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Title:
KÖHLER BEAM SHAPING ELEMENT
Document Type and Number:
WIPO Patent Application WO/2022/207389
Kind Code:
A1
Abstract:
The invention provides a Köhler beam shaping element (100) comprising an entrance face (110) and an exit face (120), wherein the entrance face (110) comprises a plurality of entrance lenslet shapes according to an entrance surface pattern (115), and wherein the exit face (120) comprises a plurality of exit lenslet shapes according to an exit surface pattern (125), wherein: the exit surface pattern (125) comprises an exit tessellation of a plurality of rectangles (121) having a length L and a width W, wherein L/W > 4, wherein the rectangles (121) are arranged in a plurality of rows (123) having a width W, and wherein for at least two rows (123) applies that the two rows (123) are shifted relative to one another; the entrance surface pattern (115) comprises an entrance tessellation, wherein the entrance tessellation comprises n seeds (112) and n corresponding regions (111), wherein each set of a seed (112) and corresponding region (111) define a region function ri(θ) for values of θ from the range of 0 – 360º, wherein the entrance tessellation defines a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(θ), wherein: (formula (I)); wherein the virtual average region seed function R(θ) comprises a largest distance Rmax and a smallest distance Rmin, wherein (formula (II)); and wherein in a superposition of the entrance surface pattern (115) and the exit surface pattern(125) the seeds (112) of the entrance tessellation coincide with central points (122) of the rectangles (121).

Inventors:
BELTMAN RENÉ (NL)
HAENEN LUDOVICUS (NL)
VISSENBERG MICHEL (NL)
IJZERMAN WILLEM (NL)
Application Number:
PCT/EP2022/057325
Publication Date:
October 06, 2022
Filing Date:
March 21, 2022
Export Citation:
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Assignee:
SIGNIFY HOLDING BV (NL)
International Classes:
G02B3/00; F21V5/00; G02B19/00; G02B27/09; G03B21/20
Domestic Patent References:
WO2014124814A12014-08-21
Foreign References:
US5594526A1997-01-14
US20160327236A12016-11-10
Other References:
TASSO R M SALES ET AL: "Engineered microlens arrays provide new control for display and lighting applications", PHOTONICS SPECTRA, 1 June 2004 (2004-06-01), XP055395315, Retrieved from the Internet [retrieved on 20170802]
Attorney, Agent or Firm:
PET, Robert, Jacob et al. (NL)
Download PDF:
Claims:
CLAIMS:

1. A Kohler beam shaping element (100) comprising an entrance face (110) and an exit face (120), wherein the entrance face (110) comprises a plurality of entrance lenslet shapes according to an entrance surface pattern (115), and wherein the exit face (120) comprises a plurality of exit lenslet shapes according to an exit surface pattern (125), wherein: the exit surface pattern (125) comprises an exit tessellation of a plurality of rectangles (121) having a length L and a width W, wherein L/W > 4, wherein the rectangles

(121) are arranged in a plurality of rows (123) having a width W, and wherein for at least two rows (123) applies that the two rows (123) are shifted relative to one another; the entrance surface pattern (115) comprises an entrance tessellation, wherein the entrance tessellation comprises n seeds (112) and n corresponding regions (111), wherein each set of a seed (112) and corresponding region (111) define a region function h(q) for values of Q from the range of 0 - 360°, wherein the entrance tessellation defines a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(6), wherein:

W) = å?=in(0) ; wherein the virtual average region seed function R(6) comprises a largest distance Rmax and a smallest distance Rmin, wherein Rmax/Rmin < y¾ and wherein in a superposition of the entrance surface pattern (115) and the exit surface pattern (125) the seeds (112) of the entrance tessellation coincide with central points

(122) of the rectangles (121).

2. The Kohler beam shaping element (100) according to claim 1, wherein each region (111) is a polygon comprising a plurality of interior angles (a), wherein each angle in the plurality of interior angles (a) > 90°.

3. The Kohler beam shaping element (100) according to any one of the preceding claims, wherein the entrance tessellation is a Voronoi tessellation (116).

4. The Kohler beam shaping element (100) according to any one of the preceding claims, wherein for each set of two adjacent rows (123) applies that the two adjacent rows (123) are shifted relative to one another along an axis parallel to the rows (123) by an independently selected distance (dn) selected from the range of 0.05*L - 0.95*L.

5. The Kohler beam shaping element (100) according to any one of the preceding claims, wherein at least 70% of rows (123) are shifted relative to at least one adjacent row (123), and wherein n is at least 30.

6. The Kohler beam shaping element (100) according to any one of the preceding claims, wherein L/W > 4.5, and wherein for at least 50% of the region functions r,(0) applies that h(q) comprises a largest region distance Umax and a smallest region distance rimin, wherein rimax/rimin <· \(2.

7. The Kohler beam shaping element (100) according to any one of the preceding claims, wherein the Kohler beam shaping element (100) has an element length LI and an element width W 1 having a first aspect ratio R1 of at least 2.

8. A lighting device (1200) comprising the Kohler beam shaping element (100) according to any one of the preceding claims 1-7 and a linear light source (10), wherein the Kohler beam shaping element (100) is configured downstream of the linear light source (10).

9. The lighting device (1200) according to claim 8, wherein the lighting device comprises a second optical element (20) configured downstream of the linear light source (10) and upstream of the Kohler beam shaping element (100).

10. The lighting device (1200) according to any one of the preceding claims 8-9, wherein the second optical element (20) is selected from the group of Fresnel lenses (21),

TIR Fresnel lenses, lenses, reflectors, and TIR collimators.

11. The lighting device (1200) according to any one of the preceding claims 9-10, wherein the second optical element (20) comprises a 2D optical element, and wherein the linear light source (10) comprises a plurality of solid state light sources.

12. The lighting device (1200) according to any one of the preceding claims 8-11, wherein the Kohler beam shaping element (100) has an element length LI, wherein the linear light source (10) defines a light source length L2, and wherein 0.5<L2/L1<1.

13. The lighting device (1200) according to any one of the preceding claims 8-12, wherein the lighting device comprises an indoor illumination device selected from the group comprising office lighting, industry lighting, and retail lighting, or an outdoor illumination device selected from the group comprising pedestrian lighting and area lighting.

14. A method for providing the Kohler beam shaping element (100) according to any one of the preceding claims 1-8, wherein the method comprises: defining an exit surface pattern comprising a tessellation of a plurality of rectangles (121) having a length L and a width W, wherein L/W > 4, wherein the rectangles (121) are arranged in a plurality of rows (123) having a width W, and wherein for at least two adjacent rows (123) applies that the two adjacent rows (123) are shifted relative to one another; defining an entrance surface pattern comprising providing a Voronoi tessellation with central points (122) of the plurality of rectangles (121) as seeds (112); providing a Kohler beam shaping element (100) having an entrance face (110) patterned according to the entrance surface pattern (115) and an exit face (120) patterned according to the exit surface pattern (125); wherein in a superposition of the entrance surface (110) and the exit surface (120) the seeds (112) of the Voronoi tessellation coincide with the central points (122) of the rectangles (121).

15. The method according to claim 14, wherein the Voronoi tessellation comprises n seeds (112) and n corresponding Voronoi regions (111), wherein each set of a seed (112) and corresponding Voronoi region (111) define a region function h(q) for values of Q from the range of 0 - 360°, wherein the Voronoi tessellation defines a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(9), wherein: wherein the virtual average region seed function R(9) comprises a largest distance Rmax and a smallest distance Rmin, wherein Rmax/Rmin < y/2.

Description:
Kohler beam shaping element

FIELD OF THE INVENTION

The invention relates to a Kohler beam shaping element. The invention further relates to a lighting device comprising the Kohler beam shaping element. The invention further relates to a method for providing the Kohler beam shaping element.

BACKGROUND OF THE INVENTION

Light integrators are known in the art. For instance, US20160327236A1 describes a shell integrator having a hollow transparent body with inner and outer surfaces formed as arrays of lenslets. Each lenslet of the inner surface images a common source region in the middle of the hollow body onto a respective lenslet of the outer surface. Each lenslet of the outer surface forms a virtual image of the respective lenslet of the inner surface at the common source region. One integrator has a light-guide following the surface of the hollow body from an inlet end at a central region of the surface to an outlet end at a rim of the hollow body. The light-guide inlet end is shaped to receive light from the common source region and direct such light along the light-guide. Another integrator is generally elongated, and may be semicylindrical. Any of these integrators may have a stepped surface forming a Fresnel lens.

SUMMARY OF THE INVENTION

Linear lens designs may provide freedom in the number of light sources, especially LEDs, and the position of these light sources along a lens axis. Such a linear lens may also cheap to produce, such as via extrusion. Linear lenses may be purely refractive lenses, but they may also contain reflective surfaces (such as TIR surfaces) or combinations of these elements, such as TIR lenses or TIR Fresnel lenses. The use of linear lenses in luminaires may be attractive for these reasons, but it may be challenging to control the beam of a linear lens. In particular, it may be challenging to collimate the light well in a direction along the linear lens. This challenge in light control may hamper the use of linear lenses in luminaires requiring a more-or less symmetric collimated beam profile. With a linear lens it may be particularly difficult to change the angle between a ray of light and the linear lens axis. Thus, although the prior art may provide options to collimate light in a cross-sectional plane, shaping the light (bundle) in the direction along the lens axis may remain challenging.

The prior art may describe approaches for post-shaping light using a Kohler integrator plate that reshapes the light. A Kohler integrator plate may, for instance, consist of a 2D array of spherical lenslets focusing on each other. In particular, the prior art may describe lenslets known as etendue squeezers or etendue shapers that reshape/squeeze a light beam considered as a set of points in phase space.

The Kohler integrators described in the prior art may, however, have exit lenslet shapes with a relatively low aspect ratio. These integrators may not be suitable to post-shape light when placed behind a linear lens. In particular, a light beam created by a linear lens may be uncollimated (or not very well collimated) along the length direction of the linear lens. The Kohler integrators in the prior art may have exit lenslets with relatively low aspect ratio and therefore the uncollimated beam may give crosstalk between the different lenslets. This may prevent the use of such integrators for linear lenses. A higher aspect ratio may be beneficial to prevent crosstalk between unpaired lenslet, i.e., to prevent that light that enters through the entrance-surface of a certain lenslet pair exits through the exit-surface of another lenslet pair, which could otherwise result in loss of light beam control.

Further, the Kohler integrators described in the prior art may have rectangular entrance surfaces with the same aspect ratio as their rectangular exit surfaces (albeit with the rectangle 90 degrees rotated. The high aspect ratio of the rectangular entrance surface may lead to a, possibly undesirable, rectangular beam shape.

It may, however, generally be desirable to provide a cumulative output with a circular or elliptical beam shape. Hence, it is an aspect of the invention to provide an alternative Kohler beam shaping element, which preferably further at least partly obviates one or more of above-described drawbacks. The present invention may have as object to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative.

Hence, in a first aspect, the invention may provide a Kohler beam shaping element (also “beam shaping element”). The beam shaping element may comprise an entrance face and an exit face, especially wherein the entrance face comprises a plurality of entrance lenslet shapes according to an entrance surface pattern, and especially wherein the exit face comprises a plurality of exit lenslet shapes according to an exit surface pattern. In particular, the exit surface pattern may comprise an exit tessellation of a plurality of rectangles. The rectangles may have a length L and a width W, especially wherein L/W > 4, i.e., the rectangles may have an aspect ratio > 4. In embodiments, the rectangles may be arranged in a plurality of rows having a width W, i.e., the rectangles may define the width of the rows. In further embodiments, for at least two (adjacent) rows (of the plurality of rows) applies that the two (adjacent) rows are shifted relative to one another. In embodiments, the entrance surface pattern may comprises an entrance tessellation. The entrance tessellation may comprises n seeds and n corresponding regions. In embodiments, each set of a seed (of the plurality of seeds) and corresponding region (of the plurality of corresponding regions) may define a region function h(q) for values of Q from the range of 0 - 360°. In particular, for each region, h(q) comprises the distance between the seed and region boundaries for the different values of Q, and each seed may located in the corresponding region. The entrance tessellation may further define a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(9), wherein:

R(0) = åf-in« .

Hence, the virtual average region seed function may comprise a sum of the h(q) functions for the n sets of a seed and corresponding region. Thereby, R(9) may reflect an average region shape of the entrance tessellation. Optionally, R(9) may be normalized by dividing the sum through n. In particular, the virtual average region seed function R(9) comprises a largest distance R ma x and a smallest distance Rmin, wherein Rmax/Rmin < y[2. In embodiments, in a superposition of the entrance surface pattern and the exit surface pattern the seeds of the entrance tessellation coincide with central points of the rectangles. In particular, the locations of the seeds may be defined by the locations of the central points of the rectangles.

The Kohler beam shaping element of the invention may provide the benefits that it has a high aspect ratio at the exit surface, and thus little crosstalk, as well as regions in the entrance surface with, on average, a rounded shape, which may facilitate acquiring a circular or elliptical beam shape. In particular, the invention may facilitate providing a large degree of freedom in generating a useful far-field intensity, while avoiding crosstalk between different lenslet pairs.

In particular, the beam shaping element of the invention may provide more extreme aspect ratios for the exit surface rectangular lenslets, while the entrance lenslet shapes are, on average, rounded, i.e., the entrance lenslets shapes may have a low aspect ratio. In specific embodiments, the entrance lenslets shapes may be shaped according to a Voronoi tessellation, i.e., the entrance tessellation may comprise a Voronoi tessellation. This may imply that the height of adjacent lenslets at their common boundary is the same and may result in a continuous lens surface without steps.

The invention may provide a Kohler beam shaping element comprising a plate comprising an exit face and an entrance face. The exit face may comprise a plurality of rectangular exit lenslet shapes configured in a first 2D array, especially wherein each exit lenslet shape defines an exit lenslet central point in the first 2D array. The rectangular exit lenslet shapes may have aspect ratios of exit lenslet lengths (L) and exit lenslet widths (W) of larger than 4. In particular, the rectangular exit lenslet shapes may define length lines parallel to the exit lenslet lengths (L), wherein for a first subset of a plurality of rows of exit lenslet shapes applies that at least two of the rows are shifted relative to one another (along an axis parallel to the length lines), especially by a distance (dn) selected from the range of 1*L with 1 from the range (0,1) excluding 0 and 1. In embodiments, the entrance face may comprise a plurality of entrance lenslet shapes. Each entrance lenslet shape may have an entrance lenslet point, corresponding in position to the exit lenslet central points in a superposition of the exit face and the entrance face. In embodiments the entrance lenslets shapes may be defined by a Voronoi diagram based on the entrance lenslet points (or “seeds”). In embodiments, for a subset of p adjacent entrance lenslets shapes applies that the entrance lenslet points do not form a regular second 2D array, or, when they form a regular second 2D array i.e., an array with two regular pitches, at least one second array pitch does not have a mutual angle b with the length lines selected from k*90°, wherein k is an integer, and wherein p is at least 7.

In specific embodiments, the invention may provide a Kohler beam shaping element comprising an entrance face and an exit face, wherein the entrance face comprises a plurality of entrance lenslet shapes according to an entrance surface pattern, and wherein the exit face comprises a plurality of exit lenslet shapes according to an exit surface pattern, wherein: the exit surface pattern comprises a tessellation of a plurality of rectangles having a length L and a width W, wherein L/W > 4, wherein the rectangles are arranged in a plurality of rows having a width W, and wherein for at least two rows applies that the two rows are shifted relative to one another; the entrance surface pattern comprises an entrance tessellation, wherein the entrance tessellation comprises n seeds and n corresponding regions, wherein each set of a seed and corresponding region defines a region function h(q) for values of Q from the range of 0 - 360°, wherein the entrance tessellation defines a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(0), wherein: m) = å n - wherein the virtual average region seed function R(0) comprises a largest distance R ma x and a smallest distance R m in, wherein Rmax/Rmin < V2; and wherein in a superposition of the entrance surface pattern and the exit surface pattern the seeds of the entrance tessellation coincide with central points of the rectangles.

Hence, the invention may provide a Kohler beam shaping element. The term “beam shaping element” may herein especially refer to an element configured to (re-)shape a beam of light. Specifically, a Kohler beam shaping element may comprise two arrays of coupled lenslets focusing on each other. In embodiments, the Kohler beam shaping element may especially comprise a Kohler integrator.

The Kohler beam shaping element may comprise an entrance face and an exit face. Specifically, the beam shaping element may be configured to receive (light source) light at the entrance face and to provide beam-shaped (light source) light from the exit face, i.e., the beam shaping element may be configured to beam shape (light source) light received at the entrance face and to provide beam-shaped (light source) light emanating from the exit face.

The entrance face may comprise a plurality of entrance lenslet shapes according to an entrance surface pattern. In particular, the entrance face may be provided by a plurality of entrance lenslets, wherein each entrance lenslet has an entrance lenslet shape. The entrance lenslet shapes may especially be according to an entrance surface pattern, i.e., an entrance surface pattern may define the shape of (at least part of) the plurality of entrance lenslets.

Similarly, the exit face may comprise a plurality of exit lenslet shapes according to an exit surface pattern. In particular, the exit face may be provided by a plurality of exit lenslets, wherein each exit lenslet has an exit lenslet shape. The exit lenslet shapes may especially be according to an exit surface pattern, i.e., an exit surface pattern may define the shape of (at least part of) the plurality of exit lenslets.

The phrase “shapes according to a pattern” and similar phrases, may herein especially refer to the shapes approximating, especially conforming to, at least part of the pattern. For instance, the exit pattern may comprise a tessellating grid of rectangles. The exit face may, however, also be rectangular, and may, for example, in embodiments, have rounded comers. Hence, at an edge of the exit face, the exit face may deviate from the exit surface pattern. In embodiments, along the edges of the exit face, the exit lenslet shapes may be non-rectangular (to account for the rectangular exit face). In further embodiments, along the edges of the exit face, the exit face may be (partially) devoid of the exit lenslet shapes (to account for the rectangular exit face), i.e., the exit face may comprise a plurality of rectangular exit lenslet shapes according to the exit surface pattern, especially wherein exit lenslet shapes are only provided if the entire rectangle fits on the exit face.

Especially, in embodiments, a rectangle may be defined as a single shape of which 100% of the area is within a smallest mathematical rectangle (i.e. 90 ° angles and non- rounded angles) enclosing the entire rectangle, wherein the rectangle overlaps for at least 95% with the area of the mathematical rectangle, like at least 96,%, such as at least 98%, such as at least about 99%.

The term “approximate” and its conjugations herein, such as in “to approximate a shape”, refers to being nearly identical to, especially identical to, the following term, for example a shape in a (regular) pattern. For example, an entrance lenslet may have an entrance lenslet shape that is nearly identical to a region in the entrance face pattern, but for a defect. In particular, an object approximating a first shape may herein refer to: a first shape realization encompassing the object, wherein the first shape realization is defined as the smallest encompassing shape of the (2D or 3D, respectively) object wherein the first shape realization has the shape of the first shape, wherein a ratio of the area (volume) of the first shape realization to the area (volume) of the object is < 1.1, such as <1.05, especially <1.02, such as < 1.01, including 1. Further, if the dimensions of the first shape are defined, the term approximate may refer to the object and the first shape being superimposable (in 2D or 3D, respectively) such that an intersection between the object and the first shape covers at least s% of the object and at least s% of the shape, wherein s is at least 90%, such as at least 95%, especially at least 98%, such as at least 99%, including 100%.

In particular, in embodiments, the entrance face may comprise a plurality of entrance lenslet shapes according to an entrance surface pattern, wherein each entrance lenslet shape approximates a region in the entrance surface pattern, and wherein on average (by number) an intersection between the entrance lenslet shape and the approximated region covers at least si% of the entrance lenslet shape and at least si% of the approximated region, wherein si is at least 90%, such as at least 95%, especially at least 98%, such as at least 99%, including 100%.

For instance, in embodiments, the entrance surface pattern may comprise a Voronoi tessellation, and the entrance face may comprise a plurality of entrance lenslet shapes approximating the Voronoi tessellation of the entrance surface pattern, wherein each entrance lenslet shape approximates a region in the Voronoi tessellation, especially wherein on average (by number) an intersection between the entrance lenslet shape and the approximated region covers at least si% of the entrance lenslet shape and at least si% of the approximated region, wherein si is at least 90%, such as at least 95%, especially at least 98%, such as at least 99%, including 100%. The entrance lenslet shapes may thus provide a Voronoi-like tessellation, such as a Voronoi tessellation but for some small defects, such as a Voronoi tessellation but for some rounded corners.

In further embodiments, the exit face may comprise a plurality of exit lenslet shapes according to an exit surface pattern, wherein each exit lenslet shape approximates a rectangle in the exit surface pattern, and wherein on average (by number) an intersection between the exit lenslet shape and the approximated rectangle covers at least S2% of the exit lenslet shape and at least S2% of the approximated region, wherein S2 is at least 90%, such as at least 95%, especially at least 98%, such as at least 99%, including 100%.

In embodiments, the exit surface pattern comprises a tessellation of (a plurality of) rectangles, i.e., the exit surface pattern may comprise a tessellating grid of rectangles. The rectangles may especially having a length L and a width W, wherein L/W > 4. In particular, at least 80% of the rectangles may have the same length L and width W, especially at least 90%, including 100%. In general, the rectangles all have the same dimensions. The rectangles may be arranged in a plurality of rows having a width W. Hence, each row may comprise a subset of the rectangles arranged along their length L. In particular, for at least two rows, especially two adjacent rows, applies that the two rows are shifted relative to one another, especially shifted along a length dimension parallel to the length L of the rectangles. In particular, for the two rows, the edges of the rectangles perpendicular to the length dimension are not aligned.

The term “tessellation” may herein especially refer to a pattern of (repeated) shapes, especially polygons, that fit together closely without gaps or overlapping.

In further embodiments, at least 3 rows may be shifted relative to an adjacent row, especially at least 5 rows, such as at least 8 rows.

In embodiments, at least 20% of the rows may be shifted relative to an adjacent row, such as at least 50%, especially at least 70%. In further embodiments, at least 80% of the rows may be shifted relative to an adjacent row, such as at least 90%, especially at least 95%, including 100%. Two rows may herein be considered adjacent if they are arranged without another row in between the two rows.

In embodiments, the rectangles may have a width W selected from the range of 0.15 - 20 mm, especially from the range of 0.25 - 10 mm, such as from the range of 0.5 - 5 mm.

In further embodiments, the rectangles may have a length L, wherein L >

4*W, such as > 4.5*W, especially > 6* W. In further embodiments, L may be selected from the range 4*W - 20*W, such as from the range of 4*W - 15*W, especially from the range of 4.5*W - 10*W, such as from the range of 5*W - 8*W.

In embodiments, the entrance surface pattern may comprise an entrance tessellation of polygons, especially of convex polygons. In particular, the entrance tessellation may comprise n seeds and n corresponding regions, wherein the regions have a (convex) polygon shape. In embodiments, each set of a seed (of the plurality of seeds) and corresponding region (of the plurality of corresponding regions) may define a region function h(q) for values of Q from the range of 0 - 360°. In particular, h(q) may comprise a vector comprising a distance between the seed and the region boundary at an angle Q for values of Q selected from the range of 0 - 360°, especially for a full circle around the seed. For instance, h(q) may comprise a distance for every full degree, for every other full degree, or may contain multiple distances per degree, such as a distance for each 0.2 degree. In particular, h(q) may comprise differences for a plurality of values of Q selected from the range of 9 - 360° at a regular interval, especially for at least 360 values of Q. It will be clear to the person skilled in the art that although each set of a seed and a region has a corresponding n(9), that the values for Q are identical, and that the angles for Q are defined relative to a common axis (in plane with the pattern).

Hence, for each seed and region, n(9) may comprise the distance between the seed and region boundaries (of the region) for different values of Q.

In embodiments, the entrance tessellation may defines a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(9). In particular, R(9) may be defined according to: ftm = Iίi h(q) wherein each of the n regions corresponds to a different value for i. In embodiments, n may be at least 39, such as at least 59, especially at least 199.

Hence, R(9) may comprise a vector representative of an average region shape in the entrance face. R(9) may comprise a largest distance R max and a smallest distance R min , especially wherein R max /R min £ /2, such as < 2, especially < 1.3, more especially < 1.15. The ratio of R max /R min may be indicative of a roundness of the average region shape. In particular, 1 , the region is circular, whereas for a square R max /R min = v% and for a rectangle with unequal adjacent sides R max /R min > V2.

In embodiments, for at least 50%, such as at least 60%, especially at least 80% of the sets of a seed and a region may apply that h(q) comprises a largest distance r max and a smallest distance r min , especially wherein r max /r min < 2, especially < 1.3, such as < 1.15. In further embodiments, for at least 85%, such as at least 90%, especially at least 95%, including 100%, of the sets of a seed and a region may apply that h(q) comprises a largest distance r max and a smallest distance r min , especially wherein rmax/rmin £ L 2, such as < 2 especially < 1.3, more especially < 1.15.

In embodiments, in a superposition of the entrance surface pattern and the exit surface pattern the seeds of the entrance tessellation may coincide with central points of the rectangles. In particular, the central points of the rectangles in the exit surface pattern may define the locations of the seeds in the corresponding entrance surface pattern.

The regions (in the entrance surface pattern) may especially be polygons, such as convex polygons.

In embodiments, for at least 60%, such as at least 80%, especially at least 90%, including 100% of the regions may apply that the region comprises a plurality of interior angles a wherein each angle in the plurality of interior angles a > 90°. In further embodiments, each region may comprise a plurality of interior angles a, especially wherein each angle in the plurality of interior angles a > 90°. Such regions may especially have a more rounded shape, which may be preferable in terms of providing a circular or elliptical beam.

The entrance tessellation may especially be a Voronoi tessellation. In a Voronoi tessellation, regions may be defined according to a plurality of seeds in a plane. In particular, for each seed there is a corresponding region consisting of all points of the plane closer to that seed than to any other. Hence, the points that are equidistant to two (or more) seeds define region boundaries. Hence, in embodiments, the regions may comprise Voronoi regions (or “Voronoi cells”).

It will be clear to the person skilled in the art that the entrance lenslet shapes and the exit lenslet shapes may vary in height, specifically, an entrance lenslet shape may be higher at the seed than at a region boundary, and, similarly, an exit lenslet shape may be higher at its center than at its boundaries.

In embodiments, each entrance lenslet shape may have a seed axis, wherein the seed axis is perpendicular to the entrance face and wherein the seed axis passes through the (respective) seed of the entrance lenslet shape, wherein the height of the entrance lenslet shape is rotationally symmetric with respect to the seed axis. In particular, the height of the entrance lenslet shape may reduce as a function of (in-plane) distance to the seed axis.

In further embodiments, each entrance lenslet shape may have the same height at the seed, and the height of each entrance lenslet shape may vary, especially reduce, according to a (same) function of (in-plane) distance to the seed axis.

In particular, in embodiments, the entrance lenslet shapes may be according to a Voronoi tessellation, the entrance lenslet shapes may be rotationally symmetric in height (with regards to the seed axis), and the entrance lenslet shapes may have the same height at their (respective) seeds. In such embodiments, then at the region boundary between two lenslets/Voronoi-regions the height of the neighboring lenslets may be equal (as the region boundary is equidistant to the seeds of the bordering regions). As a result, the entrance face of the Kohler beam shaping element may be continuous. This rotational symmetry may, for example, be satisfied when spherical lenslets are used, i.e., when a surface of each entrance lenslet shape is a segment of a sphere with the center lying on the seed axis.

In particular, in such embodiments, the entrance surface may beneficially be devoid of jumps when the lenslets form a Voronoi tessellation, i.e., the entrance lenslet shapes may provide a continuous lens surface. Hence, Voronoi tessellation in combination with rotationally symmetric entrance lenslet shapes, especially with spherical lenslets, may result in a Kohler beam shaping element without discontinuities at lenslet boundaries.

In further embodiments, the entrance lenslets, especially the entrance lenslet shapes, may comprise spherical lenslets.

In embodiments, each exit lenslet shape may have a central axis, wherein the central axis is perpendicular to the exit face and, wherein the central axis passes through the (respective) central point of the exit lenslet shape, wherein the height of the exit lenslet shape is rotationally symmetric with respect to the central axis. In particular, the height of the exit lenslet shape may reduce as a function of (in-plane) distance to the central axis.

In further embodiments, each exit lenslet shape may have the same height at the central point, and the height of each exit lenslet shape may vary, especially reduce, according to a (same) function of (in-plane) distance to the central axis. It will be clear to the person skilled in the art that a phrase such as “the entrance lenslet shape has a seed axis, wherein the seed axis passes through the (respective) seed of the entrance lenslet shape” and similar phrases, refers to the entrance lenslet shape being shaped according to a region in the entrance surface pattern, and the seed axis passing through a location in the entrance lenslet shape that corresponds to the seed of the region in the entrance surface pattern according to which the entrance lenslet shape is shaped.

In embodiments, the Kohler beam shaping element may comprise a plurality of lenslet pairs, wherein each lenslet pairs comprises an entrance lenslet shape and an exit lenslet shape focused on each other, especially wherein the seed axis of the entrance lenslet shape and the central axis of the exit lenslet shape are (essentially) the same axis. In embodiments, the seed axis and the central axis may have a mutual angle < 3°, such as < 2°, especially < 1°, including 0° (i.e., parallel). In further embodiments, the seed axis of an entrance lenslet shape may pass through the (corresponding) exit lenslet shape at a distance of < 0.1 *L from the central point (of the exit lenslet shape), such as at a distance < 0.05*L, especially < 0.01 *L, such as through the central point.

It will be clear to the person skilled in the art that the heigh variation in an entrance lenslet shape (or in an exit lenslet shape) may depend on the distance between the entrance face and the exit face of the Kohler beam shaping elements. For instance, for spherical lenslets, the focal distance inside a medium with refractive index n may be F=nR/(n-l) wherein R may be the radius of the lenslet. For example, for n=1.5, F=3R. When the distance between the entrance face and the exit face is d, and with the Kohler condition that F=d, then R=d/3 may be a rough estimate for the radius of a lenslet. With a spacing P between seeds (or central points) of the lenslets, the height difference of the spherical surface in the center and at the edge may be

For example, with d=5 mm and P=3 mm, the height difference may be 0.9 mm. With a smaller pitch and a thicker plate, the difference may be smaller: e.g. for d=10 mm, P=2 mm the height difference may be 0.15mm.

In embodiments wherein the seeds of the entrance surface pattern are arranged according to an irregular pattern, and wherein the entrance lenslet shapes are spherical, the largest height difference of the spherical surface at the seed and at the edge of a region may be

In embodiments, the entrance face and the exit face may be arranged at a distance d, wherein d is selected from the range of 1 - 50 mm, especially from the range of 2 - 40 mm. In further embodiments, d may be at least 1 mm, such as at least 2 mm, especially at least 3 mm. In further embodiments, d may be at most 50 mm, such as at most 40 mm, especially at most 30 mm, such as at most 20 mm.

In embodiments, the two (adjacent) rows may be shifted relative to one another along an axis parallel to the rows by an independently selected distance (dn) selected from the range of 0.01 *L - 0.99*L, such as from the range of 0.05*L - 0.95*L, especially from the range of 0.1 *L - 0.9*L. In further embodiments, at least 20%, such as at least 50%, especially at least 70% of rows may be shifted relative to at least one adjacent row along an axis parallel to the rows by an independently selected distance (dn) selected from the range of 0.01 *L - 0.99*L, such as from the range of 0.05*L - 0.95*L, especially from the range of 0.1 *L - 0.9*L. In further embodiments, at least 80%, such as at least 90%, especially at least 95% of rows, including 100%, may be shifted relative to an adjacent row along an axis parallel to the rows by an independently selected distance (dn) selected from the range of 0.01 *L - 0.99*L, such as from the range of 0.05*L - 0.95*L, especially from the range of 0.1*L - 0.9*L.

In embodiments, the distances dn may be independently, especially randomly, selected from the range of 0.01 *L - 0.99*L, such as from the range of 0.05*L - 0.95*L, especially from the range of 0.1 *L - 0.9*L. However, in further embodiments, consecutive rows may be shifted according to a regular pattern. For instance, each row may be shifted to an adjacent row for dn=L/3. Alternatively, for example, rows may be consecutively shifted relative to a previous row according to a sequence of o different values, such as [0.1 *L, 0.34*L,0.8*L,0.65*L] for o=4, such that each row is aligned with every o other rows, i.e., row #1 may be aligned with rows #5, #9, #13, etc.

In embodiments, the exit surface may comprise at least 10 exit lenslet shapes, such as at least 30 exit lenslet shapes, especially at least 50 lenslet shapes. In further embodiments, the exit surface may comprise at most 500000 exit lenslet shapes, such as at most 250000 exit lenslet shapes, especially at most 100000 exit lenslet shapes. In further embodiments, at least 80% of the exit lenslet shapes approximate a rectangle in the exit surface pattern, such as at least 90%, especially at least 95%, including 100%.

In particular, the exit surface and the entrance surface may comprise the same number of lenslet shapes, i.e., the number of exit lenslet shapes may be equal to the number of entrance lenslet shapes.

Hence, in embodiments, the entrance surface may comprise at least 10 entrance lenslet shapes, such as at least 30 entrance lenslet shapes, especially at least 50 lenslet shapes. In further embodiments, the entrance surface may comprise at most 500000 entrance lenslet shapes, such as at most 250000 entrance lenslet shapes, especially at most 100000 entrance lenslet shapes. In further embodiments, at least 80% of the entrance lenslet shapes approximate a rectangle in the entrance surface pattern, such as at least 90%, especially at least 95%, including 100%.

The exit face may, in embodiments, have an area a x (in plane) selected from the range of 0.5 cm 2 - 2 m 2 , such as from the range of 1 cm 2 - 1 m 2 . In particular, the entrance face may have an entrance area a n selected from the range of 0.95*a x - 1.05 a x , especially from the range of 0.99 a x - 1.01 a x , more especially wherein a n and a x are (essentially) equal.

Hence, as follows from the exit face and the entrance face having essentially the same area as well as essentially the same number of lenslet shapes, the average area of an entrance lenslet shape may be (essentially) equal to the average area of an exit lenslet shape, i.e., in embodiments, the exit lenslet shapes may have an average lenslet area ai x (in plane), and the entrance lenslet shapes may have an average lenslet entrance area ai n selected from the range of 0.95* ai x - 1.05 ai x , especially from the range of 0.99 ai x - 1.01 ai x , more especially wherein ai n and ai x are (essentially) equal.

In embodiments, the Kohler beam shaping element may have an element length LI and an element width W1 having a first aspect ratio R1 of at least 2, such as at least 3, especially at least 5. In further embodiments, R1 may be at most 50, such as at most 30, especially at most 20.

In further embodiments, W 1 may be at least 1 mm, such as at least 5 mm, especially at least 10 mm. In further embodiments, W1 may be at most 5 m, such as at most 3 m, especially at most 1 m, such as at most 0.5 m.

In a further aspect, the invention may provide a lighting device comprising the Kohler beam shaping element according to the invention. In embodiments, the lighting device may especially a (linear) light source, especially an elongated light source, especially a light source collimated in a single direction, or especially a plurality of light sources arranged along an axis of elongation. The lighting device may further comprise a second optical element configured downstream of the light source and upstream of the Kohler beam shaping element. The term “second optical element” may also refer to a plurality of second optical elements.

The second optical element may especially be selected from the group comprising Fresnel lenses, TIR Fresnel lenses, lenses, reflectors, and TIR collimators, especially from the group comprising Fresnel lenses and TIR Fresnel lenses.

The thickness of the beam shaping element along an optical axis of the lighting device may (essentially) linearly scale with the corresponding focal distance, which may result in inconveniently thick plates for large aspect ratios. In such embodiments, the second optical element may especially comprise a (TIR) Fresnel lens as such optical element may facilitate providing a large aspect ratio with a thinner plate.

In further embodiments, the lighting device may further comprise a third optical element configured downstream of the light source and downstream of the Kohler beam shaping element.

The third optical element may especially be selected from the group comprising Fresnel lenses, TIR Fresnel lenses, lenses, reflectors, diffusers, clear cover plates, and TIR collimators.

In embodiments, the Kohler beam shaping element may have an element length LI, and the lighting device may comprise a light source defining a light source length L2, especially wherein L2 > 0.2*L1. In embodiments, 0.4<L2/L1<1.1, such as 0.5<L2/L1<1, especially 0.6<L2/L1<1. The term “light source” may also refer to a plurality of light sources. Hence, the light source length L2 may also refer to a length defined by a plurality of light sources. For instance, in further embodiments, the lighting device may comprise a plurality of light sources arranged in a (linear) array defining a light source array length L2, wherein 0.4<L2/L1<1.1, such as 0.5<L2/L1<1, especially 0.6<L2/L1<1.

In embodiments, the lighting device may comprise a plurality of (solid state) light sources defining L2, i.e., L2 may be defined by a first and last (solid state) light source in the plurality of light sources.

In further embodiments, L2 may be defined by edges of an elongated light source. In embodiments, the light source may comprise a linear light source, especially an elongated light source. In further embodiments, the linear light source may comprise a plurality of solid state light sources, especially 2-100 (solid state) LED light sources, such as especially at least 10. Larger number of solid state light sources, such as over 100, may also be possible.

In further embodiments, the second optical element may comprise a 2D optical element.

In embodiments, the lighting device may be configured for general indoor illumination, such as for office lighting, industry lighting, and retail lighting, and/or for outdoor lighting, such as pedestrian lighting, and area lighting. In further embodiments, the lighting device may comprise an indoor illumination device, especially an illumination device selected from the group comprising office lighting, industry lighting, and retail lighting. In further embodiments, the lighting device may comprise an outdoor illumination device, especially an outdoor illumination device selected from the group comprising pedestrian lighting and area lighting.

In a further aspect the invention may provide a method for providing the Kohler beam shaping element according to the invention. The method may comprise defining an exit surface pattern comprising a tessellation of a plurality of rectangles having a length L and a width W, especially wherein L/W > 4. The rectangles may especially be arranged in a plurality of rows having a width W, for at least two adjacent rows may apply that the two adjacent rows are shifted relative to one another. The method may further comprise defining an entrance surface pattern comprising providing a Voronoi tessellation with central points of the plurality of rectangles as seeds. In embodiments, the method may further comprise providing a Kohler beam shaping element having an entrance face patterned according to the entrance surface pattern and an exit face patterned according to the exit surface pattern, especially wherein in a superposition of the entrance surface and the exit surface the seeds of the Voronoi tessellation coincide with the central points of the rectangles.

The method may especially comprise one or more of injection molding or hot embossing to provide the beam shaping element.

In embodiments, the method may comprise providing a precursor element having an exit face and an entrance face, and patterning the entrance face according to the entrance surface pattern, and patterning the exit face according to the exit surface pattern, i.e., providing entrance lenslet shapes in the entrance face according to the entrance surface pattern, and providing exit lenslet shapes in the exit face according to the exit surface pattern. In further embodiments, the (entrance tessellation comprising the) Voronoi tessellation may comprise n seeds and n corresponding regions, especially wherein each set of a seed (of the plurality of seeds) and corresponding region (of the plurality of corresponding regions) may define a region function n(0) for values of Q from the range of 0 - 360°. In embodiments, the Voronoi tessellation may define a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(0), wherein:

RW - å"=i ii W

In embodiments, the virtual average region seed function R(0) may comprise a largest distance R ma x and a smallest distance R m in, wherein Rmax/Rmin < V2.

In embodiments, the method may comprise defining a plurality of seeds according to a regular second 2D array according to a first pitch vector vi and a second pitch V2, especially wherein vrv2 > 0, and wherein the method may comprise defining an entrance surface pattern comprising providing a Voronoi tessellation with the seeds. In further embodiments, the method may comprise defining an exit surface pattern comprising a plurality of rectangles, wherein the method comprises: defining a plurality of parallel lines passing through the seeds, wherein sets of two adjacent parallel lines define a strip between them, wherein the parallel lines have a slope equal to mvi - V2, wherein m is an integer selected from the range of > 2, especially wherein 2 < m < 10; translating the parallel lines by ½ vi or by ½ V2; and adding line segments in each strip orthogonally to the parallel lines and in the center between two adjacent seeds in the strip to provide the plurality of rectangles, wherein the rectangles are defined by the parallel lines and the line segments. In further embodiments, the method may further comprise providing a Kohler beam shaping element having an entrance face patterned according to the entrance surface pattern and an exit face patterned according to the exit surface pattern, especially wherein in a superposition of the entrance surface and the exit surface the seeds of the Voronoi tessellation coincide with the central points of the rectangles.

In particular, the rectangles resulting from the method may have a length L and a width W according to:

L = \rnVi — t¾ | In particular, in embodiments wherein the Voronoi tessellation is a tessellation of squares, the aspect ratio of the rectangles may be equal to 1+m 2 .

The embodiments described herein are not limited to a single aspect of the invention. For example, an embodiment describing the beam shaping element may, for example, further relate to the method for providing the beam shaping element. For instance, embodiments of the method may relate to defining entrance and/or exit patterns according to described embodiments of the beam shaping element, such as with regards to the dimensions and or number of the rectangles. Similarly, an embodiment of the method describing the construction of the beam shaping element may further relate to embodiments of the beam shaping element.

The terms “upstream” and “downstream” relate to an arrangement of items or features relative to the propagation of the light from a light generating means (here especially the light source), wherein relative to a first position within a beam of light from the light generating means, a second position in the beam of light closer to the light generating means is “upstream”, and a third position within the beam of light further away from the light generating means is “downstream”.

The lighting device may be part of or may be applied in e.g. office lighting systems, household application systems, shop lighting systems, home lighting systems, accent lighting systems, spot lighting systems, theater lighting systems, fiber-optics application systems, projection systems, self-lit display systems, pixelated display systems, segmented display systems, warning sign systems, medical lighting application systems, indicator sign systems, decorative lighting systems, portable systems, automotive applications, green house lighting systems, horticulture lighting, or LCD backlighting.

As indicated above, the lighting unit may be used as backlighting unit in an LCD display device. Hence, the invention provides also a LCD display device comprising the lighting unit as defined herein, configured as backlighting unit. The invention also provides in a further aspect a liquid crystal display device comprising a back lighting unit, wherein the back lighting unit comprises one or more lighting devices as defined herein.

In a specific embodiment, the light source comprises a solid state LED light source (such as a LED or laser diode or a superluminescent diode). More especially, the (linear) light source comprises a plurality of light sources.

The term “light source” may also relate to a plurality of light sources, such as 2-20 (solid state) LED light sources. Hence, the term LED may also refer to a plurality of LEDs. The term white light herein, is known to the person skilled in the art. It especially relates to light having a correlated color temperature (CCT) between about 1800 and 20000 K, especially 2700-20000 K, for general lighting especially in the range of about 2700 K and 6500 K, and for backlighting purposes especially in the range of about 7000 K and 20000 K, and especially within about 15 SDCM (standard deviation of color matching) from the BBL (black body locus), especially within about 10 SDCM from the BBL, even more especially within about 5 SDCM from the BBL.

In an embodiment, the light source may also provide light source light having a correlated color temperature (CCT) between about 5000 and 20000 K, e.g. direct phosphor converted LEDs (blue light emitting diode with thin layer of phosphor for e.g. obtaining of 10000 K). Hence, in a specific embodiment the light source is configured to provide light source light with a correlated color temperature in the range of 5000-20000 K, even more especially in the range of 6000-20000 K, such as 8000-20000 K. An advantage of the relative high color temperature may be that there may be a relative high blue component in the light source light.

The terms “visible”, “visible light” or “visible emission” refer to light having a wavelength in the range of about 380-780 nm.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which corresponding reference symbols indicate corresponding parts, and in which:

Fig. 1 A-B schematically depict embodiments of the Kohler beam shaping element.

Fig. 2A-E schematically depict embodiments of the entrance and exit surface patterns.

Fig. 3 schematically depicts an embodiment of a region.

Fig. 4A-B schematically depict embodiments of the lighting device. The schematic drawings are not necessarily on scale.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Fig. 1 A-B schematically depict a Kohler beam shaping element 100 comprising an entrance face 110 and an exit face 120. In particular, the entrance face 110 comprises a plurality of entrance lenslet shapes according to an entrance surface pattern 115 and the exit face 120 comprises a plurality of exit lenslet shapes according to an exit surface pattern 125. Fig. IB further schematically depicts an optical element 20, especially a (linear) Fresnel lens 21, arranged upstream from the Kohler beam shaping element 100 with respect to light source light 11 (not depicted for visualization purposes).

In embodiments, the Kohler beam shaping element 100 may be configured to beam shape (light source) light 11 received at the entrance face 110 and to provide beam shaped (light source) light 101 emanating from the exit face 120.

Fig. 2A-C schematically depict embodiments of exit surface patterns 125 and entrance surface patterns 115.

Specifically, Fig. 2A depicts (on the left) an exit surface pattern 125 comprising an exit tessellation of a plurality of rectangles 121 having a length L and a width W, wherein L/W > 4. The rectangles 121 are arranged in a plurality of rows 123 having a width W. In the depicted embodiment, for at least two (adjacent) rows 123 applies that the two (adjacent) rows 123 are shifted relative to one another, especially along a length dimension parallel to the length L of the rectangles 121. In particular, in the depicted embodiment, all rows 123 are shifted relative to at least one adjacent row 123.

Specifically, in the depicted embodiment, for each set of two adjacent rows 123 applies that the two adjacent rows 123 are shifted relative to one another along an axis parallel to the rows 123 by an independently selected distance dn selected from the range of 0.05*L - 0.95*L.

Further, Fig. 2A depicts (on the right) an entrance surface pattern 115 comprising an entrance tessellation. The entrance tessellation may comprise n seeds 112 and n corresponding regions 111, especially wherein each set of a seed 112 and corresponding region 111 may define a region function h(q) for values of Q from the range of 0 - 360°. In particular, for seed and region i, h(q) may comprise the distance between the seed 112 and region boundaries for the different values of Q. The entrance tessellation may further define a virtual average region shape with a virtual average region seed according to a virtual average region seed function R(9), wherein:

*(*) = åL nW

The virtual average region seed function R(9) may comprise a largest distance Rmax and a smallest distance R m in, especially wherein Rmax/Rmin < yf2. In the depicted embodiment, in a superposition of the entrance surface pattern 115 and the exit surface pattern 125 the seeds 112 of the entrance tessellation coincide with central points 122 of the rectangles 121. In particular, in the depicted embodiment, the entrance tessellation comprises a Voronoi tessellation 116.

In the depicted embodiment, wherein L/W > 4.5, especially about 5.5. Further, in the depicted embodiment applies for at least 50% of the region functions hq that r,0 comprises a largest region distance Umax and a smallest region distance rimin, wherein rimax/rimin

< 42.

Fig. 2A further schematically depicts a method for providing the Kohler beam shaping element 100, specifically with regards to defining the exit surface pattern 125 and the entrance surface pattern 115. In the depicted embodiment, the method defining an exit surface pattern 125 comprising a tessellation of a plurality of rectangles 121 having a length L and a width W, wherein L/W > 4, wherein the rectangles 121 are arranged in a plurality of rows 123 having a width W, and wherein for at least two adjacent rows 123 applies that the two adjacent rows 123 are shifted relative to one another. In the depicted embodiment, the method further comprises defining an entrance surface pattern 115 comprising providing a Voronoi tessellation with central points 122 of the plurality of rectangles 121 as seeds 112 (right side of Fig. 2A).

In embodiments, the method may further comprise providing a Kohler beam shaping element 100 having an entrance face 110 patterned according to the entrance surface pattern 115 and an exit face 120 patterned according to the exit surface pattern 125. In particular, as depicted, in a superposition of the entrance surface 110 and the exit surface 120 the seeds 112 of the Voronoi tessellation coincide with the central points 122 of the rectangles 121.

Fig. 2B-E schematically depict further embodiments of entrance surface patterns 115 and exit surface patterns 125 of the Kohler beam shaping element 100. Specifically, Fig. 2B schematically depicts an embodiment wherein the entrance surface pattern 115 comprises a tessellation of regular hexagons, which is a Voronoi tessellation 116. Fig. 2C schematically depicts an embodiment wherein the entrance surface pattern comprises a tessellation of squares, which is also a Voronoi tessellation 116. Fig. 2D schematically depicts an embodiment wherein the entrance surface pattern 115 is a non-Voronoi tessellation. Fig. 2E schematically depicts an embodiment wherein the entrance surface pattern 115 comprises a Voronoi tessellation 116, wherein Voronoi seeds for the Voronoi tessellation 116 are distanced from the central points 122 of the rectangles 121 (and thus from the seeds 112 in the entrance surface pattern 115). For each of Fig. 2B-E, the aspect ratio of the rectangles 121 in the exit surface pattern 125 is > 5. Fig. 3 schematically depicts a set of a seed 112 and corresponding region 111 defining a region function n(0) for values of Q from the range of 0 - 360°. In particular, for seed and region i, n(0) comprises the distance between the seed 112 and region boundaries for the different values of Q.

In the depicted embodiment the region 111 may be a (convex) polygon. Further, the region 111 may comprise a plurality of interior angles a, al, a2, a3, a4, a5, a6, wherein each angle in the plurality of interior angles a, al, a2, a3, a4, a5, a6, > 90°.

Fig. 4A-B schematically depict embodiments of the lighting device 1200. The lighting device 1200 may comprise the Kohler beam shaping element 100 according to the invention.

In embodiments, the lighting device 1200 may comprise a light source 10, especially an elongated light source, especially a light source collimated in a single direction, or especially a plurality of light sources arranged along an axis of elongation. The light source 10 may especially be configured to provide (light source) light 11. In the depicted embodiments, the lighting device 1200 comprises a (linear) array 15 comprising a plurality of (solid state) light sources 10.

Fig. 4A depicts an embodiment of the lighting device 1200 comprising a plurality of light sources 10 arranged along an axis of elongation, and a second optical element 20 configured downstream of the light sources 10 and upstream of the Kohler beam shaping element 100. In particular, the light sources 10 are configured to provide (light source) light 11 to the Kohler beam shaping element 100 via the second optical element 20, wherein the Kohler beam shaping element 100 is configured to receive the light 11 at the entrance face 110 and to provide beam-shaped light 101 from the exit face 120. Hence, the lighting device 1200 may provide beam-shaped light 101.

In the depicted embodiment, the lighting device 1200 comprises an indoor illumination device selected from the group comprising office lighting, industry lighting, and retail lighting.

In embodiments, the light source may define a light source length L2 (or L2), and the Kohler beam shaping element may have an element length LI (or Li) (parallel to the light source length L2, wherein 0.5<L2/L1<1. In the depicted embodiment, L2 < LI.

In further embodiments, the second optical element 20 has an optical element length L3 (parallel to the light source length). In further embodiments, L2 < L3 < LI, especially L2 < L3, or especially L3 < LI. Specifically, Fig. 4B schematically depicts an embodiment of a luminaire 2 comprising the lighting device 1200 as described above. Reference 301 indicates a user interface which may be functionally coupled with a control system 300 comprised by or functionally coupled to the lighting device 1200. Fig. 4 also schematically depicts an embodiment of a lamp 1 comprising the lighting device 1200. Reference 3 indicates a projector device or projector system, which may be used to project images, such as at a wall, which may also comprise the lighting device 1200. Hence, reference 1200 refers to a lighting device, which may e.g. be selected from the group of a lamp 1, a luminaire 2, a projector device 3. The lighting device 1200 may comprise the beam shaping element 100. Fig. 4 also schematically depicts an embodiment of the lighting device 1200 comprising a wall light device (such as especially wall washers). The lighting device 1200 may also comprise a cove lighting device (for illuminating a cove).

The term “plurality” refers to two or more. Furthermore, the terms “a plurality of’ and “a number of’ may be used interchangeably.

The terms “substantially” or “essentially” herein, and similar terms, will be understood by the person skilled in the art. The terms “substantially” or “essentially” may also include embodiments with “entirely”, “completely”, “all”, etc. Hence, in embodiments the adjective substantially or essentially may also be removed. Where applicable, the term “substantially” or the term “essentially” may also relate to 90% or higher, such as 95% or higher, especially 99% or higher, even more especially 99.5% or higher, including 100%. Moreover, the terms ’’about” and “approximately” may also relate to 90% or higher, such as 95% or higher, especially 99% or higher, even more especially 99.5% or higher, including 100%. For numerical values it is to be understood that the terms “substantially”,

“essentially”, “about”, and “approximately” may also relate to the range of 90% - 110%, such as 95%-105%, especially 99%-101% of the values(s) it refers to.

The term “comprise” also includes embodiments wherein the term “comprises” means “consists of’.

The term “and/or” especially relates to one or more of the items mentioned before and after “and/or”. For instance, a phrase “item 1 and/or item 2” and similar phrases may relate to one or more of item 1 and item 2. The term "comprising" may in an embodiment refer to "consisting of but may in another embodiment also refer to "containing at least the defined species and optionally one or more other species".

Furthermore, the terms first, second, third and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a sequential or chronological order. It is to be understood that the terms so used are interchangeable under appropriate circumstances and that the embodiments of the invention described herein are capable of operation in other sequences than described or illustrated herein.

The devices, apparatus, or systems may herein amongst others be described during operation. As will be clear to the person skilled in the art, the invention is not limited to methods of operation, or devices, apparatus, or systems in operation.

The term “further embodiment” and similar terms may refer to an embodiment comprising the features of the previously discussed embodiment, but may also refer to an alternative embodiment.

It should be noted that the above-mentioned embodiments illustrate rather than limit the invention, and that those skilled in the art will be able to design many alternative embodiments without departing from the scope of the appended claims.

In the claims, any reference signs placed between parentheses shall not be construed as limiting the claim.

Use of the verb "to comprise" and its conjugations does not exclude the presence of elements or steps other than those stated in a claim. Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, “include”, “including”, “contain”, “containing” and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.

The article "a" or "an" preceding an element does not exclude the presence of a plurality of such elements.

The invention may be implemented by means of hardware comprising several distinct elements, and by means of a suitably programmed computer. In a device claim, or an apparatus claim, or a system claim, enumerating several means, several of these means may be embodied by one and the same item of hardware. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

The invention also provides a control system that may control the device, apparatus, or system, or that may execute the herein described method or process. Yet further, the invention also provides a computer program product, when running on a computer which is functionally coupled to or comprised by the device, apparatus, or system, controls one or more controllable elements of such device, apparatus, or system. The invention further applies to a device, apparatus, or system comprising one or more of the characterizing features described in the description and/or shown in the attached drawings. The invention further pertains to a method or process comprising one or more of the characterizing features described in the description and/or shown in the attached drawings. Moreover, if a method or an embodiment of the method is described being executed in a device, apparatus, or system, it will be understood that the device, apparatus, or system is suitable for or configured for (executing) the method or the embodiment of the method, respectively.

The various aspects discussed in this patent can be combined in order to provide additional advantages. Further, the person skilled in the art will understand that embodiments can be combined, and that also more than two embodiments can be combined. Furthermore, some of the features can form the basis for one or more divisional applications.