OPTICAL DEVICES FOR RADIATION CONCENTRATION.

COLLIMATION OR HIGH-FIDELITY IMAGING

Field of the Invention

This invention relates generally to high efficiency optical devices that concentrate, collimate, redirect, image or otherwise manipulate a beam or source of electro -magnetic radiation, such as concentrators, collimators, reflectors, or imaging systems.

Background of the Invention

Publications and other reference materials referred to herein are numerically referenced in the following text and respectively grouped in the appended Bibliography which immediately precedes the claims.

Perfect imaging has long been a goal in geometric optical design. Beyond the issue of image fidelity, perfect imaging will also ensure realization of the fundamental limit for radiative transfer in the concentration or collimation of light. In the small-source limit, this is approached by satisfying the conditions for aplanatism (i.e., the complete elimination of both spherical aberration and coma - the two leading orders of geometric aberration), to wit, both Fermat's principle of constant optical path length and the Abbe sine condition. This condition can be achieved by optical devices with a minimum of two contours (reflective and/or refractive). The notation 'R' for a refractive surface and 'X' for a reflective surface (in accordance with the notation as disclosed in US 6,639,733) will be used here.

The most compact configurations have been realized by 'XX' (dual-mirror) aplanats - originally developed in the quest for better image quality and wider fields of view in telescopes. The complete mathematical problem was solved analytically in [l]. Recently, XX aplanats were revisited and analyzed in depth, revealing eight possible design categories, most of which had remained unrecognized [2]. Such devices have been explored as both solar concentrators and illumination collimators that can approach the thermodynamic limit for radiative transfer at high collection efficiency, as described in [3] and as disclosed in US 8,063,300B2 and US 6,639,733B2.

'RR' (dual-refraction) aplanats were first rigorously analyzed by Head [4], but recognized only two categories of RR aplanatic lenses. Herein below the inventors will demonstrate that, of the eight fundamental design categories for RR aplanats, three yield practical designs, out of which one had not been discovered before.

' RX' (optics with a refractive primary and a reflective secondary) non ^¬ imaging concentrators (designed for extended rather than point sources) that approach the thermodynamic limit were first introduced as a basic class of the Simultaneous Multiple Surfaces (SMS) method, with the acknowledgement that its point-source limit yields the corresponding aplanat [5-7]. This pioneering work turns out to constitute only one design category of RX aplanatic designs. The full panorama of 8 possible fundamental design categories remained unrecognized, and will be elaborated in this application. A special emphasis is put on RX designs that will achieve reflection at the secondary surface by satisfying total internal reflection (TIR). Such designs will be especially attractive not only in avoiding the need for mirrored surfaces, but also in eliminating mirror absorptive losses (typically 5-15% per reflection). Such devices have not been discovered to date, and will be presented for the first time in this application. 'XR' (optics with a reflective primary and a refractive secondary) non ^¬ imaging concentrators that approach the thermodynamic limit were also first introduced as a basic class of the SMS method in [7 and as disclosed in US. 6,639,733B2. That invention turns out to constitute only one category of XR aplanatic designs. From the full panorama of 8 fundamental categories, of which five yield practical designs, four remained unrecognized, and will be elaborated in this application.

All of the cases that have been described up to this point related to the far- field limit (source at infinity). 'XX' far-field designs have been generalized to the near-field case, namely for a point source that is situated at a finite distance from the optic [8]. Herein the inventors also provide similar near- field generalizations for all of the design categories of the RR, RX and XR aplanats, which have not been reported before.

Additional motivations for using aplanats (relative to SMS designs) include: (a) their optical performance being essentially as good as that of the corresponding non-imaging SMS devices for many cases. An example is far- field concentrators close to the maximal concentration limit (maximal output numerical aperture) with a source angular radius up to ~2°, and (b) solutions for the optical contours being analytic (with the associated advantages in the design and optimization process) whereas the SMS method engenders a point-by-point computational scheme.

It is therefore a purpose of the present invention to provide an imaging system that completely eliminates both spherical aberration and coma by using two optical surfaces (refractive or reflective) as degrees of freedom.

Another purpose of the present invention is achieving maximum performance, namely approaching nature's basic limiting relation between flux concentration Cmax and optical tolerance. Further purposes and advantages of this invention will appear as the description proceeds.

Summary of the Invention

In a first aspect the invention is an aplanatic optical system comprised of: a) at least one aplanatic device comprised of two surfaces surrounding a transparent medium and

b) an absorber when the system is used in a concentrator mode or a light source when the system is used in an illumination mode.

The surfaces are either reflective (X) or refractive (R) and the system is configured in one of the following ways: RX, XR, and RR.

In embodiments of the system the two surfaces of the aplanatic device surround a transparent dielectric material. In these embodiments the aplanatic device can be a complementary aplanatic device obtained by interchanging the refractive indexes of the surrounding medium and the dielectric substrate. In these embodiments the RX, XR, and complementary RR configurations, the absorber or the light source can be optically bonded to the transparent dielectric material. In these embodiments having the RR, complementary RX, and complementary XR configurations the focus can lie outside of the dielectric. In these embodiments the having RX, RR, and complementary XR configurations the system can constitute a monolithic dielectric structure that is manufactured as a single lens element via the shaping of two surfaces.

In embodiments the system is employed in one of- an imaging application and a non-imaging application. In these embodiments the non-imaging application can be pure radiative transfer. In embodiments the system is employed in one of: a 2D system having a line focus and a 3D axis-symmetric system.

In embodiments of the system for XR, complementary RX and complementary RR configurations the system comprises two components, each shaped with one of the aplanatic surfaces, the two components separated by a medium that lies in between them.

Embodiments of the system can be configured as one of: a near- field aplanat and a far- field aplanat.

In embodiments of the system the RX and complementary XR configurations satisfy Total Internal Reflection (TIR) at the reflective surface, such that no mirror coating need be applied.

In embodiments of the system the RX and complementary XR configurations satisfy Total Internal Reflection (TIR) at part of the reflective surface, such that no mirror coating need be applied at that part of the reflective surface, while a mirror coating is applied to the remainder of the surface.

Embodiments of the system are configured as a hybrid aplanatic device formed by merging at least two different aplanatic devices, either from the same family of aplanatic devices or from different families of aplanatic devices.

Embodiments of the system are configured as a Fresnel aplanatic device formed from a large number of aplanatic sections that are merged together to form a single aplanatic device.

In a second aspect the invention is a non-imaging optical system comprised of: a) at least one aplanatic device comprised of two surfaces surrounding a transparent medium and

b) an absorber when the system is used in a concentrator mode or a light source when the system is used in an illumination mode! wherein the surfaces are either reflective (X) or refractive (R) and the system is configured in one of the following ways: RX _; XR _; XX _; and RR.

In embodiments of non-imaging optical system the aplanatic device is a complementary aplanatic device obtained by interchanging the refractive indexes of the surrounding medium and the transparent medium between the two surfaces.

In embodiments of non-imaging optical system the system is configured as a hybrid non-imaging optical system formed by merging at least two different aplanatic devices, either from the same family of aplanatic devices or from different families of aplanatic devices.

In embodiments of non-imaging optical system the system is configured as one of a near-field non-imaging optical system and a far-field non-imaging optical system.

In embodiments of non-imaging optical system the system is configured as a Fresnel non-imaging optical system formed from a large number of aplanatic sections that are merged together to form a single non-imaging optical system. All the above and other characteristics and advantages of the invention will be further understood through the following illustrative and non-limitative descriptions of embodiments thereof, with reference to the appended drawings.

Brief Description of the Drawings

— Fig. 1 provides a cross -sectional schematic of the far-field RX aplanat geometry with illustrative ray trajectories;

— Fig. 2 provides a panorama of cross -sectional diagrams of all of the far- field RX aplanatic design options that require a mirrored secondary. Two ray trajectories are drawn for illustration for each design;

— Fig. 3 provides a panorama of cross -sectional diagrams of all of the far- field RX aplanatic design options that utilize total internal reflection for the reflection of the secondary. Two ray trajectories are drawn for illustration for each design;

— Fig. 4 provides a cross sectional schematic of the near-field RX aplanat geometry with illustrative ray trajectories;

— Fig. 5 provides two examples of the generalization of the far-field RX aplanats to the near-field case, at an input numerical aperture NA=0.5;

— Fig. 6 provides a cross -sectional schematic of the far-field XR aplanat geometry with illustrative ray trajectories;

— Fig. 7 provides a panorama of cross -sectional diagrams of all of the XR aplanatic design options. Two ray trajectories are drawn for illustration for each design;

— Fig. 8 provides a cross-sectional schematic of the near-field XR aplanat geometry with illustrative ray trajectories;

— Fig. 9 provides an example of the generalization of the far-field XR-1 aplanat to the near-field case, at input numerical aperture NA=0.5;

— Fig. 10 provides a cross-sectional schematic of the far-field RR aplanat geometry with illustrative ray trajectories; — Fig. 11 provides a panorama of cross-sectional diagrams of all of the RR aplanatic designs. Two ray trajectories are drawn for illustration for each design;

— Fig. 12 provides a cross -sectional schematic of the near-field RR aplanat geometry with illustrative ray trajectories;

— Fig. 13 provides an example of the generalization of the far-field RR-3 aplanat to the near-field case, at input numerical aperture NA=0.5;

— Fig. 14 provides a panorama of cross -sectional diagrams of all of the complementary RX aplanatic design options. Two ray trajectories are drawn for illustration for each design;

— Fig. 15 provides a panorama of cross -sectional diagrams of all of the complementary XR aplanatic design options. Two ray trajectories are drawn for illustration for each design;

— Fig. 16 provides a panorama of cross -sectional diagrams of all of the complementary RR aplanatic design options. Two ray trajectories are drawn for illustration for each design;

— Fig. 17 provides an illustration of the RX4-RX5A-Complemetary RRIA hybrid aplanat.

— Fig. 18 provides an illustration of a RR Fresnel aplanat and a comparison to a standard aplanat.

— Fig. 19 provides an illustration of a RX Fresnel aplanat and a comparison to a standard aplanat.

— Fig. 20 provides the geometry of the hybrid concentrator design of Fig.

3(e);

— Fig. 21 provides a semi-log flux map for the hybrid concentrator design of Fig. 20; Results are presented for for the solar spectrum and for a monochromatic source, for 3 source sizes.

— Fig. 22 provides the efficiency as a function of the absorber area for the hybrid concentrator design of Fig. 20; Results are presented for for the solar spectrum and for a monochromatic source, for 3 source sizes. — Fig. 23 provides the raytracing simulation result for the hybrid collimator design of Fig. 3(e), for the case of a monochromatic lambertian emitter;

— Fig. 24 provides the collimation efficiency for the hybrid collimator of Fig. 3(e) for a monochromatic lambertian emitter, as a function of the ratio of the projected solid angle (at far field) Ω relative to its value at the thermodynamic limit (collimation efficiency). Results are presented for hybrids which were designed for several collimation angles.;

— Fig. 25 demonstrates the superiority of the hybrid aplanatic collimator of figure 3(e) over a standard collimator;

— Fig. 26 provides the geometry and illustrative ray trajectories for the RX- 6 concentrator design of Fig. 3;

— Fig. 27 provides a flux map (concentration versus the radial coordinate in the absorber plane) for the RX-6 concentrator design of Fig. 26;

— Fig. 28 provides the geometry and illustrative ray trajectories for the RX- 1 concentrator design of Fig. 2;

— Fig. 29 provides a flux map for the RX- 1 concentrator design of Fig. 28, for the case of a monochromatic source;

— Fig. 30 provides a flux map for the RX- 1 concentrator design of Fig. 28, for the case of the solar spectrum, together with the efficiency as a function of the absorber size;

— Fig. 31 provides the geometry, together with sample ray trajectories for the XR-3 and complementary RR-1A hybrid design;

— Fig. 32 provides the efficiency versus projected solid beam angle for the XR-3 and complementary RR- 1A hybrid concentrator design of Fig. 30 for the cases of a monochromatic and a solar source;

— Fig. 33 schematically shows a cross-section of an RR non-imaging device;

— Fig. 34 schematically shows an example of a contour of a close to ideal RR- 1 A non-imaging device, designed for an acceptance angle of 5 degrees and compared with an aplanatic design; and — Fig. 35 schematically shows a 2D flux map of the device of Fig. 34 and comparison to the aplanatic design.

Detailed Description of Embodiments of the Invention

This invention relates to new types of aplanatic optical systems. In some embodiments, these optical devices are based on a purely imaging design strategy, but can also be employed to closely approach the thermodynamic hmit for radiative transfer (in concentrator or illumination mode) even when the application is not inherently imaging, e.g., solar or infrared concentration, and LED collimation that achieve flux transfer near the thermodynamic limit. In other embodiments, such systems can be employed as imaging systems, forming a near-perfect on-axis image of an on-axis object. Excellent image quality is provided for a relatively large numerical aperture - superior to that of conventional plano-convex and bi-convex lenses.

The specific designs illustrated here are formed by two optical surfaces, reflective or refractive, where the optical device may be an RX, XR or RR. The aplanatic designs are relevant for 2D systems, namely systems that have a line focus, and 3D axis -symmetric systems. The designs are also axisymmetric, but (a) are rigorous for two-dimensional, linear devices where the optical control is in one plane only; and (b) non- axisymmetric generalizations are possible (e.g. with a square footprint). All of the aplanatic designs that are presented herein also include a complementary set of designs which are obtained by interchanging the refractive indexes of the surrounding medium and the dielectric substrate.

For the RX, XR and complementary RR aplanats, the concentrator's absorber (or, equivalently, the light source in illumination mode) is optically bonded to the transparent dielectric, with the added advantage of increasing flux concentration by a factor of n ² at fixed optical tolerance (where n denotes the refractive index of the lens dielectric, e.g., n ~ 1.5 for glass and transparent polymers in the visible, and n ~ 3.5 for silicon in the infrared), or, alternatively, relaxing optical tolerance angles (assumed small) by a factor of n at fixed concentration. For illuminators, the equivalent statement is that light source area can be reduced by a factor of n ² for a given degree of collimation, or the collimation angle (assumed small) can be reduced by a factor of n for a given light source size. For the refractive -refractive (RR) aplanats, the focus lies outside the lens (in air).

All of the fundamentally new RX, RR and complementary XR aplanatic designs constitute a monolithic dielectric structure! hence they can be manufactured as a single lens element via the shaping of two surfaces. In another embodiment, the complementary RX, XR and complementary RR aplanatic lens can be formed in an opposite way, by two separated components, each shaped with one of the aplanatic surfaces, with some medium that lies in between, e.g. air.

Several of the RX designs can satisfy TIR at the reflective contour (Fig. 3), such that no mirror coating need be applied, and the optical losses associated with light absorption in mirrors and additional cost can be obviated, thus providing significant benefits over prior art, as disclosed in US 6,639, 733B2. However such designs can also be fully or partially mirror coated (when TIR is not fulfilled) in order to improve compactness.

Different designs can be combined into a single device in order to provide a superior performance over a single design, e.g. the hybrid design in Fig. 3(e) is generated by merging the RX-4 and RX-5A designs, and in another example in Fig. 30, the XR3 and complementary RR1A aplanats are combined to form a single device. Other combinations are also possible. Depending on the aplanat category and the input design parameters, the full construction range of 0 < X _p < R _p may be precluded (see Figs. 3,7) by (a) the paucity of a physical solution over finite regions as X _p approaches either the rim of the primary or the optic axis, as in RX-4 and RX-5, respectively, (b) the secondary blocking rays refracted from the primary, as in RX-6, or (c) the slope of the primary diverging, as in RX-3. In these cases, the construction is truncated, i.e., contours are generated only for a limited range of X _p , as indicated in Table 1 herein below. These limitations, and the associated loss of collectible radiation, grow more pronounced as one tries to achieve more compact concentrators. In some cases, much of this loss can be recovered (if desired) by filling the central gap with a suitable confocal lens contour, e.g. Fig. 30 depicts a hybrid design which is composed of an aplanat of type XR3 which is combined with a complementary RR1A aplanatic lens as depicted in Fig. 30 (other types of lenses are also applicable). In the case of the RX aplanats, the lens can be shaped on the central part of the primary contour, which is otherwise unutilized.

The general aplanatic designs relate to the near-field case, namely a point source (equivalent to the concentration mode case) or a point target (in illumination mode) at a finite distance from the optic. The present invention relates in general to near-field aplanatic designs and to their limiting case - far-field aplanatic designs, where the source/target distance from the optic becomes very large and the radiation approaches collimation at the thermodynamic limit.

As will be described herein below, all of the new aplanatic designs depicted in this application can be further generalized to non-imaging designs, e.g. based on the SMS method [5], or the dual-surface functional method [9], much as the known SMS designs depicted in prior art can be designed for the aplanatic limit. The RR aplanatic designs depicted here can be further coupled to an additional concentrator, in a similar way to what is disclosed in US 2012/0048359 Al for an XX aplanatic concentrator.

An aplanat is an imaging system that completely eliminates both spherical aberration and coma by using two optical surfaces (refractive or reflective) as degrees of freedom. The present invention covers three general types of aplanatic optics: RX, XR and RR, with 'R' referring to a refractive surface and 'X' to a reflective surface. The 4 ^th type - XX aplanats - was researched comprehensively [2,3] and hence not addressed herein.

Aplanats allow achieving maximum performance, namely approaching nature's basic limiting relation between flux concentration Cmax and optical tolerance [3]:

with ni being the refractive index of the medium of the incident radiation at the entry and n2 being the refractive index of the transparent medium filling the concentrator, NA _exit is the concentrator's exit numerical aperture (at the absorber), NA _entry is the numerical aperture at the entry from the far-field source, θ _exit is the maximum exit half angle (at the absorber), and θ _s is the effective source half-angle (e.g., for solar concentration, it comprises the convolution of the sun's intrinsic angular radius of 4.7 mrad with imperfections in alignment, contour shape, and mirror specularity). Equation (l) also describes the basic limit in illumination mode for achieving a collimation half-angle θ _s at a given ratio of aperture to source area (C _max ). For simplicity and without loss of generality examples throughout this application will relate to the practical case having a device made of refractive index n (e.g. glass) and an air medium with refractive index of unity. These examples can be easily generalized by persons skilled in the art to devices made of material and/or any surrounding medium having any refractive index.

Out of the types of aplanatic optics, the RX, XR and complementary RR optics have the advantage of realizing the factor of n ² (Eq. (l)), provided the absorber/emitter is optically bonded to the dielectric filling the aplanat.

The aplanatic optics that is commonly described [1,4] and is presented first here, relates to far-field aplanats, the case where the source lies at infinity (in concentration mode). They are the limiting case of the general near-field case that is also covered here: the case of a point source situated at a finite distance from the optic, along the optic axis (equivalent to the concentration mode case). For illuminators, the equivalent statement is valid for a point target.

Far-field Refractive-Reflective - RX aplanatic optics

A schematic of a cross-section of a far-field RX optical device is presented in Fig. 1. It is formed by a single dielectric piece and includes two optical surfaces^ a refractive primary surface and a reflective secondary surface. For collimated radiation input/output, a receiver/emitter is placed at the focal plane, which is situated on the optic axis between the two optical surfaces. Aplanatism is achieved by satisfying the following conditions (Fig. 1):

a. Fermat's principle of equal optical path for all on-axis rays, L _x + n · L ₂ + n · L ₃ = const.

b. Snell's law of refraction at the primary surface, transition Li to L2. c. The Abbe sine condition (constant magnification for all paraxial rays),

d. Snell's law of reflection at the secondary surface, transition L2 to L3. Li, L2 and L3 are ray trajectory sections, r is the radial position on the primary entry, and φ is the angle of ray L3 with the optic axis at the focus f. F is the Abbe sphere radius, which is obtained by connecting the focus along L3 to the extension of Li and is related to

Conditions (a)-(c) are sufficient for the solution of the problem (with (d) being redundant):

with Χρ,Υρ being the coordinates of the primary, X _S ,Y _S the coordinates of the secondary, and with the following definitions: m¾ = (Y _s - Y _P )/( X _s ^_ Xp), c, p, s = ±1, and the boundary conditions: Y _P (R _P ) = H _p and Y _S (R _S ) = H _s .

There are 8 possible solution classes corresponding to c,p,s = ±1 individually, out of which only 6 are physically admissible. The physical significance of parameter 'c' is whether the optical path crosses the optic axis in the 2D cross-section of Fig. 1 (c=l for axis crossing). The parameter 'p' determines whether the slope of the primary monotonically increases (p= ^_ l) or decreases (p=l) as r approaches the optic axis. The parameter 's' determines the sign of the Abbe radius F defined as positive when its construction from the focus along L3 to the extension of Li lies below the focus and negative otherwise. Designs which demand a mirrored secondary - namely, that cannot satisfy Total Internal Reflection (TIR) at the secondary - are presented in Fig. 2 together with sample ray trajectories. Table 1 provides the exact parameters for generating each design of Fig. 2.

Table 1

Design RXl has a refractive concave primary contour and a reflective concave secondary contour. For the RXl, the optical ray trajectories don't cross the optical axis.

Design RX2A has a refractive convex primary contour and a reflective concave secondary contour. For the RX2A, the optical ray trajectories don't cross the optical axis.

Design RX2B has a refractive convex primary contour and a reflective convex secondary contour. For the RX2B, the optical ray trajectories don't cross the optical axis.

Design RX3 has a refractive convex primary contour and a reflective concave secondary contour. For the RX3, the optical ray trajectories cross the optical axis.

Of the designs in Fig. 2, only design RX-2A has been discovered before, as a non-imaging concentrator which approaches an aplanatic solution in the point source limit [8], while the rest of the designs are - RX-1, RX-2B and RX-3 - are presented here for the first time. Designs that can satisfy TIR at the secondary (for realistic refractive indices of transparent media filling the aplanat design) - thereby obviating the need for a mirrored secondary - are presented in Fig. 3, with the exact parameters for generating each design provided in Table V

Design RX4 has a refractive primary contour with a descending slope towards the optic axis (the center of the primary), and an inward facing TIR side contour. For the RX4, the ray trajectories don't cross the optical axis.

Design RX5A has a refractive primary contour with an ascending slope towards the optic axis (the center of the primary), and a bottom TIR side contour. For the RX5A, the ray trajectories don't cross the optical axis. - A hybrid design is obtained by merging designs RX4 and RX5A to form a single continuous design. For the hybrid design, the optical ray trajectories don't cross the optic axis.

Design RX5B has a refractive primary contour with an ascending slope towards the optical axis (the center of the primary), and an outward facing TIR side contour which is obtained by a void in the dielectric. For the RX5B, the optical ray trajectories don't cross the optic axis.

Design RX6 has a refractive primary contour with an ascending slope towards the optic axis (the center of the primary), and an inward facing TIR side contour. For the RX4, the ray trajectories cross the optical axis.

All of the designs that are presented in Fig. 3, RX-4, RX-5A, RX-5B and RX- 6 haven't been described before and do not necessarily require a mirror coated secondary as for the non-imaging RX concentrator of [6], and as disclosed in US 6,639,733B2.

Near-field Refractive -Reflective - RX aplanatic optics

A schematic cross-section of a near-field RX optical device is presented in Fig.4. It has similar characteristics to the far-field RX aplanatic device, with the main difference being a point source for a case equivalent to concentration mode (target for a case equivalent to illumination mode) that is situated at a finite distance h and view angle Θ from the optic. The far- field RX aplanat is the limiting case where the source distance is very large, with the incident rays L1, in Fig. 1 approaching perfect collimation. Eqs. (2) - (4) are generalized for this case, with the Abbe sine condition taking the

The same notation as used in Eqs. (2)-(4) is used here. Solutions of Eq. (5)- (7) follow the same classification scheme as for the far-field RX aplanat case. Illustrative examples of RX near-field aplanats are presented in Fig. 5, at an input numerical aperture of NA=0.5 (in concentrator mode): RX- 1 aplanat has a mirrored secondary and RX-6 aplanat has a TIR secondary.

Far-Field Reflective -Refractive - XR aplanatic optics

A schematic cross-section of an XR aplanat is presented in Fig. 6. The XR aplanat includes two separate optical components: a reflective primary surface component and a refractive secondary surface component, which is formed on the facet of a transparent dielectric piece, such as a lens. A source or receiver is placed at the focal plane, which is situated on the optic axis inside the dielectric. Aplanatism is achieved by satisfying the following conditions, according to Fig. 6 - a. Fermat's principle of equal optical path for all on-axis rays,

b. Snell's law of reflection at the primary surface, transition L1 to L2. c. The Abbe sine condition (constant magnification for all paraxial rays), F = r/sincp = const\

d. Snell's law of refraction at the secondary surface, transition L2 to L3.

As before for the RX aplanats, conditions (a)-(c) are sufficient for the solution of the problem (with (d) being redundant):

The same notation as in Eqs. (2)-(4) is used here.

Out of the 8 possible solution classes (again corresponding to c, p and s individually assuming the values ±1), only 5 turn out to be physically admissible; they are presented in Fig. 7. Table 2 provides the exact parameters for generating each design. Table 2

Design XR1 has an upward facing concave reflective primary contour and a downward facing refractive convex secondary contour. For the XR1, the ray trajectories don't cross the optical axis.

Design XR2 has an upward facing concave reflective primary contour and a downward facing refractive convex secondary contour. For the XR2, the ray trajectories cross the optical axis.

Design XR3 has an inward facing side reflective primary contour and an upward facing refractive convex secondary contour. For the XR3, the ray trajectories don't cross the optical axis.

Design XR4 has an inward facing side reflective primary contour and an upward facing refractive convex secondary contour. For the XR4, the ray trajectories cross the optical axis.

Design XR5 has an outward facing side reflective primary contour and an upward facing refractive convex secondary contour. For the XR5, the ray trajectories don't cross the optical axis.

Out of these design types, only the non -imaging version of design XR- 1 has been formerly described [5], however it has not been designed as an imaging aplanat. The rest of the designs, XR-2, XR-3, XR-4 and XR-5, have not been discovered before.

Near-Field Reflective-Refractive - XR aplanatic optics

A schematic of a cross-section of a near-field XR optical device is presented in Fig. 8. The near-field XR device has similar characteristics to the far-field XR aplanatic device, with the main difference being a point source for a case equivalent to concentration mode (target for a case equivalent to illumination mode) that is situated at a finite distance from the optic. The far-field XR aplanat is the limiting case where the source distance is very large, with the incident rays Li in Fig. 6 approach perfect collimation. Eqs. (8) - (10) are generalized for this case, with the Abbe sine condition taking

The same notation as in Eqs. (2)-(7) is used here.

Solutions of Eqs. (l l) - (13) follow the same classification scheme as for the far-field XR aplanat. An illustrative example of the near-field XR- 1 aplanat, at an input numerical aperture of NA=0.5 (in concentrator mode) is presented in Fig. 9.

Far-Field Refractive -Refractive - RR aplanatic optics

A schematic of a cross-section of an RR optical device is presented in Fig. 10. The RR device includes two optical surfaces: a refractive primary surface and a refractive secondary surface. A source or receiver is placed at the focal plane, which is situated on the optic axis below the two optical surfaces. The RR device can be made of a single transparent dielectric piece, with the optical surfaces formed on opposite facets, namely a lens. For the RR device, aplanatism is achieved by satisfying the following conditions, according to (Fig. 10):

a. Fermat's principle of equal optical path for all on-axis rays,

b. Snell's law of refraction at the primary surface, transition Li to L2. c. The Abbe sine condition (constant magnification for all paraxial

d. Snell's law of refraction at the secondary surface, transition L2 to L3.

Again, conditions (a)-(c) are sufficient for the solution of the problem (with (d) being redundant):

With the same notation as in Eqs. (2)-(4) being used here.

There are 8 possible solution classes, out of which only 3 are physically admissible as presented in Fig. 11. Table 3 provides the exact parameters for generating each design.

Table 3

Design RR1A has an upward facing convex refractive primary contour and an upward facing concave refractive secondary contour. For the

RR1A, the ray trajectories don't cross the optical axis.

Design RR1A has an upward facing concave refractive primary contour and an upward facing concave refractive secondary contour. For the

RR1A, the ray trajectories don't cross the optical axis.

Design RR1B has an upward facing convex refractive primary contour and an upward facing convex refractive secondary contour. For the

RR1B, the ray trajectories don't cross the optical axis.

Design RR2 has an upward facing concave refractive primary contour and an upward facing concave refractive secondary contour. For the RR2, the ray trajectories don't cross the optical axis.

Design RR3 has an upward facing convex refractive primary contour and an upward facing concave refractive secondary contour. For the RR3, the ray trajectories cross the optical axis.

Out of these designs, RR- 1A, RR- 1B, and RR-2 have been previously described [4], while design RR-3 has not been described before.

Near-Field Refractive-Refractive - RR aplanatic optics

A schematic of a cross-section of a near-field RR optical device is presented in Fig. 12. The near-field RR device has similar characteristics to the far- field RR aplanatic device, with the main difference being a point source for a case equivalent to concentration mode (target for a case equivalent to illumination mode) that is situated at a finite distance from the optic. The far-field RR aplanat is the limiting case where the source distance is very large, with the incident rays Li in Fig. 10 approaching perfect collimation. Eqs. (14)-(16) are generalized for this case, with the Abbe sine condition

The same notation as for Equations (2)-(7) is used here. Solutions of Equations (17)-(19) follow the same classification scheme as for the far-field RR aplanat case. An illustrative example of the RR-3 near-field aplanat at an input numerical aperture, NA=0.5 (in concentrator mode), is presented in Fig. 13.

Complementary aplanatic designs

All of the aplanatic designs, Far-Field and Near-Field that have been presented in the former sections also include a complementary set of designs which are obtained by interchanging the refractive indexes of the surrounding medium and the dielectric substrate.

A) The complementary RX aplanat is composed of two components: a primary lens and a secondary mirror, with a medium e.g. air in between. Fig. 14 presents all of the complementary RX aplanat classes. B) The complementary XR aplanat is composed of single monolithic piece with a mirrored secondary. For some designs the secondary reflection can rely on TIR and do not require a mirrored secondary. Fig. 15 presents all of the complementary XR aplanat classes.

C) The complementary RR aplanat comprises two separate transparent dielectric pieces for each surface, with a medium, e.g. air, in between. Fig. 16 presents all of the complementary RR aplanat classes.

The characterizing equations for each of these cases: complementary RX, XR, and RR, can be simply obtained by interchanging the expression for the refractive index 'n' by Ί/η'.

Hybrid aplanatic designs

A hybrid aplanatic design can be formed by merging different aplanatic designs, either from the same family of designs (e.g. the RX Hybrid of Fig. 3) or from different families (e.g. the XR-RR Hybrid of Fig. 30). Each of the designs handles a certain section of the entry, while continuity is achieved by tuning the parameters of the aplanatic sections. Hybrid designs can be made for Far-Field designs as well as Near-Field designs.

A hybrid design can offer several benefits, such as allowing high concentration (high Numerical Aperture) with high performance, eliminating central gap losses which often appear in aplanatic designs (a central part of the entry which is not covered by the aplanat), reducing the aspect ratio of the device and material savings. An example which allows demonstrating all of the benefits is the RX4-RX5A-complementary RRl triple hybrid, as described in Fig. 17 for an illumination mode (source at the focal point). The RX hybrid of Fig. 3 which is composed of the RX4 and RX5A aplanats is designed for a reduced aspect ratio (relative to the design in Fig, 3). The consequence of this reduction is a far greater central gap loss. The complementary RRl aplanat is combined in the central part of this RX hybrid in order to recover the central gap loss. Since the complementary RR- 1 design requires an air gap in between the primary and secondary, the overall design has a void in the middle which leads to material savings and lower weight.

Fresnel aplanatic designs

The notion of Fresnel zone aplanats is an elaboration of the concept of Hhybrid aplanats. Fresnel aplanats constitute a large number of aplanatic sections that are merged together to form a single aplanatic design. The main motivation of such design is achieving relatively flat optical surfaces and aspect ratio reduction which is often desired in optical designs, as well as material savings.

Each aplanatic section of a specific class (c,p,s) requires 4 parameters for solution which determine the boundaries of the primary and secondary: Rp, Hp, Rs and Hs. A Fresnel aplanatic design with maximal performance can be achieved when the Abbe sphere radius, which is determined by the Abbe sine condition, is identical for all zones (equal magnification). This requirement serves as a constraint, leaving 3 degrees of freedom for design, therefore there are many options for the realization of Fresnel aplanats, e.g. with primary zones with equal heights (flat optic), primary zones with equal widths, primary zones with a custom distribution of boundary conditions (e.g. a circle), similarly requirements can be made on the secondary boundary conditions or on both the primary and secondary together.

Fresnel aplanats can be made for Far-Field designs, Near-Field designs and also hybrid design that are composed of different aplanatic families, e.g. RX and RR.

Fig. 18 presents an example of an RRl Fresnel aplanat with equal Fresnel zone heights at the external surfaces of the lens for both the primary and the secondary. On the left the Fresnel aplanat is compared to the standard aplanat with the same parameters and a clear advantage is demonstrated by reducing the volume of the lens substantially and by flatteningy the optics. On the right, the Fresnel aplanat is presented with sample ray trajectories.

Fig. 19 presents an example of an RX-2A Fresnel aplanat with equal Fresnel zone heights at the external surface of the primary and the internal surface of the secondary. On the left the Fresnel aplanat is compared to the standard aplanat with the same parameters and an advantage is demonstrated by reducing the volume of the lens substantially and by flattening the optics. On the right, the Fresnel aplanat is presented with sample ray trajectories.

Sample embodiments

The optical devices of described above can be used for the collimation, concentration or high-quality imaging of radiation, with applications in solar and infrared concentration, collimation e.g. light emitting diode, discharge or arc filament lamps, as well as sharp image fidelity at high target irradiance in imaging systems.

Several sample embodiments are provided in order to illustrate some uses of these inventions and their performance. All of the examples were designed for a dielectric with a refractive index of 1.52 (BK7 glass)), and analysed using a ray tracing simulation, for both a monochromatic source and the solar spectrum. Illustrative results for a small number of rays, for the monochromatic case, are presented. Ray trajectories follow from right to left.

For sample concentrators, flux maps were generated by tracing ~10 ⁷ rays distributed uniformly in area and projected solid angle, using a top-hat angular distribution input, at optical tolerances θ _S = 5, 10 and 20 mrad, for both monochromatic and solar input. Local concentration is plotted against radial position r on the absorber normalized by its respective thermodynamic limit rth. Ideal concentrators will exhibit a step function with a cut-off at an abscissa value of unity.

A. Far-field RX4-RX5A hybrid aplanat as a solar concentrator

The hybrid concentrator of Fig. 3 is created by merging the RX4 and RX-5A designs (see Table 1 for the design parameters). There is still an intrinsic optical loss for this hybrid device due to the absence of a physically admissible solution for the primary contour as it approaches the optic axis. The particular design for which raytrace evaluation is presented here incurs a gap loss of 5%, which is a somewhat arbitrary choice for the maximum acceptable loss, moderated by the requirement of a reasonable lens aspect ratio. However, most of this loss can be obviated, e.g., by filling the gap with a suitable confocal ellipsoidal-cap lens, or by using a high aspect ratio design.

Fig. 20 provides raytrace results for the hybrid concentrator. Flux maps (semi-log plot) for the hybrid concentrator are provided in Fig. 21 for a range of realistic θ _S values: θ _S = 5, 10 and 20 mrad, for both monochromatic and solar radiation, toward distinguishing the contributions of geometric and chromatic aberration.

Fig. 22 presents the efficiency (the fraction of incident radiation concentrated onto a given focal spot area) of the device as a function of absorber area, A, normalized to its thermodynamic limit value Ath). Ideal concentrators will exhibit a strict proportionality, up to unit efficiency. For a typical practical case for solar concentration, at θ _S = 20 mrad (composed of the sun's angular radius and optical and tracking tolerances), the hybrid concentrator demonstrates excellent performance. B. Far-field aplanatic optics: the RX4-RX5A hybrid as an LED collimator

A monochromatic Lambertian light source is placed at the focus of the RX4-RX5A hybrid device of Fig. 3 (see Table 1 for the design parameters) - a coarse approximation for common light emitting diodes, LEDs, which can be bonded to, or embedded within, such monolithic RX lenses. Raytrace simulation results are illustrated in Fig. 23, demonstrating its collimation capability. Only a small fraction of the rays are not collimated by the device (such rays can be blocked using, e.g. an iris, in applications where stray light reduction is of importance). The thermodynamic limit of Eq. (l) still pertains, for the design degree of collimation θ _S given the ratio of aperture- to-source area C.

Far-field flux map results are presented in Fig. 24 as efficiency (the fraction of emitted radiation within a given far-field projected solid angle Ω corresponding to polar half-angle θ, Ω= n sin ² ( θ)) against Ω normalized by Qth = nsin ² (θs). The quasi-monochromatic emission of LEDs basically eliminates dispersion losses and accounts for especially good performance. The nominal optical losses here stem principally from the angular range over which emitted rays miss the secondary and are emitted at far larger angles, which is a function of source size.

Fig. 25 demonstrates the superiority of the hybrid aplanatic colhmator of Fig. 3(e) over a standard collimator by showing graphs of the relative intensity vs. off-axis angle for collimation using a standard off the shelf collimator and the aplanatic collimator.

C. Far-field aplanatic optics of type RX-6 as a concentrator

The RX-6 concentrator of Fig. 3 was simulated as an optical concentrator for monochromatic radiation (see Table 1 for the design parameters). The results are illustrated in Figs. 26 to 27, showing near-ideal performance. The RX-6 device can also serve as an exceptional colhmator. The high aspect ratio also ensures than only a small fraction of emitted rays is not collimated, rays which are emitted from the source and intersect the primary without meeting the secondary.

D. Far-field aplanatic optics of type RX-1 as a solar concentrator

Fig. 28 provides raytrace results for the RX-1 concentrator of Fig. 2, (see Table 1 for the design parameters). Fig. 29 presents the flux map of the RX- 1 for a monochromatic source, demonstrating close to ideal performance. Fig. 30 depicts the flux map and efficiency performance of the RX-1 as a solar concentrator for a source with an angular radius of 5mrad. In addition to the normalized local concentration, the efficiency (the fraction of incident radiation concentrated onto a given focal spot area) is also presented, demonstrating that for only a small 20% increase of the absorber radius beyond the thermodynamic limit, ~90% of the power can be collected.

E. Far field hybrid aplanatic optics of type XR3- Complementary RR1 as a solar concentrator

The basic XR-3 design of Fig. 7 has the advantage of allowing the implementation of large devices with only small dielectric bulk, thus allowing a more lightweight and flexible device, unlike the hybrid concentrator of Fig. 3, which is entirely dielectric. Another significant advantage is having an upward facing configuration which allows cooling the absorber using a heat sink that is situated behind the absorber and optic, unlike the XR concentrator of [5], as disclosed in US 8, 101,855, which has a downward facing configuration which severely limits the heat sink options, since it has to be placed in front of the optic, thus creating some blockage. At the same time, the disadvantage of the XR-3 design is a large optical gap loss at low aspect ratios (incident power which is not accommodated by the optic). In order to overcome this limitation, a hybrid design can be formed from a low aspect ratio XR-3 aplanatic design (which accounts for -80% of the incident power) and by a central complementary RR1 type aplanatic lens (which accounts for the remaining 20% of the power).

The complementary RR1 of this case is composed as follows. A lens with a flat top and a bottom contour shaped as the primary of the complementary RR1 design is placed at the entry of the device. The secondary contour is designed for the otherwise unutilized center of the XR dielectric secondary. Air separates the two elements.

Fig. 31 provides the geometry and a ray tracing simulation of the XR- 3-complementary RR1 concentrator.

Fig. 32 provides flux maps for the XR3-RR1B hybrid in illumination mode for a monochromatic source with different angular radii. The performance can be further adjusted by controlling the aspect ratio and the fraction of the entry that is covered by the lens, and by using different lens designs.

Non- imaging generalization of aplanatic optics

Dual surface non-imaging concentrators (designed for extended rather than point sources) that approach the thermodynamic limit, designed by the SMS method for example, have been shown to reduce to their corresponding Aplanats under the limit of a point source [5-7]. This section demonstrates how in an opposite approach, an aplanatic design, such as the ones that have been presented herein above can be extended to a non-imaging design.

A schematic of a cross-section of an RR non-imaging device is presented in Fig. 33. Unlike the aplanatic RR optic which is presented in Fig. 10 which has a single incident wavefront with an incidence angle of 0° that is focused to a single focal spot at the center of the coordinate system, here the wavefronts of the edge rays with acceptance angles θa and -θa are each focused to a different focal spot, -f and f correspondingly. Each point on the primary intercepts two edge rays with incident angles θa and -θa.

Each of these rays is then refracted by the primary and intersects the secondary at different points accordingly. The

rays are then refracted by the secondary to their corresponding focal spots: - f and f. The focal spot, namely the size of the absorber in concentration mode (or emitter in illumination mode), is obtained by the thermodynamic limit of Eq. (l), for the design degree of concentration θa, given the concentration C, which is the ratio of optic aperture to the absorber aperture with radius f.

In a similar manner to the aplanatic problems that have been presented in the former sections, the general non-imaging two surface problem can be also characterized by a governing set of Eqn. 20-24.

1) Fermat's principle for edge rays θ _α :

3) Snell's law of refraction for edge rays θ _α at the secondary:

4) Snell's law of refraction for edge rays -θ at the secondary:

5) Snell's law of reflection for edge rays θ _α at the primary.

This equation is derived in the same way as Eqn. 15. Since it is redundant in this analysis it will not be presented.

6) Snell's law of reflection for edge rays -θ _α at the primary:

This equation is derived in the same way as Eqn. 15. Since it is redundant in this analysis it will not be presented. 7) Self- similarity:

X2 and Y2 are the same secondary contour for both edge rays, therefore points PI and P2, the intersection of the edge rays with the secondary are related with a shift

(24)

This set of equations is reduced to the same set of equations for the RR Aplanat device Eq. 14- 16, in the limit of θ _a →0.

In principle an exact solution can be obtained for the non-imaging problem, however since this set of equations is extremely challenging to solve, a different solution algorithm which is based on a seed of an aplanatic solution is presented here.

The procedure goes as follows, demonstrated here for an RR optic, but can be equally applied to the case of RX, XR and XX optics. In a similar manner this procedure can be followed mutatis mutandis for illumination and concentration modes as well as for near-field, far-field, complementary and Fresnel aplanats.

1. Generate a standard RR aplanatic design using Eq. 14-16.

2. Solution setup :

A) Use a polynomial approximation (e.g. fourth order) of the aplanatic secondary of step 1 as a first guess for the secondary of the RR Non-imaging design, (xs,ys).

B) For the next steps, use the same primary parameters ^: H _p , R _p as for the aplanatic design of step 1.

3. Calculate the primary contour:

A) Calculate the primary contour (X ,y ) for the case of edge rays θ _α using Equations 20, 22 using the known secondary of step 2. In this case the equations reduce to a simple set of 2 non-linear equations.

B) Calculate the primary contour (Xp,yp) for the case of edge rays -θ _α using Equations 21, 23 using the known secondary of step 2.

In this case the equations reduce to a simple set of 2 non-linear equations.

4. Optimization:

The goal here is to optimize the parameters of the problem until an excellent match is obtained between the primary contours that are calculated independently for each set of edge rays. The outcome, a single contour that performs well for both sets of edge rays is a valid non-imaging design.

A) Change the primary parameters (Hp,Rp) for one of the edge rays set of equations: θ _α or -θ _α , and repeat step (3), to obtain a good match between the primary contours which are calculated for both sets of edge rays.

B) Tune the polynomial coefficients of step (2) to obtain a good match between the primary contours which are calculated for both sets of edge rays.

C) Repeat steps A,B until the design is optimized and a good match is obtained between the primary contours that are calculated for both edge rays sets. This is preferably accompanied by a ray tracing simulation that allows evaluating the performance of the device for both sets of edge rays.

By using the equations for the Snell's law of reflection instead of refraction, as was described herein using Eq. 20-23, the procedure can be performed in an opposite manner by replacing the primary by a polynomial approximation and calculating the secondary. There are several benefits for this method over other existing methods :

a) It allows obtaining continuous contours to any desired resolution, unlike the SMS method for example.

b) It allows obtaining a complete solution which includes also the edges (inner and outer) of the optic, without the necessity for additional construction as with the SMS method.

c) For cases for which ideal non-imaging solutions cannot be obtained, e.g. where the SMS method fails, here a non-ideal, but optimized, i.e. close to ideal, non-imaging solution can still be obtained and serve as a valid device.

Fig. 34 schematically shows an example of a contour of a close to ideal RR- 1A non-imaging device, designed for an acceptance angle of 5 degrees and compared with an aplanatic design. The design parameters of the RR-lA Aplanat are: The aplanat secondary is approximated by a 6 ^th order polynomial:

Ys=3.23Xs ⁶ +10.55Xs ⁵ +11.75Xs ⁴ +6.22Xs ³ +1.47Xs ² +0.03Xs ¹ +0.198.

The close to ideal non imaging design that is presented in Fig. 34 is simply obtained by changing the 1 ^st order coefficient of the aplanat polynomial from 0.03 to 0.05. A good match is obtained between the primary contour that was computed by both sets of edge rays: θ _α and -θ _α .

A 2D flux map of the same device is presented in Fig. 35 and compared to the aplanatic design. This non-imaging device demonstrated more power inside the core region and sharp slopes in the thermodynamic limit radius. An even better performance can be obtained with further optimization of the polynomial coefficients. Although embodiments of the invention have been described by way of illustration, it will be understood that the invention may be carried out with many variations, modifications, and adaptations, without exceeding the scope of the claims. It is to be understood that aplanatic designs labelled "prior art" are not to be considered as included within the scope of the claims.

Bibliography

US PATENT DOCUMENTS

US 6,639,733 B2 10/2003 Minano et al

US 8,063,300 B2 11/2011 Home et al

US 8,101,855 B2 1/2012 Benitez et al

US20120048359 Al 3/2012 Winston et al

OTHER PUBLICATIONS

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