Absolute calibration of null correctors using twin computer-generated holograms

Transcription

1 Absolute calibation of null coectos using twin compute-geneated hologams Poteep C.V. Mallik a, Rene Zehnde a, James H. Buge a, Alexande Poleshchuk b a College of Optical Sciences, The Univesity of Aizona, Tucson AZ b Institute of Automation and Electomety, Russian Academy of Sciences, Pospect ak., Koptyuga, 1, Novosibisk , Russia ABSTRACT We pesent a method fo a cascading null test using twin compute-geneated hologams to calibate eos in null coectos. This will allow us to test lage asphees an ode of magnitude bette than cuent limits. We discuss vaious souces of CGH eos and how to calibate them. We also mention some ways to measue and calibate the eos in the test optics. 1. INTRODUCTION CGHs ae vey poweful optical elements because they can encode a wavefont of any desied shape. Thus, they ae vey useful in the null test of asphees [1]. Fo high-accuacy testing of lage asphees, the eos in the CGH need to be caefully chaacteized [2]. Cuent limitations in testing have pevented tests of lage aspheic mios to bette than 8-10nm ms. This pape is divided into the following sections: 1.1 Definition of types of eos, 1.2 Twin-CGHs, 1.3 Tansfe of eos fom sphee to asphee, 2 Eos, 2.1 Calibating CGH eos, 2.2 Calibating test system eos, 2.3 Mapping distotions, 3 Cascading test, 4 Initial esults, 5 Futue wok and 6 Conclusions. 1.1 Definition of types of eos Calibation of null coectos must be done vey caefully. Buge [3] has shown how CGHs may be used to cetify null coectos. A detailed eo analysis must be made of such a test. Eos fom such a test can be divided into 2 categoies: 1. High fequency eos, and 2. Low fequency eos. Futhemoe, the low fequency eos can be divided into axisymmetic and non-axisymmetic pats as shown in figue 1. Eos in null test High-fequency eos Low-fequency eos Axisymmetic eos Non-axisymmetic eos Figue 1. Above is a flowchat of the diffeent types of eos in a test and calibation of a null lens. It isn t fully clea what the dividing line between high-fequency and low-fequency eos ae and that is pat of ou investigations. mallik@ .aizona.edu phone: (520) Intefeomety XIII: Techniques and Analysis, edited by Katheine Ceath, Joanna Schmit, Poc. of SPIE Vol. 6292, 62920H, (2006) X/06/$15 doi: / Poc. of SPIE Vol H-1

2 1.2 Twin-CGHs A method fo absolute intefeometic testing of axially symmetic asphees has been devised by Reichelt et al [4]. This method involves the use of a specially designed CGH that econstucts both the aspheical and spheical auxiliay waves. Such a CGH is efeed to as a twin-cgh. The twin-cgh is segmented into 4 quadants as shown in figue 2. The spheical and aspheical pattens ae encoded onto the CGH simultaneously, and thus the eos in the spheical patten can be tansfeed to the aspheical patten diectly (see figue 3). The eos in the spheical patten ae measued absolutely [5]. Spheical Pesciption Segmented Hologam Aspheic Pesciption 1.3 Tansfe of eos fom sphee to asphee Figue 2. The twin-cgh is segmented into 4 quadants as shown above. Knowledge of the eos fom the spheical quadants of the CGH can be tansfeed in a staightfowad manne to the eos in the aspheical quadants as shown in figue 3. Wavefont Eos in Sphee Line Spacing fo Sphee Line Spacing Eos in Sphee W S/λ * = X = W*S/λ Line Spacing Eos in Asphee X Line Spacing fo Asphee S/λ = Wavefont Eos in Asphee W W = *λ/s Figue 3. The tansfe of knowledge of eos in the spheical quadants to the aspheical quadants will allow us to calibate the aspheic wavefonts accuately. Poc. of SPIE Vol H-2

3 2. ERRORS 2.1 Calibating CGH eos Thee ae seveal methods of measuing and calibating CGH eos. It is impotant to be able to sepaate figue eos and patten eos of the CGH. Patten eos ae caused due to etching depth, duty cycle and patten distotion vaiations fom ideal [6]. Figue eos in the CGH substate ae the most citical eos fo phase econstuction. Recent expeiments on CGHs with diffeent duty cycles and etching depths have given us a bette idea of how these vaiations influence wavefont eos. A paametic model has been developed by Ping Zhou et al (to be published) that elates CGH fabication eos with wavefont eos. 2.2 Calibating test system eos Removal of eos in the test optics is citical to ou being able to make measuements to bette than lambda/1000. These eos can be divided into otationally symmetic and non-otationally symmetic eos [7]. Non-otationally symmetic eos may be emoved by otating eithe the test pat o the efeence pat to N equally spaced positions. Anothe convenient method to calibate eos in the intefeomete involves using a ball [8]. A ball is placed such that its cente is at the cente of cuvatue of the efeence sphee. By otating the ball to seveal positions and by aveaging the measuements, the eos in the efeence sphee can be detemined. 2.3 Mapping distotions Thee ae mapping distotions caused by the mapping of the asphee position onto the CGH plane [9]. Fo a CGH at paaxial focus, the ays map fom the mio to the CGH accoding to 3 K x(), 2 2R and the wavefont ceated by the CGH can be appoximated as 4 3K OPD =, 3 8R whee = adial asphee position R = paaxial adius of cuvatue of asphee K = conic constant of asphee x() = ay intecept position on CGH coesponding to on asphee The above fomulas ae tuncated tems in a powe seies, and fo accuate calibation of these eos moe tems may need to be used. We plan on using the methods mentioned above to caefully calibate the eos of ou test system. 3. CASCADING TEST To test lage asphees to a high degee of accuacy (bette than lambda/1000) we have devised a cascading null test. We will fist calibate the eos of the twin-cgh absolutely. Using these calibation esults we will use the twin-cgh to test the null coecto. Once the eos in the null coecto ae calibated, we can use it to test the asphee. Thee ae at least 2 easons why a cascading null test is essential fo the success of ou measuements. A CGH may be used as a null lens diectly. Howeve, due to the inheent natue of witing a CGH, high-fequency eos may be pesent in the patten. This will esult in ou being unable to sepaate high fequency eos in the aspheic mio fom those in the CGH. Secondly, asphees of a lage diamete have lage aspheic depatues fom the best fitting sphee. This esults in vey lage mapping eos fom the CGH to the test mio. Poc. of SPIE Vol H-3

4 A test stand is being assembled to enable us to measue the twin-cgh and the null coecto. The twin-cgh is 220mm in diamete with a wavefont adius of cuvatue (RoC) of 7600mm fo the aspheical quadants and wavefont RoC of 350mm fo the spheical quadants. The aspheical quadants of the twin-cgh simulate a mio with a diamete of 4.5 metes and a focal atio of f/ INITIAL RESULTS The lage, 220mm diamete, CGHs have been fabicated. Below is a pictue of the finge patten of the substate fo one of the CGHs. Also shown is a photogaph of the fabicated CGH. 220mm substate -n i Figue 4: Intefeogams (on eflection, 150mm field) of 220mm substates and locations of intefeogams on substate Poc. of SPIE Vol H-4

5 Figue 5: Photogaph of fabicated CGH 2 pototype twin-cghs wee fabicated and the quadants with the spheical pesciption wee tested. These twin-cghs ae 35mm in diamete, with a wavefont RoC of about 60mm. The wavefonts fom the spheical quadants of the 2 CGHs tested ae shown in figue 6. Below the wavefont map coesponding to each CGH is the line spacing eo and the esulting wavefont eo. As shown in figue 6, the CGH line spacing is obtained fom the test wavefonts. The line spacing eo is then calculated. The CGH suface eo is obtained fom the line spacing eo. The oveall eos fom the 2 CGHs match to about 10nm oot mean squae (ms), which will esult in the wavefont eos matching to bette than 2nm ms. These esults ae plotted in figue 7. This gives us confidence that we can calibate the twin-cgh eos and the null coecto eos to a high degee of accuacy. CGH_SSARS9_9Odeg Suface CGH_SSI_2R67 Suface 1000 t \ ms = 8.1nm ms = 7nm -151 I I I I I I I I I I I I I I I I I I Suface map (in nm) Poc. of SPIE Vol H-5

6 mm A1iwusw nfl mm nfl Line spacing: y-axis is line spacing; x-axis is adial position on CGH in mm. mm - xi? 4Aiidusbd uiw tim mm COHA1170d.g.txl Bp.clng Tn In mm U 1b ms = 38.7nm l 18 U l I / ms = 59.5nm Line spacing eo: y-axis is line spacing eo; x-axis is adial position on CGH in mm. mm 4,AIidusbd a I Il 4A1idusbd a I Il - x Id' mm 2\pIms = 3.8nm va1 ms = 3.2nm ID ID 14 ID 10 Suface eo: y-axis is CGH suface eo; x-axis is adial position on CGH in mm. Figue 6: The CGH suface map, line spacing, line spacing eo and the suface eo ae shown above. The wavefont eos ae calculated and shown in figue 5 below. Poc. of SPIE Vol H-6

7 -0.1 CGH adial eo in µm Sphee 1 Sphee adial position in mm Figue 7: CGH wavefont eos ae plotted above. Sphee 1 and Sphee 2 efe to each CGH. Only the quadants with spheical pesciption wee tested. 5. FUTURE WORK The test stand needs to be assembled and the lage twin-cghs need to be tested. The aspheic quadants of the twin- CGH will simulate a lage asphee. This will be tested using the null coecto. Caefully keeping tack of all ou test eos, we should be able to test lage asphees (~4m in diamete) to bette than lambda/ CONCLUSIONS We have descibed a cascading null test fo lage asphees. This type of test is paticulaly useful fo measuing lage asphees with lage aspheic depatues fom the ideal best-fit sphee. In fact, ou scheme is essential in being able to test such asphees to bette than lambda/1000. This will futhe the limits of aspheic testing. ACKNOWLEDGEMENTS This eseach was suppoted in pat by a gant fom JPL/NASA. The authos would also like to thank Comic Mele and Ei Cohen fo thei help and suppot with the expeiments descibed. REFERENCES 1. J. Wyant and V. Bennett, Using compute geneated hologams to test aspheic wavefonts, Appl. Opt. 11(12), (1972) 2. J. Buge, Applications of compute-geneated hologams fo intefeometic measuement of lage aspheic optics, in Intenational Confeence on Optical Fabication and Testing, ed. Toshio Kasai, Poc. SPIE 2576, (1995) 3. J. Buge, Ceification of null coectos fo pimay mios, in Advanced Optical Testing and Manufactuing IV, ed. Victo Dohety, Poc. SPIE 1994, (1994) 4. S. Reichelt et al, Absolute intefeometic test of asphees by use of twin compute-geneated hologams, Appl. Opt. 42(22), (2003) 5. S. Reichelt et al, Absolute intefeometic test of Fesnel zone plates, Opt. Comm 200, (2001) 6. Yu-Chun Chang, Diffaction wavefont analysis of compute-geneated hologams, Ph.D. Dissetation, Optical Sciences Cente, The Univesity of Aizona, (1999) 7. C. Evans and R. Kestne, Test optics eo emoval, Appl. Opt. 35(7), (1996) Poc. of SPIE Vol H-7

8 8. U. Giesman et al, A simple ball aveage fo efeence sphee calibations, in Optical Manufactuing and Testing IV, ed. H. Philip Stahl, Poc. SPIE 5869, (2005) 9. J. Buge, A null test fo null coectos: eo analysis, in Quality and Reliability of Optical Systems, eds. James Bilbo and Robet paks, Poc. SPIE 1993, (1993) Poc. of SPIE Vol H-8