Patent Application: US-86027310-A

Abstract:
one optical system comprises a first optical surface , a faceted second optical surface , and a faceted third optical surface . the optical system is operative to convert a first bundle of rays that is continuous in phase space outside the first optical surface into a second bundle of rays that is continuous in phase space outside the third optical surface . between the second and third optical surfaces the rays making up the first and second bundles form discrete sub - bundles each passing from a facet of the second optical surface to a facet of the third optical surface . the sub - bundles do not form a continuous bundle in a phase space that has dimensions representing the position and angle at which rays cross a surface transverse to the bundle of rays .

Description:
a better understanding of various features and advantages of the present invention will be obtained by reference to the following detailed description of the invention and accompanying drawings , which set forth illustrative embodiments in which certain principles of the invention are utilized . fig1 shows the geometrical definition of an upper optic of a first embodiment . the insert on the right shows a detail of the mid section of the optic and the paths of some light rays . cartesian oval 101 concentrates to point 102 the parallel rays 103 perpendicular to flat wavefront 104 . wall 105 , starting at one edge of cartesian oval 101 , concentrates to point 102 a first portion of light rays emitted from point 106 , at one edge of bundle of parallel rays 103 , and propagated through cartesian oval 101 , as shown by exemplary ray 107 . wall 108 , continuing on from wall 105 , reflects a second portion of light rays emitted from point 106 and propagated through 101 , so that those rays proceed in a direction perpendicular to flat wavefront 109 . this is the case , for example , of ray 110 . these rays then reflect on wall 111 towards the top surface 112 where ray 110 is refracted in a direction perpendicular to flat wavefront 113 . wall 114 , continuing from wall 111 , concentrates light rays perpendicular to flat wavefront 116 , after refraction at the top surface 112 , to point 115 ( propagating in the opposite direction from the rays previously discussed ). this is the case , for example , of ray 117 . wall 118 , continuing from point 115 , reflects to point 102 a further portion of the light rays perpendicular to wavefront 116 . this is the case of exemplary ray 119 . between point 120 , at the end of cartesian oval 101 further from wall 105 , and point 102 there is no optical wall , so that section of wall may be defined using some other criteria ( as long as this wall is above the straight line connecting points 120 and 102 ). fig2 shows a combination of optics like the one in fig1 into a stepped flow - line concentrator . the top portion of the side surfaces 114 and 118 , closest to top surface 112 , has little optical effect , so part of them was removed so that several of these optics can be combined into a single piece . this resulting single piece is upper optic 201 . it is combined with lower optic 202 , which is a parabolic mirror . the receiver is at flat surface 203 , extending from the pole to the focus of the parabolic mirror . surfaces 204 on the upper optic , corresponding to the section between points 102 and 120 in fig1 , are non - optical . parabolic mirror 202 has focus 205 and axis parallel to parallel rays 206 , corresponding to rays 103 in fig1 . the optics are aligned so that ray 103 or 206 from the upper end 120 of cartesian oval 101 of one optic just passes the lower end of cartesian oval 101 of the next optic . cartesian ovals 101 of fig1 are combined in fig2 to form a discontinuous faceted surface . top surfaces 112 of fig1 are combined in fig2 to form a faceted surface . a larger number of optics can be combined in the upper optic . in that case , the lower optic and receiver must be scaled accordingly ( their shape does not change , only their size changes ). fig3 shows an example of a mold 301 for extruding the upper optic 201 of fig2 . the upper optic 201 is then uniform and of indefinite length perpendicular to the plane of fig2 . the light rays shown in fig1 may then be projections onto the plane of fig1 of rays that are oblique to that plane . the number of linked cavities in the mold of fig3 may be varied in order to vary the number of linked optics in the upper optic 201 of fig2 . fig4 shows a collimator for a source 401 . the collimator is composed of two parts : a lower optic 402 and an upper optic 403 , separated by a layer of low refraction index material 404 ( which may be air ). the lower optic is a piece of solid , transparent material ( dielectric ) bounded by the low refractive index material 404 at the top and by a stepped flow - line at the bottom . this stepped flow - line is composed of lines 406 that follow the flow lines and ejectors 407 that cross the flow lines . light enters the lower optic confined to an angular aperture 405 and travels inside it confined by total internal reflection ( tir ) between the bottom surface lines 406 and the low refraction index layer 404 . as it travels , this light encounters mirrors 407 , which cross the flow lines , and reflect light upwards towards the upper optic . this reflected light can cross the low refraction index layer 404 because the angle of incidence it forms with the low refraction index layer 404 is not enough for tir . this reflected light is then collimated by lenses 408 , exiting the optic with collimation in the vertical direction . mirrors 407 and lenses 408 may also be designed simultaneously using , for example , the sms design method . in general the mirrors 407 will be curved . when designing with the sms method for 2 surfaces , two input and two output bundles of rays have to be prescribed . the sms method provides the profile of the two optical surfaces that couple the input bundles to the output bundles . in this case , the two surfaces to design are the lenses 408 and the mirrors 407 . the two input bundles can be selected as the two edge ray bundles coming from the source , i . e ., the two bundles travelling inside the lower optic 402 with the maximum angles with respect to the flow lines 404 , 406 . the two output bundles are the two edge ray bundles defining the collimation after refraction at the lenses 408 . in general , lenses 408 are different from each other , and mirrors 407 are different from each other . the sms is not the only possible design method . another possibility is , for instance , to design lenses 408 to form a good image of the edges of mirrors 407 , and to design the mirrors 407 to cast the light inside their corresponding lenses . this design is of interest for those applications needing a sharp cut - off of the illumination pattern , such as automotive applications . as in all other cases , fig4 can also be used as a light concentrator , in particular for photovoltaic applications , replacing the source 401 by a solar cell and facing the vertical direction towards the sun . fig5 shows a similar optic to the one in fig4 , but in which all mirrors 506 of the lower optic are now at the same level , with the flow line surfaces sloping down from the top edge of each mirror 506 to the bottom of the next mirror . lenses 505 are all also at the same level , and therefore at the same distance from their respective mirrors 506 . the lenses 505 all have the same focal distance . this allows the use of the same lens and the same mirror design for the whole array . the upper and lower optics are separated by low refraction index layer 504 , which is parallel to the flow lines of collimated light and sloping relative to the levels of lenses 505 and mirrors 506 . light comes from a source 502 , enters the optic confined to an angular aperture 503 and leaves the optic collimated around the vertical direction . in this and similar embodiments , the reflective surface formed by low refraction index layer 504 and the discontinuous reflective surface 507 together form a first optical surface ( distributor surface if 502 is a source , collector surface if 502 is a receiver ). facets 506 form a discontinuous , faceted second optical surface , and facets 505 together form a faceted third optical surface with a discontinuous first derivative ( cusped or kinked ). fig5 a shows the same optic as fig5 , but now also shown is a revolution axis 5 a 01 . revolving the optic around this axis results in a device with circular symmetry . “ black hole ” optic 5 a 03 collects the light coming in radially from all sides and concentrates it onto receiver 5 a 02 . fig5 b ( not to scale ) shows an optic similar to the one in fig5 , but with curved elements in the lower optic 5 b 01 . now there is no air gap between source 5 b 06 and the optic . upper optic 5 b 02 is covered by an array of lenses 5 b 03 . these two optics are separated by a layer of low refractive index material 5 b 04 shaped as a parabola with focus 5 b 05 at the edge of the source 5 b 06 and axis parallel to the flat flow - lines 5 b 07 . as it travels inside the lower optic , light is confined ( by tir ) between layer 5 b 04 and flow lines 5 b 07 and extracted by steps 5 b 08 ( crossing the flow lines ) towards the lenses 5 b 03 on the upper optic , which lenses collimate this light as it exits the device . portion 5 b 09 of the top surface of the lower optic is part of the same parabola as 5 b 04 and needs to be mirrored since tir will not occur at this surface close to the source 5 b 06 . the lower optic is completed with circular arc 5 b 10 centered at edge 5 b 05 of the source 5 b 06 . this geometry with a parabolic separation between upper and lower optics minimizes the number of reflections inside the lower optic ( and has flat flow lines 5 b 07 ). this has practical implications , since reflections always produce some scattering of the light . minimizing the number of reflections therefore increases the efficiency of the system . each one of the steps 5 b 08 and corresponding lens 5 b 03 can be designed using the sms method . typical concentrators are designed by imposing constant optical path length between the input wavefronts of the edge rays and the edges of the receiver . that is the case , for example , of the ( unstepped ) rxi concentrator . stepped flow - line optics ( sfl ), however , do not fulfill this condition . the result is that light entering at points further away from the receiver will travel a longer optical path length ( and distance ) than the corresponding light inside an rxi . also , light entering at points closer to the receiver will travel a shorter distance inside the sfl concentrator than the corresponding distance inside an rxi . in two - dimensional geometry this is not an issue and both the rxi and the sfl are ideal concentrators . let us now consider the case in which these optics are given circular symmetry . consider also a pinhole on the entrance aperture of each one of these concentrators . in the case of the rxi , two rays contained on the sagittal plane through the pinhole will travel inside the optic and end up ( approximately ) at the edges of the receiver . that is true , independent of the radial distance of the pinhole . in the case of the sfl optic , however , light entering a pinhole further away from the center will travel a longer distance than it would in the comparator unstepped rxi and , therefore , illuminate a spot with a larger radius , increasing the size of the receiver and reducing concentration . on the other hand , light entering a pinhole closer to the center will travel a shorter distance than it would in the rxi and , therefore , illuminate a spot with a smaller radius , generating a hotspot in the center . the result is that the sfl optic with circular symmetry needs a larger receiver and will illuminate it non - uniformly , creating a hotspot in the center . note that the concentration at the center of the sfl receiver cannot be higher than the comparator rxi generates , since the rxi is assumed to be fully optimized and ( almost ) reaches the maximum limit of concentration . an sfl concentrator with circular symmetry can be obtained , for example , by giving the optic in fig5 b circular symmetry around axis 5 b 11 . choosing a revolution axis further to the left ( away from the optic ) will result in a concentrator with a receiver shaped as a hollow ( annular ) disk , or a collimator with a source shaped as a hollow disk . fig6 shows a collimator that accepts light confined to cone 601 and emits collimated light 602 . the collimator is composed of two dielectric parts , the lower optic 603 and the upper optic 604 , separated by a low refraction index material 605 ( which may be air ). light inside part 603 is confined by stepped flow - surface 606 at the bottom and the low refraction index layer at the top , which together form a first or distributor surface . as light travels inside lower optic 603 , it encounters tilted mirrors 607 ( which cross the flow lines ) and is reflected upwards . mirrors 607 together form a discontinuous , faceted second optical surface . the flow - surfaces that arrive at the bottom edges of mirrors 607 , continue backwards from the top edges of mirrors 607 . light reflected by these mirrors in the lower optic is collected and collimated by lenses 608 on the upper optic . in fig6 , only one of these lenses is shown so that the interior of the collimator can also be seen . in a real optic , however , there is one of these lenses 608 for each mirror 607 . an array of lenses 608 completely covers the top surface 609 of the upper optic and forms a faceted third optical surface . lenses 608 and mirrors 607 may be free - form , designed using , for example , the sms - 3d design method . fig7 shows a lower optic 701 and an upper optic 702 separated by a low refraction index layer 703 . the upper optic is covered with lenses 704 , one for each mirror 705 in the lower optic . fig8 shows a detail of a lower optic light guide similar to the lower optics of fig6 and 7 . the lower optic of fig8 results from tiling several parts , such as 801 side by side . of course , a commercial embodiment of the lower optic may be made in a single piece or in larger tiles , depending on its size . however , recognizing that the upper and lower optics are each formed from a repeating pattern of smaller elements is still useful . the result is a stepped flow - surface in which each step results from introducing mirrors 802 that cross the flow lines of the radiation traveling inside the guide . fig9 shows an optic similar to that in fig6 , but now with the tilted mirrors 901 much smaller relative to their spacing on the bottom surface of the lower optic . this results in lenses 902 that are much larger than the tilted mirrors and , therefore , in an optic that emits light 904 much more collimated than the incoming light 903 , or a concentrator with a high concentration factor . the mirrors 901 collectively still form a discontinuous faceted surface , even though the discontinuities are now large compared with the facets . fig1 shows another possible geometry for the stepped flow - surface forming the bottom of the lower optic . now light is confined by horizontal walls 1001 and vertical walls 1002 and extracted by mirrors 1003 . the bottom surface of the lower optic is in this case obtained by a rectangular tiling of several pieces 1004 . fig1 shows a tiling similar to that in fig1 , but with the corresponding lenses 1101 on top of the extraction mirrors 1102 . pieces 1103 with extraction mirrors 1102 and corresponding lenses 1101 are tiled side by side . fig1 shows an embodiment for a compact concentrator . it is composed of an upper optic 1201 and a two surface lower optic . in this example the lower optic is composed of two mirrors 1202 and 1203 . we denote each reflection by an x and call this lower optic an xx . the optic has a receiver 1204 . a vertical ray 1205 is deflected by the upper optic 1201 towards the first mirror 1202 of the lower optic and from there towards the second mirror 1203 of the lower optic and finally towards the receiver 1204 . although in this example the receiver 1204 is shown well above the lower tip 1207 of mirror 1202 , they can be much closer together and receiver 1204 may even be below tip 1207 of mirror 1202 . also , mirror 1202 may be truncated close to the optical axis 1206 ( since it is shaded by mirror 1203 ), exposing receiver 1204 to the outside environment ( for electrical connection , cooling , and mechanical support ) even if receiver 1204 is above mirror 1202 . in the limiting case in which the acceptance angle of the optic goes to zero ( aplanatic limit ), the path of the rays fulfills x = m sin ( α ) where m is a constant , x is the horizontal coordinate at which the ray enters the optic and α is the angle with which the ray hits the receiver 1204 . this condition guarantees that , in this limit case , the meridional acceptance of the concentrator equals its sagittal acceptance when the optic has circular symmetry about vertical axis 1206 through receiver 1204 and tip 1207 , which is then the pole of the circular mirror 1202 ( although the optic may also have linear symmetry ). in that case , the mirrors 1203 , 1202 in the lower optic are designed so that , if traced backwards ( as if light were being emitted from the receiver 1204 ), the light rays would hit the upper optic 1201 at an angle given by a function ψ ( x ). this function is a parameter of the design . for different functions ψ ( x ), different upper and lower optics result . the upper optic may in this case be designed as a fresnel lens closer to the optical axis 1206 and as a tir lens further away , just like in the case of a regular tir lens . in the case of a finite acceptance angle the incoming light has an angular aperture 20 and it exits the upper optic with an angular aperture β ( x ) that fulfills θ = arcsin ( sin ψ ( x ) sin β ( x )) [ see ref . 3 ]. in that case , the optical surfaces in the upper optic are designed with the sms design method [ see ref 3 ]. the two optical surfaces ( two mirrors in this example ) of the lower optic are also designed with the sms design method . this configuration thus makes it possible to shape the lower optic mirrors 1202 , 1203 so that each point of the faceted lens 1201 has the same acceptance angle 2θ ( for a concentrator ) or emission beam angle ( for a collimator ) for rays to and from the receiver or source 1204 without needing an explicit second faceted surface . alternatively , as explained below with reference to fig1 a to 13c , two distinct faceted surfaces can be integrated into a single faceted optical element . the edge rays of the acceptance cone of angle 2θ in fig1 correspond to the rays of two extreme wavefronts , as shown at 113 and 116 in fig1 . fig1 a shows two elements of an upper optic , each one composed of a top refractive surface 13 a 01 , a reflective surface 13 a 02 and another refractive surface 13 a 03 . it is , therefore an rxr optic ( where r stands for refraction and x for reflection ). this example shows the particular case of the upper optic in fig1 in which β = ψ , although the sms design method can be used the same way in designs for other parameter values of these angles . as may be seen from the rays shown in fig1 a , the refractive surfaces 13 a 01 of all the elements together form a faceted optical surface with a discontinuous first derivative ( cusped or kinked ) and the reflective surfaces 13 a 02 of all the elements together form a faceted optical surface with a discontinuous surface . in this particular example , the edge rays perpendicular to wavefront 13 a 04 are concentrated onto point 13 a 06 at the lower tip of the next optic to the left of the one under consideration , while the edge rays perpendicular to wavefront 13 a 05 exit the optic in a direction perpendicular to wavefront 13 a 07 . also in this example , second refractive surface 13 a 03 was prescribed and surfaces 13 a 02 and 13 a 01 calculated using the sms design method . other options include prescribing the shape of 13 a 01 and calculating 13 a 02 and 13 a 03 or prescribing surface 13 a 02 and calculating surfaces 13 a 01 and 13 a 03 . an option with special practical interest is when top surface 13 a 01 is chosen as flat and horizontal since this results in an upper optic with a flat top surface . fig1 b shows a similar optic to the one in fig1 a , but now in the more general case in which angle β is different from angle ψ . this optic is bound by optical surfaces 13 b 01 , 13 b 02 and 13 b 03 . edge rays perpendicular to input wavefront 13 b 04 are either concentrated to point 13 b 07 ( at the lower tip of the optic to the left — not shown ) or exit the optic in a direction perpendicular to wavefront 13 b 06 . edge rays perpendicular to wavefront 13 b 05 exit the optic in a direction perpendicular to wavefront 13 b 08 . fig1 c shows an optic similar to the one in fig1 in which the upper optic 1201 is now made of optical elements similar to the ones in fig1 a or fig1 b , resulting in upper optic 13 c 01 . in general , the shape and use of the optical surfaces of these optical elements will vary along the upper optic 13 c 01 . similar optical elements may be used in the devices of fig1 to 21 . fig1 shows a special case of an embodiment in the general shape of fig1 . its upper optic 1401 is designed as a fresnel lens while the lower optic is composed of two mirrors , 1402 and 1403 . the optic has a receiver 1404 . exemplary vertical ray 1405 at radius x is deflected towards the first mirror 1402 where it is reflected towards the second mirror 1403 and then again reflected toward the receiver 1404 . the upper optic may also be designed as a fresnel lens closer to the optical axis 1406 and as a tir lens further away , just like in the case of a regular tir lens . the conditions of design are the same as in fig1 . fig1 shows another case of an embodiment similar to that in fig1 . in this example the upper optics 1501 is designed as a fresnel lens , while the lower optics is a dielectric solid piece with refractive index n & gt ; 1 , with three optically active surfaces , 1502 , 1503 and 1504 . the embodiment has a receiver 1505 . the incoming vertical ray 1506 is deflected by the fresnel lens 1501 towards the solid entry aperture 1502 , where it is refracted towards the surface 1503 where is reflected towards surface 1504 . the surface 1504 reflects the ray towards the receiver 1505 . the surfaces 1503 and 1504 can work by total internal reflection , or can be metalized in areas where the condition of tir is not accomplished . as in the case of fig1 the upper optic can be designed also as a fresnel lens closer to the optical axis and as a tir lens further away . fig1 shows a similar concept to that in fig1 . this example is composed of a single dielectric piece that has three optically active surfaces 1601 , 1602 and 1603 , and a receiver 1604 . the first optical surface , 1601 , has integrated teeth ( that can be either fresnel or tir ) and it deflects the incoming vertical ray to the first reflective surface 1602 that reflects the ray towards the second reflective surface 1603 , which reflects the ray to the receiver 1604 . the reflective surfaces can work by total internal reflection , or be metalized in areas where the condition of tir is not accomplished . fig1 shows another special case of an embodiment similar to fig1 . the first optic of this embodiment consists of a curved tir lens 1701 , while the lower optics is composed of two mirrors 1702 and 1703 . in this example the condition of flatness of the upper optic is removed , which gives another degree of freedom in the design and allows a better control of the teeth size . the top surface of 1701 is shown as curved ( to minimize the thickness of this optical component ), but it may also be flat . the teeth are on the underside of the lens 1701 , so that the upper surface is smooth , even if not flat , and is easier to keep clean . the teeth are protected from damage because they are inside the device . fig1 shows a particular case of the embodiment shown in fig1 . first mirror 1202 of the lower optic is now chosen to be flat , resulting in flat mirror 1801 . for a given acceptance angle and concentration , this condition defines function ψ ( x ). upper optic 1802 is either a fresnel lens or a combination of fresnel ( closer to the receiver 1803 ) and a tir lens ( further away from the receiver ). light is deflected at upper optic 1802 , bounces off mirror 1801 and then off mirror 1804 on its way towards receiver 1803 . fig1 shows a variation on the embodiment in fig1 . the device is made of two parts : upper optic 1901 and dielectric lower optic 1902 , bounded by flat surfaces 1903 and 1904 ( which may be parallel ) and mirror 1905 . mirror 1905 may have to be metalized in the area closer to the receiver 1906 . fig2 shows a particular case of the embodiment in fig1 . this device is composed of upper optic 2001 ( shown diagrammatically ) and dielectric lower optic 2002 . second mirror 1203 of the lower optic in fig1 is now chosen as flat , resulting in flat surface 2003 . for a given acceptance angle and concentration , this condition defines function ψ ( x ). different areas of optic 2001 may be designed either a fresnel lens or a combination of fresnel and a tir lens . incoming light is first deflected by upper optic . the light then refracts at flat surface 2003 into the lower optic 2002 . the light then bounces off bottom surface 2004 ( by tir ), then again off flat surface 2003 ( again by tir ) to the receiver 2005 . surfaces 2003 and / or 2004 may have to be mirrored in the area closer to the receiver 2005 . fig2 shows an optic similar to the one in fig1 , but in which the second mirror of the lower optic 1203 is replaced by a refractive surface 2103 . the resulting optic is now composed of an upper optic 2101 and a lower optic composed of a mirror 2102 and a refractive surface 2103 . in fig2 , the space between upper optic 2101 , mirror 2102 , and refractive surface 2103 is air , and the receiver 2104 is in optical contact with a dielectric material bounded by surface 2103 . fig2 shows a mirror 2201 that collects the light from a point source 2202 and distributes it on a line 2203 . its shape is such that each ray fulfills x ( α )= m sin ( α ) where m is a constant , x is the horizontal coordinate at which the ray hits line 2203 and α is the angle with which the ray leaves the receiver . in general , this mirror can be calculated to obey a different law x ( α ). fig2 shows a similar situation to that in fig2 , but now for an extended light source 2302 . mirror 2301 collects light from extended source 2302 and distributes it on a line 2303 . the shape of mirror 2301 is such that it generates on 2303 a prescribed etendue distribution u ( x ) and the shape may be calculated by the same method used to calculate luminaires for extended sources . the description of that method in ref . [ 3 ] is incorporated herein by reference . if the path of the trailing edge ray 2307 , reflected at known point 2305 , is known , function u ( x ) determines the leading edge ray 2306 and a new point 2304 at which ray 2306 is reflected on mirror 2301 . particularly interesting is a uniform etendue distribution u ( x )= constant . line 2303 is shown in fig2 as a straight line , but in the more general case , line 2303 may be curved . fig2 shows an optic composed of an upper optic 2401 and a lower optic 2402 , separated by a low refractive index layer 2403 . the low refractive index layer is calculated according to the method described in fig2 and fig2 . the upper optic 2401 has a microstructure on top , composed of many convex surfaces 2404 . the lower optic has another microstructure at its bottom composed of surfaces 2405 and 2406 . this last microstructure follows line 2203 of fig2 or 2303 of fig2 . incoming rays 2407 are deflected at one of the top surfaces 2404 towards one of the bottom surfaces 2405 . from there these rays are deflected towards the low refractive index layer , which reflects them ( by tir ) towards the receiver 2408 . the bottom surface of the low refractive index layer 2403 may have to be mirrored on the area closer to the receiver if tir fails . vertical light 2409 that hits the intersection between two surfaces 2410 and 2411 may either be refracted by 2410 towards 2412 or by 2411 towards 2413 . however , after reflection of 2412 or 2413 , this light is again reassembled as 2414 in its way towards the receiver . each pair of surfaces 2405 and corresponding surface 2405 may be designed as aplanats ( in the case of an infinitesimal receiver size ) and a vertical ray entering the optic at a distance x from the optical axis arrives at the receiver making an angle α , also to the optical axis . these quantities are related by x = m sin ( α ) where m is a constant . when the receiver is of a finite size , the sms design method may be used to simultaneously design a surface 2404 and its corresponding 2405 . lines 2406 are flow - lines of the source or receiver 2408 when reflected off the low refractive index layer 2403 . these guide the light after reflection off surfaces 2405 on its way towards the receiver if the device is used as a concentrator , or away from the source 2408 towards the surfaces 2405 if the device is used as a collimator . macroscopically ( including many surfaces 2404 on top and the corresponding 2405 at the bottom ), the etendue distribution across the top surface of the upper optic 2401 is the same as the etendue distribution across the bottom surface of the bottom optic 2402 . fig2 a shows a vertical section through a concentrator similar to the one in fig2 when given circular symmetry . the axis 24 a 01 in fig2 a corresponds to the vertical axis through source or receiver 2408 at the left edge of fig2 . fig2 shows an embodiment similar to that in fig2 in which surfaces 2406 along the flow lines are replaced by arbitrary shaped surfaces 2501 that do not intersect the light as it travels inside the device . this is usually a better arrangement if these optics are used for imaging applications , because reflections off the flow - lines would redirect light rays from one edge of the image to the other , destroying image formation for the rays reflected off the flow lines . fig2 shows a device similar to the one in fig2 , but now designed as an integrator . each one of the optical surfaces 2601 on the upper optic images the light source onto the corresponding surface 2602 on the lower optic . surface 2602 , in its turn , images surface 2601 onto the receiver 2603 ( after reflection in the low index layer corresponding to layer 2403 ). fig2 shows an optical device composed of upper optic 2701 and lower optic 2702 . surface 2703 on the lower optic is similar to the one in fig2 , but designed for a given function x ( α ) in which x ( 0 )= x 0 with x 0 & gt ; 0 , that is , a ray 2704 emitted vertically ( α = 0 ) from the receiver 2705 and reflected off surface 2703 hits horizontal line 2706 at a coordinate x 0 . any given ray 2707 , however , satisfies the condition of aplanatism , that is , it complies with r = m sin ( α ) where m is a constant and r is the distance from the optical axis to the point the light ray enters the optic . the advantage of this configuration is that light rays hitting surface 2703 at points closer to the optical axis ( such as point 2708 ) do so at wider angles , opening the possibility of the whole device working by tir . however , if necessary , the region from point 2709 to 2710 can be mirrored since the incoming light does not cross it . this design method can also be used in the geometries presented from fig1 through fig2 . fig2 a shows an optic with receiver 2801 . the optic is composed of a single piece . there may ( or may not ) be an air gap between the receiver and the optic . top surface 2802 may have to partially mirrored if there is no tir at the central area . to the extent that top surface 2802 works by tir , the inner part of the bottom face of the optic ( shown as flat in fig2 a ) may be made into a concave mirror to collect light entering through the tir surface 2802 . in general , this configuration can be used as a collimator , a concentrator or an imaging device . if used as a collimator , 2801 would be a light source ( such as an led ). fig2 b shows one side of an optic similar to that in fig2 a , but in greater detail . if used as a collimator , it has a source 28 b 02 separated from the optic 28 b 01 by an air gap 28 b 03 . therefore , as the light from this source enters the optic , it will be confined to the critical angle . this light is reflected at top surface 28 b 04 . the central part of surface 28 b 04 may have to be mirrored , but the outer region will work by tir . light then proceeds towards the bottom structure of optic 28 b 01 where it encounters walls 28 b 05 that guide it along the flow lines . eventually light reaches steps 28 b 06 that reflect it towards the top lenses 28 b 07 . the light finally exits from lenses 28 b 07 as a collimated beam 28 b 08 . the whole optic has circular symmetry around axis 28 b 09 . depending on the geometry , steps 28 b 06 may or may not have to be mirrored . the optic is made of a single dielectric part and it may be produced by the methods used to produce compact disks ( cds ) or digital video disks ( dvds ). fig2 shows a similar device to that in fig2 . also in this case the optic is a single piece , with receiver 2901 separated from the optic by an air gap . additional central lens 2902 concentrates some light onto the receiver . lens 2902 may also be used in some other embodiments . fig3 shows a construction method similar to that in fig2 , but now for the case in which the emitted light appears to come from a virtual point source . a light ray 3001 emitted from a point source 3002 at an angle α to the vertical ( optical axis ) is reflected by tir at a low - index surface 3003 towards microstructured bottom surface 3004 , which the ray meets at point 3008 . from here this ray is reflected upwards , passing through low - index layer 3003 towards top surface 3005 , where the ray is refracted , exiting in a direction 3006 making an angle β to the vertical , as if coming from a virtual source 3007 . the shape of low - index reflective surface 3003 can be calculated if , for example , we assume surface 3005 to be flat and that angles α and β are related , for example , by sin β = m sin α where m is a constant . for a given ray emitted from 3002 at an angle α to the vertical , we can calculate angle β and the path of ray 3006 since its extension must intersect virtual point source 3007 . ray 3006 may then be refracted at surface 3005 and continued to intersect with surface 3004 , giving us point 3008 . using this method , for each ray emitted from 3002 we can determine to what point 3008 on 3004 it must be reflected and therefore the shape of mirror 3003 can be determined . this is similar to what happens in fig2 . fig3 a shows an example of a design based on the overall geometry in fig3 . optic 3101 creates a virtual image 3102 of the source 3103 . the optic is composed of two parts 3104 and 3105 separated by a low refractive index layer 3106 . in this figure , insert 3107 shows a detail of the optic 3101 . a light ray 3108 emitted from the source 3103 is reflected by tir at surface 3106 . from there it is redirected towards bottom microstructure . reflective surface 3109 of the bottom microstructure and corresponding refractive surface 3110 of the top surface are calculated simultaneously so that incoming ray 3108 exits the optic as if coming from virtual source 3102 . the relationship between emission angle α at the actual source and exit angle β ( see fig3 ) is given by sin β = m sin α as stated above . surfaces 3111 follow the flow lines of the light emitted by the source and reflected at surface 3106 . fig3 b shows another detail of the same optic 3101 shown in fig3 a . again , the light emitted from source 3103 exits the optic as if coming from virtual source 3102 . the optical surfaces of the top microstructure may form a continuous surface , as is the case at point 3112 , or there may be discontinuities , as is the case at point 3113 . the central portion of surface 3106 ( directly above source 3103 ) that cannot achieve tir , and the associated portion 3114 of the undersurface of the top part of the optic may be calculated simultaneously so that a ray emitted from source 3103 is refracted at surface 3106 , then at surface 3114 , then at ( flat ) top surface 3116 , exiting the device as if coming from virtual source 3102 . various changes are possible without departing from the scope of the invention as defined in the claims . although specific embodiments have been described , the skilled reader will understand how features of different embodiments may be combined . even where not explicitly stated , the skilled reader will understand how the two - dimensional sections shown in the drawings may be translated perpendicular to the plane of the paper to form an elongated “ trough ” configuration , rotated to form a circularly symmetric configuration , or otherwise expanded into a three - dimensional device . various terms of orientation have been used , for ease of reference to the drawings , which are mostly oriented with the collimated beam aimed directly upwards away from the collimator or downwards towards the concentrator . however , those orientations are not limiting , and the various optical devices disclosed may be used in any expedient orientation . for example , a concentrator used in a solar photovoltaic collector will usually be used with the collimated beam aligned on the sun . a collimator used in an automobile headlight will usually be used with the collimated beam aligned approximately horizontally , and the exact alignment chosen to comply with relevant laws and regulations . when analyzing a constructed optical device , the wavefronts used to construct the device can be determined , either notionally or physically , by placing a light source at the source ( or receiver ) position , placing a pinhole in the exit ( or entrance ) aperture , and determining the edge rays of the cone of light that emerges through the pinhole . by repeating this process for different pinhole positions , the phase space representation of the wavefronts outside the exit aperture can be reconstructed . the preceding description of the presently contemplated best mode of practicing the invention is not to be taken in a limiting sense , but is made merely for the purpose of describing the general principles of the invention . the full scope of the invention should be determined with reference to the claims . 1 . julio chaves , manuel collares - 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