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a new technique for testing large opticl flat A NEW TECHNIQUE FOR TESTING LARGE OPTICAL FLAT Qing Wang, Jinbang Chen, Rihong Zhu, Lei Chen, Yiguang Zhang Department of Photoelectronics Nanjing University of Science & Techno1ogyD, Xiaolingwei 200, Nanjing, P.R.China LABSTRACTI This paper developed a n...

a new technique for testing large opticl flat
A NEW TECHNIQUE FOR TESTING LARGE OPTICAL FLAT Qing Wang, Jinbang Chen, Rihong Zhu, Lei Chen, Yiguang Zhang Department of Photoelectronics Nanjing University of Science & Techno1ogyD, Xiaolingwei 200, Nanjing, P.R.China LABSTRACTI This paper developed a new technique (including theory, methed and equipment etc. )for testing larger optical flat only by means of a smaller interferometer. That is Overlapping Subaperture Interference Testing ( OSIT ) technique. Author had established a mathematics model for OSIT to retrieve surface of full aperture. The theoretical accuracy of retrieved sur- face of full apertrue reached 2 / 200( p— v) . The relationship between accuracy of retrieved wavefront of full apertrue and errors (such as system error of interferometer or position error of subapertrues etc.) had been investigated. A computer program was established to simulate the real procedure from testing surface data of subapertrue to retrieved wavefront of full apertrue. The limit of expanding apertrue was discussed and it's less than 2.5—times old apreture of interferomter with the accracy of retrieved wavefront of full apertrue better than 0.05 wave- length (p— v) at the same time. Author successfully applied OSIT technique to a " phase shift- ing digital flat interferometer " and expanded the testing apertrue from 250mm to 500mm with the accuracy in expanding apertrue better than A 120 (p—v). 1. INTRODUCTION To test an optical flat of larger aperture by a smaller reference standard flat is the general method used in optical workshop. Simular to other two methods ( the spherical—wavefront interferometer test and knife —edge test), the accuracy of these methods is only qualitative and it depends on the experience of the tester, So that the method isn't appliable in moden high accu- racy optical test. In generally, to test an optical flat , we need an interferometer with similar dimension to the tested flat at least. But if the optical flat is larger than 3OOmm, the test is dif- ficult, because the ordinary interferometer is too small to test such large falt. The interferomet- er only test a smaller subaperture in the large optical flat each time. thus, we have developed a technique to deduce the measuring interferograms of subapertures which is measured respectively and used to retrieve the wavefront of allaperture. that is Overlapping Subaperture Interference Testing(OSIT) Techniques. It is the quantity test and used widely. cDOriginal name: East China Institue of Technology O-8194-1252-X/93/$6.OO SPIE Vol. 2003 Interferometry VI (1993) / 389 Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms 2.PRINCIPLE The conception subaperture,introduced by W.Chow and G. lawrance is used to solve the problem of measuring a large optical system"2. Where the reference flat is replaced by an array of smaller optical mirrors called subapertures. they separate from each other, the processes of measuring are finished at the same time. Reversedly,the subapertures,used in the OSIT measurement, are the parts of the same test- ed flat and overlap in part. They are tested by interferometer respectivly ( as shown in fig.l, where S is the number of subaperture). The overlap is important in two reasons : One is that the subapertures can cover the most areas of the tested flat in order to reduce the error which is caused by the omit area. The other is that the OSIT measurement needs the part of overlap be- tween one subaperture and another to determine and eliminate the relative piston and tilts in order to unify the data of two subapertures. Fig.1 Subapertures spread Suppose that the same subaperture of a flat is measured two times by useing a Phase Digital interferometer, so the overlapping scope full of measuring aperture. The optical path difference data D1[X,Y] and D2[X,Y] (n = I ,2,'.,N) can be obtained by this two measurements.Where D1(i = 1,2) is the optical path difference at point(X,Y) and N is the total sample points in each measurement. It is obvious that D1is different from D2in two measurements,because the relative position and tilts between the reference standard flat and tested flat are changed(as shown in fig.2),but the surface shape of tested flat is not changed. The function W(X,Y) of optimum fit- ting surface can be found by the lest—square algorithm: = 1=1,2 (1) Where the function W1(x,y) of the optimum fitting surface is formed by 390 I SPIE Vol. 2003 lnterferometry VI (1993) tested &urfrce overlapping rc Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms w (X, Y) = P + T, • X+ T, • Y i = I ,2 (2) Where i is the order of measurment, P is piston, This X—tilt and Tis y—tilt. By this time, a group of parameters (P1,T1, T1) can be obtained and suited to every data of measurement. tetlflg aperture: I reference 8urface 1 subapertu're i I reference Burface 2 I subeperture 2 ; tested surface fitting surface , (a) two measurements (b) two measurements in same subaperture in diferent subapertures Fig.2 The change ofreference surface When the piston and tilts are eliminated from each datum,the results of the tested wavefront are equal: D1[X,Y]— W1(X,Y)=D2[X,Y]— W2(X,Y) n= l,2,'••,N (3) Eq.3 means that the relative change of the optimum fitting surface can be used to substitute for the relative change of the tested wavefront in two measurements: AW(X,Y)=W2(X,Y)— W1(X,Y) (4) where the AW(X,Y) is the relative change wavefront AW(X,Y)=AP +AT • X+AT • Y (5) where the AP,AT4Tis the coefficients of piston and tilts. During the OSIT experiments, the overlapping scope is reduced, because the 2th subaperture substiutes for the frist one in the second measurement, and only the part of subapertures overlaped. But if the errors is ignored, two wavefront configurations which are part of the overlapping area are also similar in two measurements. Therefore the previous meth- od can be used in the processs of OSIT measurement, and it means that the relative change of the optimum fitting surface in the overlapping area can be substiuted for the change of the test- ed flat in two subapertures measurments. Frist at all, the data of subapertures need to be processed simply by unifying in the same plane coordinate, then by useing equation(1) , the optimum fitting surfaces can be obtained by two group of data in their overlapping areas: SPIE Vol. 2003 Interferometry VI (1993)! 391 Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms 1 =(W(X,Y ) — Di[XmYm 3)2 1,2 (6) Where Mis the total sample points of ith subaperture in its overlap area, and the function W.(X,Y) of the optimum fitting surface are formed by equition(2). The coefficients(Pi,Txi,Tyi) of Wi(X,Y) can be obtained by miminizing o. Because x and y are free variations , the relative change coefficients of the reference standard flat AW(x,y) can be obtained by the following three equations: AP=P2 —P1 AT =T —T (7)x x2 xl AT =T —T y y2 yl These parameters are suit to all the data of two subapertures, so the relative piston and tilts in the data of the 2nd subaperture can be eliminated by these paraments: D2{X,Y2]=D2[X,Y2]—(AP+AT •X+AT • Y) n=l,2,,N2 (8) Where N2is the total sample points in the 2th subaperture. And the optical path difference D;is unified with D1 in the same reference standard flat. Thus, the unified process of subapertures is finished, and the previous process is used repeatly to unify more subapertures. 3. COMPUTER SIMULATION AND RESULTS To test the method, the computer program OSIT is used to simulate a numerical subaperture interferogram and retrieve the wavefront of allapertures(shown in fig.3). the map of OPD Di[Xn1Ynl to determined P, of subapertures sampled ATxand 1Ty by by mnterferoineter equactIona(6), (7) . : u:i 1 1 retrieve the unify the map of OPD — a avefront of two Di Xn, Yn] r- T subaperture by eq, 8 prodted by position errof — ________ computer or arnp1e erruc — :zzzzzzzizzi:::± .IZIIIIIZZZ next suhuper turd original wavefront gauge thein(XY) and H-- accuracy — output the retrieve location paranient8 E=out-n wavefront Vout(XY)L J L J __________ _____ Fig.3 The chart of program OSIT To simulate the method errors, the input wavefront Win(X,Y) is the Zernike polynomials, 392 /SPIE Vol. 2003 Interferometry VI (1993) Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms the coefficients are nonzero and the highest term ofZernike polynomials is Ja. w Y) = E Z 1(X, Y) (9) To simulate the random change of adjestment of the tested flat , we use different and arbi- trary piston and tilt coefficients (j = I ,2,3) for the different subapertures. The remaining Zernike cofficients are equal for all the subapertures. here we select the coefficients A1=(—1)''A A=O.l, 0.2, 0.3, /4 (10) where A will stand for the peak—to--valley of Win , and the different Ja will stand for Win in different complex level of aberration (show in Table 1). TABLE 1 the complex of input wavefront Ja Terms Description I 2 3 Zi Zi-Z2 Zl-Z2+Z3 plane 4 6 6 ZI-Z2+Z3-Z4 Z1-Z2+' +Z5 ZI-Z2+ -Z6 add 2nd order aberrations 7 S 9 10 Z1-Z2+ +Z7 ZI-Z2+" -Z8 Zl-Z2+' +Z9 Zi-Z2+" -Z1O add 3nd order aberrations The another input into the program OSIT is the location for each subaperture, which in- cludes the position of centre points and directions of subapertures in the plane coordinate. Then a final wave—front can be obtained by OSIT program, and it is also formed by zernike polynomials: W01(X,Y) = EB1 • ZJ(X,Y) (11) We gauge the accuracy of the method by looking at the relative Peak—to—Valley wavefront error: A— PV[E(x,y)J >< l00°/ (12)PV[W1(x,y)J 0 where PV[ ] is the peak—to—valley value of wavefront, E(x,y) is the residual error: E(X, Y) = W Y) — W (K, Y) (13) SPIE Vol. 2003 Interferometry VI (1 993) I 393 Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms It shows in calculation that the accuracy is influenced by the complex level of Win, and inconcerned in PV{Win]. To correspond to reality, we select: A1=(—l)''A (14) In the absence of error, our method performs extremly well for a wide range of input aberrations. Figure 4 is a plot of L versus A. Note that the relative accuracy is better than 1O% . With the order of aberration raising, the relative accuracy is reduced, but it is irrelevant to A and less than 0.5% for 4 order aberration. So our method suit for the high accuracy piano surface measuring, and if the Peak—to-—Valley of the input wavefront is 12, the theoritical accu- racy is better than A I 200 (%) :: %L L L T 124367S91O111213141AJ Fig.4 The accuracy of method To simulate the effect of errors which exist in actual measuring program. There are two im- portant errors must be considered, one is the position errors due to the location system error, the other is the sample errors that means the residual error of interferometer and sample ran- dom error. To simulate the position errors of subapertures, we add different tiny movement dx with the subapertures location parameter, and select three difference input wavefront with Ja=2,4,10. Fig.SA is a plot of L versus dx / D. Where D is the diameter of subaperture(the measuring aperture of interferometer). Shows that the effects of position errors depands on the configura- tion of the input wavefront, means that the more the complex configuration of the tested surfer is, the more the accuracy disturbed bigger by position errors is. The residual error of interferometer is similar to each subaperture, because the aperture of interferometer is the subaperture of the tested surface, but the sample random error is difference on each sample point , so they need to be considered together. The disturbing wavefronts G1(X,Y) are added into each subaperture, and they include two errors: one is the fixed system error and the other is the random error which is produced randomly by computer.Their 394 /SPIE Vol. 2003 Interferometry VI (1993) Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms Peak—to—Valley are equal,and it's signed as 5(ö =PV[G1(X,Y)]. I rd o:der d order I irt order •1 2 '3 4 Fig.5 (a) The influence of position errors (b) theinfluence of sample errors It shows in calculation that the accuracy is irrelevant to the configuration of the input wavefront, but it relates closely to the P—V of sample errors. Fig.5B is a plot of z versus ö / PV[ Win] . It shows that the relation of L and ö / PV[Win] is linear and its slope is between 2 and 2.5. Therefore, in ordinary accuracy of location (I %), the important disturbing error is the sam- pie error of interferometer. 4. EXAMPLE OF TESTING By the previous analysis, we can know that an interferometer with high accuracy is the es. sential condition. A Phase Shifting Digital Flat Interferometer whose aperture is 25Omm and accuracy is 2/ 504is choosed and shown in fig.6. Fig. 6 Schmatic diagram of phase shifting digital flatinterferometer The special bear table( shown in fig.7) of OSIT is built by three layers: the frist is the x— y tilts adjuster. The second is the location machine which can move in one dimension and rotate in perigon. The location error is less than O.5%(O.O2mm and 4'). The third is the flat bearer which SPIE Vol. 2003 Interferometry VI (1993) /395 - t%) 3 fixed svs:ern error sample errors random error 1. 2 E !PVtIn (%) ____ I [1f Cont1IcJ Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms has nine bear points. The bear points can balance automatically to minimize the deformation of large flat(eq .500mm). Fig.7 The OSIT special tabel There are two tested flats , one is 250mm and the other is 430 mm. The results of meas- uring processes are showed in table 2 and fig.8. It is successful that OSIT technique is applied into the Phase—Shifting Digital interferomet- er and enlarge its measuring aperture from 25Omm to 5O0mm, with the accuracy of 2/20. 5% 396 ISPIE Vol. 2003 lnterferometry Vi (1993) Fig.8 the configuement of three—dimension fiet ba1arce bearer rotating p1iie .d,i&tiLg 9-point (A) standard wavefront (B) all of retrieved wavefront (C) centre of retrieved wa.vefront (B) residual wavefront Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms Table 2 the results of testing flat tt2bOmm (1)424mm aubaperture 1)lbOmm t1)2öOmm tandurd wttvefrand PVO 1BÔ RM80, 051 IVO 20? ftMSO 040 (D2SOnjm Fig1 8A retr ieved avefrand PVO. 1'18 RMS0, 047 PVO, l 2 RM801 200 (1)424mm Fig 8B) PVI). 206 R1S0 042 (P2SOmm Fig SC) re8idutil error ve PVO 051 R1S0 010 PV0 048 RMS0 010 1ii center of 250mm fig SD) accuracy 27% 23% . SUMMARY AND CONCLUSION From the above arguments, it would seem that the technique will enlarge the aperture fur- ther with more subapertures. But the accuracy descends along with it. The degree of overlap be- tween two subapertures and the ratio between the allaperture to the full—covering area of subapertures are important too. We will discuss all of them detailed in another papers. 6. REFERENCE [1]. W.W.Chow and G.N.Lawrance "A Mathod for Subaperture Testing interferogram re- duction" Opt. Lett. , vol. 8 , 468(1 983) [2]. W.W.Chow and G.N.Lawrance U Influence of High Order Noise in Wavefront Reconstruction" Proc. SPIE , vol. 440 ,31(1983) [3]. M.Y.Chen etc. UMulti.aperture Overlap— scanning Technique for Large Aperture Test "Proc. SPIE , vol. 1553(1991) [4] J.B.Chen D.Z.Song etc."Large aperture—high accuracy phase shifting digital flat interferometer" ,SPIE Vol. 2003 (to be published). SPIE Vol. 2003 Interferometry VI (1993) /397 Downloaded from SPIE Digital Library on 01 Apr 2010 to 222.190.117.220. Terms of Use: http://spiedl.org/terms
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