FIELD OF THE INVENTION

This disclosure relates to a method for designing a pupil intensity mask for light-sheet microscopy, a method for fabricating a pupil intensity mask for light-sheet microscopy and a pupil intensity mask for light-sheet microscopy.

BACKGROUND

Light-sheet microscopy has advantages over laser-scanning confocal microscopy in many applications, due to parallelized imaging and flexibility in optics design. Early instrument designs in light-sheet microscopy generated a 2-dimensional sheet with a cylindrical lens. This method was called Selective Plane Illumination Microscopy (SPIM) [Huisken et al, Science 305, 1007-1009 (2004) ; Verveer, P. J. et al, Nature methods 4, 311 (2007).] This method is schematically depicted in figure 2A. Cylindrical lens 2 creates a light-sheet 4 in a sample 6. The light sheet 4 causes excitations in only a section of the sample 6. As a result, emission light 8 originates from the sample 6, which is captured by a detection lens 10 of an optical system, such as an imaging system. As shown, the light forming light sheet 4 propagates in the y direction and the light sheet is parallel to the x-y plane. Further, the detection axis is parallel to the z axis. As used in this disclosure, the y axis is parallel to the propagation direction of the illumination light and the z axis is parallel to the detection axis. Typically, the light sheet is parallel to the x-y plane. Further, the width of the light sheet is a dimension of the light sheet along the x axis, whereas the length of the light sheet is a dimension of the light sheet along the y axis and the thickness of the light sheet is a dimension of the light sheet along the z axis.

Soon it was demonstrated that scanning a spherical focused beam in one dimension could generate a "virtual" sheet, as seen by the camera, with the major advantage of reducing light exposure to the sample [Keller, P. J., et al , Science 322, 1065-1069 (2008).]. This approach is alternately called digital scanned light-sheet microscopy (DSLM), digital light-sheet, scanned light-sheet, or 1 D light- sheet. Scanned beam approaches also made nonlinear excitation feasible because the spherical focus can generate a high peak intensity for a given power, extending light-sheet microscopy to imaging in highly scattering samples [Truong et al, Nature methods 8, 757 (2011)]. This method is schematically shown in figure 2B, wherein the spherically focused beam 12, which may be formed by a spherical lens 14, is scanned in a direction parallel to the x axis in order to create a virtual light sheet.

Further developments have focused on adding a second excitation path to improve the uniformity of the virtual sheet [Huisken et al, Opt. Lett. 32, 2608-2610 (Sept. 2007).], and later a second detection path, for isotropic resolution in the "multi-view" light-sheet design [Krzic et al, Nature methods 9, 730 (2012).]. Auto-focus, adaptive excitation power, and automated beam alignment features have made long-term multi-view imaging of live samples practical [Royer et al Nature biotechnology 34, 1267 (2016)]. A theoretical framework was recently developed by Sheppard et al, Optics express 21 , 6339- 6345 (2013): he showed that using a 2D, binary phase mask (0; TT) it is possible to obtain longer, conned excitation profiles. This approach was has been recently implemented and refined [Wilding,

D., et al, Optics Letters 41 , 1205-1208 (2016)], applying adaptive optics to correct for sample induced aberration and misalignment.

A similar solution has been adopted with the so called "magic carpet" [Golub et al, Optics letters 40, 5121-5124 (2015) & Haouas et al JOSA A 36, 124(131 (2019)], where authors increase only slightly the complexity of the original SPIM setup, using a Powell lens to focus line profiles onto a cylindrical lens: this results in very long (hundreds of microns) carpet beams, with a trade-off on the confinement (e.g. 240 micrometer length with 6 micrometer thickness).

The most immediate improvement for obtaining longer 1-D uniform excitation profiles comes as a trade-off with temporal resolution: tiling the excitation light sheet allows, in principle, to select only the central uniform region of the excitation profile, stitching together multiple images over an arbitrary field of view [Dean et al, Biophysical journal 108, 2807-2815 (2015); Meinert, T. & Rohrbach, Biomedical optics express 10, 670-681 (2019)].

A significant milestone in one-dimensional beam-shaping has been the introduction of quasi non-diffracting beams: in particular Bessel-like beams [Planchon, T. A. et al. Nature Methods 8, 417 EP - (Mar. 2011); Gao, L. et al. Cell 151 , 1370-1385 (2012); Lu et al, Biomedical optics express 9, 1964-1976 (2018)] and Airy beams [Vettenburg, T. et al, Nature Methods 11 , 541 EP - (Apr. 2014)]. The common characteristic of these approach is that these new engineered beams possess a tightly focused main lobe (that maintains higher confinement and longer uniformity than the classic Gaussian beam) surrounded by unwanted side lobes. In fact, researchers aimed to improve on those characteristics: on one hand trying to extend even more the uniformity of the central core (to investigate even larger volumes with high resolution), on the other "curing" the presence of unwanted side lobes excitation (increasing contrast and decreasing the amount of light on sample).

A considerable step forward that has been proposed consists in engineering an optical lattice to exploit interference between multiple Bessel-like beams to reduce unwanted side lobes while preserving all the useful characteristics of the beam. In the first implementation of lattice light-sheet microscopy [Chen, B.-C. et al. Science 346, 1257998 (2014)], the lattice is formed by a diffraction grating generated by a phase-modulating SLM, followed by filtering with an annulus mask in the pupil plane. This results in an extremely tight focus that extends well beyond the capabilities of a Gaussian beam: the destructive interference from adjacent beams cancels the undesired side lobes of a single Bessel beam, increasing the contrast. This kind of setup persists at the core of numerous new arrangements, that on one hand try to reduce the apparatus complexity, on the other to extend even more uniformity and increase confinement. [Chen, B.-C. et al. Science 346, 1257998 (2014)] acknowledges US7,894,136 B2 disclosing a method for creating a periodic interference pattern of coherent waves in two or three dimensions, US 8,711 ,211 B2 disclosing techniques for performing Bessel beam plane illumination microscopy and U.S. Patent application 13/844,405 relating to structured plane illumination microscopy. Exploiting lattice geometry and tiling approach [Gao, et al, Optics express 27, 1497-1506 (2019)], it has been demonstrated that, again, at the price of slower acquisitions, there could be no intrinsic limitation to the extent that could be explored (excluding the impact of heavy aberrations).

To simplify the setup, [Ellefsen et al, Cell calcium 71 , 34-44 (2018)] exploits the fact that, when not directly trying to correct for aberrations, when fixing the desired geometry and the investigation volume in the sample, the SLM is not really necessary, and it can be substituted by fixed diffractive elements.

Fahrbach et al. Optics express 21, 11425-11440 (2013)]: shows that by modifying the annular mask, it is possible to obtain a single, quasi-Bessel beam, where side fringes have a reduced impact. Another example of using a more complex amplitude mask to generate optical lattices is defined in Chen et al. Applied Physics Letters 109, 061107 (2016)]. Gao et al, Optics express 23, 6102-6111 (2015)] describes an implementation wherein a photomask is conjugated with a binary SLM.

Chang, B.-J. et al. Nature methods 16, 235 (2019) discloses a method for generating arbitrary beam profiles by sampling a pupil mask with a scanned line focused, supported by a theoretical framework dubbed "field synthesis". The authors also demonstrated that scanning a line on an annular pupil and then incoherently summing the excitation profile can achieve the same geometry as a scanned lattice light-sheet. The authors disclose a custom-made microscope that scans a line focus over an annular mask to sequentially produce multiple Bessel beams during the exposure of a single camera frame. An advantage of this technique is that no spatial light modulator, diffraction optics, or polarization optics are required. Disadvantages are that no coherent lattice is generated, and the scanning of the laser must be coordinated with the camera frame.

[Olarte et al , Advances in Optics and Photonics, vol. 10, no. 1 , 111-179, (March 2018)], hereinafter referred to as “Olarte”, describes that, in a simulation, an optical lattice is created using a pupil amplitude mask, wherein the pupil amplitude mask is formed by superimposing an opaque mask containing a set of slit apertures over a Bessel beam ring aperture.

Thus, in light of the above, there is a need in the art for improved methods for designing an optical setup for forming a light sheet in a sample, in particular for designing pupil intensity masks for forming a light sheet in a sample.

SUMMARY

To that end a method for designing a pupil intensity mask for an optical system, such as a light- sheet microscope, is disclosed. The intensity mask is configured to create a predetermined illumination light sheet in a sample and is obtainable by superimposing a first intensity mask onto a second intensity mask. The second intensity mask is for example an annular aperture and the first intensity mask is for example a set of slit apertures. The second intensity mask is configured to modulate the intensity of incident illumination light such that the illumination light, when focused by an optical system, causes a particular light distribution in a plane that is substantially perpendicular to the illuminations light’s propagation direction. This plane may also be referred to as the focal plane of the illumination lens. This particular light distribution is for example a transverse profile of a Bessel beam, such as a zeroth order Bessel beam. In any case, the particular light distribution may comprise a maximum amplitude in the center, associated with a maximum light intensity peak in the center. The method for designing the pupil intensity mask further comprises determining an arrangement in said plane of copies of said particular light distribution thus determining a composite light distribution in said plane. The method also comprises, based on the composite light distribution, determining the pupil intensity mask.

This method enables to design appropriate pupil intensity masks and therefore enables to design optical systems that create lattice light sheets in a sample having properties as desired. Examples of such properties include the length of the lattice light sheet, the thickness of the sheet, the confinement of the light sheet et cetera. Once designed and fabricated, the pupil intensity mask can simply be placed at the lens pupil of an optical system. The method obviates the need to apply a (virtual) trial and error approach for finding the intensity mask that can generate a desired light sheet.

In this manner, any 1 D virtual light sheet microscope can be made into a microscope that can produce a lattice light sheet. As described by Chen, B.-C. et al. Science 346, 1257998 (2014), such a lattice light sheet can be used for high-speed optical sectioning as well as for Structured Illumination Microscopy (SIM) techniques.

The method steps described herein may be performed by a data processing system. The methods described herein may be computer-implemented methods.

The method may comprise determining the second intensity mask. In an example, the second intensity mask is an annular aperture and determining the second intensity mask comprises determining the inner and/or outer radius of the annular aperture.

A pupil intensity mask is typically positioned in the pupil plane of a lens or in a plane conjugated thereof. The pupil plane of a lens may also be referred to as the back focal plane of the lens. An intensity mask may comprise any device that spatially modulates the intensities of incident light.

Herein spatially modulating incident light may be understood as influencing the intensity in a spatially varying manner. Spatially modulating incident light for example comprises blocking the center part of an incident light beam and letting pass the rest of the incident light beam. The pupil intensity mask may be a spatial light modulator that modulates the intensity of the light beam.

The arrangement of copies of the particular light distribution may be understood to be a virtual, spatial arrangement of the copies in said plane, for example in the focal plane of the illumination lens. The particular light distribution may be regarded as building block for forming the composite light distribution.

When the optical mask is implemented in an optical system and has created a lattice light sheet as desired, the lattice light sheet may be subsequently scanned in order to create a virtual light sheet as is for example the case when the lattice light sheet is used for high-speed optical sectioning. Preferably, at least one scanning direction is perpendicular both to the propagation direction of the illumination light and to the detection axis, i.e. scanned in a direction parallel to the x axis lattice light sheet may also be scanned in a direction parallel to the z-axis, for example to be able to render a three dimensional image of the sample. When the optical mask is implemented in an optical system and has created a lattice light sheet as desired, the lattice light sheet may subsequently be used for Structured Illumination Microscopy, which may entail shifting the light sheet, for example in the x direction.

An illumination light sheet as used herein may be understood to be light distribution that is substantially confined to a plane, e.g. the x-y plane, and only has limited extension into the direction perpendicular to this plane, e.g. limited extension into the z-direction. The thickness of the light distribution is typically much smaller than the light distribution’s dimensions in this plane.

It should be understood that the light-sheet may have a varying, non-uniform light intensity in this plane (x-y plane). In an example, the intensities of the light sheet in this plane form a pattern, i.e. show a regularity.

In an embodiment, the second intensity mask comprises an annular aperture and determining the second intensity mask comprises determining a width of the annular aperture based on a desired length of the light sheet. Optionally, the width of the annular aperture is further determined based on a wavelength of the illumination light and/or based on a refractive index of the medium after the illumination lens and/or on the numerical aperture of the illumination lens. The illumination lens may be understood to be the lens that focuses the illumination light in order to create the light sheet in the sample. This embodiment allows to design appropriate pupil intensity masks that form light sheets having a desired length.

The length of the sheet may be understood to be the dimension of the sheet along the propagation direction of the illumination light. The length of the sheet may be understood to be the distance - along the propagation direction of the sheet - in which the thickness of the sheet remains within a factor of its waist thickness Wo, for example remains within V(2)* Wo Herein, thickness may be understood to be the dimension of the sheet along the detection axis (z axis). The waist thickness of a sheet may be the minimum thickness of the light sheet.

The width of an annular aperture may be defined by R _ext - R _lnt , wherein R _ext is the external radius of the aperture and R _lnt is the internal radius of the aperture. (Also see figure 3B.) In an embodiment, R _ext is determined based on the numerical aperture of the optical system. Typically, R _ext is preferably as large as possible, and thus limited by the numerical aperture of the illumination system, because this yields as thin as possible light sheets. Of course, thin light sheets are desirable as they have better optical sectioning capabilities than thick light sheets.

However, there may be situations where a thicker light sheet is desired. In such case, R _ext , or R _lnt , may be determined based on a desired thickness. If the length of the light sheet is given, then R _ext - Rin _t ) i ^s fixed. In such case, determining R _ext means determining R _lnt and vice versa.

In an embodiment wherein the internal radius or the external radius is determined based on desired thickness of the light sheet, the internal or external radius may be found based on a trial and error approach. For several values of R _ext or R _lnt , the thickness of the sheet may be calculated numerically to see if one of them yields a desired thickness. Note that by reducing R _ext the effective NA of the illumination system is also reduced. In an embodiment, the method further comprises determining the particular light distribution based on the determined second intensity mask. In an example, this step comprises Fourier transforming the second intensity mask. Once the particular light distribution has been determined, the arrangement of copies of said particular light distribution in said plane can be determined. This step may be performed numerically and may be computer-implemented.

In an embodiment, determining the pupil intensity mask comprises Fourier transforming the composite light distribution. The Fourier transform of a light distribution in the focal plane of a lens namely yields the light distribution in the pupil plane of the lens. Thus, by Fourier transforming the composite light distribution, which may be understood to be the desired light distribution, the associated light distribution in the pupil plane can be determined as well as the pupil intensity mask that is required to achieve that light distribution in the pupil plane.

In an embodiment, Fourier transforming the composite light distribution comprises Fourier transforming a function, wherein a two-dimensional convolution of the function with said particular light distribution describes the composite light distribution.

This embodiment greatly simplifies the calculations. In this embodiment, the Fourier transform of the particular light distribution is known, because it is the second intensity mask, which may be an annular aperture. Hence, only the particular function has to be Fourier transformed.

Convolving one function with another function may be understood as determining a third function expressing how the shape of the first function is modified by the third function.

In an embodiment, the particular light distribution comprises a maximum amplitude in a center of the particular light distribution. In this embodiment, said function is a two-dimensional comb function having its impulses positioned on the respective centers of the copies of the light distribution. The two- dimensional convolution of the two-dimensional comb function and the particular light distribution describes the composite light distribution.

In an embodiment, the particular light distribution comprises a maximum amplitude in a center of the particular light distribution and a secondary maximum amplitude in a ring around said center. The copies of the particular light distribution are arranged in the composite light distribution such that respective centers of copies of the light distribution are positioned on a central illumination line in said plane and such that destructive interference occurs that suppresses at least parts of the secondary maximum amplitude rings of the respective copies on the central illumination line. Preferably parts in regions away from the central illumination line are suppressed.

The composite light distribution may comprise further copies of the particular light distribution having respective centers that lie above and/or below this central illumination. The respective light fields of the further copies of the particular light distribution may also interfere destructively herewith causing suppression of the secondary maxima of the copies of the light distribution that are positioned on the central illumination line.

The central illumination line may be understood to be perpendicular to the detection axis and perpendicular to the illumination light’s propagation direction. The central illumination line may be parallel to the x axis. In an embodiment, the copies of the particular light distribution are arranged in the composite light distribution such that said destructive interference suppresses parts of the secondary maximum rings of the respective copies on the central illumination line, wherein the suppressed parts are positioned away from the central illumination line. This embodiment allows to achieve high confinement of the lattice light sheet that is created by the pupil intensity mask. Herein, a high confinement of a light sheet may be understood to mean that the light sheet has high intensities at the central illumination line, wherein these high intensities are centered on the central illumination line, yet that the other high intensities of the light sheet, that are not centered on the central illumination line, are all positioned relatively far away from the central illumination line. It is typically undesirable to have high intensities near the central illumination line, as viewed from the y-direction, because they reduce the sectioning capabilities. Preferably, only a thin light section of the sample is illuminated.

In an embodiment, the copies of the particular light distribution have a hexagonal arrangement in the composite light distribution. This allows to closely pack the copies of the particular light distribution in the arrangement, which allows to form a very thin lattice light sheet. In another embodiment, the copies of the particular light distribution have a square arrangement in the composite light distribution.

In an embodiment, determining the pupil intensity mask comprises performing a binarization such that the pupil intensity mask at each position has either full light transmittance (100%) or no light transmittance (0%). This embodiment enables to design pupil intensity masks that can be very easily fabricated, for example by 3D printing techniques.

In an embodiment, after the composite light distribution has been determined in the focal plane of the illumination lens, the composite light distribution is Fourier transformed in order to determine the associated light distribution at the pupil plane. This associated light distribution may be understood to determine a light transmittance for each position on the pupil intensity mask that is to be placed at the pupil plane and typically defines a partial light transmittance for some positions on the mask. In an embodiment, in order to design a pupil mask that can be easily fabricated, this associated light distribution is binarized. The binarized light distribution can have either one of two values, e.g. either 0 for no light transmittance or 1 for full light transmittance, corresponding to a pupil intensity mask that fully blocks incident light except at positions where an aperture is present in the mask, which aperture fully transmits the light.

In an embodiment, the method comprises determining instructions which, when executed by a fabrication system such as a three-dimensional printing system, cause the fabrication system to fabricate the determined pupil intensity mask. In particular, the method may comprise outputting and/or storing a computer file comprising these instructions. Such computer file may have a file format suitable for 3D printing. The computer file is for example an STL file and/or VRML file and/or AMF file and/or a GCode file.

STL stands for “stereolithography” - it is a 3D rendering that contains only a single color. VRML (“vermal”, .WRL file extension) stands for “Virtual Reality Modeling Language” - it is a newer digital 3D file type that also includes color, so it can be used on desktop 3D printers with more than one extruder (i.e. two more nozzles that each can print with a different color plastic), or with full-color binder jetting technology. Additive Manufacturing File Format (.AMF) is a new XML-based open standard for 3D printing. Unlike STL, it contains support for color. They may also be compressable to about half the size of a compressed STL file.

One aspect of this disclosure relates to instructions being obtainable by the method for determining the above-mentioned instructions.

One aspect of this disclosure relates to a method for fabricating a pupil intensity mask for an optical system. Such method comprises designing the pupil intensity mask by performing one or more of the methods as described herein and fabricating the designed pupil intensity mask.

In an embodiment, the method fabricating the designed pupil intensity mask comprises 3D printing the pupil intensity mask, for example based on the above-mentioned instructions. The pupil intensity mask could also be fabricated by a subtractive manufactor, e.g., milling the holes in a solid disk.

One aspect of this disclosure relates to a pupil intensity mask that is obtainable by performing one or more of the methods for fabricating the pupil intensity mask as described herein.

One aspect of this disclosure relates to an optical setup comprising a pupil intensity mask described herein.

One aspect of this disclosure relates to a computer comprising a computer readable storage medium having computer readable program code embodied therewith, and a processor, preferably a microprocessor, coupled to the computer readable storage medium, wherein responsive to executing the computer readable program code, the processor is configured to perform one or more of the method steps described herein.

One aspect of this disclosure relates to a computer program or suite of computer programs comprising at least one software code portion or a computer program product storing at least one software code portion, the software code portion, when run on a computer system, being configured for executing one or more of the method steps described herein.

One aspect of this disclosure relates to a non-transitory computer-readable storage medium storing at least one software code portion, the software code portion, when executed or processed by a computer, is configured to perform one or more of the method steps described herein.

As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, a method or a computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system." Functions described in this disclosure may be implemented as an algorithm executed by a processor/microprocessor of a computer. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied, e.g., stored, thereon.

Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a computer readable storage medium may include, but are not limited to, the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of the present invention, a computer readable storage medium may be any tangible medium that can contain, or store, a program for use by or in connection with an instruction execution system, apparatus, or device.

A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber, cable, RF, etc., or any suitable combination of the foregoing. Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java(TM), Smalltalk, C++ or the like and conventional procedural programming languages, such as the "C" programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer, or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor, in particular a microprocessor or a central processing unit (CPU), of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer, other programmable data processing apparatus, or other devices create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

The flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

In one aspect, embodiments of the present invention may relate to a computer-implemented method for determining a pupil intensity mask.

Moreover, a computer program for carrying out the methods described herein, as well as a non- transitory computer readable storage-medium storing the computer program are provided. A computer program may, for example, be downloaded (updated) to existing data processing systems or be stored upon manufacturing of these systems.

Elements and aspects discussed for or in relation with a particular embodiment may be suitably combined with elements and aspects of other embodiments, unless explicitly stated otherwise. Embodiments of the present invention will be further illustrated with reference to the attached drawings, which schematically will show embodiments according to the invention. It will be understood that the present invention is not in any way restricted to these specific embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the invention will be explained in greater detail by reference to exemplary embodiments shown in the drawings, in which:

FIG. 2A schematically shows a set up for Single Plane Illumination Microscopy;

FIG. 2B schematically shows a set up digital scanned light-sheet microscopy; FIG. 3A schematically shows an optical set up and pupil intensity mask according to an embodiment;

FIG. 3B shows a pupil intensity mask according to an embodiment;

FIG. 4A illustrates a particular light distribution according to an embodiment;

FIG. 4B shows an intensity plot associated with a particular light distribution according to an embodiment;

FIG. 4C shows a composite light distribution according to an embodiment;

FIGs. 5A and 5B shows details of composite light distributions according to embodiments;

FIG. 6 schematically shows the width of a light sheet according to an embodiment;

FIGs. 7A and 7B illustrate how the second intensity mask may be determined according to an embodiment;

FIG. 8 shows intensity plots caused by pupil intensity masks according to embodiments;

FIG. 9 is a flow chart illustrating methods steps according to an embodiment;

FIG. 10 illustrates a data processing system according to an embodiment.

DETAILED DESCRIPTION OF THE DRAWINGS

Figure 1 schematically shows an embodiment of an optical setup 200 in which a pupil intensity mask 24 as described herein can be used. In particular, optical setup 200 is a light-sheet microscope. This system 200 can also be used to test pupil intensity masks that have been designed and fabricated as described herein.

A illumination light source 201 , such as laser source, for example a laser source that is configured to generate 488nm wavelength light, may iluminate an axicon lens 202. The axicon lens 202 generates a diverging conical profile. A lens L may be configured to collimate the beam. Herewith a a hollow cylindrical profile may be created that impinges onto the pupil intensity mask 24. The mask plane 204 may be relayed to the pupil plane 206 of the objective 2 using three telescopes T1 , T2 and T3. Hence, the pupil intensity mask 24 may be understood to be positioned in the pupil plane of lens 2. T1 copies the mask plane onto the first galvanometric mirror g1 ; T2 does the same towards the second galvanometric mirror g2; and finally T3 copies the plane to the pupil plane 206 of the objective 2. In the figure, the stars shows the copies of the pupil plane. The objective 2 has its focal plane in or near the sample 6.

The detection path comprises an objective 10, alsa referred to as a detection lens 10. The detection path may also comprise a tube lens 208, and may also comprise a unitary magnification telescopic module T4, optionally with and electrically tunable lens 210 at the commons focus. The electically tunable lens may be used to apply a custom defocus during volumetric scans, following the movement of the excitation plane. Emission light from the sample 6, such as fluorescence light, finally reaches imaging system 212, which may be a CMOS camera.

This optical system creates an illumination light sheet in the sample in the x-y plane and the created light sheet may subsequently be scanned, for example in the x-direction, in order to create a digital scanned light sheet as described above. The scan may be performed by galvanometric mirrors g1 and g2, one for each direction, x-direction and z-direction in figure 1 , perpendicular to the propagation axis of the light. In a typical configuration, the first mirror g1 is imaged on the second g2 with a telescope T2, and the second is imaged on the mask, that is finally imaged to the pupil plane of the lens. In this way, the galvanometric mirrors’ movement may add an angle, i.e. a phase, to the field. From the pupil 206 to the sample (due to the Fourier Transform’s properties), the amplitude mask 24 generates the geometry, while the angle adds a linear shift in one direction, again, x, or z, or both if both mirrors are moving.

Figure 3A schematically depicts a lattice light sheet microscope system comprising a pupil intensity mask 24 according to an embodiment. The microscope system comprises an illumination lens 2 that is configured to focus illumination light 16 and create a light sheet 19, such as a lattice light sheet, in sample 6. The illumination lens 2 preferably has its focal plane 18 in sample 6. The lattice light sheet 19 may cause emission light 8 from the sample 6 that is captured by detection lens 10.

Such emission light 8 is for example the result of optical excitations in the sample caused by the light sheet 19. Detection lens 10 preferably has its focus on the plane of the light sheet 19 as shown. Further, preferably, the depth of focus of the detection lens is equal to the thickness of the light sheet 19. The emission light 8 after being collected by detection lens 10 may subsequently be focused onto an image plane (not shown) of an imaging system, such as a camera, e.g. a CCD camera.

The pupil intensity mask 24 is preferably positioned in the pupil plane of the illumination lens 2. The pupil plane may also be referred to as the back focal plane. In an embodiment, the illumination light 16 incident on the intensity mask 24 has a uniform intensity.

Figure 3B shows a pupil intensity mask 24 according to an embodiment. As shown, such a pupil intensity mask is obtainable by superimposing a first intensity mask 20 onto a second intensity mask 22. An intensity mask may be understood to have a certain transmittance value for each position (x,y) on the mask. The transmittance value for position (x,y) indicates the ratio between the transmitted light intensity at position (x,y) and the light intensity that is incident at position (x,y). Thus, “0” for example indicates that no light is transmitted, i.e. the light is completely blocked, and “1” for example indicates that all light is transmitted.

Each position (x,y) on the first intensity mask 20 has a corresponding position (x,y) on the second intensity mask. The transmittance for position (x,y) on the first intensity mask 20 may be denoted by Ti(x,y) and the transmittance for position (x,y) on the second intensity mask 22 by T2(x,y). The transmittance of the pupil intensity mask 24 may then be given by T(x,y) = Ti(x,y) * T2(x,y).

It should be appreciated that pupil intensity mask 24 being obtainable by superimposing two intensity masks onto each other does not mean that fabricating pupil intensity mask 24 necessarily involves fabricating two pupil intensity masks and superimposing them onto each other.

Figure 4A schematically depicts a particular light distribution 29 in the focal plane 18 of the illumination lens. The particular light distribution 29 is the light distribution that the second intensity mask causes if placed in the pupil plane of illumination lens 2. If the second intensity mask would be the mask 22 as shown in figure 3B, then the particular light distribution is the transverse profile of a zeroth order Bessel beam as shown in figure 4A.

The dot 30’ in the center indicates the region where the particular light distribution has the highest amplitude, and thus the highest intensity. The particular light distribution further exhibits a high amplitude, and thus a high intensity, at further concentric rings around the center, such as first concentric ring 32’ and second concentric ring 34’. In practice, even more concentric rings are present. However, these are not shown in figure 4A.

Figure 4B shows the intensity of the light distribution corresponding to the particular light distribution of figure 4A along line 31 indicated in figure 4A. The maximum intensity peak 30 is associated with the center 30’ of figure 4A. Side peaks 32 are associated with the first concentric high amplitude ring 32’ and side peaks 34 are associated with the second concentric high amplitude ring 34’.

Figure 4C schematically shows the center lobe 30 of the light beam, which may be a Bessel-like beam, that causes the particular light distribution 29 shown in figure 4A. The thickness, also referred to as the waist, of the beam is indicated by 33. Typically, the beam has its waist at the focal plane of the illumination lens 2, thus in plane 18. Further, D indicates the length of the beam, and thus the length of the light sheet that will be constructed using the particular light distribution shown in figure 4A. In particular, D indicates the distance between the first zero intensity points on either side of the beams’ waist and D may be calculated using equation (3) below.

As explained above, the beam waist has a minimum bound defined by the NA of the illumination lens. It is possible to choose a larger beam waist by selecting a set {Rint, Rext} having smaller values that reduce the effective NA.

Figure 4D shows a composite light distribution according to an embodiment. Figure 4D shows the determined arrangement 35 in an x-z plane- for example in the focal plane 18 of the illumination lens- of copies 38 - 76 of the particular light distribution that is shown in figure 4A. In figure 4D, only the center and first concentric ring of each copy are shown for clarity. In this example, the copies of the light distributions have a hexagonal arrangement in the composite light distribution, however, other arrangements are also possible as will be shown below.

Figure 4D illustrates that the particular light distribution that is created by the second intensity mask, can be regarded as a building block for determining the composite light distribution. In the depicted example, the respective centers of copies 52 - 62 lie on a central illumination line 36. The central illumination line may be regarded as the center of the composite light distribution in the z- direction.

Preferably, the separation between high light intensities at the central illumination line 36 and other high light intensities is large. This namely reduces out of focus contributions. To illustrate, the region between 78 and 80 may represent the depth of focus of the detection lens. The further away high light intensities, other than the high light intensities at the central illumination line, are removed from this depth of focus region, the less these high light intensities cause undesired out-of-focus contributions. Thus, the further removed these other high light intensities are from the central illumination line, the better the sectioning capabilities of the system are and the higher the quality of the obtained images.

Note that if only a single particular light distribution would be formed, which would be subsequently scanned in the x-direction as for example shown in figure 2B, then the first concentric ring, also referred to as the secondary maximum ring, would cause relatively high intensities near the central illumination line. An advantage of using a composite light distribution is that the copies of the particular light distribution can be arranged such that parts of the first concentric rings are suppressed due to destructive interference of the light fields of the respective copies of the particular light distribution. Preferably parts that lie above and/or below the central illumination line are suppressed, more preferably such parts that lie within the depth of focus of the detection lens.

The copies of the particular light distribution are preferably arranged in the composite light distribution such that said destructive interference suppresses parts of the secondary maximum rings of the respective copies on the central illumination line, wherein the suppressed parts are positioned away from the central illumination line.

On the sample, the real profile is a 0th order Bessel function of the first kind; the phase, since these are real signals, is 0 when the real part is positive, or p when the real part is negative. The center and first concentric ring of the particular light distribution are typically 180° out of phase with respect to each other. In fact, all the concentric rings, the first, second, third ring, et cetera, of the particular light distribution alternate in phase (0, 180, 0, 180...). The reason for this is in the “reality condition” of the Fourier transform, as described in Chen, B.-C. et al. Science 346, 1257998 (2014)]. However, the respective first concentric rings of the respective copies of the particular light distribution in the composite light distribution are in phase with each other.

Figure 5A shows for one copy of the particular light distribution in which regions constructive interference occurs and in which regions destructive interference occurs. When the outer ring touches other rings, they reinforce each other, since they are in phase. But there are many regions where this does not happen, and the small shifts make things superimpose not precisely, so that parts with opposite phases meet. The practical advantage of such destructive interference is that the first ring tends to “disappear sooner” in the z-direction, so that the central line is better separated from the others, and the separation persists when scanning is performed. This is an improvement over the simple Bessel beam, where the full circle would shine light around when scanned.

Figure 5B shows a composite light distribution wherein the copies of the particular light distribution are arranged in a square geometry.

Several definitions for respective functions are as follows. somb = 2/ _x p0 / p0, wherein Ji is the Bessel function of the first kind 5 ⁵ f r) = \b\[S(x - x ₀ + b) + S(x - x ₀ - b)] d _d p0 = \b\[S(x - x ₀ + b) - d(c - x ₀ - b)]

Figures 6A and 6B illustrate how the second intensity mask can be determined. Figure 6A shows the unitary pupil. Unitary pupil means that its radius is considered 1 , that is the “f in the picture. In figure 6A a 2D spherical wave is depicted that is cut by the binary annular aperture 22. The geometry follows the explanation given by C. W. McCutchen, J. Opt. Soc. Am. 54, 240-244 (1964)]. In particular, McCutchen says: “A lens, like a cookie cutter, is assumed to chop out a chunk of spherical wave which is regarded as a Huygenian source”.

The ’’shadow on the axis” created by the pupil is defined as a, where a = A/f _0t>j , A is the annulus width in meters, and f _0t>j is the focal length of the objective. If we assume a unitary sphere, as in McCutchen’s formulation, where the focal length of the lens is normalized, a can be represented by rectiiy - y ₀ )/a). Then its Fourier Transform gives the intensity along the y axis as sinc ² yan/A ₀ ).

The method may comprise imposing a desired axial length for the illumination, defining it as the distance between the first zero-intensity points along the propagation axis. This distance D may be calculated by

D 2 * y fi _rs t zero (1)

Since sine ²

V _{0 /} = 0 for ^ A ₀ = k, wherein k is simply an integer, so k«º N, the position of the first zero is given by k=1 , meaning that the position of the first zero is given by l ₀ y irst zero (2) an and

2L, o

D = (3) an

A ₀ is the excitation wavelength (in vacuum), and n is the refractive index of the medium after the excitation lens. Inverting (3) that we find the required annulus width shadow a:

2A _n a = (4) nD

This parameter a may be understood to fix the actual annulus width A as it can be geometrically calculated. The position of the annulus (that is, external and internal radii) may be defined both from the excitation lens NA and the shadow value a (referring to figure 6B):

Herein f _obj is the focal length of the illumination lens. Equation 5 is based on the definition of NA = nsin d) and the commonly used approximation sin(i9) * R _ext /f·

In an embodiment, the method comprises determining the second intensity mask, the second intensity mask comprising an annular aperture, wherein determining the second intensity mask comprises determining a width of the annular aperture based on a desired axial length of the light sheet. The desired axial length may be understood to be D given by formula (3), based on which parameter a can be determined. Preferably, the axial length is sufficient to cover the Field of View of the detection system. Then, the internal radius of the annulus of the second intensity mask can be determined geometrically. The outer radius of the annulus may be determined irrespective of the desired axial length. The outer radius can be determined based on for example the NA of the detection system, for example in accordance with equation (5). The width of the of the central peak, i.e. the smallest possible light confinement, depends in general on the numerical aperture (NA) of the illumination lens. Once the lens has been determined, the minimum central peak is also defined. It may be beneficial to determine the external radius of the annulus aperture based on an NA value that is slightly less than the actual NA of the illumination lens. This may be easier to experiment with.

The internal and external radius of the annulus may be understood to define the second intensity mask that may be configured to generate a Bessel beam profile with the desired axial length.

The transverse profile of the generated beam profile, i.e. the particular light distribution, may be determined using McCutchen’s theorem in 2D. C.W. McCutchen - J. Opt. Soc. Am. 54, 240-244 (1964). In an embodiment, this step is performed numerically, which may be beneficial if Bessel functions of the first kind are involved, because the analytic functions described the Bessel functions are quite cumbersome to manipulate.

The method preferably further comprises determining the particular light distribution based on the determined second intensity mask. In an example, this step may comprise Fourier transforming the second intensity mask. This may be performed as follows.

The intensity profile of a plane wave at the pupil may be written as: wherein, f(c,g) = f ₀

So that the light field at the sample plane may be written as: and the real part of this function, representing the electric field may be written as:

Equation 10 is the squared modules of equation 9 and describes the light intensity at the sample.

Then the position of the first local minimum and first local maximum may be found, i.e. their distance from the center. For example, aiming at a length of 160 micrometer, considering l =

0.488nm, excitation NA = 0.29, lens focal length f _0t>j = 20 mm, water immersion, we get r _firstmin = 0.6 micrometer, and rnrstmax = 0.96 micrometer, with a total central peak width of = 1.2 micrometer. A such, the particular light distribution may be determined. Apparently, these parameters yield a particular light distribution in which the secondary maximum ring is positioned 0.96 micrometer from the center. Further, the particular light distribution has a central peak that is 1.2 micrometers width, i.e. two times r _firstmin . This value may be compared with the depth of focus of the detection lens that we have: 1.2 mth (11)

Herein, M is the detection magnification. Eq. 11 is a standard formula usually employed to describe the basic parameters of an objective

For the illumination lens and detection lens to work best together, preferably the depth of focus of the detection lens is as close as possible to the total excitation central peak width.

Now that the annular geometry for the pupil has been determined, as well as the particular light distribution, the composite light distribution may be engineered. Considering just the center and first ring of the Bessel profile as a building block, we can imagine a 2D arrangement on which we superimpose the rings, making them interfere and partially cancel or reinforce each other. In fact, a 2D array of excitation points, capable of uniformly filling all the space, can be obtained describing a spatial sampling with comb functions. One geometry (highest ratio covered area / perimeter) that is possible is a hexagonal configuration, as found in honeycombs.

The math of this model can be condensed with a convolution of comb functions with the building block. Instead of one (skewed) comb function, it may be easier to work with a sum of two Cartesian comb functions to describe the same sampling. Moreover this description underlines more clearly the constructive and destructive interference of the final pattern.

A closely packed lattice arrangement can be described (in the most general case) by a skewed, scaled, and shifted comb functions. The periods and the shifts that we employ could be general, but we choose shifts equal to half the periods, both because the formulae result easier and can be greatly simplified, and because this case encompasses suitable geometries.

In such case, it may be easier to describe such spatial sampling with a sum of two comb functions: one centered at the origin, and a shifted one, both with the same periodicity.

Herein, parameters A and B are indicated in figure 4D. Note that the values for A and B can be determined based on the particular light distribution. In the composite light distribution of figure 4D, A is for example equal to twice rnrstmax of the particular light distribution.

Preferably, the composite light distribution only comprises copies of the particular light distributions near the central illumination line. The further removed copies are from the central illumination line, the more the Gaussian characteristic of the illumination will contribute to reduce the intensity. Also, the less information is defined in the sample plane (at least in one direction) the more accurate will be the result in the pupil plane.

Convolving the two-dimensional comb function with the particular light distribution, which distribution in this example is the Bessel profile, yields:

Here, ** denotes two-dimensional convolution. Explicitly writing the impact of the rect cut, the extent of the sampling can be reduced in the following way: Formula (14) describes the composite light distribution. In particular, it describes a two- dimensional convolution of the part between brackets, which is a two-dimensional comb function having its impulses positioned on the respective centers of the copies of the light distribution, with the particular light distribution, which in this case is the Bessel profile. In an embodiment, the composite light distribution is Fourier transformed in order to determine the pupil intensity mask. In the above example, such Fourier transform can be determined by separately Fourier transforming the part between brackets and the Bessel profile. The Fourier transform of the latter is the second intensity mask, in this example the determined annulus mask. Fourier transforming (14) yields: which is equal Herein, comb{A()e ^~2m ^ can be re-written in a more useful way:

, since the sine is identically 0 when sampled by the comb. On the other hand, the interplay between the periods of comb and cosine gives:

When the n is highlighting the index of the comb sampling (different from the one that may be used for the other sampling function along x). The common A term may be dropped if a normalization is performed with a binarization step. Therefore, equation ((16) may be written as:

Equation (19) may be understood to describe the light transmittance of the pupil intensity mask.

In an embodiment, determining the pupil intensity mask further comprises performing a binarization such that the pupil intensity mask at each position has either full light transmittance or no light transmittance. Now a binarization criterion: the result of the sampling can be just 1 or 0. Then both normalization and the following rule may be applied: the binarization of a function f(x) is a new function g(x) that behaves in the following way

Therefore to binarize the pupil intensity mask may mean to rewrite the 1 + 2(— l) ⁿ cos (2p^h^ part of (19) as a new function 6(h,h,B) as in the following. Once normalized, it retains only the behaviour of the cosine. Therefore this binarization results in

The only difference for the case of n odd is that the cosine results shifted of half a period.

Finally getting to: comb _n (Ax) C(n,p,B ) · A _nnulus (25)

This formula completely specifies the sampling in the pupil space and therefore defines the pupil intensity mask. A change from frequency to spatial variable can be made, defining also reciprocal lattice spacings with

Figure 7 shows exemplary pupil intensity masks (bottom) together with the associated light intensity distribution that these pupil intensity masks may cause (top). Herein, the bright areas represent high intensities and dark areas low intensities.

Figure 8 is a flow chart illustrating an embodiment of the method. Herein, steps 802, 804 and 810 are optional. Step 802 comprises determining the second intensity mask based on a desired length of the light sheet. Such length may be input by a user in a data processing system that is configured to perform one or more of the steps of the methods described herein. Step 804 comprises determining the particular light distribution. This step may be performed by Fourier transforming the determined second intensity mask. Step 806 comprises determining a composite light distribution. This step may comprises virtually arranging copies of the particular light distribution. Step 808 comprises determining the pupil intensity mask based on the composite light distribution. This step may comprise Fourier transforming the composite light distribution.

Fig. 9 depicts a block diagram illustrating a data processing system according to an embodiment. As shown in Fig. 9, the data processing system 100 may include at least one processor 102 coupled to memory elements 104 through a system bus 106. As such, the data processing system may store program code within memory elements 104. Further, the processor 102 may execute the program code accessed from the memory elements 104 via a system bus 106. In one aspect, the data processing system may be implemented as a computer that is suitable for storing and/or executing program code. It should be appreciated, however, that the data processing system 100 may be implemented in the form of any system including a processor and a memory that is capable of performing the functions described within this specification.

The memory elements 104 may include one or more physical memory devices such as, for example, local memory 108 and one or more bulk storage devices 110. The local memory may refer to random access memory or other non-persistent memory device(s) generally used during actual execution of the program code. A bulk storage device may be implemented as a hard drive or other persistent data storage device. The processing system 100 may also include one or more cache memories (not shown) that provide temporary storage of at least some program code in order to reduce the number of times program code must be retrieved from the bulk storage device 110 during execution.

Input/output (I/O) devices depicted as an input device 112 and an output device 114 optionally can be coupled to the data processing system. Examples of input devices may include, but are not limited to, a keyboard, a pointing device such as a mouse, or the like. Examples of output devices may include, but are not limited to, a monitor or a display, speakers, or the like. Input and/or output devices may be coupled to the data processing system either directly or through intervening I/O controllers.

In an embodiment, the input and the output devices may be implemented as a combined input/output device (illustrated in Fig. 9 with a dashed line surrounding the input device 112 and the output device 114). An example of such a combined device is a touch sensitive display, also sometimes referred to as a “touch screen display” or simply “touch screen”. In such an embodiment, input to the device may be provided by a movement of a physical object, such as e.g. a stylus or a finger of a user, on or near the touch screen display.

A network adapter 116 may also be coupled to the data processing system to enable it to become coupled to other systems, computer systems, remote network devices, and/or remote storage devices through intervening private or public networks. The network adapter may comprise a data receiver for receiving data that is transmitted by said systems, devices and/or networks to the data processing system 100, and a data transmitter for transmitting data from the data processing system 100 to said systems, devices and/or networks. Modems, cable modems, and Ethernet cards are examples of different types of network adapter that may be used with the data processing system 100.

As pictured in Fig. 9, the memory elements 104 may store an application 118. In various embodiments, the application 118 may be stored in the local memory 108, the one or more bulk storage devices 110, or apart from the local memory and the bulk storage devices. It should be appreciated that the data processing system 100 may further execute an operating system (not shown in Fig. 9) that can facilitate execution of the application 118. The application 118, being implemented in the form of executable program code, can be executed by the data processing system 100, e.g., by the processor 102. Responsive to executing the application, the data processing system 100 may be configured to perform one or more operations or method steps described herein.

Various embodiments of the invention may be implemented as a program product for use with a computer system, where the program(s) of the program product define functions of the embodiments (including the methods described herein). In one embodiment, the program(s) can be contained on a variety of non-transitory computer-readable storage media, where, as used herein, the expression “non-transitory computer readable storage media” comprises all computer-readable media, with the sole exception being a transitory, propagating signal. In another embodiment, the program(s) can be contained on a variety of transitory computer-readable storage media. Illustrative computer-readable storage media include, but are not limited to: (i) non-writable storage media (e.g., read-only memory devices within a computer such as CD-ROM disks readable by a CD-ROM drive, ROM chips or any type of solid-state non-volatile semiconductor memory) on which information is permanently stored; and (ii) writable storage media (e.g., flash memory, floppy disks within a diskette drive or hard-disk drive or any type of solid-state random-access semiconductor memory) on which alterable information is stored. The computer program may be run on the processor 102 described herein.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of embodiments of the present invention has been presented for purposes of illustration, but is not intended to be exhaustive or limited to the implementations in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the present invention. The embodiments were chosen and described in order to best explain the principles and some practical applications of the present invention, and to enable others of ordinary skill in the art to understand the present invention for various embodiments with various modifications as are suited to the particular use contemplated.