A NEW INSTRUMENT FOR ROUTINE OPTICAL TESTING OF GENERAL ASPHERICS

Transcription

1 A NEW INSTRUMENT FOR ROUTINE OPTICAL TESTING OF GENERAL ASPHERICS A NEW INSTRUMENT FOR ROUTINE OPTICAL TESTING OF GENERAL ASPHERICS Peter M. Emmel Tropel c. Fairport, New York and Kang M. Leung Honeywell Corporate Materials Sciences Center Bloomington, Minnesota Peter M. Emmel Tropel c. Fairport, New York and Kang M. Leung Honeywell Corporate Materials Sciences Center Bloomington, Minnesota Abstract Abstract A unique and versatile laser interferometer has been jointly developed by Honeywell, Tropel and University of Arizona. The system is designed for routine non-contact testing of aspheric optical surfaces (using a Computer-Generated Hologram [CGH] to provide aspheric component of reference wavefront) while retaining features and capabilities of standard Tropel Vertical terferometer. Thus it is capable of measuring radius and/or optical figure of spheres, flats, conies and general aspherics. The instrument provides convenient interchangeability among Fizeau, Twyman-Green, CGH and Lateral Shearing modes of operation in a single compact unit. It is also capable of direct interfacing with a computer for wavefront measurement or analysis. The operation of system is described and data is presented from a CGH test of an f/2 paraboloid (using a spherical test wavefront) for which independent comparative data is also given. A unique and versatile laser interferometer has been jointly developed by Honeywell, Tropel and University of Arizona. The system is designed for routine non -contact testing of aspheric optical surfaces (using a Computer- Generated Hologram [CGH] to provide aspheric component of reference wavefront) while retaining features and capabilities of standard Tropel Vertical terferometer. Thus it is capable of measuring radius and /or optical figure of spheres, flats, conics and general aspherics. The instrument provides convenient interchangeability among Fizeau, Twyman- Green, CGH and Lateral Shearing modes of operation in a single compact unit. It is also capable of direct interfacing with a computer for wavefront measurement or analysis. The operation of system is described and data is presented from a CGH test of an f/2 paraboloid (using a spherical test wavefront) for which independent comparative data is also given. troduction troduction Precision lens molding and, more recently, ultraprecision machining techniques are narrowing gap in production costs between spherical and non-spherical optical surfaces. deed, from fabrication standpoint, in eir of se technologies, re is little difference between making a sphere and making an asphere. However, when it comes to measuring surface figure, aspherics have always posed serious problems. The rapid commercialization of aspheric manufacturing technology requires a corresponding development in measurement capability. Precision lens molding and, more recently, ultraprecision machining techniques are narrowing gap in production costs between spherical and non -spherical optical surfaces. deed, from fabrication standpoint, in eir of se technologies, re is little difference between making a sphere and making an asphere. However, when it comes to measuring surface figure, aspherics have always posed serious problems. The rapid commercialization of aspheric manufacturing technology requires a corresponding development in measurement capability. terferometric equipment for non-contact testing of various optical surfaces has been in use for many years. However, with a few exceptions, commercially available instruments have been limited to testing of flats and concave spheres. The exceptions are those offering a variety of focusing lenses, with reasonably large apertures, for testing a useful range of convex spheres. Using simple auxilliary optics, most available instruments can also test conic surfaces such as paraboloids, ellipsoids and hyperboloids. General aspherics, however, with more than a few waves departure from nearest conic, usually exceed capability of se instruments to even view, let alone accurately measure. terferometric equipment for non -contact testing of various optical surfaces has been in use for many years. However, with a few exceptions, commercially available instruments have been limited to testing of flats and concave spheres. The exceptions are those offering a variety of focusing lenses, with reasonably large apertures, for testing a useful range of convex spheres. Using simple auxilliary optics, most available instruments can also test conic surfaces such as paraboloids, ellipsoids and hyperboloids. General aspherics, however, with more than a few waves departure from nearest conic, usually exceed capability of se instruments to even view, let alone accurately measure. The literature contains many laboratory setups for overcoming difficulties in testing aspherics.(1>2) The most promising are those using holographic techniques to generate a reference wavefront which matches wavefront reflected by aspheric test surface.'-^) The resulting interference fringes are interpreted in same way as those in conventional two-beam interferometers. The literature contains many laboratory setups for overcoming difficulties in testing aspherics.(1,2) The most promising are those using holographic techniques to generate a reference wavefront which matches wavefront reflected by aspheric test surface.(3) The resulting interference fringes are interpreted in same way as those in conventional two -beam interferometers. Anor method for testing aspherics is lateral wavefront shearing, where test beam is divided into two identical beams with a slight lateral displacement, terference between se displaced beams produces a fringe pattern which, for small displacements, is directly related to slope of wavefront, but only indirectly related to its total depth. Obtaining accurate depth information from such a fringe pattern requires numerical analysis best performed by a computer.(4) Anor method for testing aspherics is lateral wavefront shearing, where test beam is divided into two identical beams with a slight lateral displacement. terference between se displaced beams produces a fringe pattern which, for small displacements, is directly related to slope of wavefront, but only indirectly related to its total depth. Obtaining accurate depth information from such a fringe pattern requires numerical analysis best performed by a computer.(4) This paper describes implementation of both of se techniques - holography and shearing - in a commercially oriented laser interferometer, thus adding aspherics to its or surface testing capabilities. The interferometer was developed jointly by Honeywell, Tropel and University of Arizona. The intent was to provide a single instrument versatile enough to satisfy needs of several groups for a convenient interferometric means of testing a variety of optical materials and surfaces including aspherics. Since se groups were engaged in developing various production technologies, system had to be practical in routine production-level use where ease of setup and adjustment are key factors. It was also intended to be adaptable to possible future needs, such as real-time holography and direct computer interfacing. This paper describes implementation of both of se techniques - holography and shearing - in a commercially oriented laser interferometer, thus adding aspherics to its or surface testing capabilities. The interferometer was developed jointly by Honeywell, Tropel and University of Arizona. The intent was to provide a single instrument versatile enough to satisfy needs of several groups for a convenient interferometric means of testing a variety of optical materials and surfaces including aspherics. Since se groups were engaged in developing various production technologies, system had to be practical in routine production -level use where ease of setup and adjustment are key factors. It was also intended to be adaptable to possible future needs, such as real -time holography and direct computer interfacing. SPIE Vol. 171 Optical Components: Manufacture & Evaluation (1979) / 93 SPIE Vol. 171 Optical Components: Manufacture & Evaluation (1979) / 93

2 EMMEL, LEUNG The Tropel Model 4000 was chosen as a starting point because of its convenient vertical test beam and its Fizeau testing capability for flats, spheres and conics. conies. The internal layout of Model 4000 along with its single-frequency HeNe laser and its relatively small internal beam diameter, all proved to be particularly advantageous. The interferometer design was modified to allow use of of computer-generated holograms (CGH) and lateral wavefront shearing for testing of known and unknown aspherics having up to several hundred waves departure from nearest sphere. The design also permits gener- gener ation of real-time holograms in cases where a master aspheric surface is available. The range of radius and figure measurement was extended to 450mm and a motor drive was added to vertical slide. All or features of standard interferometer were retained. Several additional features were necessary in order to implement CGH mode of opera opera- tion. The most important of se was that a real image of test surface had to be pro pro- jected onto hologram plane. Failure to satisfy this condition causes systematic measurement errors which increase in proportion to asphericity of surface under test. Accuracy was maintained over full range of radii by providing variable (stepwise) magnification and independent focusing between test surface and hologram plane. System Description The system is essentially a two-beam interferometer with its test and reference beams separated according to ir polarization states. order to minimize system wavefront deformation and maximize repeatability, system was designed so that all lenses are used on-axis. To achieve efficient use of light, polarizing beam splitters are used with quarter-wave retardation plates appropriately located to obtain desired beam paths, as shown in figure 1. VERTICAL SLIDE TEST PC POSITION LASER TILT STAGE Lam_ ATTACHMENT FOCUSSING LENS BEAM EXPANDER,-BEAM EXPANDER RETRORE F L ECTION MIRROR TV CAMERA VARIABLE BEAM >- EXPANDER 6" TRAVEL--7 TEST BEAM RELAY- RELAY^ CALCITE SHEARING PLATE POLARIZER SPATIAL FILTER HOLOGRAM RELAY -HOLOGRAM PLATE a--hw ADJ ARM \`RM -I RM-2' SHUTTER Figure 1, 1. System Schematic 94 / SPIE Vol. 171 Optical Components: Manufacture & 8- Evaluation (1979)

3 A NEW INSTRUMENT FOR ROUTINE OPTICAL TESTING OF GENERAL ASPHERICS A NEW INSTRUMENT FOR ROUTINE OPTICAE TESTING OF GENERAE ASPHERICS The layout is best described by identifying its five "arms": source arm, test arm, relay arm, reference arm, and viewing arm. source arm linearly polarized beam is expanded and collimated. Its plane of polarization is rotated according to half-wave plate (HW) adjustment. The first polarizing beamsplitter (BS-1) reflects S-polarized component, which becomes reference beam, and transmits P-polarized component, which becomes test beam. Quarter-wave plates (QW), located in test and relay arms, control polarization of test beam and thus determine wher it is transmitted or reflected on each succeeding encounter with BS-1. The layout is best described by identifying its five "arms ": source arm, test arm, relay arm, reference arm, and viewing arm. source arm linearly polarized beam is expanded and collimated. Its plane of polarization is rotated according to half -wave plate (HW) adjustment. The first polarizing beamsplitter (BS -1) reflects S- polarized component, which becomes reference beam, and transmits P- polarized component, which becomes test beam. Quarter -wave plates (QW), located in test and relay arms, control polarization of test beam and thus determine wher it is transmitted or reflected on each succeeding encounter with BS -1. The vertically oriented test arm consists of a series of interchangeable beam expanding and focusing lenses. A particular combination is chosen to provide an appropriate spherical (or plane) wavefront to nearly match test surface. The test surface, positioned for best "fit" to this wavefront, reflects beam back through test arm optics. Any mismatch between test surface and illuminating wavefront is captured as a deformation of returning wavefront. Three beam sizes may be selected by adjusting variable beam expander, which also varies viewing magnification. The vertically oriented test arm consists of a series of interchangeable beam expanding and focusing lenses. A particular combination is chosen to provide an appropriate spherical (or plane) wavefront to nearly match test surface. The test surface, positioned for best "fit" to this wavefront, reflects beam back through test arm optics. Any mismatch between test surface and illuminating wavefront is captured as a deformation of returning wavefront. Three beam sizes may be selected by adjusting variable beam expander, which also varies viewing magnification. The returning test beam is reflected by BS-1 and enters relay arm. The relay is a retroreflector consisting of a lens with a plane mirror located at its focus. It reflects a real image of test surface back through beamsplitter toward hologram in viewing arm. The relay is adjusted along its track to bring test surface into sharp focus at hologram plane, without affecting its magnification. The returning test beam is reflected by BS -1 and enters relay arm. The relay is a retroreflector consisting of a lens with a plane mirror located at its focus. It reflects a real image of test surface back through beamsplitter toward hologram in viewing arm. The relay is adjusted along its track to bring test surface into sharp focus at hologram plane, without affecting its magnification. space between two beamsplitters test and reference beams are recombined, but y are still orthogonally polarized. They are separated by second beamsplitter (BS-2), which transmits reference beam and reflects test beam along axis of viewing arm. The viewing arm contains hologram, a second relay lens and a closed circuit television camera. Figure 2 gives a more detailed view of reference and viewing arms of interferometer. The path of reference beam is determined by two sets of quarter-wave plates and adjustable plane mirrors (RM-1 and RM-2). Adjustment of mirrors gives necessary reference beam angle at hologram. space between two beamsplitters test and reference beams are recombined, but y are still orthogonally polarized. They are separated by second beamsplitter (BS -2), which transmits reference beam and reflects test beam along axis of viewing arm. The viewing arm contains hologram, a second relay lens and a closed circuit television camera. Figure 2 gives a more detailed view of reference and viewing arms of interferometer. The path of reference beam is determined by two sets of quarter -wave plates and adjustable plane mirrors (RM -1 and RM -2). Adjustment of mirrors gives necessary reference beam angle at hologram. ZERO-ORDER REF ZERO -ORDER REF T -VIDICON i(.analyzer VIDICON ANALYZER (SPATIAL FILTER SPATIAL FILTER AZERO-ORDER TEST 8c FIRST-ORDER REF ZERO-ORDER TEST FIRST-ORDER REF COMBINED TEST AND REF BEAMS -C COMBINED TEST AND REF BEAMS -HOLOGRAM RELAY LENS II HOLOGRAM BS-2 QW ty. QWRM-I BS-2 QW Figure 2. ^-HOLOGRAM RELAY LENS COMPUTER GENERATED ^-COMPUTER GENERATED ' HOLOGRAM RM-2 RM-2 Figure 2. Viewing Arm Schematic Viewing Arm Schematic SPIE Vol. 171 Optical Components: Manufacture & Evaluation (1979) / 95 SPIE Vol. 171 Optical Components: Manufacture 8- Evaluation (1979) / 95

4 EMMEL, LEUNG EEUNG The hologram itself is a fringe pattern, up to 14mm 14nun diameter, plotted from a computer raytrace of complete interferometer system and recorded on film. Some of energy in test and reference beams is diffracted by hologram into plus and minus first-order beams. These are brought to focus, along with zero-order beams, on a white pinhole plate (spatial filter) where y are easily viewed. When reference beam is properly adjusted, first-order reference and zero-order test beams are superimposed. The pinhole is adjusted to block all but se two beams. The TV camera is located behind pinhole, at image of hologram. A rotatable linear analyzer is mounted on front of camera with its axis oriented at This allows two beams to form visible interference fringes which are displayed on video monitor. These fringes are interpreted as ordinary Twyman-Green fringes, showing con con- tour of any mismatch between test surface and desired figure "encoded" in hologram. The accuracy of this testing technique is limited mainly by geometric accuracy of hologram and is currently estimated to be within 1% of total aspheri- city for any particular surface. A surface whose asphericity exceeds limit for CGH testing (currently about 300 waves per radius slope) may be measured by lateral wavefront shearing. To do this, reference beam is blocked by closing shutter, and a calcite block is installed in viewing arm ahead of hologram relay lens. Proper adjustment of analyzer gives lateral shearing fringes which can be digitized for computer analysis. The shear distance is measured by inserting a reticle in hologram holder and measuring separation of its double images. Flat or spherical surfaces require neir a hologram nor a shearing block, and are generally tested in Fizeau mode. this case reference arm is again blocked and appropriate Fizeau reference attachment is installed in test arm. The top surface of such an attachment is a partial reflector polished to an extremely accurate flat or spherical figure. The fraction of beam reflected by this surface becomes refer- reference beam. Since it follows essentially same path as does test beam, system wave- - front deformations do not show up in observed fringe pattern. The accuracy of this test is 1/10 wave or or better, but its range is limited to surfaces within a few waves of being flat or spherical. If a suitable high quality auxilliary mirror is used, conic surfaces may also be tested in Fizeau mode. Aspheric Surface Test This has been an extremely brief discussion of interferometer. A case history will serve to better illustrate use of instrument to test a particular aspheric surface. A 4-inch diameter f/2 paraboloid was chosen because it is a conic and could be relatively easily fabricated and independently tested for comparison. The surface equation for test surface (parabola) was entered into raytrace program along with optical design data for interferometer system. For this particular surface f f/1.8 setting of variable beam expander was used. The program found best position for surface in test beam and calculated fringe pattern that would be produced at hologram plane if test beam were interfered with a plane reference beam at a particular nonzero incidence angle. The incidence angle was chosen to be about three times maximum slope angle of test wavefront, so that diffracted orders would be sufficiently separated at pinhole. This fringe pattern was output in form of plotter commands on magnetic tape. The tape was n transferred to a Dicomed Digital Image Recorder which plotted pattern on a high resolution, low distortion CRT and recorded it it on on 35mm 35mm Plus Plus-X film. This image was n rephotographed on Kodak SO at correct magnification to give a 14mm pattern at full beam diameter using a fiducial mark. The resulting negative was bleached to enhance its diffraction efficiency. After installing appropriate test arm lenses (125mm diameter f/1 in this case) and checking alignment of interferometer, test surface was installed and adjusted to correct position as specified by computer raytrace. The relay was adjusted for a sharp image of test surface and hologram was installed. The reference beam was adjusted to superimpose proper orders at pinhole and obtain a fringe pattern on monitor. Fine adjustment of hologram centration and reference beam tilt resulted in best "fit" leaving a fringe pattern, shown in figure 3c, representing residual error in parabola. Figures3a,b illustrate asphericity of test surface by showing Twyman-Green fringe patterns produced independently by surface (in-position on interferometer) and by hologram alone. The "asphericity" measured in this example was actually difference between parabolic test surface and spherical test wavefront illuminating it. Thus, hologram removed about 40 waves of spherical aberration and defocus from fringe pattern, allowing residual figure error to be accurately measured. Digitization of lower fringe pattern showed an rms surface deviation of 0.03 waves and a peak-to- 96 I / SPIE Vol. 171 Optical Components: Manufacture 8 & Evaluation (1979)

5 ASPHERICS GENERAL ASPHERICS OFGENERAL TESTINGOF OPTICALTESTING ROUTINE OPTICAL FOR ROUTINE INSTRUMENTFOR NEW INSTRUMENT A NEW at test was ation test valley depth of 0.15 waves. independent autocollim waves. An An independent autocollimation was made made at valley depth flat a precision and a interferometer and University of of Arizona Arizona using using aa different different interferometer precision optical optical flat. University interf^rothis of on The in interferogram from this Digitizati 4 ' Digitization f±gure 4. of this interferoin figure Sh Wn in 1S shown tsst is thls test gram shows waves rms and 0.17 waves -to- valley agreeing with with CGH CGH results results "«* agreeing *»*-*> W peak a^ave!' within a few hundredths of a wave. Figure 3a Figure 3b Figure 3b 3c Figure 3c 4" Dia. Dia. F/2 F/2 Parabola 4" gram en terf'ero Twyman -Green terferogram Twyman-Gre Wavefront Diffracted by enerated Hologram ComputerHologram Computer-GGenerated F/2 perfect F/2 To Simulate perfect Parabola and Compensate Error strumental strumental Error F/2 F/2 of CGH Test of Parabola is: Deviation is: Surface Deviation ( &) RMS (63288) 0.03 waves wave s RMS waves PP-V 0.15 waves -V Figure 44 F/2 of F/2 Test of ation Test Autocollim Autocollimation Parabola is: Deviation, is: Surface Deviation RMS waves RMS 0. waves PP-V waves -V {J979I // Evaluation (1979) SPIE Vol. Vol. 171 Optical Components: Components: Manufacture Manufacture & 8 Evaluation 171 Optical SPiE 97 97

6 EMMEL, LEUNG EMMEL, LEUNG also tested tested in shearing shearing mode. mode. terferograms were taken taken with The paraboloid was also terferograms shear shear in in orthogonal directions, directions, as as shown shown in in figure figure Aberration ory ory predicts predicts waves of of spherical waves spherical aberration for for this this setup. setup. For shearing and and For comparison both shearing Twyman-Green respectivetwyman -Greeninterferograms interferograms were were measured, measured, giving giving values values of of and and waves waves respectively. It was fine fringe fringe spacing spacing that that hampered aspheric It was extremely extremely fine hampered measurement of aspheric Twyman-Green Twyman -Greenfringe fringe patterns patterns and and led led us us to to seek seek better better ways ways of of testing testing aspherics aspherics in first place. place. lateral lateral shearing shearing technique technique this this problem is is controlled because fringe fringe spacing spacing is is partially partially aa function function of of shear shear distance, distance, which which can can be be varied. varied. The CGH ique comp1e te1y e1imin a t e s rob1em for for aspherics a few hundred waves. waves. CGH techn technique completely eliminates pproblem aspherics up up to to a Figure 5a 5a Figure 5b terferogram Lateral Shearing terferogram Calclte Block to test Using Calcite F/2 Parabola Lateral Lateral Shearing terferogram (Calclte Block Block Rotated Rotated9090 ) (Calcite ) These comparative results confirm confirm soundness soundness of techniques techniques and and quality quality of of These equipment. Anor very important important comparison comparison is is time time required required to to obtain obtain results results in in each of se modes. all all cases cases setup setup and adjustment adjustment of of interferometer was was straightforward and convenient. convenient. terms terms of turnaround time time from scratch for for testing testing a new took by far longest because time required for for calnew surface, surface, CGH CGH mode mode took by far because of of Howculating hologram (a (a matter days with present arrangements). arrangements). culating and and making making matter of of days with ever, fringe fringe pattern a few few minutes. ever, once once hologram was was ready, ready, pattern was was observed in minutes. If several of available, y y could several of parabolas parabolas had had been been available, could all all have have been measured, measured, using same hologram, period, comparable comparable with with any any or or productionproduction-oriented inte.rfe.rosame hologram, in a time period oriented interferometer. me t e r. I n oorder r de r to obtain ob t a in comparable c omp a r able results, r e s u 11 s, both bo t h t h e Twyman Twy m a n --Green Green (when (wh e n. fringes f r i n ge s are are resolvable) and shearing shearing modes modes require require fringe digitization and data reduction for resolvable) and fringe digitization for each surface tested. tested. Clearly CGH mode is preferable for for situations situations where several several nominally identical surfaces to be shearing is Is most practical for occasional occasional or identical surfaces are are to be measured, measured, while while shearing one of a kind surfaces. surfaces. Furr Considerations There ways in which CGH turnaround time could be drastically There are are a a few ways drastically reduced. reduced. At various operations operations are are not notall allinin-house. Under roof, turnaround moment moment various house. Under one one roof, time Even shorter be realized if time could be less less than than hours. hours. Even shorter times times could be if hologram were exposed exposed directly directly from mag tape tape onto onto This were from mag final final film film (or (or rmoplastic). rmoplastic). This is within ccapability a pab11i ty of a (hopefully) (hopefully) growing grow g number numbe r of of XX-Y -Y laser beam be am recorders. re c or de rs. If required, re re are are If aa quantitative, quantitative analysis analysis of of residual residual fringe fringe pattern pattern Is is required, two sophisticated techniques currently currently in in use. use. One One of m is is fringe fringe digitization, digitization, in in two which intersections of fringes fringes in in. a particular interferogram terferogram with aa. set set of of parallel, parallel, equally supplied to to computer computer for for curve curve fitting fitting or or or or analysis. analysis. equally spaced lines are supplied The least least tedious tedious way way of of getting getting this this fringe data into into computer computer is The fringe data is to let computer computer help by using an interactive video terminal with software that can find find most of fringes fringes for itself. The technique is is direct phase interthe or or analysis analysis technique phase measurement, measurement, in which interferometer -based System ferometer is is connected directly to to computer. computer. Tropel's minicomputer minicomputer-based System 70, 70, for of over over interferograms interferograms during during its its 66-second for example, example, measures measures equivalent of second data data 98 SP/E Vol. Vol Optical Optical Components: Components: Manufacture Manufacture &8-Evaluation Evaluation(1979) { // SPIE

7 A NEW INSTRUMENT FOR ROUTINE OPTICAL TESTING OF GENERAL ASPHERICS A NEW INSTRUMENT FOR ROUTINE OPTICAL TESTING OF GENERAL ASPHERICS taking period and has wavefront data (32 X 32 grid) available for analysis or redisplay in less than one minute. This gives it a very high signal to noise factor and tends to eliminate transient effects which are often "frozen" in a single interferogram. taking period and has wavefront data (32 X 32 grid) available for analysis or redisplay in less than one minute. This gives it a very high signal to noise factor and tends to eliminate transient effects which are often "frozen" in a single interferogram. It is not hard to visualize interferometer, CGH recorder, and keyboard, all connected to computer, with access to software for ray tracing, CGH calculation and wavefront analysis. When one considers eauipment that is now being developed for fabricating precision aspherics, a surface measurement system like this is clearly an essential, independent measurement tool compatible with machine control systems in both accuracy and data format. It is not hard to visualize interferometer, CGH recorder, and keyboard, all connected to computer, with access to software for ray tracing, CGH calculation and wavefront analysis. When one considers eauipment that is now being developed for fabricating precision aspherics, a surface measurement system like this is clearly an essential, independent measurement tool compatible with machine control systems in both accuracy and data format. Acknowledgement Acknowledgement The authors wish to acknowledge valuable personal assistance of Dr. James C. Wyant, at University of Arizona's Optical Sciences Center. His work in field of aspheric surface testing formed basis for design of instrument we describe. The authors wish to acknowledge valuable personal assistance of Dr. James C. Wyant, at University of Arizona's Optical Sciences Center. His work in field of aspheric surface testing formed basis for design of instrument we describe. References References 1. Polster, H. D., et al, "New Developments in terferometry", Applied Optics, Vol. 8, pp Wyant, J. C., "Testing" Aspherics Using Two-Wavelength Holography", Applied Optics, Vol. 10, pp MacGovern A. J., and J. C. Wyant, "Computer Generated Holograms for Testing Optical Elements", Applied Optics, Vol. 10, pp Rimmer, M. P., and J. C. Wyant, "Evaluation of Large Aberration Using a Lateral- Shear terferometer Having Variable Shear", Applied Optics, Vol. 14, pp Polster, H. D., et al, "New Developments in terferometry", Applied Optics, Vol. 8, pp Wyant, J. C., "Testing Aspherics Using Two- Wavelength Holography ", Applied Optics, Vol. 10, pp MacGovern A. J., and J. C. Wyant, "Computer Generated Holograms for Testing Optical Elements ", Applied Optics, Vol. 10, pp Rimmer, M. P., and J. C. Wyant, "Evaluation of Large Aberration Using a Lateral - Shear terferometer Having Variable Shear ", Applied Optics, Vol. 14, pp SPIE Vol. 171 Optical Components: Manufacture & Evaluation (1979) / 99 SPIE Vol. 171 Optical Components: Manufacture 8- Evaluation (1979) I 99