Differential wavefront curvature sensor

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1 Dfferental wavefront curvature sensor Weyao Zou and Jannck Rolland College of Optcs and Photoncs: CREOL& FPCE, Unversty of Central Florda Orlando, Florda ABSTRACT In ths paper, a wavefront curvature sensor s presented. Ths sensor s based on the measurements of the dfferentals of wavefront slopes, where the wavefront slope measurements can be acheved by a Shack-Hartmann sensor. A Shack- Hartmann sensor wth three output collmated beams wll be ntroduced wth a lenslet array nstalled n each beam. By shftng two of the Shack-Hartmann grds n the x- and n the y- drectons ndependently compared to the thrd grd, we can measure the slope dfferences and obtan the wavefront curvatures at each grd pont. A wavefront reconstructon can be performed wth the wavefront curvature measurements. Keywords: wavefront sensng, Shack-Hartmann, dfferental measurement, curvature sensor 1. SHACK-HARTMANN SLOPE SENSOR Currently the Shack-Hartmann sensor s a popular wavefront slope sensor, whch s orgnated from the Hartmann test nvented by Hartmann n Roland Shack mproved ths test by ntroducng a lenslet array n Wavefront slopes are measured n Shack-Hartmann (S-H) test by quanttatvely comparng the Hartmann grd from the measurement beam wth the Hartmann grd from the reference beam. A CCD camera s usually used to record the coordnates of the Hartmann grd, and a computer s employed for data reducton and wavefront reconstructon. Fg. (1) The schematc of Shack-Hartmann sensor and Hartmann grd Fg. 1 s a schematc layout of a Shack-Hartmann sensor. The wavefront (.e. ether the reference wavefront or the measurement wavefront) s collmated by a collmaton lens and then passes through a lenslet array. The Hartmann screen dvdes the wavefront nto many sub-apertures. The lenslet array focuses the wavefront wthn the sub-apertures nto a Hartmann grd. The reference beam s generated by a pn-hole lght source and njected nto the system as an deal wavefront to calbrate any systematc error. Comparng the coordnate dfferences between the measured and the reference wavefronts, we can obtan the wavefront slopes by The correspondng author s emal: wzou@creol.ucf.edu. Optcal Manufacturng and Testng VI, edted by H. Phlp Stahl, Proc. of SPIE Vol (SPIE, Bellngham, WA, 005) X/05/$15 do: / Proc. of SPIE

2 W x W y x y (1) (1) x f y f (0) (0), (1) where (x (0), y (0) )( 1,,,m) s the Hartmann grd coordnates of the reference beam; (x (1), y (1) ) (1,,,m) s the Hartmann grd coordnates of the measurement beam, f s the focal length of the lenslet array, and m s the total number of the grd ponts. Compared wth the Hartmann test, the Shack-Hartmann wavefront test offered better photon effcency. Also the poston of S-H grd spot s only proportonal to the average wavefront slope over each sub-aperture, and s ndependent of hgher-order aberratons and ntensty profle varatons due to the extracton of the pupl centrodng and background thresholdng. The Shack-Hartman sensor s a real-tme and parallel wavefront sensor. It has wde applcatons n actve and adaptve optcs, optcal testng, telescope mage analyss, and characterzatons of atmosphere and random meda. In ths paper, a dfferental Shack-Hartmann curvature sensor (DSHCS) s developed. In Secton, we detal the prncple and mplementatons of dfferental Shack-Hartmann curvature sensor; In Secton 3, we ntroduce an expermental setup under development for the dfferental Shack-Hartmann curvature sensor; In Secton 4, we compare the dfferental Shack-Hartmann curvature sensor wth the exstng arts; In Secton 5, we conclude the technque and talk about future work.. DIFFERENTIAL SHACK-HARTMANN CURVATURE SENSOR.1. Prncple Curvature at any part of the wavefront s the dervatve of the slope, whch can be computed n any drecton. One metrc of the curvature s the Laplacan curvature, whch s computed from the second dervatve of the wavefront n the x-and y-drectons. If we can measure the dfferentals of the wavefront slope at each Hartmann grd pont, we can compute the wavefront curvatures or Laplacan that can be expressed as W (x,y) W (x,y) W (x,y) +. () x y For the case of a Shack-Hartmann sensor, f we could make the Hartmann grd move a known dfferental dstance n the x-drecton (or n the y-drecton) and measure the slopes at each grd pont before and after the dfferental movement, we wll obtan the slope dfferentals of the wavefront n the x-drecton (or n the y-drecton),.e. wavefront curvature. The dea of ths dfferental measurement s llustrated n Fg.. To mplement the dea, we can make the Hartmann grd shft a lateral dfferental dstance s x (or s y ), for example, n the x and n the y drectons as shown n Fg., and we can measure the slopes at each pont before and after the dfferental shft. Wth Eq.(1), the wavefront curvatures can be computed by W cx() x W cy() y 1 s x 1 s y W x W y W x W y 1 f 1 f ( x ( y 1 ) 1 ) x s x y s y ( 1 ) ( 1 ) 1 1 (3) Proc. of SPIE

3 V1' V Sy 4 Sx Fg. The Hartmann grd dfferental shears made n the x- and y-drectons.. Implementatons To mplement the dea of slope dfferental wth Hartmann grds, we ntroduce a Shack-Hartmann sensor wth three output beam channels. Suppose the output wavefront travels n the z drecton, t s splt nto three channels along three drectons: one stll travels n the z-drecton, one travels n the x-drecton, and the other one n the y-drecton. Lenslet arrays A, B and C are put n the three beams separately: C s n the z-drecton beam, A s n the x-drecton beam, and B s n the y-drecton beam only. Lenslet array A s conjugated to lenslet array C, and lenslet array B s conjugated to lenslet array C. (a) Proc. of SPIE

4 (b) (c) Fg. (3) Implementatons of the dfferental Shack-Hartmann curvature sensor Usng a fne mcro-screw we can move the lenslet array A a dfferental dstance n the x-drecton, and usng another mcro-screw, we can move the lenslet array B a dfferental dstance n the y-drecton. Thus, the lenslet arrays A and C Proc. of SPIE

5 are shearng each other n the x-drecton, and lenslet arrays B and C are shearng each other n the y-drecton. Measurng the coordnates of the Hartmann grd ponts generated by A, B and C, and applyng them n the Eq. (3), we obtan the wavefront curvatures n the x- and n the y-drectons. In these three beam channels, three CCD cameras are needed for measurng the Hartmann grd coordnates, so the constant (namely s 1 n Eq.(3)) should be obtaned by calbraton. A drect mplementaton layout s shown n Fg. 3(a). Other mplementatons where the shearng elements are replaced wth glass plates nstead of mcro-screws are shown n Fg. 3(b) and Fg. 3(c). In Fg.3(b), two optcal parallel plates are only used as shearng elements to make dfferental dsplacements between the three lenslet arrays. In Fg.3(c), the optcal parallel plates are also actng as beam spltters. 3. EXPERIMENTAL SETUP An expermental system for the dfferental Shack-Hartmann curvature sensor s beng developed n the ODA lab of the College of Optcs and Photoncs at the Unversty of Central Florda. The layout of ths expermental system s shown n Fg.4. Fg. 4. Expermental system for the dfferental Shack-Hartmann curvature sensor A 3-nch dameter, 18-nch focal length commercal qualty mrror s used as an optcal element n ths expermental system. A Φ5mm achromatc lens wth a focal length of 10 mm s used to collmate the output beam nto a parallel beam. Two mm 3 cube beam spltters are used to splt the collmated beam nto three channels channel 0, channel 1 and channel. Another cube s used to make a 90 o mage rotaton n channel. A s lenslet array wth mm sub-apertures and focal length of 90mm (Adaptve Optcs Assocates Inc.) s used n each output channel to generate the Shack-Hartmann grds n ts focal plane. An optcal de-magnfyng system wth the reducng power of 3.3:1 s used n each channel to convert the Hartmann grd to a CCD camera target. Fg.(5) shows a Shack-Hartmann grd n a channel. A pont lght source used s made of a 635-nm laser dode module wth a pnhole. The pont lght source O 1 s used to generate the beam for measurement and the pont lght source O s used to generate the beam for calbraton. After calbraton, no reference lght beam s needed. All the optcal elements customzed for ths setup are the common commercal products from the catalogue of Edmond Optcs. Proc. of SPIE

6 The expermental setup beng developed s shown n Fg. (6). Fg.(5) Hartmann grd for curvature measurement I] I 1JF J Fg. (6) Expermental Setup for the DSHCS Proc. of SPIE

The three CCD cameras used n ths setup are Watec LCL-90 Monochrome CCD cameras, whch have resoluton of 768 494 pxels wth pxel sze of 8.4 9.8 µm (EIA, RS-170), a sensng area of 6.4 4.

7 The three CCD cameras used n ths setup are Watec LCL-90 Monochrome CCD cameras, whch have resoluton of pxels wth pxel sze of µm (EIA, RS-170), a sensng area of mm and lght senstvty of 0.01 Lux. The NI-IMAQ PCI-1409 mage acquston board (Natonal Instruments) s used as a frame grabber to acqure mages from the CCD cameras. It s compatble wth double-speed 60 frames per second progressve scan cameras and delvers up to 60dB dynamc range, whch corresponds to 10 bts or 104 gray scales. It has 16 MB of onboard memory used to temporarly store the mage beng transferred to the PCI bus. The PCI_1409 board has four nput ports, so we can connect our three CCD cameras located n the three output channels to ths board. The NI-IMAQ Vson development module can provde LabVew related functons, whch allows us to perform varous operatons on the acqured mages. LabVew s a graphcal programmng development envronment based on the G programmng language for data acquston and control, data analyss, and data presentaton. Fg.(7) shows the Graphc User Interface that s desgned for the expermental setup. Channel 3 l S-H Grd Pol,t 104 J nr Dfferental Shack-Harlmann Curvature Sensor Fg.(7) GUI of the expermental setup for the DSHCS 4. COMPARISONS WITH PREVIOUS ARTS In 1988, Francos Rodder proposed a method to measure the local curvature of the wavefront surface by measurng the dfference n llumnaton between the two planes before and after the focal pont. The dea of the curvature sensor s that the normalzed dfferental ntensty change along the optcal axs provdes the nformaton of the local curvature of the wavefront. For some reasons, Rodder s curvature sensor has not been wdely commercally avalable yet, whle the dfferental Shack-Hartmann curvature sensor can be quckly commercalzed. Proc. of SPIE

8 Interferometry s a technque makng the wavefront under test to nterfere wth tself or an deal wavefront to obtan an nterferogram. It s especally good for measurng hgh spatal frequency aberratons and low ampltude aberratons. However, ar moton and mechancal vbratons make t dffcult to obtan an mage, and magnfcaton errors makes t dffcult to nterpret the nterferogram, especally for testng large optcs. The dfferental Shack-Hartmann curvature sensor, on the other hand, measures the second dervatves of the wave front, so t s nsenstve to the wave front tp/tlt and the whole body movements. The commercal nterferometers are usually expensve (typcally cost $100,000 or more), whle a Shack-Hartmann-based curvature sensor can be made relatvely low cost. One of the nterferometers that shares some smlarty to the dfferental Shack-Hartmann technque s called the shearng nterferometer, whch splts the wavefront nto two parts, makng them sheared wth each other, and then recombnes them to generate an nterferogram. However, the shearng nterferometer s a slope sensor, and t s senstve to the tp/tlt of the wavefront; whle the dfferental Shack-Hartmann sensor proposed here s a curvature sensor, and t s not senstve to the tp/tlt of the wavefront and the whole body movement. 5. CONCLUSIONS In concluson, the Dfferental Shack-Hartmann curvature sensor shares the mportant features of the Shack-Hartmann sensor, such as 1) It s a real-tme wavefront measurement and measurements are nherently two-dmensonal and parallel; ) t s ndependent of hgher-order aberratons and ntensty profle varatons, 3) t has good photon effcency and 4) good for the all wavelength band. In addton, the dfferental Shack-Hartmann curvature sensor also provdes some unque features, such as 1) no external reference s needed for all tests after one-tme calbraton; ) t s ndependent of vbratons, tlt and whole body movements, so t s good for measurements wth movng objects; 3) t s a tlt-removed wavefront estmaton, and 4) t s scale tunable by changng dfferental values. Based on curvature measurement, we can estmate the wavefront ether by a zonal Least-squares-based wavefront estmaton algorthm 3 or a zonal Fourer transform-based teratve algorthm 4 or even a model estmaton algorthm. The expermental setup s stll under development, and more results wll be publshed n the near future lterature. A US patent about ths nventon has been fled and s now n pendng REFERENCES 1. Shack, R. V. and B. C. Platt, Producton and use of a lentcular Hartmann screen, J. Opt. Soc. Am. 61, p656 (abstract only), F. Rodder, Curvature sensng and compensaton: a new concept n adaptve optcs, Appl. Opt. 7, pp13 15, Gary Chanan, Wavefront sensng and reconstructon, Center for Adaptve Optcs Proceedngs: Summer school on adaptve optcs 000, Santa Cruz, July 8-14, F. Rodder and C. Rodder, "Wavefront reconstructon usng teratve Fourer transforms", Appl. Opt., 30, pp , Dfferental Shack-Hartmann curvature sensor, US patent n pendng, 005. Proc. of SPIE

Stitching of off-axis sub-aperture null measurements of an aspheric surface

Stitching of off-axis sub-aperture null measurements of an aspheric surface Sttchng of off-axs sub-aperture null measurements of an aspherc surface Chunyu Zhao* and James H. Burge College of optcal Scences The Unversty of Arzona 1630 E. Unversty Blvd. Tucson, AZ 85721 ABSTRACT