阅读说明：本技术 光学器件、照明器以及制造光学器件的方法 (Optical device, luminaire and method of manufacturing an optical device ) 是由 M·布兰德 于 2019-03-06 设计创作，主要内容包括：一种使光源所发射的入射光变换以在投影面上形成辐照图案的光学器件具有由非球面透镜与笛卡尔卵形线集合的并集形成的自由形式表面。各个笛卡尔卵形线是将入射光聚焦到点的透镜,并且笛卡尔卵形线集合将入射光引导到形成辐照图案的边界的点集合。非球面透镜是折射透镜的引导入射光以形成辐照图案的内部的部分。非球面透镜与笛卡尔卵形线集合组合以形成所述并集,使得各个笛卡尔卵形线共享折射透镜的辐射焦点并且在单个点处与非球面透镜的表面切向接触。(An optical device that transforms incident light emitted by a light source to form an irradiance pattern on a projection surface has a free-form surface formed by a union of an aspheric lens and a set of cartesian ovals. Each cartesian oval is a lens that focuses incident light to a point, and the set of cartesian ovals directs incident light to a set of points that form the boundary of the irradiance pattern. The aspheric lens is the portion of the refractive lens that directs incident light to form the interior of the irradiance pattern. The aspheric lens is combined with a set of cartesian ovals to form the union such that each cartesian oval shares a radiation focus of the refractive lens and makes tangential contact with a surface of the aspheric lens at a single point.)

1. An optical device for converting incident light emitted by a light source to form an irradiance pattern on a projection surface, wherein the optic has a free-form surface formed by a union of an aspheric lens and a set of Cartesian ovals, wherein each Cartesian oval is a lens that focuses the incident light to a point, and wherein, the set of cartesian ovals directs the incident light to a set of points forming a boundary of the irradiance pattern, and wherein the aspheric lens is a portion of a refractive lens that directs the incident light to form an interior of the irradiance pattern, wherein the aspheric lens is combined with the set of Cartesian ovals to form the union, such that the respective cartesian ovals share the radiation focus of the refractive lens and make tangential contact with the surface of the aspheric lens at a single point.

2. The optic of claim 1, wherein the intensity of the incident light follows lambertian cosine law such that the light source is a lambertian light source, wherein the refractive lens is a lambertian uniform point lens that reverses lambertian cosine law to generate a uniform irradiance on the projection surface forming the interior of the irradiance pattern in response to illumination by the lambertian light source.

3. The optic of claim 2, wherein each cartesian oval shares the radiation focus of the lambertian uniform lens, wherein each cartesian oval has a unique focus on the boundary of the irradiance pattern defined by the optical axis of the cartesian oval, and wherein each cartesian oval is in tangential contact with the surface of the aspheric lens at a unique point.

4. The optic of claim 1, wherein at least some of the set of cartesian ovals have different geometric parameters defined by a focal point of the cartesian ovals on the boundary of the irradiation pattern and a location of tangential contact with the refractive lens.

5. The optic of claim 1, wherein the free-form surface of the lens formed by the union of the aspheric lens and the cartesian oval set is a surface of the refractive lens having a cutout that conveys rays of the incident light that pass through the cutout from outside the irradiance pattern to the boundary of the irradiance pattern.

6. The optical device of claim 1, wherein the incident light is collimated, the refractive lens has a flat surface, each of the cartesian ovals comprises a hyperbolic shape and is in tangential contact with a surface of the aspheric lens at a vertex of the hyperbolic shape.

7. The optical device of claim 1, wherein the irradiance pattern comprises a glyph.

8. The optical device of claim 1, wherein the irradiance pattern comprises letters forming words.

9. The optical device of claim 1, wherein the irradiance pattern comprises a bi-tonal image.

10. The optical device of claim 1, wherein a surface of the optical device opposite the free-form optical surface is frosted such that the irradiation pattern is formed on the frosted surface.

11. A luminaire, comprising:

the optical device of claim 1; and

a light source arranged in the illuminator to emit light onto the free-form optical surface to generate the irradiance pattern.

12. The luminaire of claim 11 wherein the light source comprises a Light Emitting Diode (LED).

13. The luminaire of claim 12 wherein the shape of the free form optical surface is a function of the arrangement of the LEDs relative to the free form optical surface.

14. A method for manufacturing an optical device, the method comprising the steps of:

determining a free-form optical surface that transforms incident light emitted by a lambertian light source into an irradiance pattern on a projection plane, wherein the free-form optical surface of the optic is formed by a union of a portion of a lambertian uniform point lens that, in response to illumination by the lambertian light source, generates uniform irradiance on the projection plane that forms an interior of the irradiance pattern and a set of cartesian ovals that focus light from the lambertian light source along boundaries of the irradiance pattern; and

fabricating the optical device having the free-form optical surface.

15. The method of claim 14, further comprising the steps of:

determining the Lambertian uniform point lens that transforms the incident light emitted by the Lambertian light source into a uniform irradiance of the projection surface;

determining a portion of the Lambertian uniform spot lens that contributes to irradiance of an interior of the irradiance pattern;

determining a volume formed by the set of cartesian ovals focusing light from the lambertian light source along the boundary of the irradiance pattern; and

combining the portion of the Lambertian uniform-point lens with the volume to form the free-form optical surface of the optic such that each Cartesian oval is in tangential contact with the portion of the Lambertian uniform-point lens at a single unique point.

16. An optical device, comprising:

an aspheric lens formed of a portion of the lambertian uniform point lens that transforms incident light emitted by the lambertian light source into uniform illumination; and

a union of cartesian ovals, wherein each cartesian oval is a lens that focuses incident light to a point, wherein each cartesian oval shares a radiation focus of the lambertian uniform lens and makes tangential contact with a surface of the aspheric lens at a single unique point.

17. A luminaire, comprising:

the optical device of claim 16; and

a lambertian light source disposed in the illuminator to emit light onto the optics, wherein the lambertian uniform point lens transforms the incident light emitted by the lambertian light source into uniform irradiance forming an interior of an irradiance pattern, and wherein each cartesian oval transforms the incident light emitted by the lambertian light source onto a corresponding point at a boundary of the irradiance pattern.

18. The illuminator of claim 17, wherein the irradiance pattern comprises letters such that a union of the cartesian ovals directs the incident light to form a profile of the letters and the lambertian uniform point lens directs the incident light inside the profile.

Technical Field

The present invention relates to optics, and more particularly, to optics having a free-form optical surface that transforms incident light to generate an illumination pattern.

Background

The field of non-imaging optics has sought a way to design an optical surface that transforms incident light emitted by a light source into an arbitrary illumination pattern. In the past two decades, substantial progress has been made in the idealization of rays that are either perfectly parallel or that diverge completely from a single point for the zero etendue case. This idealization allows for a one-to-one correspondence between the light rays in the emitted light and the light rays in the target illumination pattern. This one-to-one correspondence reduces design issues, deciding on reflection or refraction of an optical surface enables a one-to-one mapping between the spatial density of rays in a cross-section of the emitted light and the spatial density of rays in the target illumination pattern. If a smooth mapping between the initial density and the target density is possible (which is almost always the case for zero etendue systems), the mapping can be found using methods from the best quality delivery domain. The resulting optics can generate detailed illumination patterns (e.g., projection capture images). These optical surfaces are often referred to as free-form optical surfaces simply because their shape is more complex than any simple algebraic surface typically associated with lenses and mirrors.

In fact, zero etendue light sources are not present. Practical light sources, e.g. Light Emitting Diodes (LEDs), have a spatial extent, i.e. light rays are emitted from areas rather than points, and these light rays cross during their propagation, so that a one-to-one mapping is not possible and the problem is out of range for which the best quality transport can be resolved. If the free-form optical surface is illuminated by a spatially extended light source, the resulting illumination pattern is significantly blurred, as shadows on cloudy days become soft and unsharp. This ambiguity is inevitable according to the second law of thermodynamics.

Thus, when designing free-form optics for spatially extended light sources, the goals of the optical engineer are much gentler — typically achieving near uniform illumination only in circular or polygonal border areas. Furthermore, it is generally believed that there will be a blurry halo of uncontrolled illumination decay outside this region, even though this may be undesirable in some applications. Some researchers have also attempted to control this halo and achieve sharp attenuation. The simultaneous multiple curved surface (SMS) method provides some control over the boundary by routing light rays from the edge of the light source to the intended target; optimal mass transport combined with approximate deblurring can sometimes achieve sharp edges in the irradiation pattern. However, in both approaches, the final irradiation pattern suffers from an uncontrolled trade-off between blurred edges and undesirable texture artifacts within the irradiation pattern.

Since the advent of high power LEDs, the problem of obtaining uniform irradiance from a lambertian light source has received much attention. To date, all design approaches have been approximated. Furthermore, many of the methods proposed for designing free-form surfaces rely on simplifying assumptions about the light source, most commonly it provides a uniform light flux through the lens. Most modern light sources are lambertian light sources, the luminous flux intensity along any ray being proportional to the cosine of the angle between the ray and the optical axis. This must be very carefully modeled at optimization, otherwise the irradiance image will have fairly significant artifacts.

Therefore, there is a need for a method that can transform incident light from a spatially extended light source into a target illumination pattern with sharp edges. These methods may be beneficial for many optical applications, such as optics for identification lighting and special lighting.

Disclosure of Invention

It is an object of some embodiments to provide an optical device that can generate complex irradiation patterns with sharp boundaries and no overflow in the background outside those boundaries. It is another object of some embodiments to provide an optical device that can generate complex irradiance patterns with uniform illumination inside.

Some embodiments are based on the recognition that: one particular type of lens, referred to herein as a cartesian oval, focuses incident light to a point without any light contamination outside of that point. To this end, a set of cartesian ovals may direct incident light to a set of points. When an extended light source is used, the points are also extended, but they retain a sharp boundary and the set of points can similarly form an extended shape with a sharp boundary. For example, such a set of points may form an irradiation pattern and/or a boundary of an irradiation pattern. Such an irradiation pattern may have a complex form to include glyphs, letters forming words, and/or logos.

Some embodiments are based on another recognition: the refractive lens transforms incident light to illuminate a projection surface. Typical refractive lenses direct incident light into and out of the desired irradiance pattern (glyph-like). The portion of the refractive lens that directs light onto the desired irradiance pattern is useful for forming the irradiance pattern. The remainder of the refractive lens illuminates the projection surface outside the desired irradiance pattern, and is useless for forming the irradiance pattern.

Some embodiments are based on the recognition that: the "useless" portion of the refractive lens may be replaced by a collection of cartesian ovals that direct light previously collected by the "useless" portion of the refractive lens to a point on the boundary of the irradiation pattern. In this way, a two-tone image can be formed by the interior formed by the "useful" portion of the refractive lens and the boundary illuminated by incident light refracted by the set of cartesian ovals.

Some embodiments are based on the recognition that: many light sources, such as LED Light Emitting Diodes (LEDs), are lambertian light sources that emit light according to the lambertian emission law, which states that the intensity of radiation or luminescence observed from an ideal diffuse reflective surface or an ideal diffuse radiator is proportional to the cosine of the angle θ between the direction of incident light and the surface normal. To this end, the projection surface illuminated by the lambertian light source shows radiation with intensity dissipated from the bright center. Thus, a typical lens shaped to direct incident light emitted by a lambertian light source to form a particular irradiance pattern (resembling a glyph or logo) generates the irradiance pattern such that there is uneven irradiance inside the irradiance pattern and/or the background is contaminated by light that spills outside the desired irradiance pattern.

Some embodiments are based on the recognition that: a lens having a refractive surface that uniformly illuminates the disk in response to illumination by a lambertian light source may be designed. Such lenses are referred to herein as lambertian uniform spot lenses. For this reason, when the refractive lens is a lambertian uniform-spot lens, a two-tone image having a uniform interior, a bright boundary, and a dark exterior may be displayed on a projection plane illuminated by a lambertian light source.

In geometry, the cartesian oval named Ren descales is a plane curve, a linear combination of distances from two fixed points (called focal points) with the same set of points. In optics, a cartesian oval is a lens with refractive surfaces formed by rotating the cartesian oval around an axis passing through its two focal points. Light from either focal point is refracted to focus on the other focal point. Some embodiments are based on the recognition that: a set of cartesian ovals may be used to redirect emitted light away from the outside of the desired irradiance pattern onto the boundaries of the irradiance pattern.

In this manner, the optics for transforming the emitted incident light into a bi-tonal irradiance pattern may be formed from the union of the portion of the lambertian uniform point lens that generates the interior of the irradiance pattern and the set of cartesian ovals that focus the remaining light from the lambertian light source along the boundaries of the irradiance pattern. In the optics that generate such a bi-tonal irradiance pattern, each cartesian oval shares the radiation focus of the lambertian uniform lens, and each cartesian oval is in tangential contact with the surface of the lambertian uniform lens at a single point.

Notably, the shape of the lambertian uniform point lens and the set of cartesian ovales can be determined analytically. In this way, the resulting optics used to generate the bi-tonal image can also be determined analytically.

Accordingly, one embodiment discloses an optic that transforms incident light emitted by a light source to form an irradiance pattern on a projection surface, wherein the optic has a free-form surface (freeform surface) formed by a union of an aspheric lens and a set of cartesian ovals, wherein each cartesian oval is a lens that focuses incident light to a point, and wherein the set of cartesian ovals directs incident light to a set of points that form a boundary of the irradiance pattern, and wherein the aspheric lens is a portion of a refractive lens that directs incident light to form an interior of the irradiance pattern, wherein the aspheric lens and the set of cartesian ovals combine to form the union such that each cartesian oval shares a radiation focus of the refractive lens and is in tangential contact with the surface of the aspheric lens at a single point.

Another embodiment discloses a method for manufacturing an optical device, the method comprising the steps of: determining a free-form optical surface that transforms incident light emitted by the lambertian light source into an illumination pattern on the projection surface, wherein the free-form optical surface of the optic is formed by a union of a portion of a lambertian uniform point lens that, in response to illumination by the lambertian light source, generates a uniform irradiance on the projection surface that forms an interior of the irradiance pattern and a set of cartesian ovals that focus light from the lambertian light source along a boundary of the irradiance pattern; and fabricating an optical device having the free-form optical surface.

Another embodiment discloses an optical device, including: an aspherical lens formed by a portion of the lambertian uniform point lens that transforms incident light emitted from the lambertian light source into uniform irradiation; and a union of cartesian ovals, wherein each cartesian oval is a lens that focuses incident light to a point, wherein each cartesian oval shares the radiation focus of a lambertian uniform lens and makes tangential contact with the surface of the aspheric lens at a single unique point.

Drawings

[ FIG. 1A ]

Fig. 1A is a schematic diagram of an irradiation pattern illustrating principles used by some embodiments.

[ FIG. 1B ]

Fig. 1B is a schematic diagram of an optical device having a free-form optical surface designed by some embodiments using the principles disclosed with respect to fig. 1A.

[ FIG. 2A ]

FIG. 2A is a schematic view of some embodiments of a Cartesian oval lens for refracting light.

[ FIG. 2B ]

Figure 2B is a schematic diagram of a set of cartesian ovals forming a boundary directing light from outside of an irradiance pattern to the irradiance pattern, according to one embodiment.

[ FIG. 3]

FIG. 3 is a cross-section of a lens formed by a combination of a refractive lens and a set of Cartesian ovals, according to one embodiment.

[ FIG. 4A ]

Fig. 4A is a schematic diagram of forming an optical device according to some embodiments.

[ FIG. 4B ]

Fig. 4B is an exemplary schematic diagram illustrating the lambertian uniformity principle employed by some embodiments.

[ FIG. 5]

FIG. 5 is a block diagram of a method of manufacturing an optical device that projects a pattern onto a projection surface, according to one embodiment.

[ FIG. 6A ]

FIG. 6A is an example of an illuminator with optics determined in accordance with various embodiments of the invention.

[ FIG. 6B ]

Figure 6B is an example of an illuminator with optics determined in accordance with various embodiments of the invention.

[ FIG. 6C ]

Figure 6C is an example of an illuminator with optics determined in accordance with various embodiments of the invention.

[ FIG. 7A ]

Fig. 7A is a different non-limiting example of various target illumination patterns generated by some embodiments.

[ FIG. 7B ]

Fig. 7B is a different non-limiting example of various target illumination patterns generated by some embodiments.

[ FIG. 7C ]

Fig. 7C is a different non-limiting example of various target illumination patterns generated by some embodiments.

[ FIG. 8]

FIG. 8 is a graph of light intensity for sharp-edged boundaries of a target illumination pattern, in accordance with some embodiments.

Detailed Description

Fig. 1A shows a schematic diagram of an irradiation pattern illustrating the principle used by some embodiments. Some embodiments are based on the recognition that: a typical refractive lens transforms incident light into an illumination disk 110 that is projected onto a projection surface. However, it is an object of some embodiments to modify the refractive lens to transform incident light into a particular irradiance pattern, similar to the pattern within the profile 130. Some embodiments are based on the recognition that: typical refractive lenses direct incident light both inside 140 and outside 120 the irradiance pattern 130. The portion of the refractive lens that directs light within the interior 140 of the irradiance pattern 130 is useful for forming the irradiance pattern. The remainder of the refractive lens illuminates the projection surface outside 120 (i.e., outside of the outline 130) of the desired irradiance pattern, which is useless for forming the irradiance pattern.

Some embodiments are based on the recognition that: the "useless" portion of the refractive lens may be replaced by a collection of cartesian ovals that direct light previously collected by the "useless" portion of the refractive lens to a point on the boundary 150 of the irradiation pattern. In this way, the interior formed by the "useful" portion of the refractive lens and the boundary illuminated by incident light refracted by the set of cartesian ovals form a two-tone image.

Some embodiments are based on the recognition that: many light sources, such as LED Light Emitting Diodes (LEDs), are lambertian light sources that emit light according to the lambertian emission law, which states that the intensity of radiation or luminescence observed from an ideal diffuse reflective surface or an ideal diffuse radiator is proportional to the cosine of the angle θ between the direction of incident light and the surface normal. To this end, the projection surface illuminated by the lambertian light source shows radiation with intensity dissipated from the bright center 155.

Some embodiments are based on the recognition that: a lens having a refractive surface that uniformly illuminates 160 the projection surface in response to illumination by the lambertian light source may be designed. Such lenses are referred to herein as lambertian uniform spot lenses. To this end, some embodiments design an optical device to transform incident light to form an irradiance pattern having a uniform interior 160 confined within the boundaries 150 of the irradiance pattern.

Fig. 1B shows a schematic diagram of an optical device having a free-form optical surface designed by some embodiments using the principles disclosed with respect to fig. 1A. According to some embodiments, the optics 170 transform incident light emitted by the light source 175 to form an irradiance pattern 180. The optic has a free-form surface formed by the union of a collection of cartesian ovals and a portion of a refractive lambertian uniform point lens.

The cartesian ovals are lenses that focus incident light to points such that the set of cartesian ovals reflect incident light to at least the set of points forming the boundary 190 of the irradiance pattern. This portion of the refractive lens directs incident light to form an interior 195 of the irradiance pattern surrounded by the boundary 190. In some implementations, when the refractive lens is a lambertian uniform-spot lens, a two-tone image having a uniform interior, a bright boundary, and a dark exterior can be displayed on a projection surface illuminated by a lambertian light source.

FIG. 2A illustrates some embodiments for directing light from a focal point F of radiation ₀205 to a radiation focus point F ₁215 of a cartesian oval lens 210. The nature of the definition is that the light takes the same time from F, regardless of the path₀Is propagated to F₁. This may be because the light slows down by a factor n inside the lens. Thus, the top 220 and bottom 225 paths have a travel time np + q ═ nv + r, where p, v and q, r are the straight line travel distances inside and outside the lens for the two different paths, respectively. It is noted that the length v of the central ray from the focal point to the apex of the lens, the two focal points F₀、F₁Is sufficient to fully determine the shape of the cartesian oval 210.

Figure 2B illustrates a schematic diagram of forming a set of cartesian ovals directing light from outside of an irradiance pattern to a boundary of the irradiance pattern, in accordance with one embodiment. If the embodiment rotationally sweeps the 2D cartesian oval line 210 about its optical axis 230, the resulting 3D cartesian oval line focuses light from point F0205 to the point at F1215. If the embodiment then rotationally sweeps the 3D cartesian oval line about another line 240 passing through the focal point F0, the embodiment obtains a union of the cartesian oval lines 250. In this example, the union of the cartesian ovals 250 focuses the light from the focal point F0 into a perfect circle on the projection surface. In constructing the swept volume, the central axis of the 3D cartesian oval traces the path of the projected circle.

Notably, the front face of the resulting union of the cartesian oval collections includes missing pieces (divot) 260. The lack transmits any light passing through it away from the interior of the ring, keeping the area dark. Various embodiments use this principle to form irregular patches formed by sweeping a cartesian oval through an irregular path controlled by the shape of the irradiation pattern and use these patches to keep the irregular areas of the projection plane dark.

FIG. 3 illustrates a cross-section of a lens formed by a combination of a refractive lens and a union of Cartesian oval collections, according to one embodiment. In this illustrative example, the cross-section of the refractive lens 340 (thick curve) has a lack 345 (gray), which lack 345 causes portions of the irradiance image 355 on the projection plane 350 to be dark. In this example, the desired irradiation pattern is an illuminated disc with the dark letter "I". To this end, the portion 342 of the lens 340 that refracts incident light inside the desired irradiance pattern (i.e., outside the desired dark letter I) is considered to be a "useful" portion, and the portion 345 of the lens 340 that refracts incident light inside the desired dark letter I is considered to be a "useless" portion. A useful portion of refractive lens 340 is referred to herein as an aspheric lens. To this end, the aspheric lens is the portion of the refractive lens that directs incident light to form the illuminated interior of the irradiance pattern.

Dark lines 315 and 317 are rays from the light source 310 to the projection plane 350. Two cartesian ovals 320 and 330 (depicted in thin curves) are superimposed on the lens 340. Each oval is tangent to the aspheric lens where a ray to the boundary of "I" exits the lens, and the cartesian oval is scaled and oriented to focus light at the end point of the ray. This means that the central axes 325 and 335 of the cartesian ovals point to the corresponding end points. These two ovals are part of a sweep of a similarly configured oval that the focal point tracks the boundary of the "I". So that the surface of the lens follows the lack 345 formed by this sweep.

Some embodiments combine the useful portion of refractive lens 340 that directs incident light inside the irradiance pattern (i.e., an aspheric lens) with a set of cartesian ovals that direct incident light to the boundaries of the irradiance pattern. This combination results in a free-form lens having respective cartesian ovals 320 and 330 that share a focal point of radiation 310 with a refractive lens 340. Light is placed at the radiation focus point 310. In this manner, both the refractive lens and the cartesian oval project light onto the same plane of projection 350. Additionally, in some embodiments, each cartesian oval is in tangential contact with a useful portion of the refractive lens at a single and/or unique point. For example, the cartesian oval 320 makes tangential contact with the aspheric lens at point 327. Similarly, the cartesian oval 330 makes tangential contact with the aspheric lens at point 337. In this way, the combined optics remain smooth and easy to manufacture.

As can be seen in fig. 3, the optic is formed at least in part by the union of the cartesian oval sets that merge the cartesian oval sets together. The union of the cartesian oval sets ensures that incident light entering at least one cartesian oval is directed at the contour or boundary of the desired irradiance pattern. In various embodiments, the geometry relative to each cartesian oval in the set of refractive lens geometries is uniquely defined by the focal point 310, the direction of the optical axis 325 and/or 335, and the location of the tangent point 327 and/or 337. Different cartesian ovals may have different geometric parameters. In various embodiments, the cartesian oval continuously tracks the shape of the boundary of the irradiance pattern to ensure that the boundary is sharply, continuously, and brightly illuminated.

Fig. 4A illustrates a schematic diagram of forming an optical device according to some embodiments. In those embodiments, the useful portion of the refractive lens (i.e., aspheric lens 410) is combined 430 with a set of cartesian ovals 420. In various implementations, the cartesian oval 420 has a surface formed by the union of the cartesian oval 420 to ensure continuity of the boundaries of the irradiation pattern. The aspherical lens 410 is a lens whose surface profile is not a part of a sphere or a cylinder. This is because the aspherical lens 410 is only a part of the refractive lens. The combination 430 of the aspheric lens 410 and the set of cartesian ovals 420 is performed such that the respective cartesian ovals share the radiation focus of the refractive lens and make tangential contact with the surface of the aspheric lens at a single point, as shown in fig. 3.

In some embodiments, the intensity of the incident light follows lambertian cosine law, such that the light source is a lambertian light source and the refractive lens is implemented as a lambertian uniform point lens that reverses lambertian cosine law. In various embodiments, a lambertian uniform spot lens generates a uniform irradiance forming an interior of an irradiance pattern on a projection surface in response to illumination by a lambertian light source.

Fig. 4B shows an exemplary schematic illustrating the lambertian uniformity principle employed by some embodiments. In this example, a Lambertian uniform point lens with a refractor surface R (φ)460 converts light emitted by a Lambertian point source 450 at an origin into a uniformly illuminated disk 470 of radius p at a distance R480.

Some embodiments use the relationship between the emissivity of a lambertian light source and the surface area of the disk to design a lambertian uniform point lens. Specifically, a Lambertian light source radiates along the tilt angle φ 451 with an intensity proportional to cos φ, so the total luminous flux leaving the half angle φ cone is

Some embodiments are based on the recognition that: the disc can be uniformly illuminated with optics that maintain this relationship at some fixed ratio q for all radii up to some finite limit. To this end, a suitably shaped lens should refract light rays emitted at an oblique angle φ so that they are incident on the projection plane in units of q sin φ with respect to the optical axis. To generate a uniformly illuminated disc of radius p using a cone of emitted half-angle β 452, the above relationship implies q ═ p/sin β. For example, one embodiment determines angle β such that the angle of incidence of the edge ray at the refracting surface is close to brewster's angle. In this way, embodiments may ignore losses due to fresnel reflections.

The corresponding relation between the lens point and the plane point is

Where R (φ) is the radial extent of the lens surface at an angle φ relative to the optical axis, and θ is the azimuthal angle on the lens and the polar angle on the plane of projection.

To derive the lens surface, some embodiments first use 2D cartesian coordinates, where the light is at the origin (0,0), the optical axis extends in the direction { +1,0} and the perpendicular projection plane passes through (r, 0). One implementation parametrizes the lens (in 2D) to (x, y) — (R (Φ) cos Φ, R (Φ) sin Φ) and uses the cosine form of the law of refraction to parameterize the incident ray I ═ x, y) - (0,0), the emergent ray E ═ s, t) - (x, y) ═ R, p csc β sin Φ) - (x, y), and the surface tangentAre associated with:

n cos∠IT＝cos∠ET

where n is the ratio of the refractive indices on either side of the lens surface.

Writing the result in vector form as

One embodiment assumes that the lens is very small with respect to the disc radius p and the projection distance r, such that x ═ s, | y | t |, and the field of the outgoing rays is determined by the surface normal, the effect of the surface extent being negligible. In the limiting case, this is: lin_{R(φ)/min(r，p)→0}E ═ s, t. Substituting ray and tangent definition and simplifying, the embodiment obtains

Extended to Ordinary Differential Equation (ODE)

Wherein q is p csc β. The solution is in the form ofWherein p is₁，p₂Is a super-empirical polynomial summed over the roots of the fourth degree.

Alternative embodiments have no lenslet hypothesis and design a lambertian uniform point lens by approximating the exit surface as a sphere in the exit ray E, resulting in a solvable ODE. Notably, simulations confirm that this surface provides good uniformity even when the lens has a non-trivial size and there is an extended light source (provided it is small relative to the lens).

In this way, some embodiments are based on the understanding that: the shape of the lambertian uniform point lens and the set of cartesian ovals can be determined analytically. Thus, the resulting optics used to generate the bi-tonal image can also be determined analytically.

FIG. 5 shows a block diagram of a method of manufacturing an optical device for projecting a pattern onto a projection surface, according to one embodiment. The embodiment determines 510 a lambertian uniform point lens for the predefined parameter 515. For example, the predefined parameters 515 may include the desired focal length r, the spot radius p, the lens size s, and the embodiment solves for ODE (2).

In addition, embodiments establish 520 a correspondence between the boundaries of the pattern and the lens surface according to the predefined locations and boundaries of the desired pattern 525 within the disc illuminated by the lambertian uniform point lens. For example, embodiments place a graphic on a projection surface (e.g., a projection plane) and identify portions of a lambertian uniform spot lens surface that direct light outside the boundaries of the graphic. These parts are then sunk and become missing pieces so that they direct the light to the boundary.

In some implementations, the graphic is back projected from the projection plane to the lens surface using correspondence (1). Let G be a subset of the projection plane occupied by the pattern,b is the corresponding set of emission angles through the lens, i.e.,g has a boundary

Similarly, B has a boundary

Next, along a sweep 530 of the boundary trace of the graph projected on the lambertian uniform spot lens, the embodiment determines the union of the cartesian oval sets. For example, some implementations construct a new function of the lens surface depression that causes the lens to refract light out of G:

wherein C is_R(g, φ, θ) is the corresponding point where light is focused to point g and its surface is on the original lens surfaceThe radial extent at (phi, theta) of the cartesian oval tangent to R (·). The radial function of the Cartesian oval is

Where v is the distance from the light to the apex of the oval and p-r_g(c-n) + (n-1) v, and c is the cosine of the angle between the ray along (phi, theta) and the axis of the oval, which would be the distance r_gThe target point g at (a) is connected to the light at the origin.

Taking the maximum value on all these ovals generates a focusing surface corresponding to the union of the set of cartesian ovals, each point being contributed by a cartesian oval. The focusing surface replaces any unwanted refraction on the original surface of the 540 lambertian uniform point lens with refraction that transmits light to the boundary of the pattern to create a free-form optical surface 545. In some embodiments, points on the focusing surface have surface normals different from their contributing ovals, typically these normals are moderately tilted so that local ray refraction is shifted very slightly along the tangent of the boundary.

Different embodiments calculate the max function in different ways. At the boundary

In some cases, simply, the focusing surface may be derived analytically. More generally, since the surface is ultimately assigned to the manufacturing machine as a numerical sample, these samples can be calculated as: the boundary segments are represented as simple lines and circular arc segments, the oval line is swept along these segments by parsing, and the resulting expressions are used to calculate the radial extent of nearby sinks.

Next, embodiments fabricate 550 an optical device having a free-form optical surface 545. For example, one embodiment manufactures an optical device by injection molding a plastic optical device. The development of Electrical Discharge Machining (EDM) has provided a means of producing optical quality free-form surfaces in the mold metal. EDM, in turn, relies on five and six axis machining to generate the desired free form surface as a carbon electrode of the same dimensions as the part to be produced. The electrode is used to electrocautery a concavity in the metal that matches its shape, thereby providing a mold cavity that imparts the desired shape to the molten plastic. In addition to replication methods of injection molding, free-form surfaces can be directly created in some optical materials (e.g., acrylic) using multi-axis machining techniques, albeit at a greater cost per part than injection molding, and are therefore typically used for prototypes. There are many other free-form prototyping techniques including 3D printing of optical polymers and robotic deformation of metal plates.

For the case where the incident light is collimated, some embodiments take the limits of the above equation as the light source moves towards (- ∞,0) while keeping the lens-to-target distance constant. In this limit, the lens and the projection plane face an infinitely small beam cone, and therefore from its angle, lambertianThe point emitter becomes a uniform collimated beam, the uniform lens surface becomes flat, the oval becomes hyperboloid, and the tangent point is always the hyperboloid vertex. Thus, the whole construction is simplified to a height fieldIs internally zero and is in

Maximum convolution of hyperboloids outside of- ∞ (also known as gray scale expansion).

One advantage of embodiments with collimated light is that the lens and lens mold can be cut from a flat blank with little machining. In particular, a hi-fi mold can be cut using standard bagging techniques on a 3-axis milling machine using a drill bit with flat ends and hyperbolic side profiles.

Fig. 6A, 6B and 6C show examples of an illuminator with optics determined according to various embodiments and a light source 620 arranged in the illuminator to emit light onto the free-form optical surface. For example, the light source 620 may be arranged at a distance 640 from the free-form optical surface, which is taken into account when determining the free-form optical surface. For example, in some embodiments, the shape of the free-form optical surface is a function of the shape of the emission area of the extended light source and the arrangement of the light source relative to the free-form optical surface.

In various embodiments, the free-form optical surface may be single-sided or double-sided. For example, in the example illuminator 611, the optics 631 have a single-sided free-form optical surface. The free-form surface of the optics 631 is the surface furthest from the light source 620 and the nearest surface is flat. In the example illuminator 612, the free-form optical surfaces of the optics 632 are double-sided, i.e., both sides of the optics are free-form optical surfaces. In the example illuminator 613, the surface of the optics 633 closest to the light source 620 has a free form.

In some embodiments, the illuminator projects a target illumination pattern on a screen external to the illuminator. Examples of such screens include walls or any other flat surface. In an alternative embodiment, the optics of the illuminator itself may be used as the screen. For example, in one embodiment, the surface 650 of the optical device 633 opposite the free-form optical surface is frosted such that an illumination pattern is formed on the frosted surface. Additionally, or alternatively, the illuminator may have secondary optics for imaging and display purposes.

Fig. 7A, 7B, and 7C illustrate different non-limiting examples of various illumination patterns generated by some embodiments. The pattern of illumination is shown with black lines for clarity. In practice, those example images may be reversed. For example, in some embodiments, the illumination pattern includes a glyph 710 or an artistic image 720. For example, the illumination pattern may include letters that form the word 730. In some embodiments, the illumination pattern is an asymmetric pattern. The illumination pattern may also have a gradient in brightness.

FIG. 8 illustrates a graph 820 of light intensity at a sharp-edged boundary of a target illumination pattern, according to some embodiments of the invention. Boundary 810 separates the exterior from the interior of the illumination/irradiance pattern. As seen on the graph, the rate of change of light intensity causes the light intensity to change from a minimum value to a maximum value within a predetermined distance 830 from the boundary 810. Such a distance 830 is found in the focused image and is governed by the second law of thermodynamics.

The above-described embodiments of the present invention can be implemented in any of numerous ways. For example, embodiments may be implemented using hardware, software, or a combination thereof. When implemented in software, the software code can be executed on any suitable processor or collection of processors, whether provided in a single computer or distributed among multiple computers. These processors may be implemented as integrated circuits, with one or more processors in an integrated circuit component. However, the processor may be implemented using circuitry in any suitable format.

Additionally, embodiments of the invention may be embodied as a method, examples of which have been provided. The actions performed as part of the method may be ordered in any suitable way. Thus, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, although shown as sequential acts in illustrative embodiments.

Use of ordinal terms such as "first," "second," in the claims to modify a claim element does not by itself connote any priority or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.