The present invention relates to a computer-implemented method for calculating a digital twin of a spectacle lens according to the preamble of claim 1 , alternatively according to the preamble of claim 8, further alternatively according to the preamble of claim 15.

Related prior art

To realize a curved-form spectacle lens, according to ISO 13666:2019(E), section 3.6.2 (curved-form lens), a spectacle lens (3.5.2) having one surface convex in all meridians (3.2.11) and the other surface concave in all meridians, for example, a plurality of layers is inkjet printed in layers, whereby a spatial expansion in x,y direction of said plurality of layers successively increases or decreases in z direction. An increase or decrease of spatial expansion of said plurality of layers is visible as steps in plan view as well as in side view, in particular on a surface of said curved-form lens which has not been in contact with a substrate, said substrate being used as removeable support material for example. An additional processing step, for example polishing to remove said steps or applying a further layer to compensate said steps, usually is required. For example, if, to realize a convex spherical surface of a spectacle lens, the spherical surface as defined in ISO 13666:2019(E), section 3.4.1 , the spectacle lens as defined in ISO 13666:2019(E), section 3.5.2, a plurality of circular layers is inkjet printed in layers, a radius determining the circumference of each circular layer of said plurality of circular layers successively decreases from one inkjet printed circular layer to an inkjet printed circular layer on top in z direction. Considering a circular layer of said plurality of circular layers individually, said circular layer may be a continuous circular layer or a non-continuous circular layer. In said continuous circular layer the complete circular area is inkjet printed. In said non-continuous circular layer, an area in between said radius determining the circumference of said circular layer, said radius being the first radius, and a second radius smaller than said first radius is inkjet printed. Further, in said non-continuous circular layer, an area limited by said second radius is not inkjet printed. Again, due to said successively decreasing first radius in said plurality of circular layers stacked in z direction, a front surface and/or back surface of said spectacle lens comprises visible steps in plan view and in side view. These visible steps need to be removed in an additional processing step, for example by polishing the respective surface showing them or by an application of a further layer compensating them. Said respective surface may be a surface which has not been in contact with a substrate used as, for example, removable support material.

WO 2020/165439 A1 discloses a refractive optical component and a spectacle lens manufactured therefrom. An additive manufacturing method is suggested, the material may be applied droplet by droplet, and the size of the individual droplets and/or the application density may be varied within a single layer.

WO 2021/209551 A1 discloses a method for printing a three-dimensional optical structure built up from layers. In the layers the printing ink is deposited through targeted placement to match calculated thicknesses and lateral dimensions of the respective layers. Problem to be solved

Departing from the above-described disadvantage, obtaining steps on a surface of an inkjet printed spectacle lens, and in particular departing from WO 2021/209551 A1 , page 3, lines 4 to 19, disclosing that during printing a layer droplets are placed according to a dither pattern reducing a number of droplets to be placed in a part of said layer homogeneously or inhomogeneously, it has been the object of the present invention, as in WO 2021/209551 A1 , to provide a possibility avoiding the formation of steps on a surface of a spectacle lens, thus avoiding an additional processing step to remove or to compensate those steps, and in particular to provide a concrete dithering algorithm for droplet placement.

Summary of the invention

This problem has been solved by the computer-implemented method according to claim 1 , alternatively by the computer-implemented method according to claim 8, further alternatively by the computer-implemented method according to claim 15.

Preferred embodiments, which might be realized in an isolated fashion or in any arbitrary combination, are listed in the dependent claims.

In the computer-implemented method being configured for calculating a digital twin of a spectacle lens for the purpose of a use of the digital twin for a manufacture of the spectacle lens, the digital twin comprising a layer stack, the method is characterized in that one of the following conditions apply:

- when in 50% or in less than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of an adjacent layer of said layer stack a volume element is positioned then no volume element is positioned in discrete

Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions of a layer of said layer stack, a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer being directly adjacent and on top of a respective discrete X _m ,Ym,Z _m ... Xn,Yn,Zn position of said adjacent layer;

- when in more than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of an adjacent layer of said layer stack a volume element is positioned then volume elements are positioned in at least one of odiscrete Xm+1a z,Ym+ia z,Zm+1a z ... Xn+1a z,Yn+1a z,Zn+1a z positions of a layer of said layer stack, a discrete Xm+1a ...z,Ym+1a ...z,Z _m +1a z ... X _n +1a z,Yn+1a z,Z _n +1a z position of said layer not being on top of a respective discrete Xm,Ym,Zm ... X _n ,Yn,Z _n position of said adjacent layer, odiscrete Xm+1 ,Ym+1,Z _m +1 ... Xn+1,Y _n +1,Z _n +1 positions of a layer of said layer stack, a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer being directly adjacent and on top of a respective discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

Volume elements are positioned in discrete positions preferably in that each volume element is positioned in one respective discrete position.

The computer-implemented method is suitable for generating printing instructions for inkjet printing a spectacle lens. The computer-implemented method is suitable for the purpose of generating printing instructions, said printing instructions to be used for inkjet printing a spectacle lens. Preferably, in a computer-implemented method for generating printing instructions for inkjet printing a spectacle lens, said printing instructions are based on a digital twin of the spectacle lens, said digital twin being sliced into a layer stack, the method comprises the steps:

(i) positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of said layer stack, based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack; or

(ii) not positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+i,Zn+1 position of a layer of said layer stack, based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack. m,n are an indices for a respective x,y,z position in a layer of a layer stack, dependent on a number of x,y,z positions in a respective layer.

Preferably, the computer-implemented method is characterized by one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then no volume element is positioned in each of said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1,Zn+1 positions.

Preferably, in a computer-implemented method for generating printing instructions for inkjet printing a spectacle lens, said printing instructions are based on a digital twin of the spectacle lens, said digital twin being sliced into a layer stack, the method comprising the steps:

(i) positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of said layer stack, based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack, said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer being directly adjacent and on top of said discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer; or

(ii) not positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of said layer stack, based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack, said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer being directly adjacent and on top of said discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, is characterized in that one of the following conditions apply:

- when in 50% or in less than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of said adjacent layer a volume element is positioned then no volume element is positioned in discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 positions of said layer; - when in more than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of said adjacent layer a volume element is positioned then volume elements are positioned partially in discrete Xm+1 ,Ym+1 ,Zm+1 . . . Xn+1 ,Yn+1,Zn+1 positions of said layer.

Not to position a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position when in less than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of an adjacent layer a volume element is already positioned means that in two adjacent layers volume elements are not directly adjacent and not on top of each other positioned. Instead a volume element is positioned in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position which is not on top of a volume element positioned in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer.

To position a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position or not to position a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position when in 50% or more than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of an adjacent layer a volume element is already positioned means that preferably in a first step a volume element is not positioned in a discrete Xm+1 ,Ym+1 ,Zm+1 . . . Xn+1,Yn+1,Zn+1 position when in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer a volume element is already positioned. Instead a volume element is positioned in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position which is not on top of a volume element positioned in a discrete Xm,Ym,Zm ... Xn,Yn,z _n position of said adjacent layer. When volume elements are positioned in all discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a positions then in a second step a volume element is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position. Volume elements need not necessarily to be positioned in all discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a positions before a positioning of volume elements in discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions starts. Preferably, when positioning a volume element in a discrete Xm+1a,Ym+1 a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position a maximum distance between two volume elements is considered. Said maximum distance preferably corresponds to a maximum distance of two single ink droplets allowing for a coalescence of said two single ink droplets in an inkjet printed layer and thus ensuring a continuous inkjet printed layer. Preferably, when positioning a volume element (i) in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+i,Zn+1 position or (ii) in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position a variation in a distance between two adjacent volume elements in said layer is minimized. Inkjet printing a spectacle lens in layers considering said minimized variation in a distance between two adjacent ink droplets in a layer, preferably enables a smoothest possible surface or interface of said layer. Preferably, adjacent volume elements are positioned to result in a variation of a distance between adjacent volume element of less than 50%, preferably less than 25%.

“Generating” printing instructions comprises the following steps, preferably in the given order: a) Slicing a digital twin of a spectacle lens into a layer stack. Preferably, said digital twin is sliced in that an interface of a layer of said layer stack or a form of an interface of a layer of said layer stack each is a linear combination of a surface form of a front surface and a surface form of a back surface of said digital twin. Preferably, for slicing a maximum layer thickness of each layer of said layer stack is preset, said maximum layer thickness preferably being determined by a maximum layer thickness inkjet printable with a single ink droplet. Further preferably, a positioning of adjacent ink droplets in minimum distance to said single ink droplet in a same layer of said layer stack is considered for said determination of said maximum layer thickness. Said positioning of adjacent ink droplets in minimum distance preferably prevents said single ink droplet from a complete spreading. Preferably said minimum distance is preset by a print resolution of an inkjet printer, preferably by a print resolution of an inkjet print head of said inkjet printer. Preferably, for slicing a minimum layer thickness of each layer of said layer stack is preset, said minimum layer thickness preferably being determined by a minimum layer thickness still leading to a continuous layer. Further preferably, a maximum distance of two single ink droplets inkjet printed in a same layer of said layer stack is considered for said determination of said minimum layer thickness. Said maximum distance of said two single ink droplets is a maximum distance that allows for a coalescence of said two single ink droplets. Due to said coalescence a continuous layer is inkjet printable.

Preferably, slicing ensures a knowledge of a layer thickness in each discrete x,y,z position of each layer of said layer stack. A positioning of ink droplets in a minimum distance, preferably according to a print resolution of an inkjet printer, further preferably according to a print resolution of an inkjet print head of an inkjet printer, or a positioning of ink droplets in a maximum distance are tools to support slicing said digital twin of said spectacle lens in a layer stack. Preferably said spectacle lens is inkjet printed with said inkjet printer. Additionally or alternatively, knowledge of a thickness of said digital twin, i.e., a centre thickness, an edge thickness and a thickness in each discrete x,y,z position in between, preferably a distance in each discrete x,y,z position between a front surface and a back surface of said digital twin, support slicing said digital twin of said spectacle lens in a layer stack. Said centre thickness of said digital twin shall mean, analogously to the definition given in ISO 13666:2019(E), section 3.2.47, a thickness of said digital twin of said spectacle lens at its reference point, determined normal to a front surface of said digital twin. Said reference point of said digital twin shall correspond, analogously to the definition given in ISO 13666:2019(E), section 3.2.19, to a point on the front surface of the finished inkjet printed spectacle lens at which the verification power of a specific portion applies. Said edge thickness shall mean, analogously to the definition given in ISO 13666:2019(E), section 3.2.48, a thickness at a point on an edge of said digital twin of said spectacle lens. Said layer thickness in each corresponding x,y,z position of an inkjet printed layer depends on a density of ink droplets in said layer: the more ink droplets are positioned within an area element, the higher a layer thickness in said area element. Said area element preferably is preset to comprise within a layer more than ten discrete positions for ink droplets, i.e., more than ten positions in which an ink droplet (i) is placed or (ii) could be placed but is not placed. Said area element may comprise, preferably when projected in a plane held by a x direction and a y direction, for example, an area of 100 discrete positions for ink droplets, ten in x direction and ten in y direction. Phrased differently, in an inkjet printed layer, a layer thickness is defined as number of ink droplets multiplied by a volume of an ink droplet divided by an area of said area element:

Preferably, said thickness of said digital twin, i.e., said centre thickness, said edge thickness and said thickness in each discrete x,y position in between, preferably a distance in each discrete x,y,z position between the front surface and the back surface of said digital twin, is reflected in a thickness distribution of a layer of said layer stack, preferably in a thickness distribution of each layer apart from a base layer of said layer stack. Reflecting a thickness distribution shall mean that a ratio of said thickness of said digital twin between two discrete x,y,z positions is identical to a ratio of a layer of said layer stack in two discrete x,y,z positions having identical z positions as two discrete x,y,z positions of said digital twin, preferably apart from a base layer.

Preferably, said digital twin is sliced to comprise, according to the before mentioned restrictions with respect to a minimum layer thickness or a maximum layer thickness, a maximum number of layers in said layer stack. Said digital twin may also be sliced to comprise, according to the before mentioned restrictions with respect to a minimum layer thickness or a maximum layer thickness, a reasonable number of layers in said layer stack. Said reasonable number of layers may be a compromise between a possible maximum number of layers and a possible minimum number of layers in said layer stack. Said possible maximum number of layers mainly contributes to achieving a predefined power whereas said possible minimum number of layers mainly contributes to avoiding cosmetic defects when inkjet printing a respective spectacle lens in layers; b) Converting each layer of said layer stack into a spatial volume element pattern. In said spatial volume element pattern each volume element is positioned in a discrete x,y,z position. In said spatial volume element pattern each volume element represents an ink droplet. In said spatial volume element pattern a volume element serves as a virtual placeholder for an ink droplet. In said spatial volume element pattern each volume element positioned in a discrete x,y,z position serves as a virtual placeholder for each ink droplet to be positioned in a corresponding discrete x,y,z position of a spectacle lens, when said spectacle lens is inkjet printed in layers. Each volume element is a computer-readable representation of a digital positioning of an ink droplet in a discrete x,y,z position in said spatial volume element pattern of said digital twin of said spectacle lens. Preferably, for converting said digital twin into said spatial volume element pattern a print resolution of an inkjet printer, preferably an inkjet print head of the inkjet printer is considered; c) Transferring said spatial volume element pattern into printing instructions which, when the printing instructions are executed by an inkjet printer, cause the inkjet printer to print said spectacle lens in layers. Preferably, transferring said sliced spatial volume element pattern into printing instructions which, when the printing instructions are executed by an inkjet printer, cause an inkjet print head of the inkjet printer to release a jet forming an ink droplet in a corresponding discrete x,y,z position in layers. Preferably, said printing instructions are computer-readable data comprising a stack of images, one image for each layer to be inkjet printed, for example tiff images, and a text file, for example in .xml format. Said text file preferably comprises instructions for an order in which said stack of images corresponding to said layer stack is to be inkjet printed. Said text file preferably further comprises process parameters that are required to inkjet print said spectacle lens in layers like a power of pinning LEDs to cure the ink droplets, said ink droplets preferably comprising a UV- curable fluid, and an increase of the z-position of an inkjet print head after having inkjet printed a layer to avoid collision of the inkjet print head with said inkjet printed layer. A discrete x,y,z position of a volume element in a spatial volume element pattern of a digital twin of a spectacle lens is “corresponding” to a discrete x,y,z position of an ink droplet when while inkjet printing said spectacle lens in layers said ink droplet is positioned according to said discrete x,y,z position of said volume element in said spatial volume element pattern of said digital twin of said spectacle lens. Said ink droplet is positioned in that position that is in said spatial volume element patten intended for its discrete positioning. Analogously, a discrete x,y,z position of an ink droplet is “corresponding” to a discrete x,y,z position of a volume element in a spatial volume element pattern of a digital twin of a spectacle lens when while inkjet printing said spectacle lens in layers said ink droplet is positioned in that discrete x,y,z position in which said volume element had served as virtual representation or as virtual placeholder in said spatial volume element pattern of said digital twin.

A “discrete x,y,z position” or “discrete x,y,z positions” both of a digital twin of a spectacle lens and of a spectacle lens are comprised in a x,y,z coordinate system. Said x,y,z coordinate system preferably is defined as follows:

A surface normal at either an apex of a front surface of a digital twin of a spectacle lens or an apex of a back surface of a digital twin of a spectacle lens shall define an origin of a x,y,z coordinate system and a z direction. A surface normal at either an apex of a front surface of a spectacle lens or an apex of a back surface of a spectacle lens shall define an origin of a x,y,z coordinate system and a z direction. A x,y direction shall be in a tangential plane to either said front surface at the respective apex or said back surface at the respective apex. A x direction and a y direction shall be perpendicular to each other in the respective tangential plane.

Instead of the surface normal at the respective apex of the front surface or instead of the surface normal at the respective apex of the back surface an optical centre of the a) digital twin of the spectacle lens or b) spectacle lens each may define an origin of a x,y,z coordinate system and a surface normal at the respective optical centre may define a z direction. The x,y direction then is in the tangential plane to an intersection with the respective front surface. In the respective tangential plane the x direction and the z direction are perpendicular to each other. The optical centre of a digital twin of a spectacle lens is defined analogously as in ISO 13666:2019(E), section 3.2.15, as an intersection of an optical axis with a front surface of said digital twin. The optical centre of a spectacle lens is defined as in ISO 13666:2019(E), section 3.2.15, as an intersection of an optical axis (3.1.8) with a front surface (3.2.13) of a spectacle lens (3.5.2).

In case a front surface or a back surface of a a) digital twin of a spectacle lens or b) spectacle lens is for example a power-variation surface or another surface without an unambiguously definably apex, preferably a surface normal at a fitting point of the a) digital twin of the spectacle lens or b) spectacle lens each shall define the origin of the x,y,z coordinate system and a primary direction may define a z direction. The primary direction of a digital twin of a spectacle lens is defined analogously as in ISO 13666:2019(E), section 3.2.25, as direction of a virtually represented line of sight, usually taken to be a horizontal, to an object at an infinite distance assumed with habitual head and body posture when assumed looking straight ahead in unaided vision. The primary direction of a spectacle lens is defined as in ISO 13665:2019(E), section 3.2.25, as direction of a line of sight (3.2.24), usually taken to be a horizontal, to an object at an infinite distance measured with habitual head and body posture when looking straight ahead in unaided vision. In that case, a x,y direction is in a plane perpendicular to the respective primary direction. In the respective plane perpendicular to the respective primary direction a x direction and a y direction are perpendicular to each other.

“Printing instructions” are computer-readable data which, when the printing instructions are executed by an inkjet printer, cause the inkjet printer to inkjet print a spectacle lens.

Printing instructions preferably are computer-readable data based on a sliced digital twin of a spectacle lens.

Printing instructions preferably are in the form of computer-readable data and are based on a sliced digital twin of a spectacle lens; when the printing instructions are executed by an inkjet printer, said printing instructions cause the inkjet printer to inkjet print a spectacle lens.

Said printing instructions being computer-readable data or being in the form of computer-readable data preferably are (i) stored on a computer-readable storage medium or (ii) transferred via a data signal. The computer-readable storage medium may be a non-transitory tangible computer-readable storage medium.

Said printing instructions preferably are configured to, when executed by an inkjet printer, to cause the inkjet printer to inkjet print a spectacle lens. Said printing instructions preferably are computer- readable data which, when executed by an inkjet printer, are configured to cause the inkjet printer to inkjet print a spectacle lens in layers, wherein in each layer, beginning from a base layer directly adjacent to an optionally removable substrate, ink droplets are positioned in a discrete x,y,z position. Said discrete x,y,z positions of the ink droplets positioned in layers to inkjet print a spectacle lens preferably correspond to discrete x,y,z positions of volume elements in a spatial volume element pattern of a digital twin of said spectacle lens to be inkjet printed.

Said printing instructions are for the purpose of a use thereof for inkjet printing a spectacle lens. Said printing instructions are computer-readable data for the purpose of a use of said data for inkjet printing a spectacle lens in layers. The inkjet printing of said spectacle lens preferably begins with inkjet printing a base layer directly in or on an optionally removable substrate and continues with inkjet printing layer by layer until said spectacle lens is finished inkjet printed. The positioning of each ink droplet in a discrete x,y,z position in each layer is specified by a corresponding discrete x,y,z position of a volume element in a spatial volume element pattern of a digital twin of said spectacle lens to be inkjet printed.

Preferably said printing instructions, when the printing instructions are executed by an inkjet printer, cause a print head of the inkjet printer to release a jet forming an ink droplet in a corresponding discrete x,y,z position in layers.

The substrate said base layer is inkjet printed in or on, or said base layer is directly adjacent to, may be removable from the inkjet printed spectacle lens or may remain with the inkjet printed spectacle lens. Preferably, the spectacle lens and the substrate are removable from each other.

Preferably, said printing instructions are in a computer-readable data format comprising a stack of images, one image for each layer to be inkjet printed, for example tiff images, and a text file, for example in .xml format, as described before. A “spatial volume element pattern” is a digital representation in volume elements or a virtual description in volume elements of each layer of a sliced digital twin of a spectacle lens. Said digital representation or said virtual description preferably are computer-readable data or are in the form of computer-readable data. Said computer-readable data may (i) be stored on a computer-readable storage medium, or (ii) transferred via a data signal. The computer-readable storage medium may be a non-transitory tangible computer-readable storage medium. In a spatial volume element pattern each volume element is spatially positioned in a discrete x,y,z position. In said spatial volume element pattern each volume element in a discrete x,y,z position represents an ink droplet to be positioned in a corresponding discrete x,y,z position when inkjet printing said spectacle lens.

A “digital twin” of a spectacle lens is defined analogously as in ISO 13666:2019(E), section 3.5.2 (spectacle lens), a digital twin of an ophthalmic lens (3.5.1) which when transferred to physical reality is worn in front of, but not in contact with, an eyeball. The digital twin of the spectacle lens may include a design of the spectacle lens, preferably based on an ordered power as defined in ISO 13666: 2019(E), section 3.10.14. The digital twin of the spectacle lens is for the purpose of a use for manufacturing the spectacle lens, in particular for inkjet printing the spectacle lens.

For providing a concrete dithering algorithm, the digital twin of the spectacle lens preferably is a mathematical description of a lens surface of a front surface of the spectacle lens, a mathematical description of a lens surface of a back surface of the spectacle lens, said mathematical descriptions optionally including (i) a refractive index for said spectacle lens or (ii) a refractive index distribution n(x,y,z) for said spectacle lens. The lens surface of said digital twin is defined analogously to ISO 13666:2019(E), section 3.4. The front surface of the digital twin of the spectacle lens is defined analogously as in ISO 13666:2019(E), section 3.2.13, as a surface which when said digital twin is transferred to physical reality is intended to be fitted away from the eye. The back surface of the digital twin of the spectacle lens is defined analogously as in ISO 13666:2019(E), section 3.2.14, as a surface which when said digital twin is transferred to physical reality is intended to be fitted nearer to the eye. The refractive index for said spectacle lens is a refractive index said spectacle lens should have after having been inkjet printed. The refractive index distribution for said spectacle lens is a refractive index distribution said spectacle lens should have after having been inkjet printed. Preferably, the mathematical descriptions of the lens surfaces of the front surface and of the back surface include a relative orientation of the front surface and the back surface to each other, for example, in a same coordinate system and a) a refractive index for said spectacle lens or b) refractive indices for said spectacle lens. Instead of including the relative orientation of the front surface and the back surface in the same coordinate system, the mathematical descriptions may include a relative orientation of the front surface and the back surface and a distance between the front surface and the back surface, preferably in one arbitrarily selected point on one of the surfaces.

A digital twin of a spectacle lens is a mathematical description or a mathematical representation of lens surfaces of the spectacle lens, optionally including a refractive index or optionally including a refractive index distribution n(x,y,z), said mathematical description or said mathematical representation being computer-readable data or in the form of computer-readable data. Said computer-readable data may (i) be stored on a computer-readable storage medium, or (ii) transferred via a data signal. The computer-readable storage medium may be a non-transitory tangible computer- readable storage medium. Said computer-readable data may additionally contain printing instructions to inkjet print a spectacle lens. Said computer-readable data may additionally contain printing instructions which, when the printing instructions are executed by an inkjet printer, cause the inkjet printer to inkjet print a spectacle lens.

A digital twin of a spectacle lens may, additionally or alternatively, be, for the purpose of a use of the digital twin for manufacturing the spectacle lens, in particular for inkjet printing the spectacle lens, one of the following:

- an analytical description or an analytical model describing or representing said spectacle lens. Said analytical description or said analytical model preferably is a piecewise description or a piecewise representation and comprises (i) a mathematical formula describing a lens surface of a front surface of said digital twin of said spectacle lens and (ii) a mathematical formula describing a lens surface of a back surface of said digital twin of said spectacle lens and optionally (iii) a mathematical formula describing a refractive index for said spectacle lens or describing refractive indices for said spectacle lens, a relative orientation of the front surface to the back surface, as described before, preferably is included in said analytical description or said analytical model;

- an analytical description or an analytical model describing or representing said spectacle lens, said analytical description or said analytical model additionally containing printing instructions (i) to inkjet print said spectacle lens or (ii) when executed by an inkjet printer to cause the inkjet printer to inkjet print said spectacle lens;

- in the form of an analytical description or an analytical model representing said spectacle lens;

- in the form of an analytical description or an analytical model representing said spectacle lens, said analytical description or said analytical model additionally containing printing instructions (i) to inkjet print said spectacle lens or (ii) when executed by an inkjet printer to cause the inkjet printer to inkjet print said spectacle lens;

- said analytical description or said analytical model being (i) stored on a computer-readable storage medium or (ii) transferred via a data signal. The computer-readable storage medium may be a non- transitory tangible computer-readable storage medium;

- numerical data describing or representing said spectacle lens. Said numerical data preferably are comprising or being a conversion of said analytical description or said analytical model. Said numerical data preferably are comprising a pattern which comprises discrete Zfront(x,y) positions of or on a front surface of said digital twin of said spectacle lens and discrete Zback(x,y) positions of or on a back surface of said digital twin of said spectacle lens. Said discrete Zfront(x,y) positions and said discrete Zback(x,y) positions preferably are considering a print resolution of an inkjet printer, preferably a print resolution of an inkjet print head of an inkjet printer. Preferably, in each of said discrete Zfront(x,y) positions and said discrete Zback(x,y) positions a lens surface is described by a mathematical formula. So, said numerical data comprises an evaluation of analytical description or an analytical model of said lens surface in each of said discrete x,y positions, preferably meaning that said numerical data comprises a function value of the analytical description or the analytical model of a lens surface of at least one of a front and a back surface in each discrete x,y position. The function value in each discrete x,y position, i.e., the discrete x,y,z positions, of the lens surface of the front surface and of the back surface preferably are described in a same coordinate system; or a relative orientation of fer example coordinate systems of the front surface and the back surface and a distance between the front surface and the back surface, preferably in one arbitrarily selected point on one of the surfaces, is comprised in said numerical data. Optionally, a refractive index or a refractive index distribution, said refractive index distribution comprising a pattern which comprises (i) discrete x,y,z positions of or on a front surface of said digital twin of said spectacle lens (n(x,y,z)), (ii) discrete x,y,z positions of or on a back surface of said digital twin of said spectacle lens (n(x,y,z)) and (iii) discrete x,y,z positions in between said front surface and said back surface (n(x,y,z)), is comprised in said numerical data. Preferably, said numerical data are taken as a basis for slicing. Compared to taking said analytical description or said analytical model as a basis for slicing, less computing power is needed when said numerical data are taken as a basis for slicing. Phrased differently, slicing said numerical data is computationally less expensive;

- numerical data describing or representing said spectacle lens, said numerical data additionally containing printing instructions (i) to inkjet print said spectacle lens or (ii) when executed by an inkjet printer to cause the inkjet printer to inkjet print said spectacle lens;

- in the form of numerical data describing or representing said spectacle lens;

- in the form of numerical data describing or representing said spectacle lens, said numerical data additionally containing printing instructions (i) to inkjet print said spectacle lens or (ii) when executed by an inkjet printer to cause the inkjet printer to inkjet print said spectacle lens;

- said numerical data being (i) stored on a computer-readable storage medium or (ii) transferred via a data signal. The computer-readable storage medium may be a non-transitory tangible computer- readable storage medium;

- computer-readable data describing or representing said spectacle lens;

- computer-readable data describing or representing said spectacle lens, said computer-readable data additionally containing printing instructions (i) to inkjet print said spectacle lens or (ii) when executed by an inkjet printer to cause the inkjet printer to inkjet print said spectacle lens;

- in the form of computer-readable data describing or representing said spectacle lens;

- in the form of computer-readable data describing or representing said spectacle lens, said computer-readable data additionally containing printing instructions (i) to inkjet print said spectacle lens or (ii) when executed by an inkjet printer to cause the inkjet printer to inkjet print said spectacle lens;

- said computer-readable data being (i) stored on a computer-readable storage medium or (ii) transferred via a data signal. The computer-readable storage medium may be a non-transitory tangible computer-readable storage medium.

A “spectacle lens” or lens is as defined in ISO 13666:2019(E), section 3.5.2, an ophthalmic lens worn in front of, but not in contact with, the eyeball.

A front surface is as defined in ISO 13666:2019(E), section 3.2.13, a surface of a lens (3.5.2) intended to be fitted away from the eye. A back surface is as defined in ISO 13666:2019(E), section 3.2.14, a surface of a lens (3.5.2) intended to be fitted nearer to the eye. In the context of the present invention, a spectacle lens is further a physical representation of a corresponding digital twin of said spectacle lens, said spectacle lens being an inkjet printed physical representation of said corresponding digital twin. A spectacle lens results from a transfer of a digital twin of the spectacle lens to physical reality.

“Slicing” is a conversion of a digital twin of a spectacle lens into a layer stack. Preferably, slicing is a conversion of said digital twin digitally represented by numerical data, the numerical data as defined before, into a layer stack. Slicing is a digital conversion of said digital twin into a layer stack in which for each layer a layer thickness is preset. Said layer thickness is preset digitally in a centre, in an edge and in between in each x,y,z position of said layer. Preferably, each layer of said layer stack has an identical spatial expansion, in plan view, when projected in a plane held by a x direction and a y direction.

“Positioning” is a digital placement or virtual arrangement or digital distribution of a volume element in a discrete x,y,z position of each layer of a layer stack of a sliced digital twin of a spectacle lens. The positioning of a volume element in a discrete x,y,z position preferably includes (i) a digital placement or virtual arrangement within a layer as well as (ii) a digital placement or virtual arrangement in an adjacent layer, in a next but one layer, in an adjacent layer to a next but one layer, and so on. Preferably, the positioning is a digital placement of a single volume element per discrete x,y,z position. Said positioning of a volume element in a discrete x+1,y+1,z+1 position of a layer depends on or is based on a positioning of a volume element in an adjacent layer in a discrete x,y,z position. In said adjacent layer each volume element is positioned in a discrete x,y,z position. In said adjacent layer, preferably when projected in a plane held by a x direction and a y direction, in plan view, each volume element has a discrete x,y,z position. In said layer, preferably when projected in a plane held by a x direction and a y direction, in plan view, each volume element has a discrete x+1,y+1,z+1 position, when positioned directly adjacent and on top of a volume element having a discrete x,y,z position in said adjacent layer. Said layer and said adjacent layer are stacked in z direction. The z direction is perpendicular to said plane held by the x direction and the y direction.

When positioning volume elements in layers, volume elements of a first adjacent layer on whose volume element positioning a further digital placement of volume elements depend on are digitally placed. After their digital placement those volume elements form then the basis of a second adjacent layer on whose volume element positioning a further digital placement of further volume elements depends on. Those digitally placed volume elements in turn form the basis of a third adjacent layer on whose volume element positioning a further digital placement of further volume elements depend on. Said positioning in layers is repeated until volume elements in a final layer are digitally placed dependent on a volume element positioning of a then adjacent layer underneath.

Not positioning a volume element in a discrete x+1,y+1,z+1 position of a layer depends on or is based on a positioning of a volume element in an adjacent layer in a discrete x,y,z position. In said adjacent layer each volume element is (i) positioned in a discrete x,y,z position or (ii) not positioned in a discrete x,y,z position. With respect to said not positioning before given explanation for positioning apply. A digital twin of a spectacle lens is sliced in a layer stack. Said layer stack comprises a plurality of layers. Preferably said layer stack comprises up to 200 layers stacked, further preferably up to 150 layers stacked. Further preferably said layer stack comprises between 50 and 130 layers stacked, further preferably between 60 and 120 layers stacked, more preferably between 70 and 115 layers stacked and most preferably between 80 and 110 layers stacked. Preferably for slicing said digital twin of said spectacle lens the print resolution of an inkjet printer, preferably an inkjet print head of said inkjet printer, which is to be used for inkjet printing said spectacle lens is considered.

In said layer stack a volume element is

(i) positioned, i.e., digitally placed or virtually arranged or digitally distributed in a discrete Xm+1 ,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of a layer dependent on a positioning of a volume element in an adjacent layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, said discrete Xm+1 ,Ym+1 ,Zm+1 . . . Xn+1 ,Yn+1 ,Zn+1 position of said layer being directly adjacent and on top of said discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, for example in plan view, when both said layer and said adjacent layer are projected in a plane held by a x direction and a y direction, or

(ii) not positioned, i.e., not digitally placed or not virtually arranged or not digitally distributed, in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer dependent on a positioning of a volume element in an adjacent layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer being directly adjacent and on top of said discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, for example in plan view, when both said layer and said adjacent layer are projected in a plane held by a x direction and a y direction.

A volume element has a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position in a layer preferably in plan view when said layer is projected in a plane held by a x direction and a y direction. A volume element having a discrete Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position in a layer is directly adjacent and on top of a volume element having a discrete Xm,Ym,Zm ... Xn,Yn,Zn position in an adjacent layer, preferably said adjacent layer also in plan view when projected in a plane held by a x direction and a y direction, if the two volume elements differ only in their z position. In said layer stack, preferably in plan view with all layers projected in a plane held by a x direction and a y direction, volume elements are digitally placed on top of each other when having an identical x,y position but having a different z position. Digitally placed on top of each other means in a layer, Zm+1, a next but one layer, Zm+2, a layer adjacent to a next but one layer, Zm+3, and so on. Digitally placed on top of each other does not mean that in each of a layer, Zm+1, a next but one layer, Zm+2, a layer adjacent to a next but one layer, Zm+3, and so on, a volume element is digitally placed, a volume element could be digitally placed on top of each other in any layer of said layer stack in a Zm position but need not to be placed in each layer in a Zm position. In case a volume element is not digitally placed in a layer, Zm+1 , but in a next but one layer, Zm+2, or in a layer adjacent to a next but one layer, Zm+3, and so on, said volume element and a volume element digitally placed in a Zm position are, when having an identical x,y position, on top of each other but not adjacent to each other.

Positioning or not positioning “a” volume element in a discrete x,y,z position of a respective layer preferably includes positioning or not positioning more volume elements in different discrete x,y,z positions of said respective layer, preferably one volume element of the more volume elements per discrete x,y,z position. In said layer stack said positioning of volume elements preferably begins with a digital placement of volume elements in a base layer. Said base layer preferably is a digital representation of a layer directly adjacent to a substrate. Said base layer preferably is a digital representation of a layer which is inkjet printed in or on a substrate. In said base layer, preferably in plan view when projected in a plane held by a x direction and a y direction, in each discrete x,y,z position of said base layer a volume element is digitally placed. Said base layer, preferably in plan view when projected in a plane held by a x direction and a y direction, is having a constant thickness. In said layer stack said positioning of volume elements ends with a digital placement of volume elements in a final layer. In an inkjet printed spectacle lens said base layer is or forms either a front surface or a back surface of said spectacle lens, said final layer then is or forms accordingly a back surface or a front surface thereof. In between said base layer and said final layer a

(i) positioning of volume elements in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer, or

(ii) not positioning of volume elements in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer, each depends on or is based on a positioning of a volume element in an adjacent layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position.

Positioning or not positioning of volume elements in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer preferably means that more volume elements are positioned in different discrete Xm+1,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions of said layer, one volume element is positioned or not positioned in one Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said different discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions. The more volume elements preferably depend on a number of volume elements to be positioned.

In said layer stack said

(i) positioning of volume elements in a discrete Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer or first layer adjacent to said base layer, a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer or first layer being directly adjacent and on top of a respective Xm,Ym,Zm ... Xn,Yn,Zn of said base layer, preferably in plan view when both of said layer and said base layer are projected in a plane held by a x direction and a y direction, or

(ii) not positioning of volume elements in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer or first layer adjacent to said base layer, a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer or first layer being directly adjacent and on top of a respective Xm,Ym,Zm ... Xn,Yn,Zn of said base layer, preferably in plan view when both said layer and said base layer are projected in a plane held by a x direction and a y direction, each depends on or is based on a positioning of a volume element in said adjacent base layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position.

In said layer stack said

(i) positioning of volume elements in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer or second layer, a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer or second layer being on top of a respective Xm,Ym,Zm ... Xn,Yn,Zn of said base layer, preferably in plan view when both said next but one layer and said base layer are projected in a plane held by a x direction and a y direction, or (ii) not positioning of volume elements in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer or second layer, a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer or second layer being on top of a respective Xm,Ym,Zm ... Xn,Yn,Zn of said base layer, preferably in plan view when both said next but one layer and said base layer are projected in a plane held by a x direction and a y direction, each depends on or is based on a positioning of a volume element in said layer or first layer in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position. Said next but one layer or second layer is adjacent to said layer or first layer and next but one to said base layer.

In said layer stack said

(i) positioning of volume elements in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of a layer adjacent to a next but one layer or third layer, a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer being on top of a Xm,Ym,Zm ... Xn,Yn,Zn of said base layer, preferably in plan view when both said layer adjacent to said next but one layer and said base layer are projected in a plane held by a x direction and a y direction, or

(ii) not positioning of volume elements in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of a layer adjacent to a next but one layer or third layer, a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer being on top of a Xm,Ym,Zm ... Xn,Yn,Zn of said base layer, preferably in plan view when both said layer adjacent to said next but one layer and said base layer are projected in a plane held by a x direction and a y direction, each depends on or is based on a positioning of a volume element in said next but one layer or second layer in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position. Said layer adjacent to a next but one layer or third layer is a layer adjacent to said next but one layer or second layer, is a next but one layer to said layer or first layer and adjacent to the next but one layer of said base layer.

In said layer stack said (i) positioning of volume elements or (ii) not positioning of volume elements in a discrete Xm+u,Ym+u,Zm+u ... Xn+v,Yn+v,Zn+v position is repeated until volume elements in said final layer are (i) positioned or (ii) not positioned.

Said (i) positioning of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position or said (ii) not positioning of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+i,Zn+1 position, each dependent on or being based on a positioning of a volume element in an adjacent layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position results in a variation of a volume element density. Preferably, said variation of the volume element density is given in each layer of said layer stack apart from the base layer. Said variation of the volume element density in a layer of said layer stack of said sliced digital twin is a digital representation of a variation of ink droplets in a layer. Printing instructions comprising said variation of the volume element density executed by an inkjet printer, cause an inkjet printer, preferably a printhead of the inkjet printer, to release a jet forming an ink droplet according to said variation in layers. A variation of ink droplets in a layer results in a variation of a layer thickness of said layer. A variation of said layer thickness avoids issues with respect to waviness in an inkjet printed spectacle lens. In contrast to WO 2020/165439 A1 disclosing on page 25, lines 10 to 18, or on page 26, lines 23 to 30, to vary a droplet density within a single layer, the present invention not only suggests varying a density of ink droplets in a layer but to vary a volume element density, digitally representing a density of ink droplets, in a layer based on a positioning of a volume element in an adjacent layer so that the volume elements that are representing the ink droplets are preferably placed complementary to an adjacent layer. This has as decisive advantage of avoiding steps on a surface of an inkjet printed spectacle lens, both in plan view and in side view. Also, residual structures that can impact the optical quality of the spectacle lens are minimized in each layer.

The before described variation of a volume element density in a layer of a digital twin of a spectacle lens resulting from positioning or not positioning a volume element in a discrete position dependent on a positioning or not positioning of a volume element in an adjacent discrete position underneath of an adjacent layer effects that each layer of said digital twin contributes to a power of said digital twin, the power defined analogously as in ISO 13666:2019(E), section 3.1.10, as capacity of the digital twin of the spectacle lens or virtual representation of an optical surface to calculate a change of a curvature or a direction of a virtually represented incident wavefront by refraction. The contribution of each layer to the power of the digital twin depends on the number of layers the digital twin is sliced into. Thus, the contribution of each layer to the power of the digital twin is 1 /number of layers. For example, in case a digital twin of a spectacle lens is sliced in 100 layers, a contribution of each layer of said 100 layers to the power of said digital twin is 1/100. Accordingly, in an inkjet printed spectacle lens a layer thickness variation corresponding to said variation of volume element density in a respective layer of said digital twin effects that each inkjet printed layer contributes to a power of the spectacle lens, the power as defined in ISO 13666:2019(E), section 3.1.10, as capacity of a spectacle lens (3.5.2) or optical surface to change the curvature or direction of incident wavefronts by refraction. The contribution of each inkjet printed layer to the power of the spectacle lens depends on the number of layers needed for inkjet printing the spectacle. The number of layers in turn corresponds to the number of layers of the corresponding sliced digital twin. Thus, the contribution of each layer to the power of the spectacle lens is 1/number of layers. In contrast to each layer contributing to the power of the digital twin of the spectacle lens and accordingly to the power of the spectacle lens, a power of a spectacle lens disclosed in WO 2021/209551 A1 is effected by a form of a front surface and a form of a back surface. This in turn means that an inevitable superelevation of a printed layer shown in WO 2021/209551 A1 , figure 2 and disclosed on page 1 , lines 26 to 28, as occurring at edges of printed layers due to a surface tension of a printing ink adding up and resulting in a printed structure whose shape differs from the intended shape has a greater influence on the power of the spectacle lens of

WO 2021/209551 A1 than on the power of the before described digital twin or respective before described spectacle lens. Therefore, WO 2021/209551 A1 has the problem to control and minimize for example by blank spaces an always present superelevation at an edge of a layer as the power of the spectacle lens otherwise deviates due to the in WO 2021/209551 A1 described superelevations from an intended power whereas the before described digital twin and the respective before described spectacle lens do not have the problem of WO 2021/209551 A1 to this extent as here each layer contributes to the power of the digital twin and the respective spectacle lens.

“Positioning a volume element” shall include a positioning of one volume element in a discrete x,y,z position or a positioning of more volume elements in discrete x,y,z positions. A positioning of more volume elements shall include a positioning of one volume element of said more volume elements per discrete x,y,z position, i.e., as described before, one volume element is positioned in one respective discrete x,y,z position.

“Not positioning a volume element” shall mean that in a discrete x,y,z position no volume element is positioned.

“Discrete” shall mean an integer multiple of a minimum nozzle distance of an inkjet print head or an arrangement of two or more inkjet print heads.

“An inkjet print head “shall mean a single inkjet print head or an arrangement of two or more inkjet print heads.

“Layer thickness” is, preferably of a sliced digital twin of a spectacle lens projected in a plane held by a x direction and a y direction, in side view, in z direction, a shortest distance between a point

- on an outermost surface of a layer to a point perpendicular to said point in z direction on the nearest interface of said layer, or

- on an interface of a layer to another layer to a point perpendicular to said point in z direction on the nearest interface of said layer.

The above-described problem is fully solved by a computer-implemented method described in the forgoing. A targeted positioning of a volume element in a layer dependent on or based on a positioning of a volume element in an adjacent layer results in a variation of a volume element density in said layer. Said variation in volume element density results in a variation of a layer thickness when an ink jet printer, preferably a print head of the inkjet printer, releases a jet forming an ink droplet in a corresponding position to said targeted positioned volume element. Thus, in turn avoids to a formation of steps in an inkjet printed spectacle lens.

In a preferred embodiment of the invention, the computer-implemented method is characterized by one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then no volume element is positioned in each of said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions and volume elements are positioned in each of a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in osaid discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions, and o discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack; a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer being directly adjacent and on top of a discrete Xm+1,Ym+1,,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer.

When in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+ 1 positions and, volume elements are positioned partially in discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack.

Not to position a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer when in less than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of an adjacent layer a volume element is already positioned but to position a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position when in less than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of said adjacent layer a volume element is already positioned means that a volume element of said next but one layer is positioned on top of a volume element of said adjacent layer but that these two volume elements are not adjacent to each other. In said layer in between said adjacent layer and said next but one layer a volume element is positioned in a discrete Xm+1a,Ym+1a,Zm+1a ... Xn+1a,Yn+1a,Zn+1a position which is not on top of a volume element positioned in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer. Preferably, as mentioned before, when positioning a volume in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position a maximum distance between two volume elements is considered. Preferably, as explained before, in said layer a variation in a distance between two adjacent volume elements is minimized.

To position a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position or not to position a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer when in 50% or more than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of an adjacent layer a volume element is already positioned and to position a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position or not to position a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer to said adjacent layer when in 50% or more than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of said adjacent layer a volume element is already positioned means that preferably in a first step a volume element is not positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer when in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer a volume element is already positioned and a volume element is not positioned in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer when in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer a volume element is already positioned. Instead a volume element is positioned in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position which is not adjacent and not on top of a volume element positioned in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer and instead a volume element is positioned in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position of said next but one layer which is not adjacent to and not on top of a volume element positioned in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and which is not on top of a volume element positioned in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer. When volume elements are positioned in all discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a positions and in all discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b positions then in a second step a volume element is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position and in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position. Volume elements may be positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position and/or in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position before volume elements in all discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a positions and in all discrete Xm+2b,Ym+2b,Zm+2b . . . Xn+2b,Yn+2b,Zn+2b positions are positioned. Preferably, when positioning a volume in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position or in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position in each of said layer and said next but one layer a maximum distance between two volume elements is considered. Said maximum distance preferably corresponds to a maximum distance of two single ink droplets allowing for a coalescence of said two single ink droplets in an inkjet printed layer and thus ensuring a continuous inkjet printed layer. Preferably, when positioning a volume element (i) in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1,Zn+1 position, (ii) in a discrete Xm+1a,Ym+1a,Zm+1a ... Xn+1a,Yn+ia,Zn+1a position, (iii) in a discrete Xm+2b,Ym+2b,Zm+2b . . . Xn+2b,Yn+2b,Zn+2b position, Or in a discrete Xm+2,Ym+2 ,Zm+2 . . . Xn+2,Yn+2,Zn+2 position a variation in a distance between two adjacent volume elements in said layer or said next but one layer is minimized. Inkjet printing a spectacle lens in layers considering said minimized variation in a distance between two adjacent ink droplets in a layer, preferably enables a smoothest possible surface or interface of said layer or said next but one layer.

In a preferred embodiment of the invention, the computer-implemented method is characterized by the following condition:

- when in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer a volume element is to be positioned then said volume element is positioned in o a discrete Xm+2b,Ym+2b,Zm+2b ... xn+2b,Yn+2b,Zn+2b position not adjacent and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+2a,Ym+2a,Zm+2a . . . Xn+2a,Yn+2a,Zn+2a position adjacent and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position not adjacent and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,Znb position of said adjacent layer, or o a discrete Xm+2a,Ym+2a,Zm+2a . . . Xn+2a,Yn+2a,Zn+2a position adjacent and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer.

Preferably, this condition considers a positioning of volume elements in said next but one layer. Preferably, for positioning a volume element in said layer one of the above-described conditions shall apply.

Preferably, as explained before, when positioning a volume in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer or in a discrete Xm+2b,Ym+2b,Zm+2b . . . Xn+2b,Yn+2b,Zn+2b position of said next but one layer a maximum distance between two volume elements is considered. Preferably, as explained before, in each of the before mentioned layers a variation in a distance between two adjacent volume elements is minimized.

Preferably, when in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer a volume element is to be positioned then said volume element is positioned in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position not adjacent and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer. In case in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer a volume element is to be positioned and either

(i) in one of said layer or said adjacent layer a volume element is already positioned in a discrete Xm+1 ,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or

(ii) in both of said layer or said adjacent layer a volume element is already positioned in a discrete Xm+1 ,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position and in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, preferably the respective before mentioned positioning shall apply.

In a preferred embodiment of the invention, the computer-implemented method is characterized by the following condition:

- when in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer a volume element is to be positioned then said volume element is positioned in o a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,Znb position of said adjacent layer, or o a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b ... Xn+1b,Yn+1b,Zn+1b position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+3a,Ym+3a,Zm+3a . . . Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer, or o a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and not on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer, or o a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b ... Xn+1b,Yn+ib,Zn+ib position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,Znb position of said adjacent layer, or o a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer. Preferably, this condition considers a positioning of volume elements in said adjacent layer to a next but one layer. An overview with respect to possible positionings of volume elements in three layers underneath said adjacent layer to a next but one layer is given in table 1 , summarizing the before mentioned. Preferably, for positioning a volume element in said layer and in said next but one layer one of the above-described conditions shall apply.

Preferably, as explained before, when positioning a volume in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position, in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position, in a discrete Xm+1 b,Ym+1 b,Zm+1b . . . Xn+1b,Yn+ib,Zn+1b position, in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, in a discrete Xm+2a,Ym+2a,Zm+2a . . . Xn+2a,Yn+2a,Zn+2a position, in 3 discrete Xm+2b,Ym+2b,Zm+2b . . . Xn+2b,Yn+2b,Zn+2b position, in a discrete Xm+3a,Ym+3a,Zm+3a . . . Xn+3a,Yn+3a,Zn+3a position, or in a discrete Xm+3b,Ym+3b,Zm+3b . . . Xn+3b,Yn+3b,Zn+3b position in each of said layers a maximum distance between two volume elements is considered. Preferably, as explained before, in each of the before mentioned layers a variation in a distance between two adjacent volume elements is minimized.

Table 1 : Possible positionings of volume elements in layer stack underneath adjacent layer to next but one layer

Preferably, when in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer a volume element is to be positioned then said volume element is positioned in a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

In case in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer a volume element is to be positioned and (i) in one of said next but one layer, said layer or said adjacent layer a volume element is already positioned in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or

(ii) in two of said next but one layer, said layer or said adjacent layer a volume element is already positioned in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or

(iii) in each said next but one layer, said layer and said adjacent layer a volume element is already positioned in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position and in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, preferably the respective before mentioned positioning shall apply.

In a preferred embodiment of the invention, the computer-implemented method is characterized by the following condition:

- when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer, i.e., of a layer being separated by said layer, said next but one layer, said adjacent layer to said next but one layer from said adjacent layer, a volume element is to be positioned then said volume element is positioned in o a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+1b,Zm+1b ... Xn+1b,Yn+1b,Zn+1b position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm.Ym.Zm ... Xn,Yn,Zn position of said adjacent layer, or a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b . . . Xn+1 b,Yn+1 b,Zn+1 b position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,Znb position of said adjacent layer, or a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,z _n b position of said adjacent layer, or a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b ... Xn+1b,Yn+1b,Zn+ib position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a ... Xn+1a,Yn+ia,Zn+ia position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a ... Xn+1a,Yn+1a,Zn+ia position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b ... Xn+1b,Yn+1b,Zn+1b position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,Znb position of said adjacent layer, or o a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer, or o a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer, or o a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a ... Xn+1a,Yn+1a,Zn+1a position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or o a discrete Xm+4a,Ym+4a,Zm+4a ... Xn+4a,Yn+4a,Zn+4a position adjacent and on top of a volume element in a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position of said layer adjacent to said next but one layer and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer.

Preferably, this condition considers a positioning of volume elements in said layer separated by three layers from said adjacent layer. An overview with respect to possible positionings of volume elements in four layers underneath said adjacent layer to a next but one layer is given in table 2, summarizing the before mentioned. Preferably, for positioning a volume element in said layer, in said next but one layer and in said adjacent layer to said next but one layer one of the above-described conditions shall apply.

Preferably, as explained before, when positioning a volume in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position, in a Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position, in a Xm+1 b,Ym+1 b,Zm+1 b . . . Xn+1 b,Yn+1b,Zn+1 b position, in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position, in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position, in a discrete Xm+3,Ym+3,Zm+3 . . . Xn+3,Yn+3,Zn+3 position, in 3 discrete Xm+3a,Ym+3a,Zm+3a . . . Xn+3a,Yn+3a,Zn+3a position, in 3 discrete Xm+3b,Ym+3b,Zm+3b . . . Xn+3b,Yn+3b,Zn+3b position, in a discrete Xm+4a,Ym+4a,Zm+4a . . . Xn+4a,Yn+4a,Zn+4a position or in a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position, in each of these layers a maximum distance between two volume elements is considered. Preferably, as explained before, in each of the before mentioned layers a variation in a distance between two adjacent volume elements is minimized.

Table 2: Possible positionings of volume elements in layer stack underneath layer separated by three layers from adjacent layer

- = no volume positioned, + = volume element positioned

Continuation of table 2:

- = no volume positioned, + = volume element positioned

Preferably, when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer, a volume element is to be positioned then said volume element is positioned in a discrete Xm+4b,Ym+4b,Zm+4b ... Xn+4b,Yn+4b,Zn+4b position not adjacent and not on top of a volume element in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position of said layer adjacent to said next but one layer and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

In case, when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer a volume element is to be positioned and

(i) in one of said adjacent layer to said next but one layer, said next but one layer, said layer or said adjacent layer a volume element is already positioned in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position, in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or

(ii) in two of said adjacent layer to said next but one layer, said next but one layer, said layer or said adjacent layer a volume element is already positioned in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position, in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or

(iii) in three of said adjacent layer to said next but one layer, said next but one layer, said layer or said adjacent layer a volume element is already positioned in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position, in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, in a discrete Xm+1 ,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or

(iv) in each of said adjacent layer to said next but one layer, said next but one layer, said layer or said adjacent layer a volume element is already positioned in a discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 position, in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position, in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+i,Zn+1 position or in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position preferably the respective before described positioning shall apply.

In a preferred embodiment of the invention, the computer-implemented method is characterized by the following additional step:

(iii) determining a deviation of an actual value of a layer thickness in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer from a default nominal value of said layer thickness in an identical discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

As described above slicing a digital twin of a spectacle lens into a layer stack determines in each discrete x,y,z position a layer thickness of each layer of said layer stack. Said layer thickness is preset. Said layer thickness has in each discrete x,y,z position a default nominal value.

As further described above each layer of said layer stack is converted in a spatial volume element pattern in which volume elements are positioned or not positioned in discrete x,y,z positions. A volume element may be represented for example as cuboid with preset edge lengths, preferably a volume element is represented as cube with a preset edge length. Preferably, when projecting said layer stack in a plane held by a x direction and a y direction and when viewing each layer of said layer stack as spatial volume element pattern for example in side view then in each discrete x,y,z position an actual value of a layer thickness is determined. Positioning of one volume element or more volume elements in a discrete x,y,z position of a layer results, as described before one volume element per discrete x,y,z position, when viewing said layer in side view, in an actual value of a layer thickness in said discrete x,y,z position that is

- larger than a default nominal value of a layer thickness in an identical discrete x,y,z position of said layer, or

- smaller than a default nominal value of a layer thickness in an identical discrete x,y,z position of said layer, or

- equal to a default nominal value of a layer thickness in an identical discrete x,y,z position of said layer.

A deviation of said actual value to said default nominal value is a difference between these two values. In a preferred embodiment of the invention, the computer-implemented method is characterized by the following additional step:

(iv) determining a sum of said deviation and said actual value of said layer thickness.

A determination of said sum is used as valid basis for positioning or for not positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer. Thus, said determination is used for deciding if a volume element is positioned adjacent and on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

The computer-implemented method being configured for calculating a digital twin of a spectacle lens for the purpose of a use of the digital twin for a manufacture of the spectacle lens, the digital twin comprising a layer stack, the method being characterized in the step of:

- determining a sum of a deviation of a layer thickness and an actual value of a layer thickness, said deviation being a deviation of an actual value of a layer thickness in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer from a default nominal value of said layer thickness in an identical discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

Again, the computer-implemented method is suitable for generating printing instructions for inkjet printing a spectacle lens. The computer-implemented method is suitable for the purpose of generating printing instructions, said printing instructions to be used for inkjet printing a spectacle lens.

WO 2021/209551 A1 describes for example on page 8, lines 8 to 18, that to match a calculated layer thickness, i.e., a nominal thickness, during printing a layer depositing printing ink is controlled and possible deviations of a layer thickness are compensated. WO 2021/209551 A1 discloses on page 6, lines 11 to 13, to determine deviations by confocal scanning, and further page 6, line 30 to 33, to use a simulation for determining deviations of all layers to be printed before printing these layers. Thus, WO 2021/209551 A1 , uses a control of a layer thickness during printing to match a nominal layer thickness of the printed layer or a simulation to matching nominal layer thicknesses of to be printed layers. WO 2021/209551 A1 does not disclosed to decide based on a sum of a deviation of a layer thickness and an actual value of said layer thickness in an identical x,y,z position upon a positioning a volume element or, while printing, a droplet in a position directly adjacent and on top of said x,y,z position.

In a preferred embodiment of the invention, the computer-implemented method is further characterized by one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then no volume element is positioned in each of said discrete Xm+1 ,Ym+i ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+i positions;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 positions.

Reference is made to the explanations provided above. In a preferred embodiment of the invention, the computer-implemented method is further characterized by one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then no volume element is positioned in each of said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions and volume elements are positioned in each of a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in osaid discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions, and o discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack; a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer being directly adjacent and on top of a discrete Xm+i,Ym+i ,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer.

Reference is made to the description given before.

In a preferred embodiment of the invention, the computer-implemented method is further characterized in that the following condition apply:

- when in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer a volume element is to be positioned then said volume element is positioned in a. a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position not adjacent and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or b. a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position adjacent and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or c. a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position not adjacent and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,z _n b position of said adjacent layer, or d. a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position adjacent and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer.

Reference is made to the information provided before.

In a preferred embodiment of the invention, the computer-implemented method is further characterized in that the following condition apply:

- when in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer a volume element is to be positioned then said volume element is positioned in a. a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or b. a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,znb position of said adjacent layer, or c. a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b ... Xn+1b,Yn+ib,Zn+ib position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or d. a discrete Xm+3a,Ym+3a,Zm+3a ... Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and not on top of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, or e. a discrete Xm+3a,Ym+3a,Zm+3a . . . Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and not on top of a volume element in a discrete Xm+1 ,Ym+i ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer, or f. a discrete Xm+3a,Ym+3a,Zm+3a . . . Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and not on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer, or g. a discrete Xm+3b,Ym+3b,Zm+3b ... Xn+3b,Yn+3b,Zn+3b position not adjacent and not on top of a volume element in a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer and on top of a volume element in a discrete Xm+1b,Ym+ib,Zm+1b ... Xn+1b,Yn+ib,Zn+ib position of said layer and on top of a volume element in a discrete Xmb,Ymb,Zmb ... Xnb,Ynb,z _n b position of said adjacent layer, or h. a discrete Xm+3a,Ym+3a,Zm+3a . . . Xn+3a,Yn+3a,Zn+3a position adjacent and on top of a volume element in a discrete Xm+2a,Ym+2a,Zm+2a ... Xn+2a,Yn+2a,Zn+2a position of said next but one layer and on top of a volume element in a discrete Xm+1a,Ym+1a,Zm+1a . . . Xn+1a,Yn+1a,Zn+1a position of said layer and on top of a volume element in a discrete Xma,Yma,Zma . . . Xna,Yna,Zna position of said adjacent layer.

Reference is made to the further information given before.

In a preferred embodiment of the invention, the computer-implemented method is further characterized in that the following condition apply:

- when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer, i.e., of a layer being separated by said layer, said next but one layer, said adjacent layer to said next but one layer from said adjacent layer, a volume element is to be positioned then said volume element is positioned as described before.

Reference is made to the further information given before in this context.

In a preferred embodiment of the invention, the computer-implemented method is further characterized by one of the following conditions:

- when said sum is larger than half said default nominal value of said layer thickness then no volume element is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack;

- when said sum is smaller than or equal to half said default nominal value of said layer thickness then a volume element is positioned in a discrete Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack.

As mentioned before, a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer is directly adjacent and on top of a respective discrete Xm,Ym,Zm ... x,y,z position of an adjacent layer.

As the volume elements may be represented as cuboids with a preset edge lengths, preferably as cubes of a preset edge length and the layer thickness in each discrete x,y position of each layer is preset by slicing a digital twin of a spectacle lens into a layer stack,

(i) a positioning of one volume element or more volume elements in said discrete Xm+1 ,Ym+1 ,Zm+1 . . . Xn+1,Yn+1,Zn+1 position(s) or

(ii) a not positioning of one volume element or more volume elements in said discrete Xm+1 ,Ym+1 ,Zm+1

... Xn+1,Yn+1,Zn+1 position(s), each according to said condition corrects a deviation of an actual value of a layer thickness in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer from a default nominal value of said layer thickness in an identical discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer. Said correction of said deviation may

- correct said actual value to correspond to said default nominal value, or

- undercorrect said actual value not to correspond to said default nominal value, or

- overcorrect said actual value not to correspond to said default nominal value.

Preferably said correction of said deviation corrects said actual value to correspond to said default nominal value.

In case said correction of said deviation would result in either an undercorrection or an overcorrection of said actual value said undercorrection or said overcorrection is distributed in equal parts. Said distribution in equal parts is preferably done as, while printing a spectacle lens in layers, a total volume of ink droplets to be positioned in a layer is equivalent to a volume of said layer.

When (i) positioning one volume element or more volume elements or (ii) not positioning one volume element or more volume elements according to said condition

- a maximum distance between two adjacent volume elements in said layer, or

- a maximum distance between two adjacent stacks of volume elements in said layer, or

- a maximum distance between a volume element and an adjacent stack of volume elements in said layer is considered. Said maximum distance preferably is a distance corresponding to a distance allowing a coalescence of ink droplets. Said ink droplets, inkjet printed a) as two adjacent ink droplets or b) as two adjacent stacks of ink droplets or c) as an ink droplet adjacent to a stack of ink droplets, preferably after coalescence form a continuous layer.

Further, when (i) positioning one volume element or more volume elements or (ii) not positioning one volume element or more volume elements according to said condition

- a variation in a distance between two adjacent volume elements in said layer, or

- a variation in a distance between two adjacent stacks of volume elements in said layer, or

- a variation in a distance between a volume element and an adjacent stack of volume elements in said layer preferably is minimized. When inkjet printing a spectacle lens in layers considering said minimized variation in a distance

- between two adjacent ink droplets in a layer, or

- between two adjacent stacks of ink droplets in a layer, or

- between an ink droplet and an adjacent stack of ink droplets in a layer preferably enables a smoothest possible surface of said layer.

In a preferred embodiment of the invention, the computer-implemented method is further characterized by one of the following additional steps selected from:

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of a volume element and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of a volume element and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of a volume element and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of a volume element and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer.

A discrete Xo+1,yo+1,Zo+1 ... Xp+1,Yp+1 ,Zp+1 position is adjacent to a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position within in a same layer. A discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer is directly adjacent and on top of a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer.

In case said layer is a final layer of said layer stack then said transferring of said deviation is only possible within said final layer. As described before, the volume elements may be represented as cuboids with preset edge lengths, and preferably are represented as cubes of a preset edge length and the layer thickness in each discrete x,y,z position of each layer is preset by slicing a digital twin of a spectacle lens into a layer stack.

Subsequently to a

(i) positioning of one volume element or more volume elements in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position(s) of said layer, or

(ii) not positioning of one volume element or more volume elements in a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 position(s) of said layer, an actual value of a layer thickness in a discrete Xm+1 ,Ym+i ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer is determined and compared to a default nominal value of said layer thickness a discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer. A deviation from said default nominal value is

- distributed to an adjacent discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1 ,Yp+1,Zp+1 position within said identical layer, and

- transferred to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer.

Distributing said deviation to one adjacent discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1 ,Yp+1,Zp+1 position or more adjacent Xo1+1 ,Yo1+1,Zo1+1 ... Xp1+1 ,Yp1+1 ,Zp1+1 positions shall mean that when determining an actual layer thickness in said discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1 ,Zp+1 position or in said discrete Xo1+1 ,Yo1+1,Zo1+1 ... Xp1+1 ,Yp1+1 ,Zp1+1 positions said deviation is considered. In case said actual value of said layer thickness in said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer is smaller than said default nominal value of said layer thickness in said a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position then said deviation is considered for example in that in an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position the difference in layer thickness is added to an actual layer thickness in said adjacent discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1,Yp+1,Zp+1 position. In case said actual value of said layer thickness in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer is larger than said default nominal value of said layer thickness in said a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position then said deviation is considered for example in that in an adjacent discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1 ,Yp+1,Zp+1 position the difference in layer thickness is subtracted from an actual layer thickness in said adjacent discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1 ,Y _p +1,Zp+1 position. In case said actual value of said layer thickness in said discrete Xm+1,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer is equal to said default nominal value of said layer thickness in said a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position no transferring is needed.

Subsequently to the before described distribution of said deviation the computer-implemented method continues with and applies said step in said adjacent discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1,Yp+1 ,Zp+1 position, i.e., an actual value of a layer thickness in said discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1 ,Yp+1,Zp+1 position of said layer is determined and compared to a default nominal value of said layer thickness a discrete X _o +1,Y _o +1 ,Z _o +1 ... Xp+1 ,Yp+1,Zp+1 position of said layer. A deviation from said default nominal value is

- distributed to an adjacent discrete Xq+1,Yq+1 ,Zq+1 ... Xr+1,Yr+1,Zr+1 position within said identical layer, and

- transferred to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer. Said determination is continued until a deviation of an actual layer value of a thickness from a default nominal value of said layer thickness is determined for each discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer.

A sum of said deviation and the considered deviation distributed in a layer preferably is zero to ensure that in an inkjet printed lens a total volume of ink droplets is equivalent to a volume of a layer to be inkjet printed.

Transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of a next but one layer shall mean that said deviation is considered in said next but one layer to preferably position a volume element in said next but one layer in a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position not on top of a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer. Thus, said transferring contributes to achieve a smoothest possible (i) interface of a spectacle lens or (ii) surface of a spectacle when said spectacle lens is inkjet printed in layers and ink droplets are positioned according to said positioning of volume elements a discrete Xm+2b,Ym+2b,Zm+2b ... Xn+2b,Yn+2b,Zn+2b position.

The computer-implemented method being configured for calculating a digital twin of a spectacle lens for the purpose of a use of the digital twin for a manufacture of the spectacle lens, the digital twin having a front surface and a back surface, is characterized in the step of:

- calculating a total number of volume elements between each discrete Zfront(x,y) position of said front surface and a respective discrete Zback(x,y) position of said back surface, the calculation resulting in a volume element density distribution of said digital twin.

In a digital twin of a spectacle lens a distance of each discrete z(x,y) position of a front surface to a respective z(x,y) position of a back surface preferably is preset. For a respective distance in each discrete z(x,y) position between the front surface and the back surface the two discrete z(x,y) positions of the front surface and the back surface differ in their respective z position only. Phased differently, said distance between a discrete z(x,y) position of a front surface and a respective z(x,y) position of a back surface is a distance between positions having identical discrete x and y positions on the respective surface but having different z positions on the respective surface. A total number of volume elements for each respective distance between the front surface and the back surface of the digital twin, may be calculated by dividing a lens thickness at a (x,y) position by a respective thickness of a fully printed layer. Preferably, with respect to

- said preset distance in each discrete z(x,y) position between the front and the back surface, i.e., an absolute value of Zback(x,y) minus Zfront(x,y),

- a volume of one volume element,

- an area of said one volume element, usually depending on a printing resolution of an inkjet printer, preferably a printhead of said inkjet printer, said total number of volume elements is calculated as product of said preset distance and said area of said one volume element divided by the volume of said one volume element: Having calculated said total number of volume elements for each distance between a front surface and a back surface of a digital twin results in a volume element density distribution of said digital twin. Said volume element density distribution is a suitable basis for slicing said digital twin.

The computer-implemented method is suitable for generating printing instructions for inkjet printing a spectacle lens. The computer-implemented method is suitable for the purpose of generating printing instructions, said printing instructions to be used for inkjet printing a spectacle lens.

Preferably, the method being configured for calculating the digital twin of the spectacle lens for the purpose of a use of the digital twin for the manufacture of the spectacle lens, the digital twin having the front surface and the back surface, is characterized in the step of:

- determining said layer stack to comprise a minimum number of layers based on a calculated maximum total number of volume elements between a discrete x,y,z position of said front surface and a respective discrete x,y,z position of said back surface.

Preferably, said digital twin is sliced such that a minimum number of layers at a maximum distance between a front surface and a back surface is determined. Under the assumption of an identical volume and an identical area of volume elements a maximum distance between a front surface and a back surface of a digital twin corresponds to a calculated maximum total number of volume elements.

Preferably, the method being configured for calculating the digital twin of the spectacle lens for the purpose of a use of the digital twin for the manufacture of the spectacle lens, the digital twin having the front surface and the back surface, is characterized in the step of:

- uniformly distributing volume elements based on said calculated total number of volume elements o in z direction of each respective x,y,z position, and o in x,y direction of each layer of said layer stack.

Uniformly distributing volume elements in the knowledge of the calculated total number of volume elements and the minimum number of layers of said layer stack preferably comprises that in z direction between two respective x,y,z positions a front surface and on a back surface when the total number of volume elements is smaller than the minimum number of layers not the total number volume elements is distributed in subsequent layers of said layer stack but that the total number of volume elements is distributed throughout the minimum number of layers. A resulting spatial volume pattern is then the basis for inkjet printing a spectacle lens.

Preferably, the method being configured for calculating the digital twin of the spectacle lens for the purpose of a use of the digital twin for the manufacture of the spectacle lens, the digital twin having the front surface and the back surface, is characterized in that each layer of said layer stack is having an identical spatial expansion when projected in a plane held by a x direction and a y direction.

Preferably, an identical spatial expansion of all layers of a layer of a digital twin has the decisive advantage that in an inkjet printed spectacle lens, preferably inkjet printed according to a spatial volume element pattern resulting from any one of the before described volume element positionings or not positionings, has the inherent superelevations described in WO 2021/209551 A1 , for example on page 1 , lines 25 to 28, were transferred to an edge of the printed spectacle lens. If necessary, such an edge with added up superelevations may be just cut off.

The computer-implemented methods described before are further configured to manufacture the spectacle lens based on the digital twin of the spectacle lens.

A Computer according to the invention is configured to perform the step of:

- determining a volume element positioning in a layer of a layer stack of a digital twin in that

(i) a positioning a volume element in a discrete Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of said layer stack is based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack, or

(ii) a not positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of said layer stack is based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,yn,Zn position of an adjacent layer of said layer stack, said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer being directly adjacent and on top of said discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer, following the condition: when in 50% or in less than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of said adjacent layer a volume element is positioned then no volume element is positioned in discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 positions of said layer; when in more than 50% of discrete Xm,Ym,Zm ... Xn,Yn,Zn positions of said adjacent layer a volume element is positioned then volume elements are positioned partially in discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 positions of said layer, and an inkjet printer printing a spectacle lens according to said condition.

A data processing system according to the invention comprises a processor and a storage medium coupled to the processor, wherein the processor is adapted to perform the steps:

(i) positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of a layer stack, based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack, or

(ii) not positioning a volume element in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer of a layer stack, based on a positioning of a volume element in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer of said layer stack, said data processing system being configured for the purpose of a use thereof for inkjet printing a spectacle lens in layers.

Said processor adapted to perform above mentioned steps may be based on a computer program stored on a storage medium. Said storage medium may be a non-transitory tangible computer- readable storage medium. In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform the step according to one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then no volume element is positioned in each of said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1,Yn+1,Zn+1 positions.

In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform a step according to one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then no volume element is positioned in each of said discrete Xm+1 ,Ym+i ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions and volume elements are positioned in each of a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions a volume element is positioned then volume elements are positioned partially in said discrete Xm+1 ,Ym+1 ,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 positions and volume elements are positioned partially in discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack.

In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform a step according to one of the following conditions:

- when in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer a volume element is to be positioned then said volume element is positioned as described before with respect to a computer-implemented method;

- when in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer a volume element is to be positioned then said volume element is positioned as described before with respect to a computer-implemented method;

- when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer, i.e., of a layer being separated by said layer, said next but one layer, said adjacent layer to said next but one layer from said adjacent layer, a volume element is to be positioned then said volume element is positioned as described before with respect to a computer-implemented method.

In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform an additional step: (iii) determining a deviation of an actual value of a layer thickness in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer from a default nominal value of said layer thickness in an identical discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform an additional step:

(iv) determining a sum of said deviation and said actual value of said layer thickness.

In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform a step according to one of the following conditions:

- when said sum is larger than half said default nominal value of said layer thickness then no volume element is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack;

- when said sum is smaller than or equal to half said default nominal value of said layer thickness then a volume element is positioned in a discrete Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack.

In a preferred embodiment, the data processing system comprises a processor and a storage medium coupled to the processor is adapted to perform one of the additional steps selected from:

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of a volume element and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of a volume element and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of a volume element and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of a volume element and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer.

With respect to said data processing system the before with respect to a computer-implemented method given definitions shall apply. Said data processing system is replacable by a computer and an inkjet printer, in this case the before with respect to a computer-implemented method given definitions shall also apply. In a preferred embodiment, the invention comprises a computer program, said computer program comprises instructions which, when the program is executed by a computer, cause the computer to carry out the above-described computer-implemented method.

Said computer program may be stored on a non-transitory tangible computer-readable storage medium, said computer program comprising instructions which, when said program is executed by a computer, cause the computer to carry out the above-described computer-implemented method.

In a preferred embodiment, the invention comprises a computer-readable storage medium having stored thereon said computer program. Said computer-readable storage medium may be a non- transitory tangible computer-readable storage medium.

In a preferred embodiment, the invention comprises a data signal carrying said computer program.

A data set of computer-readable printing instructions according to the invention is configured to be used for inkjet printing a spectacle lens, the data set being (i) stored on a computer-readable storage medium or (ii) transferred via a data signal. Said data set is for the purpose of a use thereof for inkjet printing a spectacle lens.

Said data set comprise printing instructions which have been generated as described before.

An inkjet printer according to the invention comprises a processor configured to cause an inkjet print head

A) to release a jet forming an ink droplet in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer, or

B) not to release a jet forming an ink droplet in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer for inkjet printing a spectacle lens in layers, said release or said not release being based on an ink droplet positioning in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of an adjacent layer.

Said (A) release or (B) not release is completed when said spectacle lens is finished inkjet printed.

In a preferred embodiment, the inkjet printer is configured to comprise a step according to one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then no ink droplet is positioned in each of said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then ink droplets are positioned partially in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions.

In a preferred embodiment, the inkjet printer is configured to comprise a step according to one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then no ink droplet is positioned in each of said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions and ink droplets are positioned in each of a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then ink droplets are positioned partially in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions and ink droplets are positioned partially in discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack.

In a preferred embodiment, the inkjet printer is configured to comprise a step according to one of the following conditions:

- when in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer an ink droplet is to be positioned then said ink droplet is positioned as described before with respect to a computer-implemented method;

- when in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer an ink droplet is to be positioned then said ink droplet is positioned as described before with respect to a computer-implemented method;

- when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer, i.e., of a layer being separated by said layer, said next but one layer, said adjacent layer to said next but one layer from said adjacent layer, an ink droplet is to be positioned then said ink droplet is positioned as described before with respect to a computer-implemented method.

In a preferred embodiment, the inkjet printer is configured to comprise an additional step:

(C) determining a deviation of an actual value of a layer thickness in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer from a default nominal value of said layer thickness in an identical discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

In a preferred embodiment, the inkjet printer is configured to comprise an additional step:

(D) determining a sum of said deviation and said actual value of said layer thickness.

In a preferred embodiment, the inkjet printer is configured to comprise a step according to one of the following conditions:

- when said sum is larger than half said default nominal value of said layer thickness then no ink droplet is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack;

- when said sum is smaller than or equal to half said default nominal value of said layer thickness then an ink droplet is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack. In a preferred embodiment, the inkjet printer is configured to comprise one of the additional steps selected from:

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of an ink droplet and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of an ink droplet and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of an ink droplet and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1 ,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of an ink droplet and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer.

With respect to said inkjet printer the before with respect to a computer-implemented method given definitions shall apply.

A method for inkjet printing a spectacle lens in layers according to the invention comprises one of the following steps: a) positioning an ink droplet in a discrete Xm+1,Ym+i,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer, based on a positioning of an ink droplet in an adjacent layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position, or b) not positioning an ink droplet in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of a layer, based on a positioning of an ink droplet in an adjacent layer in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position.

According to said method said (a) positioning or (b) said not positioning is completed when said spectacle lens is finished inkjet printed.

In a preferred embodiment, the method comprises a step according to one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then no ink droplet is positioned in each of said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then ink droplets are positioned partially in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions.

In a preferred embodiment, the method comprises a step according to one of the following conditions:

- when in less than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then no ink droplet is positioned in each of said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions and ink droplets are positioned in each of a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack;

- when in 50% or more than 50% of said discrete Xm,Ym,Zm ... Xn,Yn,Zn positions an ink droplet is positioned then ink droplets are positioned partially in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 positions and ink droplets are positioned partially in discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of a next but one layer of said layer stack.

In a preferred embodiment, the method comprises a step according to one of the following conditions:

- when in 50% or more than 50% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions and in 66% or less than 66% of said discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 positions of said next but one layer an ink droplet is to be positioned then said ink droplet is positioned as described before with respect to a computer-implemented method;

- when in more than 66% of discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions and in 75% or less than 75% of said discrete Xm+3,Ym+3,Zm+3 ... Xn+3,Yn+3,Zn+3 positions of an adjacent layer to said next but one layer an ink droplet is to be positioned then said ink droplet is positioned as described before with respect to a computer-implemented method;

- when in more than 75% of discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions and in less than 80% of said discrete Xm+4,Ym+4,Zm+4 ... Xn+4,Yn+4,Zn+4 positions of a layer separated by three layers from said adjacent layer, i.e., of a layer being separated by said layer, said next but one layer, said adjacent layer to said next but one layer from said adjacent layer, an ink droplet is to be positioned then said ink droplet is positioned as described before with respect to a computer-implemented method.

In a preferred embodiment, the method comprises an additional step:

(c) determining a deviation of an actual value of a layer thickness in a discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer from a default nominal value of said layer thickness in an identical discrete Xm,Ym,Zm ... Xn,Yn,Zn position of said adjacent layer.

In a preferred embodiment, the method comprises an additional step:

(d) determining a sum of said deviation and said actual value of said layer thickness.

In a preferred embodiment, the method comprises a step according to one of the following conditions:

- when said sum is larger than half said default nominal value of said layer thickness then no ink droplet is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack;

- when said sum is smaller than or equal to half said default nominal value of said layer thickness then an ink droplet is positioned in a discrete Xm+1,Ym+1,Zm+1 ... Xn+1,Yn+1,Zn+1 position of said layer of said layer stack.

In a preferred embodiment, the method comprises one of the additional steps selected from:

- determining a deviation of a default nominal value of a layer thickness in said discrete

Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of an ink droplet and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said positioning of an ink droplet and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of an ink droplet and distributing said deviation to an adjacent discrete Xo+1,Yo+1,Zo+1 ... Xp+1 ,Yp+1,Zp+1 position within said identical layer;

- determining a deviation of a default nominal value of a layer thickness in said discrete Xm+1,Ym+1,Zm+1 ... Xn+1 ,Yn+1 ,Zn+1 position of said layer following said non-positioning of an ink droplet and transferring said deviation to a discrete Xm+2,Ym+2,Zm+2 ... Xn+2,Yn+2,Zn+2 position of said next but one layer.

With respect to said method the before with respect to a computer-implemented method given definitions shall apply.

In a preferred embodiment of the invention, a spatial expansion of said layer and said adjacent layer is identical.

An identical spatial expansion means that said layer and said adjacent layer when projected in a plane held by a x direction and a y direction, in plan view, is of identical dimensions. For example, when each layer and said adjacent layer when projected in a plane held by a x direction and a y direction, in plan view, results in results in a circle, a radius of each layer resulting in said circle is identical. Being of identical dimensions does not necessarily mean that, when projected in a plane held by a x direction and a y direction, in plan view, at every point of a perimeter of said projection an ink droplet must be placed. However, said perimeter preferably is the maximal spatial expansion each layer has. Said spatial expansion may be either a spatial expansion for a spectacle lens for which

- an edging is intended, i.e., a spectacle lens corresponding to an uncut lens as defined in ISO 13666:2019(E), section 3.8.8, a finished lens prior to edging, or

- no edging is intended, i.e., a spectacle lens corresponding to an edged lens as defined in ISO 13666:2019(E), section 3.8.9, a finished lens edged to the final size and shape.

In a preferred embodiment of the invention, an outermost of said adjacent layers is inkjet printed in or on a substrate, said substrate defining a lens surface of

- a front surface of said spectacle lens or

- a back surface of said spectacle lens.

In a preferred embodiment of the invention, a total volume of ink droplets in each layer is preset.

A total volume of ink droplets being preset means that a total volume of ink is preset for each layer, i.e., said total volume is inkjet printed in a layer. No volume of said total volume is inkjet printed in another layer. Said total volume of ink droplets to be positioned in a layer is equivalent to a volume of said layer.

Figure 1 shows a flow chart comprising preferred embodiments of the computer-implemented method. Figure 2 shows the result of a positioning on a linear gradient structure. In the upper part, the layer thickness is zero so that no volume elements are positioned, said volume elements representing ink droplets to be inkjet printed. In the lower part, all layers are to be inkjet printed with their maximum thickness so that all ink droplets are inkjet printed and all volume elements representing them positioned. In the 50% zone, the layer is to be inkjet printed with half of the maximum thickness so here only half of the ink droplets are to be inkjet printed and only half of the volume elements representing them positioned. The positioning of the volume elements in the second layer here is complementary to the positioning of the volume elements in the first layer. The positioning of the volume elements in the fourth layer here is complementary to the positioning of the volume elements in the second layer. The positioning of the volume elements in the third layer may not be complementary to the positioning of the volume elements in the second layer. This is because at this discrete position the deviation of the layer thickness of the first layer was already equilibrated by the opposing volume element positioning of the second layer. This means the volume elements in the third layer at this discrete position are mainly positioned here minimizing the distance variation to volume elements in the same layer.

In the 25% zone, one can observe that only one volume element is positioned at each position distributed over all four layers. In the 75% zone, one can observe that three volume elements are positioned at each position distributed over all four layers.