Abstract:
An apparatus for testing an optical surface comprising an array of holograms. The array includes a plurality of individual holograms arranged in an M×N format, in which M is the number of rows and N is the number of columns in the array. The array of holograms is positioned between the optical surface and a wavefront sensor. The array of holograms reflects a reference beam back to the wavefront sensor, and transmits a test beam to the optical surface. The array of holograms also receives the test beam reflected from the optical surface and transfers the test beam back to the wavefront sensor.

Description:
FIELD OF INVENTION 
     The present invention is directed toward wavefront or surface measurements of an optical surface. In particular, the present invention is directed to a system and method for performing surface measurements of an optical surface using computer generated holograms (CGHs). 
     BACKGROUND OF THE INVENTION 
     Interferometry techniques are used for testing aspheric surfaces. In one test configuration, known as a null configuration, a reference wavefront and a test wavefront are formed to produce an interference pattern. Errors in the test measurement are then interpreted directly as errors in the test surface. The Hindle test is an example of a null configuration and may be used for testing convex hyperboloidal secondary mirrors. A difficulty in this approach, however, is that the auxiliary optics are often very large and difficult to fabricate. Moreover, this type of test arrangement is subject to environmental errors. 
     Recently CGHs have been used to measure optical surfaces or the wavefronts from the optical surfaces. The CGHs usually include patterns of lines which act as diffraction gratings. These patterns are usually written onto, or etched into glass substrates. The CGHs may be written with circular symmetry to preserve the rotational symmetry of most aspheric optics. The circular symmetry type of CGH disperses the diffraction orders along the axis, bringing them to a focus at different axial positions. See “Optical Shop Testing”, second edition, K. Creath and 3. C. Wyant, D. Malacara Ed. (Wiley, N.Y., 1992), pp. 602-612, for more discussion on CGHs. 
     SUMMARY OF THE INVENTION 
     To meet this and other needs, and in view of its purposes, the present invention provides an apparatus for testing an optical surface. The apparatus includes an array of holograms and the array further includes a plurality of individual holograms arranged in an M×N format, in which M is the number of rows and N is the number of columns in the array. The array of holograms is positioned between the optical surface and a wavefront sensor. The array of holograms reflects a reference beam back to the wavefront sensor, and transmits a test beam to the optical surface. The array of holograms also receives the test beam reflected from the optical surface and transfers the test beam back to the wavefront sensor. 
     The array of holograms may include length and width dimensions, and the length dimension may include M holograms of sufficient number to extend a radial dimension of the optical surface, and the width dimension may include N holograms, where N is at least two rows. In some embodiments of the present invention, each row in the array may be staggered with respect to each adjacent row, and a hologram in a first row may be positioned between two holograms in an adjacent second row and forming the stagger between the first and second row. 
     Each hologram of the array may include a layer having a pattern of arcs of a circle and a pattern of arcs in one hologram may be phased with a pattern of arcs in an adjacent hologram. 
     In some embodiments of the present invention, the wavefront sensor may emit a beam of light of a predetermined field-of-view (FOV) that may have a footprint area sized smaller than, or similar to an area formed by the array of holograms. A linear translational device may move the FOV of the beam across a radial extent of the optical surface, and a rotational device may rotate the optical surface. The translational device and the rotational device may be configured to position the FOV of the beam across an entire area of the optical surface. 
     In some embodiments of the present invention, each hologram of the array may include opposing surfaces, and a layer on one surface may include a pattern of arcs of a circle and a layer on the opposing surface may include a wedge for reducing ghosting effect. 
     In some embodiments of the present invention the apparatus may include a rigid frame having two ends. One end may include an M×N array of openings, in which each opening may be configured to receive an individual hologram in the array of holograms and another end may include at least one opening configured to receive a hologram having a pattern configured for alignment of the rigid frame to the optical surface. 
     Embodiments of the present invention also relate to a method for testing an optical surface. The steps of this method may include directing an incident beam from a wavefront sensor toward an array of holograms which may then illuminate at least a portion of the array of holograms. Another step of the method may include modifying the incident beam by the array of holograms to produce a reference beam and a test beam and then reflecting the reference beam from the array of holograms to the wavefront sensor. Finally, yet another step may include impinging the test beam on the optical surface and then reflecting the test beam back to the wavefront sensor. 
     Embodiments of the present invention further relate to an apparatus for testing an optical surface. The apparatus includes an array of holograms and the array includes a plurality of individual holograms arranged in a two-dimensional matrix format. An incident beam from a wavefront sensor is positioned above the array of holograms and illuminates at least a portion of the array. The array of holograms modifies the incident beam to a reference beam and reflects back the reference beam to the wavefront sensor. The array further modifies the incident beam to a test beam. The test beam impinges on the optical surface which is positioned below the array of holograms. 
     It is understood that the foregoing general description and the following detailed description are exemplary, but are not restrictive, of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention may be best understood from the following detailed description when read in connection with the accompanying figures, with like elements having the same reference numerals. When a plurality of similar elements are present, a single reference numeral may be assigned to the plurality of similar elements with a small letter designation referring to specific elements. When referring to the elements collectively, or to a non-specific one or more of the elements, the small letter designation may be dropped. The letter “n” may represent a non-specific number of elements. Also, lines without arrows connecting components may represent a bi-directional exchange between these components. According to common practice, the various features of the drawings are not drawn to the scale. Also, the dimensions of the various features are arbitrarily expanded or reduced for clarity. The figures are listed below: 
         FIG. 1   a  is a block diagram illustrating an embodiment of the present invention depicting a system for wavefront measurements. 
         FIG. 1   b  is a block diagram showing an embodiment of a test system including a planar phased holographic array testplate (PHAT) covering an entire optical test piece for wavefront measurements, in accordance, with an embodiment of the present invention. 
         FIG. 1   c  is a block diagram showing a zoomed-in view of a single CGH in an array of holograms, or a phased holographic array testplate (PHAT), in accordance with an embodiment of the present invention. 
         FIG. 1   d  is a bottom view of the single CGH shown in  FIG. 1   c , in accordance with an embodiment of the present invention. 
         FIG. 1   e  is a flow-chart of a method for performing test measurements on an optical test piece, in accordance with an embodiment of the present invention. 
         FIG. 2  is a block diagram depicting a side view of a sub-aperture test system, in accordance with an embodiment of the present invention. 
         FIG. 3  is a block diagram illustrating a test system having optional rotation and translation stages, in accordance with an embodiment of the present invention. 
         FIG. 4  is a block diagram illustrating a top-view of radial and rotational motions performed by a test system of the present invention. 
         FIG. 5  is a block diagram of a test system including a planar phased holographic array testplate (PHAT), in accordance with an embodiment of the present invention. 
         FIG. 6   a  is a block diagram of a test system including a non-planar PHAT disposed above a convex shaped optical test piece, in accordance with an embodiment of the present invention. 
         FIG. 6   b  is a block diagram of a test system including a non-planar PHAT disposed above a concave shaped optical test piece, in accordance with an embodiment of the present invention. 
         FIG. 7  is a block diagram of a test system including a phased PHAT having wedged CGHs, in accordance with an embodiment of the present invention. 
         FIG. 8  is a top view of a primary hologram including alignment holograms disposed above a mirror surface under test, in accordance with an embodiment of the present invention. 
         FIG. 9  is a block diagram illustrating a test system for testing optical systems using a PHAT. 
         FIG. 10   a  is a block diagram illustrating a calibration setup for calibrating a reference beam using a PHAT, in accordance with an embodiment of the present invention. 
         FIG. 10   b  is a block diagram illustrating a calibration setup for calibrating a test beam using a PHAT, in accordance with an embodiment of the present invention. 
         FIG. 11  is a block diagram illustrating a rigid frame for holding the holograms of a PHAT, in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The CGHs have been used for some time to measure optical surfaces or a wavefront from optical surfaces. Typically, a CGH converts a spherical wavefront to an aspheric wavefront (see Burge et al., Proc. of SPIE, vol. 2576, 1995 and U.S. Pat. No. 5,737,079). 
     One limitation of CGH related interferometry testing of optical surfaces is the high cost (or unavailability) of large CGHs. This is especially true for testing large convex aspheric surfaces. In most cases, the CGH needs to be located near the surface to be tested and a single CGH must have a size as large as the surface to be tested (see FIG. 13 of Burge et al., Proc. of SPIE, vol. 2576, 1995). For example, when testing a 3-meter convex curved mirror, it is conventional to have a single CGH that also has a 3-meter diameter. 
     The present invention advantageously overcomes the size limitation in holograms by employing an array of holograms, also referred to herein as a PHAT. The PHAT allows for testing of mirror apertures that are not limited by the availability and expense of single large holograms. The PHAT provides the functionality of a large hologram by using smaller holograms on each element of the array making up the PHAT. As will be explained, the spatial relationships amongst the holograms of the array are calibrated by the present invention to form one large hologram. The PHAT of the present invention, therefore, acts as a single large hologram. 
     The present invention includes different embodiments of test systems for wavefront or surface measurements of a mirror surface or any other optical surface. Test measurements may be performed using a PHAT including an array of CGHs that cover the entire optical test surface. In addition, test measurements may be performed by using a PHAT having an array of CGHs that cover a small portion of a test surface. As will be explained, by using sub-aperture techniques, combined with mechanical motions in the test system, a complete mapping of the optical test surface obtained by the present invention. Thus, the present invention is useful for testing large optics using individual CGHs that when arrayed form a larger CGH. As will also be explained, the present invention provides calibration techniques for calibrating a PHAT using different diffraction orders and also aligning a PHAT with an optical test surface, for example. 
     Referring first to  FIG. 1   a , there is shown a side-view of an embodiment of the present invention illustrating a test system  100  for measuring optical surfaces. The test system includes an interferometer  102 , an expander  104  (optional), a PHAT  106 , and an optics under test  108 , in which the latter is shown held in place by an optics holder  110 . Also shown in the figure are optional translation stage  118  and an optional rotational stage  112 . These elements are described below. 
     The interferometer  102  outputs an incident beam and gathers interferometry data using a reference beam and a test beam. The reference beam is reflected from PHAT  106  back to interferometer  102 , whereas the test beam is reflected from optical test piece  108 , through PHAT  106  and back to the interferometer. The interferometer  102  may be, for example, a commercial Fizeau interferometer, such as those manufactured by 4D Technologies and Zygo Inc. The interferometer may also include a camera. Yet as another example, interferometer  102  may be configured as a Twyman-Greene interferometer. Alternatively, interferometer  102  may be configured as a wavefront sensor, such as a Shack-Hartman, Phase Diverse Phase Retrieval Sensor (non-interferometer sensing technology). 
     It will be appreciated that in Fizeau interferometry, two reflecting surfaces are used to combine reflecting beams from these surfaces to form interference fringes. One of the reflecting surfaces is a reference surface and the other surface is a test surface. The fringes produced from the reflecting beams may be used to measure the shape of the optical test surface. The reference surface may be realized by a diffractive optical element, such as a CGH. The CGH, illuminated by a source of light, may produce a reflected beam, for example, which is used as the reference beam. On the other hand, a first order diffraction beam may be directed toward the test surface. The reflected beams from both surfaces combine to generate test data in the form of interference fringes which are processed to produce surface measurements of the test surface. 
     The incident beam output by interferometer  102  may be a collimated coherent light beam, for example. Optionally, beam expander  104 , which is disposed between the interferometer and the PHAT, may be an afocal relay (for example). The beam expander  104  may be used to increase the size of the collimated beam output from the interferometer. For example, beam expander  104  may increase the size of the collimated beam and illuminate only a portion of the PHAT or illuminate the entire array of CGHs in the PHAT, as shown in  FIG. 1   a.    
     The PHAT of the present invention is a one or two dimensional (2-D) array of diffractive elements that are formed by computer generated holograms (CGHs) and may be arranged in a matrix format, for example. The diffractive elements may also be randomly scattered, for example. The 2-D array may be planar, as shown in  FIGS. 1   a  and  1   b , or may be non-planar, as shown in  FIGS. 6   a  and  6   b . It will be understood, however, that each hologram, for example, CGH  106   a ,  106   b , etc., is a planar hologram that is used to form the array of holograms in PHAT  106  of  FIG. 1   a , or PHAT  606  in  FIG. 6   a , or PHAT  626  in  FIG. 6   b.    
     The holograms in the PHAT may be arranged in a regular grid, or alternatively, may be staggered. In one example, the PHAT in its entirety, or in a smaller portion, may be configured to bend a collimated wavefront, prior to the beam arriving at the optical test surface. Furthermore, the returning wavefront from the PHAT, prior to the beam arriving at the interferometer, may be used to provide a null wavefront. Generally, the null wavefront, also known as an aspheric wavefront is formed by a diffractive carrier. As detailed in Burge et al., Proc. of SPIE, vol. 2576, 1995, holograms are designed and manufactured with a carrier to isolate light in a desired order of diffraction, which are then passed through a spatial filter that blocks the other orders of diffraction. Most holograms use tilt, random encoding, straight lines, or power, as the carrier to fan out the orders of diffraction. Particularly, the power carrier is a type of hologram that includes a ring pattern which axially spreads out the orders of diffraction. In one example, a transmitted 1 st  order diffraction power carrier is used. 
     The optical test piece  108  may be held in position by optic holder  110 , as shown in  FIG. 1   a . The optic holder, which fixes the optical test piece  108 , may be coupled to an optional rotational stage  112 . The rotational stage  112  may be used to rotate optical test piece  108  about an axis of rotation, in a clockwise or counter-clockwise direction. The rotational motion of the optical test surface allows the array of holograms of PHAT  106  to cover an entire 360 degrees of the test surface. Furthermore, interferometer  102 , together with beam expander  104 , may be linearly translated in order to move the beam (formed by the interferometer and the beam expander) along a radial extent of the optical test surface. This linear translation may be performed by an optional translation stage  118 , shown in  FIG. 1   a.    
       FIG. 1   b  is a side view of another embodiment of the present invention depicting a test system  120 . As shown, diverger  103 , which is a part of beam expander  104  in  FIG. 1   a , focuses a collimated beam outputted from interferometer  102  at point  103   a , and then diverges and enlarges the beam. Collimating lens  105 , which is also part of beam expander  104 , collimates the diverged beam that is received from diverger  103 . The enlarged collimated beam from collimating lens  105  is then directed towards PHAT  106 . In another example, beam expander  104  illuminates only a portion of PHAT  106  (or as shown in  FIG. 2 , only a portion of PHAT  206  is illuminated). 
       FIG. 1   c  provides a side view of a single hologram, designated as  106   n , in the array of PHAT  106 . The hologram is comprised of a substrate  111  made of glass (for example). The bottom layer of the hologram includes a patterned layer  113 . For example, patterned layer  113  may include an etching of segments of circles  113   a , as shown in a top view of  FIG. 1   d . The segments, or arcs of circles are of a predetermined density, typically having a spacing between adjacent segments of 1 micron to 1 mm. The top portion of substrate  111  is shown wedged at a wedge angle  109 . The wedge angle helps reduce ghosting effects in the collimated beam. 
       FIG. 1   e  presents a flow diagram of a method  130  for testing an optical surface according to an embodiment of the present invention. The method  130  may be better understood by reference to  FIG. 1   b . The method begins at step  140  and directs an incident beam from interferometer  102  toward PHAT  106 . The system may include beam expander  104 , as shown in  FIG. 1   b , for expanding the incident beam. Alternatively, the incident beam may be directly output toward PHAT  106 . In that case, step  150  illuminates at least a portion of the array of holograms in PHAT  106 . For example, the portion may be a sub-section of the array. Alternatively, the illuminated beam may cover the entire array of PHAT  106 . 
     At step  160 , the method modifies the incident beam by using the array of PHAT  106  to form a reference beam and a test beam. The reference beam is the beam that is reflected back from the array of holograms, whereas the test beam impinges on optical test piece  108  and then is reflected back, through the array of holograms, toward the interferometer. The wavefront of the test beam may include an aspheric wavefront formed by a first order diffraction power carrier, as described earlier. 
     At step  170 , the reference beam is reflected from the array of PHAT  106  back to interferometer  102 . At step  180 , the test beam impinges onto and is reflected from optical test piece  108  back to interferometer  102 . Thus, both the reference and the test beams are modified by the array of holograms in PHAT  106 . Both beams share a common return path back to the interferometer. The reflected beams, therefore, interfere with each other and form interference fringes, thus generating test data. Measurements of the optical test surface may then be performed, by way of step  190 , using the interference fringe data. 
     It will be appreciated that the common optical path traversed by the test and reference beams is advantageous, because alignment errors and atmospheric effects on the test data are reduced. 
       FIG. 2  depicts a side view of a test system  200  in another embodiment of the present invention. The system  200  illustrates a test system which includes interferometer  102 , an optional beam expander  204 , PHAT  206  and optical test piece  108 , which is held in place by holder  110 . The array of holograms in PHAT  206  extends across the full radial extent  208  of optical test piece  108 . The test piece  108  has a radial center  210 . If the optical test piece includes an active or an operative reflection surface across the entire diameter of the optical surface, then PHAT  206  should preferably cover the entire radius of the optical surface including radial center  210 . The interferometer  102  and beam expander  204  are configured to cover at least a portion of the array of holograms in PHAT  206 , but need not cover the entire extent of the optical test piece. 
       FIG. 3  illustrates another test system  300  which includes a rotational stage  112  and a translation stage  118 , in addition to the components of test system  200  as shown in  FIG. 2 . The translation stage  118  is configured to allow interferometer  102  and beam expander  204  to have a radial translation along line  318 , in order to view the full radial extent of optical test piece  108  and the array of holograms in PHAT  206 . The array of holograms in PHAT  206  includes M×N holograms covering at least the radial extent of the optical test piece, spanning from the center of optical test piece  108  to the radial end of the active portion of the test piece. FIG. 3 only shows one row of holograms  206   a - 206   m . Additional rows are shown, for example, in  FIG. 4 , which includes six rows of holograms. It will be appreciated that the number of rows may be varied by the tester that may impact the sampling of the surface of the optical test piece, for example; the number of columns, however, is determined by the number of holograms required to span the full radial extent of the optical test piece (assuming that the optical test piece has an active reflection surface spanning across its entire diameter). In the example of  FIG. 3 , nine columns of holograms are required. 
     In operation, interferometer  102  and beam expander  206  may, for example, illuminate elements  206   a - 206   f  of the array of holograms which are a small portion of the entire array shown in  FIG. 3 . The optical test piece is then rotated by the rotational stage  112 , which is configured to rotate about the rotational axis  210 . The optical test piece  108  may rotate in a clockwise direction  328 , or in a counter-clockwise direction. 
     In order to test another portion of optical test piece  108 , interferometer  102  and beam expander  204  are translated to the right along the direction of line  318  by translator stage  118 . In this manner, the beam from beam expander  204  may illuminate holograms  206   d - 206   m  and, thereby cover the remaining portion along the radius of the optical test piece. Again, through rotation, the inner portion of the optical test piece is illuminated and tested. It will be appreciated that the linear translation may include an overlap, as described above, by first covering holograms  206   a - 206   f  and then covering holograms  206   d - 206   m  (for example). 
     The rotational motion  328  of test piece  108  and the translational motion  318  of interferometer  102  and beam expander  204  are combined by the present invention to perform a complete optical test surface measurement of test piece  108 , thereby completely mapping the entire active surface of the optical test piece. 
     Turning now to  FIG. 4 , there is shown a better view of the radial translation and the rotational motion provided by test system  300 . As shown, PHAT  206  is overlaid above optical test piece  108 . The PHAT includes N×M holograms that may be staggered, as shown. The beam emanating from expander  204  ( FIG. 3 ) has a circular footprint, or a field-of-view (FOV), designated as  410 . In the example shown, the PHAT includes 6 rows (N) and 9 staggered columns (M). It will be observed that the 9 columns extend the full radial extent of the optical test piece. Accordingly, as described before, the radial translation is provided by moving footprint  410  along the direction of line  318  and the rotational motion is provided by rotating the optical test piece in a clock-wise direction  328  (for example). 
     Generally, the holograms of the array are arranged two-dimensionally in a staggered grid, as shown. Each hologram in array  206  is fixed in space relative to its neighbors by placing each hologram in a rigid frame. An example of such a rigid frame is shown as frame  1108  in  FIG. 11 . The staggered arrangement of the holograms may provide improved data coverage of the optical test piece and improved phase information from the test data. 
     Although not shown, the holograms of a PHAT may be arranged in a non-staggered manner, in which the columns of one row line-up with the columns of an adjacent row. 
     In another embodiment of the present invention, a test system  500  is shown in  FIG. 5 . This embodiment is similar to test system  200  of  FIG. 2 , except for the beam expander having been replaced with a diverging lens  503 . Thus, a diverging incident beam impinges on PHAT  206 . The holographic pattern of the array in the PHAT may be configured to provide additional power (focus) to bend the light towards optical test piece  108 , as shown by rays  207   a,b . Another difference in test system  500  is that interferometer  102  is not perpendicular to the array of holograms, although in one example it may be perpendicular to the array of holograms. In this configuration, axial alignment of interferometer  102  with the optical test piece may be biased. 
       FIG. 6   a  depicts another embodiment of the present invention as test system  600   a . The diverging lens  603  diverges the incident beam onto the array of holograms, or PHAT  606 . The array is conformal to the shape of the optical test piece  608 . For example, as shown, the array of holograms  606  follows the spherical convex shape of optical test piece  108 . Although each hologram in the array is planar or flat, nevertheless, the array, as a whole conforms to the convex shape of the optical test piece. 
     Similarly, in another embodiment of the present invention, the array of holograms may be conformal to the surface of a concave optical test piece  628 . In such a scenario, the array of holograms  626  conforms to the shape of the optical test piece, as shown in  FIG. 6   b , although each hologram in the PHAT is planar or flat. 
       FIG. 7  depicts another embodiment of the present invention, in which a test system  700  includes holograms of PHAT  706 , in which each hologram has a wedge or is mated to a wedged lens that is angled at a predetermined slope. For example, at least two different sized wedges are shown in PHAT  706 . The inner holograms of the PHAT include a smaller angled wedge, than the angled wedges of the outer holograms, as shown. The rays may then be refracted to a near collimated state before they impinge on the diffracting surface of the holograms. It is contemplated that this configuration is similar to coupling the PHAT with a Fresnel lens. As shown in  FIG. 7 , the transmitted rays are configured to impinge on the convex surface of the optical test piece at a perpendicular (normal) angle to the convex surface. 
     Alternatively, the holograms of the PHAT may include other light bending surface profiles. For example, they may be aspheric or spherical and they may also be on one or both sides of each hologram in the array. The surface profiles facilitates bending of the incident beam toward the optical test surface, without a collimating lens (see  FIG. 1   b ), or without additional power in the array of holograms (see  FIG. 5 ), and may be advantageously lower in cost. 
       FIG. 8  is a top view of a complete holographic pattern  113  covering an optical test surface  802 . The hologram pattern  113  generates the different diffraction orders described earlier. In addition, holographic pattern  113  includes auxiliary patterns  804 , which may be used to align the optical surface to the holographic pattern. Moreover, coordinate measurement targets  806  (for example, cross hairs, retro-reflectors) may be used to pre-align the PHAT. Alternatively, coordinate measurement targets  806  may be used for locating test hardware with the aid of photogrammetry cameras or laser trackers. 
       FIG. 9  is another embodiment of the present invention depicting a test system  900 . The test system includes an interferometer  102 , a beam expander  904 , an array of holograms  906  and an optical system to test  908 . The optical system to test may be comprised of any optical assembly. The test may be carried out according to the method described in  FIG. 1   e , in which the test beam is reflected from the optical test system and detected by the interferometer. Alternatively, a test may be carried out where a detection is carried out in the optical system to test  908 , according to a variation of the method described in  FIG. 1   e.    
     Ideally each hologram in the PHAT is phased to each other hologram, such that the PHAT acts as a single large hologram. In addition, the PHAT is aligned to the test system. In practice, however, the alignment may be relaxed so long as the components in the test system are calibrated (as described below) by characterizing any residual alignment errors and fabrication errors. These errors may then processed out of the test data. 
     The array of holograms is calibrated for different orders of diffraction. For example, the array of holograms may be calibrated by characterizing the 0 th  order of diffraction for the reference beam. An example of a calibration system is shown in  FIG. 10   a , identified as system  1000 . The system  1000  includes an interferometer  102 , a beam expander  1004 , an array of holograms  1006  and an optical flat  1001 . As described before, for example, Fizeau interferometry may be implemented for calibration and the calibration data may be detected by the interferometer. This may provide a calibration of the reference surface of the PHAT. 
     The diffracted aspheric wavefront of the PHAT may also be calibrated. The aspheric wavefronts may be characterized in a diffraction order other than the one that is used for testing the optical test piece. For example, a test system may be designed for a first order diffraction. However, the calibration may be performed for a second order diffraction, as the various diffraction orders are quantifiably related. 
     As shown in  FIG. 10   b , a test system  1010  includes an interferometer  102 , a diverging lens  1014 , an array of holograms  1006  and an aspheric corrector  1012 . The aspheric corrector may be required in the calibration test, because the wavefront may have substantial asphericity. The calibration data from the two aforementioned calibration configurations may be combined and used in the calculation of the test data obtained from an optical device under test. 
       FIG. 11  shows an example of a rigid frame for holding each hologram of a PHAT. For example, the rigid frame includes an M×N openings for receiving the M×N holograms of the PHAT. In addition, the alignment marks  1110 , as shown in  FIG. 11 , may be used to align the PHAT with an axial center of an optical test piece (for example). As such, frame  1108  covers a portion of an optical test piece (not shown) as it extends from the axial center of the optical test piece to a radial portion of the optical test piece (covered by the M×N holograms). 
     Although the present invention is illustrated and described herein with reference to specific embodiments, the invention is not intended to be limited to the details shown. Rather, various modifications may be made in the details within the scope and range of equivalents of the claims and without departing from the invention.