Abstract:
A cube corner reflector is oriented so that incident and reflected beams either entirely miss the edges at the intersections of reflective surfaces or so that the beams have only peripheral portions incident on the edges. A symmetry plane of the cube corner reflector is midway between the incident and reflected beams of the cube corner reflector and contains the central axis of the cube corner reflector and one of the edges between the reflective surfaces. For a minimum size reflector that permits the tight beam spacing, trimmed surfaces perpendicular to the symmetry plane are at different distances from the central axis. The edges, variations in the orthogonality of the reflective surfaces, and beam walk off cause less wavefront distortion that could affect measurements in systems such as interferometers.

Description:
BACKGROUND 
     Cube corner reflectors are well-known optical elements that are used in a variety of optical systems. A cube corner reflector  100  as illustrated in FIG. 1 has three planar reflective surfaces  110 ,  120 , and  130  that intersect at right angles in the same manner as the intersection of faces at the corner of a cube. Reflective surfaces  110 ,  120 , and  130  can be formed on three sides of a tetrahedral glass block that also has a transparent face  140  for input of an incident beam and output of a reflected beam. The tetrahedral glass block in cube corner reflector  100  is symmetric so that the perimeter of transparent face  140  forms an equilateral triangle and the perimeters of reflective surfaces  110 ,  120 , and  130  are congruent isosceles right triangles. 
     Cube-corner reflector  100  is a retroreflector, and therefore a reflected beam from cube-corner reflector  100  is parallel to but offset from an incident beam regardless of the direction of the incident beam. FIG. 1 illustrates an example of an incident beam  180  that enters cube corner reflector  100  through transparent face  140  and reflects from one or more of reflective faces  110 ,  120 , and  130  before exiting as a reflected beam  190 . Reflected beam  190  is parallel to incident beam  180  and offset from incident beam  180  by twice the perpendicular separation between incident beam  180  and a vertex  150  of cube corner reflector  100 . 
     The tetrahedral shape of cube corner reflector  100  includes more glass than is generally required for the optical function of cube corner reflector  100 , particularly in optical systems where the location and direction of the incident beam is well controlled. Cube corner reflector  100  can thus be trimmed to remove glass that is not required for the optical function of cube corner reflector  100 . One conventional way to trim cube corner reflector  100  is to take a cylindrical core of cube corner reflector  100 , which results in transparent face  140  having a circular perimeter. Another known trimming scheme gives transparent face  140  a rectangular boundary  145 . 
     FIG. 2 shows a cube corner reflector  200  resulting from trimming cube corner  100  at boundary  145 . Cube corner reflector  200  is small for a retroreflector capable of reflecting an incident beam  280  to provide an offset reflected beam  290 . The minimum required size of cube corner reflector  200  to perform this optical function depends on the desired offset between incident and reflected beams  280  and  290 , the diameters or areas of beams  180  and  290 , and the path of the beams inside cube corner reflector  200 . To minimize the area of the face of cube corner reflector  200 , incident beam  280  (or alternatively reflected beam  290 ) is centered at a point on an edge  235  of cube corner reflector  200 . 
     Analysis of the beam paths in cube corner reflector  200  shows the if incident beam  280  is parallel to a central axis of cube corner reflector  200  then the beam paths will remain within a band having boundaries at the upper and lower edges of beams  280  and  290  in FIG.  2 . For example, a ray  282  at a top edge of incident beam  280  reflects from a reflective face  210  toward a reflective face  230  and then reflects from a point on reflective face  230  that is at the same height as the bottom edge of incident beam  280 . From there, the ray travels horizontally to reflective surface  220  and exits as a reflected ray  292  at the bottom of reflected beam  290 . Similarly, a ray  284  at the bottom of incident beam  280  reflects from reflective surface  230  to a point on reflective surface  210  at the same height as the top of incident beam  280 , travels horizontally to the top of reflected beam  290 , and exits as reflected ray  294 . The height of cube corner reflector  200  can thus be as small as the diameter of beams  280  and  290  plus an added margin for beam variations or misalignments. 
     FIG. 3 illustrates a known multi-axis plane mirror interferometer  300  employing four cube corner reflectors  200 . U.S. Pat. No. 09/876,531, entitled “Multi-Axis Interferometer With Integrated Optical Structure And Method For Manufacturing Rhomboid Assemblies” further describes some examples of multi-axis interferometers containing retroreflectors that can be implemented using cube corner reflectors. 
     Interferometer  300  has four input beams IN 1  to IN 4  that are direction into a polarizing beam splitter  310 . Polarizing beam splitter  310  splits input beams IN 1  to IN 4  into components according to polarization. Components of one polarization from input beams IN 1  to IN 4  become respective measurement beams M 1  to M 4 , and components of an orthogonal polarization in input beams IN 1  to IN 4  become reference beams (not shown). Measurement beams M 1  to M 4  travel from polarizing beam splitter  310  to a planar measurement reflector (not shown) that is mounted on an object being measured. The measurement reflector returns measurement beams M 1  to M 4  along the same paths. 
     Polarization changing elements (e.g., quarter-wave plates)  320  are in the paths of outgoing and returning measurement beams M 1  to M 4  and change the polarization of measurement beams M 1  to M 4  so that polarization beam splitter  310  directs the returning measurement beams M 1  to M 4  to respective cube corner reflectors  200 . 
     Cube corner reflectors  200  reflect returning measurement beams M 1  to M 4  so that offset measurement beam M 1 ′ to M 4 ′ can traverse polarizing beam splitter  310  and elements  320 , reflect from the measurement reflector, and return through elements  320  and polarizing beam splitter  310  to form parts of respective output beams OUT 1  to OUT 4 . Each measurement axis of interferometer  300  corresponds to a pair of beams M 1  to M 1 ′, M 2  and M 2 ′, M 3  and M 3 ′, or M 4  and M 4 ′ and to a measured point that is halfway between the centers of the incident areas of the corresponding pair on the measurement mirror. Accordingly, cube corner reflectors  200  must be small enough to fit within the spacing of measurement beams M 1  to M 4  and M 1 ′ to M 4 ′ that is required for the desired measurement axes. 
     The reference beams have paths that include first reflections from a reference reflector (not shown), reflections from respective cube corner reflectors  200 , and second reflections from the reference reflector before the reference beams rejoin respective measurement beams M 1 ′ to M 4 ′ in output beams OUT 1  to OUT 4 . The two reflections of each measurement beam from the measurement reflector, the two reflections of each reference beam from the reference reflector, and the intervening reflections from the associated cube corner reflector  200  are well known to eliminate an angular separation that misalignment of the measurement or reference mirror might otherwise cause between the reference and measurement beams in the combined output beam. 
     A measurement along a measurement axis of interferometer  300  requires measuring and analyzing the phases of the measurement and reference beams that are within the output beam associated with the measurement axis. These measurements are most accurate if the wavefronts of measurement and reference beams are uniform because the measured phase information is generally an integral or average of the phase information over a cross-section of the output beam. Further, the integrated/analyzed portion of the measurement beam typically changes because of beam “walk-off”. Beam walk-off occurs when the object being measured changes angular orientation. The walk-off changes the matched portions of the measurement and reference beams, causing an erroneous phase shift when the beam wavefront is nonuniform. Wavefront distortion can thus cause errors and lower signal-to-noise ratios in phase information measurements and correspondingly in the measurements along the measurement axes of interferometer  300 . 
     Returning to FIG. 2, edge  235  of cube corner reflector  200  passes through the center of incident beam  280 . The reflection of a beam from edge  235  is generally nonuniform and distorts the wavefront of the reflected beam. Such non-uniformity may arise from a chamber formed to improve the safety or durability of an otherwise sharp edge and from roll off that commonly arises at the edges of polished optical surfaces. This wavefront distortion can be significant for an interferometer measurement particularly because wavefront distortion from the edge crosses through the center of the beam where light intensity is high. 
     Another source of wavefront distortion in cube corner reflector  200  arises from reflective surfaces  210 ,  220 , and  230  not being perfectly orthogonal. When incident beam  280  is incident on edge  235 , the angular errors in the orientations of reflective surfaces  210 ,  220 , and  230  cause the wavefront (i.e., the surface of uniform phase) of output beam  290  to be V-shaped. This V-shape produces measurement errors when measuring a phase for a planar cross-section of the beam. Correcting for this type of wavefront distortion is difficult because expected beam movement relative to edge  235  typically changes which side of the V-shaped wavefront corresponds to the larger portion of beam intensity. 
     In view of the limitations of current cube corner reflectors, methods and structures that reduce the wavefront distortion caused in reflections from cube corner reflectors could improve measurement signal strength and the accuracy of interferometer measurements. 
     SUMMARY 
     In accordance with an aspect of the invention, a cube corner reflector is oriented so that incident and reflected beams either entirely miss the edges at the intersections of reflective surfaces or so that the beams have only peripheral portions incident on the edges. The edges thus cause less wavefront distortion that could affect measurements in systems such as interferometers. With one such orientation, a symmetry plane that is midway between the incident and reflected beams of the cube corner reflector contains one of the edges of the reflective surfaces and a central axis that passes through the vertex of the cube corner reflector. A cube corner reflector having trimmed surfaces perpendicular to its symmetry plane can be closely spaced with other cube corner reflectors to provide a tight beam pattern in a multi-beam device. For minimum size, the trimmed surfaces that are perpendicular to the symmetry plane are at different distances from the central axis. 
     One specific embodiment of the invention is an optical element such as a cube corner reflector. The optical element has three orthogonal reflective surfaces with three edges at the intersections of the reflective surfaces. A first edge is at an intersection of the first reflective surface and the second reflective surface and is symmetrically located between an incident beam and a reflected beam of the optical element. A second edge is at an intersection of the second reflective surface and the third reflective surface, and a third edge is at an intersection of the third reflective surface and the first reflective surface. A first trimmed surface is parallel to a central plane that contains central rays of the incident and reflected beam. 
     The optical element may further have a second trimmed surface that is parallel to the first trimmed surface, but the parallel trimmed surfaces are asymmetrically located relative to the central axis through the vertex of the optical element. A perpendicular distance between the first trimmed surface and the central plane differs from a perpendicular distance between the second trimmed surface and the central plane. More specifically, a perpendicular distance between one trimmed surface and the central plane may be required to extend beyond a radius of the incident and reflected beam by at least a distance corresponding to a non-zero deflection of incident beam toward the trimmed surface in the optical element. The beam is deflected away from the other trimmed surface in the optical element so that the distance between that trimmed surface and the central plane can be about equal to the radius of the beams. 
     Another specific embodiment of the invention is a cube corner reflector. The cube corner reflector includes first, second, and third reflective surfaces, an input/output face, and at least one trimmed surface. The input/output face is perpendicular to a central axis through the vertex of the cube corner reflector and includes a first transparent aperture for an incident beam and a second transparent aperture for a reflected beam. One trimmed face intersects a first edge that is between the first and second reflective surfaces, with the first edge being in a plane that also includes the central axis of the cube corner reflector and passes midway between the first and second apertures. 
     A second trimmed surface is parallel to the first trimmed surface and is such that a second edge that is between the second and third reflective surfaces makes an angle with the second trimmed surface that is equal to the angle made with the second trimmed surface by a third edge that is between the third and first reflective surfaces. A perpendicular distance between the first trimmed surface and the central axis of the cube corner reflector can be less than a perpendicular distance between the second trimmed surface and the central axis of the cube corner reflector. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 shows a view through the face of a cube corner reflector having a tetrahedral glass body. 
     FIG. 2 shows a view through the face of a known cube corner reflector having a glass body that is trimmed to provide a rectangular face. 
     FIG. 3 is a perspective view of a known multi-axis interferometer having a tight beam spacing, which requires uses of trimmed cube corner reflectors. 
     FIGS. 4A,  4 B, and  4 C are respectively a face-on view, a perspective view, and a side view of a trimmed cube corner reflector in accordance with an embodiment of the invention. 
     FIG. 5 is a view through the face of a trimmed cube corner reflector in accordance with another embodiment of the invention. 
     FIG. 6 is a perspective view of a multi-axis interferometer employing cube corner reflectors that are trimmed in accordance with an embodiment of the invention. 
     FIG. 7 is a perspective view of a trimmed, hollow cube corner reflector in accordance with an embodiment of the invention. 
    
    
     Use of the same reference symbols in different figures indicates similar or identical items. 
     DETAILED DESCRIPTION 
     In accordance with an aspect of the invention, trimmed cube corner reflectors that permit tight beam spacing provide minimal distortion of the wavefronts of reflected beams. FIGS. 4A,  4 B, and  4 C respectively show a face-on view, a perspective view, and a side view of a cube corner reflector  400  in accordance with an embodiment of the invention. Cube corner reflector  400  includes a block of optical quality glass such as BK- 7  glass that has three orthogonal reflective surfaces  410 ,  420 , and  430  and an input/output face  440 . With the illustrated trimming, reflective surfaces  410  and  420  have the same shape and size, while the shape and size of reflective surface  430  differs from those of reflective surfaces  410  and  420 . Reflective surfaces  410 ,  420 , and  430  can be formed using conventional techniques for formation of reflective metal coatings or multi-layer highly reflective dielectric coatings. 
     Edges  415 ,  425 , and  435  between reflective surfaces  410 ,  420 , and  430  meet at a vertex  450  through which a central axis  445  of cube corner  400  passes at equal angles to edges  415 ,  425 , and  435 . As illustrated in FIGS. 4B and 4C, affordable manufacturing normally does not permit edges  415 ,  425 , and  435  to be perfectly sharp, and a sharp edge may be undesirable because of safety and durability concerns. The edges for a precision optical system such as an interferometer thus typically have a chamber about 0.2 mm or smaller when the edge may be in the beam path. A chamfer can be relatively large when the edge is away from the beam path. 
     Input/output face  440  receives an incident beam  480  and returns a reflected beam  490  that is offset from and parallel to incident beam  480 . (The roles of incident and reflected beams  480  and  490  are reversible, but beam  480  is presumed to be incident beam here for illustration.) Input/output face  440  has transparent apertures that correspond to incident beam  480  and reflected beam  490 , but these apertures may merely be undistinguished areas of input/output face  440  when input/output face  440  is transparent across its entire area. FIG. 1 shows the orientation of input/output face  440  relative to a tetrahedral cube corner  100 . 
     In addition to optical surfaces  410 ,  420 ,  430 , and  440 , cube corner  400  also has four trimmed surfaces  441 ,  442 ,  443 , and  444  that bound input/output face  440 . Trimmed surfaces  441  to  444  can be surfaces that remain after trimming processes cut an originally larger glass block. However, trimmed surfaces are more generally not functional optical surfaces and may be original surfaces that existed before cutting, grinding, and/or polishing processes formed the optical quality surfaces such as reflective surfaces  410 ,  420 , and  430  and/or input/output face  440  of cube corner reflector  400 . 
     Trimmed surfaces  441  to  444  generally can be planar or curved provided that trimmed surfaces  441  to  444  do not cut off any optically required portion of reflective surfaces  410 ,  420 , and  430  or of input/output face  440 . Trimmed surfaces  441  to  444 , in a preferred embodiment, are shown as a set of respectively orthogonal and parallel surfaces that are orthogonal to input/output face  440 . Trimmed surfaces  441  to  444  when planar act as convenient part datums for machining and/or other mechanical manufacturing processes. 
     Cube corner reflector  400  is specifically designed for incident beam  480  to be parallel to and centered a distance X from central axis  445  of cube corner reflector  400 . As a result, the beam path within cube corner  440  is set, and the geometry of cube corner reflector  400 , which controls the location of trimmed faces  441  to  444 , can minimize the size of cube corner  400  for a particular selection of beam size and desired offset. In FIG. 4A, beams  480  and  490  have a radius R and offset X from vertex  450  of cube corner reflector  400 . 
     Edges  415 ,  425 , and  435  are oriented so that a symmetry plane containing edge  415  and central axis  445  of cube corner reflector  400  lies midway between beams  480  and  490 . A perpendicular plane containing the centers of beams  480  and  490  and central axis  445  is above edges  435  and  425 , causing incident beam  480  have a larger portion that initially reflects from surface  410  and a smaller portion that initially reflects from surface  430 . The portion of beam  480  that is incident on edge  435  between reflective surfaces  430  and  410  is at an outer part of beam  480 . Edge  435  thus affects a portion of beam  480  that is shorter than the diameter of beam  280 . In comparison, edge  235  of conventional cube corner reflector  200  passes through a diameter of beam  280 . Edge  435  of cube corner reflector  400  thus affects a smaller portion of incident beam  480 , and for a beam having a Gaussian intensity distribution, edge  435  affects a smaller portion of the integrated power of incident beam  480 . Edge  425  similarly affects the same small, low-intensity portion of the beam at the reflection that produces reflected beam  490 . 
     The radius R of the clear apertures that accommodate beams  480  and  490  and variations in beams  480  and  490 , a spacing δ between the clear aperture and the optical edge for glass edge imperfections, the desired offset 2X between the centers of beams  480  and  490 , and the beam path in cube corner  400  control the minimum size of cube corner  400  and particularly control the locations or bounds of trimmed surface  441  to  444 . In the direction of the offset, the distance from central axis  445  to trimmed surface  441  or  443  of cube corner reflector  400  must accommodate the separation X between central axis  445  and the center of the beam, a radius R, and spacing δ. Equation 1 thus indicates a minimum width W for cube corner reflector  400 . 
     
       
         W=2(X+R+δ)  Equation 1 
       
     
     Central axis  445  and the centers of beams  480  and  490  are closer to trimmed surface  442  than to trimmed surface  444  because of the beam path within cube corner reflector. Reflective surface  410  reflects incident beam  480  toward reflective surface  430  and trimmed surface  444  and away from trimmed surface  442 . Accordingly, a distance Y 1  of trimmed surface  442  from the plane of central axis  445  and the central rays of beams  480  and  490  must accommodate the size of the beam (radius R) and spacing δ. The minimum distance Y 1  is given in Equation 2. 
     
       
         Y 1 =R+δ  Equation 2 
       
     
     A distance Y 2  of trimmed surface  444  from the plane of the central axis and central rays of beams  480  and  490  must accommodate the beam&#39;s size and movement of the beam toward trimmed surface  444  while still avoiding edge imperfections. FIG. 4A illustrates a ray  482  that is at outer edge (i.e., closest to trimmed surface  441 ) of beam  480  to illustrate the furthest extent of the beam path toward trimmed surface  444 . Surface  410  reflects ray  482  towards reflective surfaces  430  and  420 . The ray  482  reflected from surface  410  strikes surface  430  at a point below the profile of incident beam  480  as viewed in FIG.  4 A. To avoid unacceptable power loss from the beam, distance Y 2  must be large enough to avoid trimming away any of the reflection points of the beam from reflective surface  430 . A geometrical analysis of cube corner reflector  400  indicates that Equation 3 will give the minimum distance Y 2  in terms of separation X, radius R, and spacing δ. 
     
       
         Y 2 =(X+R)tan30°+δ  Equation 3 
       
     
     One exemplary embodiment of the invention that provides an offset of 13 mm for an incident beam having a clear aperture diameter of 9 mm with a 2-mm radial allowance for edge imperfections has a total width of about 26 mm. Minimum distance Y 1  is 6.5 mm, and minimum distance Y 2  is about 8.35 mm in this embodiment. 
     When compared to prior trimmed cube corner reflectors, cube corner reflector  400  causes wavefront distortions that have a smaller effect on interferometer measurements because edges  425  and  435  reflect a small portion of the beam and that small portion has low light intensity. 
     Trimmed cube corner reflector  400  provides better performance, and particularly less wavefront distortion, than does the conventional trimmed cube corner reflector  200  (FIG. 2) when manufactured with comparable imperfections (e.g., non-orthogonal reflective surfaces, edge roll-off, and chamfer.). In particular, in FIG. 4A, edge  425  and a reflection  435 ′ of edge  435  split the area of reflected beam  490  into three parts. If reflective surfaces  410 ,  420 , and  430  are not perfectly orthogonal, each of these parts of reflected beam  490  has uniform phase in a different plane. However, most of the beam intensity is in the central part of reflected beam  490 , even when normal beam movement is taken into account. 
     The amount or significance of both these types of wavefront distortion depends on the ratio of the beam size to the desired offset. If the desired offset is large relative to the beam diameter, reflection from edges  425  and  435  and the associated wavefront distortions can be completely avoided. FIG. 5, for example, shows a cube corner reflector  500  in which the ratio of the off-axis distance X to the radius R is large enough to avoid reflections from edges  515 ,  525 , and  535  between the reflective surfaces  510 ,  520 , and  530 . In cube corner reflector  500 , an incident beam  580  is entirely incident on reflective surface  510 . Beam  580  reflects from surface  510  onto an area  585  of reflective surface  530 . The beam then reflects from area  585  onto reflective surface  520  to form output reflected beam  590 . The minimum size of cube corner reflector  500  and particularly the minimum distances between trimmed surfaces  541 ,  542 ,  543 , and  544  and the central axis of cube corner  500  depend on off-axis beam displacement X, the radius R, the spacing δ for beam variations, and the beam path as described above. 
     FIG. 6 illustrates multi-axis interferometer optics  600  including multiple cube corner reflectors  400  for respective measurement axes. Interferometer  600  has four input beams IN 1  to IN 4  that are directed into a polarizing beam splitter  310 . As described above in regard to interferometer  300  of FIG.  3 . Polarizing beam splitter  310  splits input beams IN 1  to IN 4  according to polarization into measurement beams M 1  to M 4  and reference beams (not shown). Measurement beams M 1  to M 4  travel from polarizing beam splitter  310  to a planar measurement reflector (not shown) that is mounted on an object being measured. The measurement reflector returns measurement beams M 1  to M 4 , which pass through polarizing beam splitter  310  and enter respective cube corner reflectors  400 . From cube corner reflectors  400 , offset measurement beams M 1 ′ to M 4 ′ follow paths to reflect a second time from the measurement reflector before polarizing beams splitter  310  directs returning offset measurement beams M 1 ′ to M 4 ′ to form parts of output beams OUT 1  to OUT 4 , respectively. The reference beams have paths that similarly include first reflections from a reference reflector (not shown), reflections from respective cube corner reflectors  400 , and second reflections from the reference reflector before the reference beams rejoin respective measurement beams M 1 ′ to M 4 ′ to form output beams OUT 1  to OUT 4 . 
     The horizontal and vertical spacing of cube corner reflectors  400  match the spacing of measurement beams M 1  to M 4  or M 1 ′ to M 4 ′. Overall system requirements generally dictate this beam spacing, which is required to perform measurements along the desired axes. The trimming of cube corner reflectors  400  allows arrangement of cube corner reflectors  400  in an array that achieves tight beam spacing. When compared to the minimum size of conventional trimmed cube corner reflectors  200 , trimmed cube corner reflectors  400  are generally somewhat larger in the direction perpendicular to the beam offset because the distance Y 2  to one trimmed surface accommodates an internal beam path that departs from the band containing incident and reflected beams. However, cube corner reflectors at the edge of beam arrays can be oriented with distance Y 2  directed out of the beam array, so that the increased size has no effect on beam spacing. In larger arrays (i.e., arrays having three or more cube corner reflectors along the direction perpendicular to the reflection offsets), the increased size is typically acceptable for the required interferometer beam pattern. Thus, for little or no increase in the beam spacing, cube corner reflectors  400  provide less wavefront distortion than do conventional trimmed cube corner reflectors. Analysis of phase information from the beams after reflections from respective cube corner reflectors  400  can thus provide a higher signal-to-noise ratio and more accurate interferometer measurements. 
     A hollow cube corner reflector in which the paths of the incident and reflected beams are within a hollow portion, rather than within a glass block, can also be trimmed to provide a small size and little or no wavefront distortion. FIG. 7, for example, is a perspective view of a hollow cube corner reflector  700  in accordance with an embodiment of the invention. Cube corner reflector  700  includes orthogonal reflective planar surfaces  710 ,  730 , and a surface not shown in the view of FIG.  7 . Reflective planar surfaces  710  and  730  and the reflective surface not illustrate correspond to and have substantially the same shapes as reflective surfaces  410 ,  430 , and  420  of cube corner reflector  400  or reflective surfaces  510 ,  530 , and  520  of cube corner reflector  500 , so that a front view of cube corner reflector  700  has substantially that same appearance as illustrated in FIG. 4A or FIG.  5 . 
     Cube corner reflector  700  has a trimmed surface  742  that intersects symmetric reflective surface  710  and the reflective surface (not shown) that is symmetric with reflective surface  710 . Another trimmed surface  744  intersects reflective surface  730 . In accordance with an aspect of the invention, the distance between trimmed surface  742  and the center plane of cube corner reflector  700  can be less than the distance between the center plane and trimmed surface  744  (where trimmed surface  744  intersects reflective surface  730 .) The respective distances can, for example, be as given in Equations 1 and 2. The reduction in the distance between trimmed surface  742  and the center plane allows use of cube corner reflector  700  in systems where the beam spacing does not permit the used of a symmetrically trimmed cube corner reflector. 
     Although the invention has been described with reference to particular embodiments, the description is only an example of the invention&#39;s application and should not be taken as a limitation. In particular, although exemplary embodiments of the invention include cube corner reflectors that are separate optical functions of cube corner reflectors can be integrated into optical elements that also perform other optical functions. Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention as defined by the following claims.