Patent Publication Number: US-8531750-B2

Title: Afocal beam relay

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a Continuation-In-Part of U.S. patent application Ser. No. 12/611,320, filed on Nov. 3, 2009, entitled “CONCENTRIC AFOCAL BEAM RELAY”, which, in turn, claims priority from U.S. Ser. No. 61/152,709, provisionally filed on Feb. 15, 2009, entitled “CONCENTRIC AFOCAL BEAM RELAY”, in the name of David Kessler and incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention generally relates to beam steering and scanning systems and more particularly relates to beam scanners that provide scanning in two orthogonal directions using an arrangement of reflective surfaces. 
     BACKGROUND OF THE INVENTION 
     Many types of laser scanners and printers use a one-dimensional (1-D) beam deflector such as a spinning polygon, monogon, hologon, or a reciprocating galvo mirror, that scans the beam along a line. To provide two-dimensional (2-D) scanning with a 1-D beam deflector requires that mechanical motion be provided for scanning in the other dimension, orthogonal to the first. This is commonly done by a transport system that moves the scanned media or moves the scanning deflector. 
     Two-dimensional beam deflectors provide a simpler solution for steering the light beam for scanning along two orthogonal directions or axes. With some scanning laser systems, this is often termed Two-Axis Beam Steering (TABS). TABS scanning can use an arrangement comprised of two galvo mirrors like the ones made by Cambridge Technology, Cambridge Mass.; GSI Lumonics (previously General Scanning Inc) Bedford Mass.; Nuffield Technology Inc., Windham N.H.; and GalvoScan LLC, South Royalton Vt. Similar Fast Scanning Mirrors (FSM) systems also steer the beam in two dimensions using reciprocating reflective surfaces. Galvo mirrors are commonly used as deflectors due to their relatively wide deflection angles and high scan speed, especially when used in the resonant mode. Because galvo scanners scan only in one direction, a pair of galvo mirrors in series is used as the deflection system to accomplish 2-D scanning. 
     Laser beam scanning systems are generally classified by the arrangement of the deflection system relative to the focusing lens. When deflection system components follow the focusing lens, the system is termed a post-objective system. When the focusing or scan lens follows the beam deflector, the system is called a pre-objective scanner. Post objective scanners are usually simpler in design compared with pre-objective scanners, but are generally more limited in terms of scan fields and are more prone to distortion and field curvature. 
     The schematic diagram of  FIG. 1  shows how light is directed for 2-D scanning by components in a pre-objective scanning system  80 . A light beam  82  of beam width B, preferably collimated, is deflected by a first galvo mirror  35  that scans relative to a first axis and toward a second galvo mirror  35 A that scans relative to a second axis that is orthogonal to the first axis. A scan lens  120  then directs this 2-D scan to form a 2-D image  130 . 
     Among disadvantages of the arrangement of  FIG. 1 , second mirror  35 A must be large enough to accommodate the deflected beam from first mirror  35 , and thus cannot operate at high speed. Another disadvantage relates to mirror positioning. With a pre-objective system, the beam deflector provides the best optical performance when it is positioned in an external entrance pupil of the scan lens. This is shown as pupil  30  in  FIG. 1 . However, for such a two-mirror system, this would require that both mirrors  35  and  35 A be positioned at entrance pupil  30 . As a compromise, galvo mirrors  35  and  35 A are generally positioned close to, and equidistant from, pupil  30 , displaced at a distance L as shown in  FIG. 1 . When this is done, because both mirrors  35  and  35 A are displaced from entrance pupil  30 , scan lens  120  must have an aperture large enough to accommodate the beam displacements. This adds cost and size, requiring that scan lens  120  have a higher effective numerical aperture than does a system that uses a single two-dimensional scan mirror. 
     With both mirrors displaced from the entrance pupil, the aperture diameter D of the aperture corresponding to entrance pupil  30  is given by:
 
 D=B+ 2 *L *Tan(α)
 
Where:
 
B is the beam diameter of light beam  82 ;
 
L is the distance from pupil  30 , along the axis, of the farthest mirror galvo;
 
and α is the semi beam angle.
 
     For example, with a beam diameter of 10 mm, a shift L of 20 mm, and a semi scan angle α of 15 degrees, the aperture D is 20.7 mm. Thus, the entrance pupil must be about twice the diameter of the beam. The numerical aperture (NA) of the scan lens  120  is therefore twice the NA of a scan lens where the mirror deflector is located at the entrance pupil  30 . 
     As is shown in  FIG. 2 , one approach to solve this problem and reduce the NA of scan lens  120  is to optically co-locate galvo scanning mirrors  35  and  35 A. There can be a number of ways to do this using refractive and reflective relay optics. Referring to the schematic diagram of  FIG. 2 , there is shown an example of an optical relay  90  that relays galvo mirror  35  onto galvo mirror  35 A. In the arrangement of  FIG. 2 , the pupil relay uses two off-axis concave mirrors  55  and  56  to relay galvo mirror  35  onto galvo mirror  35 A. With this type of solution, both deflectors can thus be optically positioned within the entrance pupil of scanning lens  120 . This reduces the numerical aperture requirements for lens  120 , as described earlier, and reduces the size requirements of the second galvo mirror  35 A. Actuators  32  and  32 A control the rotation of their respective scanning mirrors  35  and  35 A. 
     In spite of its advantages for reducing size and performance requirements of other components in the optical system, however, the arrangement of optical relay  90  as shown in  FIG. 2  has a number of problems that prevent its use in most laser scanner applications. Off-axis aberrations of the concave mirrors can seriously degrade the performance of such a system. Both mirrors are relatively large, requiring precision manufacture to minimize defects in maintaining exact curvatures. This solution is not particularly compact and does not scale well for large scan angles. 
     As exhibited in the example of  FIG. 2 , pupil relay optics show some promise for at least reducing some of the problems inherent to 2-D beam scanners using lasers. However, problems remain. In order for a pupil relay to satisfactorily serve 2-D beam scanning applications, the following basic set of requirements must be met:
         (i) Low aberration. While some amount of aberration is inevitable, it is important that the pupil relay solution be well corrected and have minimal aberration.   (ii) Capable of handling large deflection angles. Angles of up to 12 degrees and larger should be accommodated.   (iii) Preserves the phase of the beam wavefront. When this requirement is met, a collimated input beam with a planar phase wavefront that enters the entrance pupil of the relay, on axis or at an angle within its specified field of view, exits from the exit pupil as a collimated beam, again with planar phase wavefront. The optical path difference (OPD) between any point at the entrance pupil and its conjugate point at the exit pupil is the same. This characteristic is of particular interest for laser scanning. The capability to preserve the phase of the beam wavefront distinguishes the performance requirements of a pupil relay system from the requirements of an imaging relay system. In an imaging relay system, beam wavefront and phase considerations are unimportant and the phase of the beam wavefront is not preserved.   (iv) Capable of providing a large pupil size, effectively forming an image of a circular pupil.   (v) Afocal. For beam relay applications, it is most preferable to handle collimated light. Exit and entrance pupils should be at infinity.   (vi) Color-corrected. This requirement depends on the application. Good color correction enables use of either monochromatic light or polychromatic light over a broad spectral range.   (vii) Low cost. This relates both to precision of assembly and number of components.   (viii) Reduced size.       

     However, as seen from the example of  FIG. 2 , pupil relay solutions proposed thus far fail to satisfy all of these requirements. Instead, conventional pupil relay solutions typically compromise on one or more of these basic requirements. 
     In a paper entitled “Offner-type pupil relay optics for a scanning system” by G. C. deWit and J. J. M. Braat, in Design and Engineering of Optical Systems, SPIE vol. 2774, pp. 553-561, three possible pupil relay solutions are compared, including a spherical mirror on-axis relay, a spherical mirror off-axis relay, and an Offner-type system. These researchers conclude that the spherical mirror on-axis solution is optically superior to the other two proposed solutions. 
     Significantly, researchers deWit and Braat were intrigued with some of the advantages of an Offner-type solution, but were unable to make this arrangement work satisfactorily as a pupil relay and found the Offner-type arrangement inferior to on-axis spherical mirror designs. The authors cite the advantages of Offner optics as they relate to size, optical properties, and unlimited horizontal field of view (FOV). However, the Offner arrangement does not provide a pupil relay and is, by itself, a poor solution for directing a 2-D scanning beam, chiefly because it fails to preserve the beam wavefront, a significant needed feature of a pupil relay as noted earlier in requirement (iii). 
     It is instructive to understand more clearly why the Offner optical system, disclosed in U.S. Pat. No. 3,748,015 entitled “Unit Power Imaging Catoptric Anastigmat” to Offner, does not function as a pupil relay. This shortcoming is most readily shown by a description of the Offner optical system itself. Referring to  FIG. 3 , an Offner optical system  92  is a one-to-one object-to-image relay system using two concentric mirrors, a primary concave mirror  50  and a secondary convex mirror  60 . The system is afocal, with its entrance pupil at infinity. The aperture stop of this optical system, pupil  65 , is at secondary convex mirror  60 . This system is corrected for all third order aberrations and for a number of higher order aberrations. 
     The imaging function of Offner optics is constrained to image a specific field of a particular shape, rather than for a circular beam. The Offner optical system, as shown in the example of  FIG. 3 , is a member of a class of imaging systems that have an annular object, or a ring object  15  and, in turn, form a corresponding ring image  15 A. Because of higher order aberrations, such as fifth order astigmatism, the object shape is limited to a thin arcuate region  15  about the optical axis OA. Thus, in practice, the Offner system is used to scan across a 2-D area and form an image of the arcuate object shown as object  15  in  FIG. 3 . Examples of how the Offner optics are used for scanning are given, for example in U.S. Pat. No. 5,221,975 entitled “High Resolution Scanner” to Kessler that describes a CCD scanner for film reproduction and in U.S. Pat. No. 6,304,315 entitled “High Speed High Resolution Continuous Optical Film Printer for Duplication Motion Films” to Kessler et al. As each of these patents shows, the object of the Offner optical system is an arc of limited thickness and the optical system faithfully images that arc with little aberration, effectively scanning a 2-D image over this arcuate image area. 
     In an attempt to improve the relative size of the arc that can be imaged by this two-mirror system, Suzuki in U.S. Pat. No. 4,097,125 adjusts the positions of the two curved mirrors so that they are no longer concentric, as is required in the conventional Offner system. Even with this change, however, the width of the relatively narrow slit imaged by the Offner system can only be increased by about a factor of 2. The modified arrangement provided by Suzuki &#39;125 still images an arcuate object, not a circular beam, and would also fail as a pupil relay. 
     Another significant problem with Offner-type optics relates to the beam wavefront. When the Offner system is used as an object-to-image relay, the object points are incoherent with each other. This is not a concern for imaging, as was noted earlier. However, in order to maintain beam quality as a beam relay, the beam phase wavefront at the entrance pupil must be preserved at the exit pupil. This is not the case with Offner optics. When the Offner system is used as an object-to-image relay, five of the third-order aberrations, namely spherical, coma, astigmatism, Petzval, and distortion, are corrected. However, one of the third order aberrations, called “piston error” which particularly relates to the phase difference between different object points, is not corrected. In the type of imaging system for which the Offner optics are designed, there is no need to correct for the piston error since the object points are themselves generally incoherent with each other and phase is not important. However, for beam relay optics, such a phase difference is an aberration that severely degrades beam quality for a coherent beam and can render the optical system unusable. In summary, because it is an image relay system, and not a pupil relay system, as described in requirement (iii) above, the Offner system does not preserve phase relationships. 
     Thus, it can be appreciated by those skilled in the optical arts that the Offner system is an afocal imaging relay, not an afocal pupil relay, and it is no surprise that, in spite of their interest in some of the potential capabilities and compactness of Offner optics, researchers have been unable to adapt this arrangement for use as an acceptable pupil relay. 
     The need remains for pupil relay optics for 2-D scanning that meet requirements (i) to (viii) given earlier. In spite of some perceived advantages, however, solutions posed thus far have failed to take advantage of Offner-type optics for use as a beam relay for this purpose, due to inherent limitations of such systems. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to advance the art of laser scanning systems. With this object in mind, the present invention provides an afocal beam relay comprising:
         first and second primary concave reflective surfaces and first and second secondary convex toroidal reflective surfaces,   wherein the centers of curvature of each of the first and second primary reflective surfaces and first and second secondary reflective surfaces lie on an axis;   wherein the first and second secondary convex reflective surfaces face toward the first and second primary concave reflective surfaces and are disposed to relay a decentered entrance pupil to a decentered exit pupil; and   an aspheric corrector element that is disposed in the path of an input beam of light that is directed by the primary and secondary surfaces to the decentered entrance pupil,   wherein the directed beam of light between the first and second secondary convex mirrors is collimated in one direction and focused in mid air in an orthogonal direction.       

     It is a feature of the present invention that it adapts an optical arrangement that is conventionally used for imaging or relaying an arcuate object field for use as a beam relay. The beam relay that is formed is capable of handling large deflection angles and large pupil sizes. 
     The present invention takes advantage of the reduced third-order aberrations of concentric reflective optical designs. It is also afocal and color corrected. As pupil relays, embodiments of the present invention preserve the phase of the beam wavefront. 
     These and other aspects, objects, features and advantages of the present invention will be more clearly understood and appreciated from a review of the following detailed description of the preferred embodiments and appended claims, and by reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       While the specification concludes with claims particularly pointing out and distinctly claiming the subject matter of the present invention, it is believed that the invention will be better understood from the following description when taken in conjunction with the accompanying drawings. 
         FIG. 1  is a schematic diagram of 2-D pre-objective scanning optics. 
         FIG. 2  is a schematic diagram of 2-D pre-objective scanning optics with first and second scanning mirrors optically co-located within the pupil of the scan lens. 
         FIG. 3  is a perspective view of components and light paths for an Offner scanning system. 
         FIG. 4  is a perspective view of components in a Schmidt telescope. 
         FIG. 5  is a perspective view of a beam relay according to one embodiment of the present invention. 
         FIG. 6  is a perspective view showing a portion of the optical path for a beam relay as in  FIG. 5 . 
         FIG. 7  is another perspective view showing entrance and exit pupil positions for the beam relay of the present invention. 
         FIG. 8  is a top view, optically unfolded, of the beam relay of  FIGS. 5-7 . 
         FIG. 9  is a table giving example optical specifications for a beam relay in one embodiment. 
         FIG. 10  is a perspective view showing an alternate embodiment of a beam scanner using a prism for light redirection. 
         FIG. 11  is a perspective view showing an alternate embodiment of a beam scanning that has a two-axis deflection device. 
         FIG. 12  is a perspective view showing an alternate application of the relay in a mini laser projector using MEMS beam deflectors. 
         FIG. 13A  is a perspective view that shows a modified relay for applications with high power lasers where the beam is not focused on the secondary mirror. 
         FIG. 13B  is a top view showing a portion of the light paths for the  FIG. 13A  embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following is a detailed description of preferred, but non-limiting, embodiments of the invention, reference being made to the drawings in which the same reference numerals identify the same elements of structure in each of the several figures. It is to be understood that elements not specifically shown or described may take various forms well known to those skilled in the art. For example, conventional scanning optical systems are well known in the optical arts and are not, therefore, described in detail herein, except for those parts of systems related either directly to embodiments of the present invention or cooperating in some way with embodiments of the present invention. 
     Figures shown and described herein are provided in order to illustrate key principles of operation and component relationships along their respective optical paths according to the present invention and are not drawn with intent to show actual size or scale. Some exaggeration may be necessary in order to emphasize basic structural relationships or principles of operation. Some conventional components that would be needed for implementation of the described embodiments, such as various types of optical mounts, for example, are not shown in the drawings in order to simplify description of the invention itself. In the drawings and text that follow, like components are designated with like reference numerals, and similar descriptions concerning components and arrangement or interaction of components already described are omitted. Where they are used, the terms “first”, “second”, and so on, do not necessarily denote any ordinal or priority relation, but are simply used to more clearly distinguish one element from another. The terms “scanning” and “steering” may be used interchangeably in this document. 
     In the context of the present disclosure, the phrase “reflective surface” is used interchangeably with the term “mirror”. As is familiar to those skilled in the optical design arts, a reflective surface can be formed from a number of different materials, including metals and from dichroic and metal coatings on various substrates, for example. 
     In the context of the present disclosure, the phrase “substantially circular” describes a feature or object that appears circular or nearly circular to the unaided eye of an observer. 
     As was noted earlier in the background section and described with reference to  FIG. 3 , the Offner system is not useful as a beam relay. In order to work as a relay, the respective positions of object  15  and the entrance pupil (not shown in  FIG. 3  because it is at infinity) must be switched. Correspondingly, the placement of image  15 A and exit pupil must also be reversed. 
     The present invention addresses the problems that have thus far prevented the use of Offner-type optics as beam relays. To do this, the present invention modifies the conventional Offner design with the addition of aspheric corrector optics disposed in the path of the collimated input beam. This effects the needed change in position for both entrance and exit pupils, as just described. 
     Corrector optics are used to correct for image aberration in various types of telescope systems, such as a Schmidt telescope  70  shown in  FIG. 4 . In the catadioptric Schmidt system, a high degree of symmetry is achieved, with all components centered on optical axis OA. The object for the Schmidt telescope system is at infinity; the image is at the back focal plane of a primary spherical curved surface. An on-axis collimated beam  10  from the object field is reflected from a primary spherical mirror  72  and forms an image on a secondary spherical focal surface  74  located at the back focal plane of spherical mirror  72 . Both entrance and exit pupils are at a plane  40  that is coplanar with the center of curvature C of the curved reflective surfaces and centered about C. For reference, plane  40  may be termed the “center plane”. Spherical aberration in the Schmidt telescope is corrected by a thin refracting aspheric element  24  that is symmetric about the optical axis and positioned at the center of curvature C of primary spherical mirror  72 . Off-axis aberrations are corrected since the system is concentric about the stop, so the off-axis beams “see” the same optical system at all angles (except for small variations due to the corrector off-axis performance). 
     In order to suitably adapt Offner optics to the task of pupil relay, embodiments of the present invention employ the concept of corrective optics at the stop. However, unlike the axially symmetric corrector optics used, for example, in Schmidt telescope systems, the corrector optics  20  in  FIG. 5  of the present invention are disposed only near the decentered entrance pupil  30 . Moreover, unlike the Schmidt corrector that corrects for the spherical aberration from a single reflection from the concave mirror, corrector optics for the present invention correct for two reflections from a concave mirror or mirrors, as shown in subsequent description. Significantly, with the addition of corrector optics  20 , the phase of the beam that is being relayed is preserved. Using corrector optics, a corrector element  20  of the present invention, with the optical arrangement of  FIGS. 5-8 , the phase wavefront variation over the beam at the exit pupil is less than a quarter wave for a perfectly collimated input beam. 
     Referring to  FIG. 5 , there is shown an embodiment of a beam relay  100  that scans coherent light as part of a pre-objective laser scanning system  200  according to the present invention.  FIG. 6  gives a perspective view showing component functions in the optical path, as considered looking inward toward the curved reflective surface of primary concave mirror  50 , and shown without folding mirrors  58 . 
     Annotations A 1 -A 6  given in  FIG. 5  and following help to trace the path of light through the system of beam relay  100 . Input collimated beam  10  from the laser source (not shown) at A 1  is directed to first scanning mirror  35  through corrector element  20 . Scanning mirror  35  reflects the light A 2  to folding mirror  58  and toward primary concave mirror  50 . Primary concave mirror  50  reflects this light A 3  onto secondary convex mirror  60 . Secondary convex mirror  60  reflects this light A 4  back toward primary concave mirror  50 . The reflected light A 5  from primary concave mirror  50  is then directed, again as collimated light, to scanning mirror  35 A. This scans the beam in the orthogonal direction to that scanned by scanning mirror  35 . The scanned light A 6  is then directed through scan lens  120  that focuses the two dimensionally steered beams onto a surface, such as a scanned image surface  130  to form a scanned 2-D image. Folding mirrors  58  help to reduce the spatial footprint of the system. 
     In the perspective view of  FIG. 6 , the arrangement and geometry of secondary convex mirror  60  within relay  100  are shown in more detail. As can be seen from this view, mirror  60  can be sliced to a narrow strip as is explained in more detail subsequently. 
     As one type of scanning element, scanning mirrors  35  and  35 A are actuable devices driven by deflecting mechanisms, shown in  FIG. 5  as actuators  32  and  32 A, respectively. Although scanning mirrors  35  and  35 A are shown as galvo (galvanometer) type scanning mirrors, it is understood that polygons, monogons, hologons and other one-dimensional beam steering devices of various types, reflective and refractive, can alternately be used as scanning elements. 
       FIG. 7  shows the optical behavior of beam relay  100  in  FIGS. 5 and 6 , from the beginning to the ending of a scanned line, from the perspective of entrance and exit pupils  38  and  38 A, respectively.  FIG. 7  also shows aspects of placement for optical system components. Primary concave mirror  50  has its center of curvature C and a vertex V 1  that define optical axis OA. Mirrors  35  and  35 A, shown in  FIGS. 5 and 6  but not shown in  FIG. 7  for clarity, are correspondingly placed at pupils  38  and  38 A of relay  100 . Pupils  38  and  38 A are located on center plane  40 . The center of curvature C of primary concave mirror  50  of secondary convex mirror  60  is substantially coplanar with pupils  38  and  38 A at center plane  40 . With respect to such distance relationship, the term “substantially” can be taken to mean “within about +/−2%”. For example, if the radius of curvature of mirror  50  is 100 mm, for example, the center of curvature C is within about +/−2% of that distance from plane  40 , that is, within about +/−2 mm of plane  40 . Convex mirror  60  is located substantially half way (again, within about +/−2% of the actual half distance) between plane  40  and concave mirror  50 , as shown in  FIG. 7 , with its center of curvature substantially coincident with center of curvature C of concave mirror  50 , located substantially at plane  40 . Thus the radius of curvature of concave mirror  60  is substantially half that of convex mirror  50 . Mirror  60  has a vertex V 2  along optical axis OA. This is a basic structural relationship that parallels the Offner system of  FIG. 3 . However, the changes described herein are required in order to take advantage of aspects of the Offner design and adapt it to the challenge of beam relay operation including beam phase preservation, for which it was not originally intended and which the Offner system is incapable of providing. In the view of  FIG. 7 , the beginning of the scanned line directs light toward the top of primary concave mirror  50 . The scan in this first direction, providing the light labeled A 2 , then proceeds downward along mirror  50  (the −y direction in  FIG. 7 ). The light at A 4  that is reflected back onto primary concave mirror  50  from secondary convex mirror  60  moves in a parallel path to the A 2  light, also proceeding downward along mirror  50  as the line scan progresses. 
     It is understood that while  FIG. 7  shows the pupils  38  and  38 A and corrector  20  as having circular apertures, they could alternately have other shapes, including non-circular pupil shapes such as square and rectangular; input beam  10  could also have a non-circular cross section. 
       FIG. 8  shows a top view of beam relay  100 , optically unfolded with respect to  FIG. 5 . Annotation A 2 -A 6  again traces the light path, beginning from after aspheric corrector element  20  to scanning the 2-D image at image surface  130 . 
     In beam relay  100 , substantially collimated input beam  10  is incident on aspheric corrector element  20 , near the entrance pupil. Aspheric corrector element  20  is an off-center segment, with circular-aperture, having correction values centered on the center of curvature C as shown in  FIG. 7 . Corrector element  20  as described is a transmissive corrector, such as an aspheric lens element. However, in an alternative embodiment corrector element  20  can also be designed as an aspherical doublet using two elements with different dispersions or the corrector can be a reflective corrector, thus providing improved aspheric correction performance over a larger spectral range. A short distance following corrector element  20  (as shown more clearly in the perspective view of  FIG. 5 ), the beam is deflected in the y direction by scanning mirror  35 . 
     As mentioned earlier and shown from various perspectives in  FIGS. 5-8 , convex mirror  60  can be in the form of a narrow strip, wherein the width of its reflective surface is less than its length. This makes it possible to minimize the decenter distance S, shown in  FIG. 7 . As is best seen in the views of  FIGS. 7 and 8 , the beam is steered along primary concave mirror  50  in the y direction during scan operation; there is no beam displacement in the x direction within beam relay  100 . Thus, mirror  60  can be narrowed in the x direction with no impact on the system performance, thereby reducing separation distance S. If mirror  60  were wider in the x direction, however, this would necessitate an increased separation S that would be otherwise needed to avoid interference of mirror  60  with the incoming and outgoing beams A 2  and A 5 . In contrast to this arrangement, it can be observed that conventional Offner system optics, as shown in  FIG. 3 , require that convex mirror  60  have a circular aperture. Then, to avoid interference between mirror  60  and the beams in the conventional Offner system, the decentering distance S actually needs to be larger than the semi-diameter of mirror  60 . Notably, high order aberrations in the conventional Offner system increase with increased separation distance S. To some extent, reduced performance can be corrected by scaling up the radii of curvatures of mirrors  50  and  60  and the corresponding axial distances. However, this has the disappointing result of increasing system dimensions. 
     The table of  FIG. 9  shows a design example for beam relay  100  in one embodiment using terms used in the widely used Zemax optical design program (ZEMAX Development Corp., Bellevue, Wash.). A number of notes and observations apply for this and other exemplary embodiments:
         (i) The entrance and exit pupils are spaced apart and in a plane  40  which is 160 mm from the vertex of mirror  50 .   (ii) The off-axis decentering distance S of the pupils from the optical axis is 10 mm.   (iii) The diameter of entrance pupil  30  is 15 mm, and the beams are deflected by scanning mirror  35 , as shown on  FIG. 5 , by a total optical scan angle of 20 degrees.   (iv) Primary concave mirror  50  can be shortened width-wise, as shown in  FIG. 7 . In this example embodiment, primary concave mirror  50  is reduced to a width of 76 mm in the y scan direction and to about 40 mm in the x or cross scan direction.   (v) Convex mirror  60 , as shown on  FIG. 7 , is reduced to a width of 3.2 mm in the y scan direction by about 32 mm in the x or cross scan direction.   (vi) Silica aspheric corrector element  20  in this example, best shown in  FIG. 7 , is disposed at the entrance pupil.       

     Note that in  FIG. 5 , aspheric corrector element  20  is shown displaced along the input beam  10  from scanning mirror  35 , which is at entrance pupil  30 , so that it does not interfere with the scanning operation. This slight displacement has minimal affect on the performance of corrector  20  since input beam  10  is collimated, axial, and stationary. 
     The performance of the optical system described with respect to  FIGS. 5-9 , over the visible spectrum, is diffraction limited. Variability of the RMS wavefront is less than 0.05 waves. The OPD peak-to-peak is less than 0.25 waves and the Strehl Ratio is above 0.9. For green light only, at 586 nm, the Strehl Ratio is over 0.95 and the RMS wavefront is less than 0.025 waves. 
     As suggested in the illustrations of  FIGS. 7 and 8 , entrance pupil  38  and aspheric corrector element  20  are significantly decentered by a distance S from optical axis OA. Unlike the corrector used in Schmidt telescopes and corrective optics for similar concentric optical systems, the aspheric corrector  20  of the present invention is an off-center segment with an aspheric term that is about twice the value that is used for Schmidt and other single mirror systems. Note that aspheric corrector element  20  is depicted on  FIGS. 7 and 8  with dotted lines centered on the optical axis OA and the center of curvature C to indicate that this is a decentered circular-aperture element that is segmented from or cut from a larger, axially symmetrical element. Aspheric corrector element  20  is described in the examples given herein as a transmissive (refractive) component. However, reflective optics could also be provided, and could provide improved aspheric correction performance over larger spectral range. 
     The concave mirror is shown in  FIG. 9  with a spherical surface. It is possible to keep the axial symmetry of the system, but change the concave mirror to a torodial shape, such as having a parabolic cross section in the x direction. A mirror of this type is corrected for spherical aberration in this direction; thus, if this were used, the aspheric corrector must then correct only in the y direction (that is, the scan direction). Such an arrangement of corrector and concave mirror would be functional, but the system would be more costly to construct and more complex to align. 
     Scan lens  120  is also known as an f-theta lens, a focusing lens, or an objective lens. This is shown schematically in  FIGS. 5 and 8  and can comprise either or both refractive and reflective components. 
     When compared against the conventional Offner optical system that has some similar components and spacing relationships, beam relay  100  effectively interchanges the relationships of object/image planes and pupil planes. Thus, for example, in  FIG. 7 , the incoming beam at aspheric corrector element  20 , or entrance pupil  38 , is collimated at plane  40  and is directed to primary concave mirror  50  as collimated beam A 2 . Equivalently stated, the object point is at infinity. This runs counter to Offner optics, for which the input beam is focused at plane  40 , as was shown in  FIG. 3 . 
     It should be observed that simply adding a corrector element at plane  40  of a conventional Offner optical system, as shown in  FIG. 3 , does not affect various aspects of Offner system performance, because the marginal ray height at this position is zero, since this is its object plane. While corrective optics may have been previously applied to Offner systems for various reasons, such as the use of shell like correctors interposed between plane  40  and concave mirror  50 , and displaced along the optical axis from plane  40 , as described in U.S. Pat. No. 4,693,569 to Offner, these have been used to correct for high order field aberrations such as fifth order astigmatism, not to adapt Offner imaging for beam relay use. 
     As was noted earlier with respect to  FIG. 3 , conventional Offner optics provide a thin arcuate object field, not adaptable for use as a beam relay. The convex secondary mirror of the conventional Offner arrangement is at the pupil of such a system and commonly has a circular aperture. 
     The perspective view of  FIG. 10  shows an alternate embodiment of beam relay  100  within a scanning apparatus in which a prism  76  is used to fold the optical path and also provides a mounting position for secondary convex mirror  60 . 
     While beam relay  100  of the present invention is particularly well suited for systems that provide separate x- and y-axis scanners, such as those described with reference to  FIGS. 5-10 , embodiments of the present invention can also be used with two-axis deflection provided by a single gimballed mirror or other device. The perspective view of  FIG. 11  shows a pre-objective laser scanning system  300  having a two-axis deflector  135 , a two dimensional scanning element that scans the beam in both the x and y directions. Two-axis deflector  135  could be a gimbaled mirror capable of deflection in two orthogonal directions and able to reach the internal stop of a scanning lens. While most scanning lenses have an accessible external entrance pupil, some, especially those with high numerical aperture, may have an internal inaccessible entrance pupil. With the  FIG. 11  arrangement, the entrance pupil of scan lens  120  is placed at exit pupil  38 A of beam relay  100 . The scan lens in this case can have an internal entrance pupil, shown at  38 A, as opposed to the common external entrance pupil of other arrangements. This is conducive to increased performance and reduced cost of the scan lens. 
     Beam relay  100 , having an accessible external exit pupil, can be used with such a scan lens. When using the arrangement of  FIG. 11  for a 2 dimensional scan, secondary convex mirror  60  has a circular aperture as opposed to the thin sliced convex mirror  60  shown earlier with respect to  FIGS. 5-8 . In order for the beams to clear this enlarged convex mirror  60 , the pupil separation distance S of  FIGS. 7 and 8  must be increased (for example, from 10 mm to 24 mm). Over scan angles of 12 degrees in both x and y directions, and beam size of 6 mm, the performance of the system of  FIG. 11  is diffraction limited over the visible spectrum. 
     As noted earlier, various types of scanning elements can be used to provide the function of scanning mirrors  35  and  35 A in embodiments of the present invention. In addition to galvo mirrors, MEMS (Micro-ElectroMechanical Systems) beam deflectors can alternately be used as scanning elements. MEMS deflectors have been used, for example, with laser mini- and pico-projectors, such as the “PicoP” projector made by Microvision, Inc., Redmond, Wash. The PicoP projector uses a gimbaled TABS MEMS mirror. In one direction, the scan is performed by a small mirror that is scanned at high speed. This small mirror is mounted on a gimbal that is larger and scans the beam in the orthogonal direction at a much reduced speed. While this arrangement is workable, however, there can be inherent problems with distortion associated with gimbaled mirrors. 
     According to an embodiment of the present invention, gimbaled mirrors are not used. Instead, light from the afocal beam relay of the present invention is scanned using a pair of one-dimensional MEMS deflectors. Exemplary MEMS deflectors for this purpose include MEMS devices made by Lenoptix SA, Lausanne, Switzerland, or by Mezmeriz, Rochester, N.Y. 
     The perspective diagram of  FIG. 12  shows a laser scanning system  400  with a beam relay  402  that uses two MEMS deflectors as scanning elements, shown as deflectors  35   c  and  35   d . By comparison with system  100  of  FIG. 10 , galvo mirrors  35  and  35   a  are replaced by one-dimensional micro-electromechanical scanning elements, the MEMS deflectors  35   c  and  35   d . Reflective deflector  35   c  scans in the y direction; reflective deflector  35   d  scans in the x direction. This allows system  400  to be scaled significantly in size, to dimensions suitable for laser mini-projectors and similar devices. For example, width dimension Q 1  can be in the 6.4 mm range. Distance dimension Q 2  from the axis of symmetry K 1  of the optical system can be in the 15 mm range. Advantageously, by adjusting the distance between mirrors  50  and  60 , relay  402  can provide a focused image onto the image surface at a distance, with no scan lens being used. The image surface is not shown in  FIG. 12 . 
       FIGS. 13A and 13B  show an alternate embodiment of a laser scanning system  500  with a beam relay  502  having aspheric corrector element  20  for relaying a decentered entrance pupil to a decentered exit pupil that addresses a problem related to high power laser light, such as might be used in a writing application. At high laser power levels, there is potential for damaging the surface of the convex secondary mirror with a focused beam. Alternatives such as cooling the secondary mirror or rotating the mirror about its center of curvature can be used to mitigate high exposure levels; however, these methods require additional components and mechanical complexity. In the  FIGS. 13A and 13B  embodiment, the concave primary mirror is divided into two toroidal primary mirrors  50   a  and  50   b , both having the same curvature, monocentric about an axis AX 1  connecting scanning mirrors  35  and  35   a . The corresponding centers of curvature Ca and Cb lie on axis AX 1 . Convex secondary mirrors  60   a  and  60   b  provide a toroidal surface with a hyperbolic cross section in the plane, as best shown on  FIG. 13B . Secondary mirrors  60   a  and  60   b  are monocentric with axis AX 1  connecting scanning mirrors  35  to  35   a . Centers of curvature Ca and Cb for secondary mirrors  60   a  and  60   b  correspond to those of the primary reflective surfaces  50   a  and  50   b , respectively. The incoming beam of light at A 1 , incident on scanning mirror  35  at the entrance pupil and reflected at A 2  from primary concave mirror  50   b  is reflected as A 3  from secondary mirror  60   b  and, considered from a top view, is collimated between mirrors  60   a  and  60   b , as shown in the plan view of  FIG. 13B . Seen from the orthogonal direction, however, as is best shown in the perspective view of  FIG. 13A , the beam of light comes to focus in mid air, that is, within a region that lies half way between the mirrors  60   a  and  60   b . There is, then, no focus of the beam directly on any mirror surface. This light, reflected from mirror  60   a , then proceeds at A 4  to primary concave mirror  50   a  and is reflected from mirror  50   a  as A 5  and, from there, is reflected as A 6  to scan lens  120  and to the image surface  130 .  FIG. 13A  shows the scanned light at different scanned positions. According to an alternate embodiment of the present invention, one or more of the primary and secondary mirrors  50   a ,  50   b ,  60   a , and  60   b  are non-spherical. Using the embodiment of  FIGS. 13A and 13B , the phase wavefront variation over the beam at the exit pupil is less than a quarter wave for a perfectly collimated input beam. Entrance and exit pupils at mirrors  35  and  35   a  may be circular or non-circular. 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the scope of the invention as described above, and as noted in the appended claims, by a person of ordinary skill in the art without departing from the scope of the invention. For example, dimensional values shown are given by way of example; other dimensions could be used, depending on various factors such as beam width, scan angles, and wavelengths. While the apparatus and methods described are particularly well suited to laser light, the apparatus of the present invention can also be used with other collimated light sources. The optical path can be folded using turning mirrors or similar devices in order to allow more compact packaging for optically equivalent arrangements, for example. Using folding, entrance and exit pupils can be optically coplanar, for example, without being geometrically disposed within the same plane. Convex and concave reflective surfaces can be spherical or non-spherical, as has been described. 
     Thus, what is provided is an apparatus and method for providing a beam relay for a scanning system. 
     PARTS LIST 
     
         
           10 . Collimated beam 
           15 . Object 
           15 A. Image 
           20 . Aspheric corrector element 
           24 . Corrector element 
           30 . Stop 
           32 ,  32 A. Actuator 
           35 ,  35 A. Scanning mirror 
           35   c ,  35   d . Deflector 
           38 ,  38 A. Pupil 
           40 . Center plane 
           50 . Primary concave mirror 
           50   a  and  50   b . Concave toroidal primary mirrors 
           55 ,  56 . Mirror 
           58 . Folding mirror 
           60 . Secondary convex mirror 
           60   a  and  60   b . Convex toroidal secondary mirrors 
           65 . Exit pupil 
           70 . Schmidt telescope 
           72 . Spherical mirror 
           74  Focal surface 
           76 . Prism 
           80 . Pre-objective scanning system 
           82 . Light beam 
           90 . Optical relay 
           92 . Offner optical system 
           100 . Beam relay 
           120 . Scan lens 
           130 . Image surface 
           135 . Two-axis deflector 
           200 . Laser scanning system 
           300 . Laser scanning system 
           400 . Laser scanning system 
           402 . Beam relay 
           500 . Laser scanning system 
           502 . Beam relay 
         OA. Optical axis 
         A 1 , A 2 , A 3 , A 4 , A 5 , A 6 . Annotation 
         AX 1 . Axis 
         B. Beam width 
         Ca, Cb. Center of curvature 
         L, S. Distance 
         K 1 . Axis of symmetry 
         Q 1 , Q 2 . Dimension 
         V 1 , V 2 . Vertex 
         α Angle