Measurement of the dynamic deformation of a high frequency scanning mirror using a Shack-Hartmann wavefront sensor

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1 Mesurement of the dynmic deformtion of high frequency scnning mirror using Shck-Hrtmnn wvefront sensor * b** b Mrgret Brown, Timothy Gong, Dniel R. Nel, Jmes Roller, Selso Lunv nd Hkn Urey Inc., North Creek Prkwy S., Bothell, WA WveFront Sciences, Centrl Ave SE, Albuquerque, NM ABSTRACT Scnning mirrors for micro-disply systems typiclly require opertion t frequencies over 1 5 khz. These mirrors undergo lrge dynmic stresses nd inerti relted deformtions. We report here on the mesurement of these dynmic deformtions using commercilly vilble Shck-Hrtmnn wvefront sensor with dt reduction softwre. The mesured deformtions using the Shck-Hrtmnn wvefront sensor re shown to gree with mesurements obtined using stroboscopic interferometer. Advntges of the Shck Hrtmnn wvefront sensor re discussed. 1. INTRODUCTION The dynmic deformtion of high frequency opticl scnning mirrors limits system opticl resolution by imposing wvefront errors on the scnning opticl bem tht ultimtely result in n increse in the smllest 123 chievble opticl To chieve mirror design with minimum dynmic deformtion, the pproch tken here is to optimize the design using detiled finite element nlysis (FEA) of the mechnicl design of the mirror structure. The mirror is then fbricted nd the wvefront deformtion mesured. Mesurements re compred with the FEA predictions nd used to improve subsequent mirror designs. This design process requires routine, ccurte nd relible mesurements of the minor deformtion. Two different instruments hve been used to mesure the dynmic deformtion of our opticl scnning mirrors. The first instrument is custom-built stroboscopic interferometer ' with custom designed dt reduction softwre to infer the mirror deformtion. This instrument performed with high sptil resolution nd noise floor estimted to be 2JlO. However, the collection nd reduction of dt is time consuming. To fcilitte the rpid mesurement nd nlysis of the dynmic deformtion of the scnning mirrors, we replced the stroboscopic interferometer with commercilly vilble Shck-Hrtmnn wvefront sensor. This instrument enbled routine nd ccurte dynmic deformtion mesurements while mintining the sensitivity nd ccurcy of the stroboscopic interferometer. In this pper, we summrize the theoreticl predictions of the dynmic deformtion developed from the FEA. We then describe the experimentl test beds nd procedures for both the interferometer nd Shck- * Mrgret_brownmvis.com; phone ; fx ; Microvision mc, p.o. Box 3008, Bothell, W 98011; ** drnel@wvefrontsciences.com; Ph: (505) (X107);Fx: (505) ;: WveFront Sciences, Inc.,14810 Centrl SE., Albuquerque, NM Opticl Mnufcturing nd Testing IV, H. Philip Sthl, Editor, Proceedings of SPIE Vol (2001) 2001 SPIE X/01/$15.00

2 Hrtmnn wvefront sensor mesurements. The mesurements nd FEA nlysis predictions re then compred. 2. SHACK-HARTMANN SENSOR The Shck Hrtmnn sensor nd dt cquisition nd reduction softwre used here is model CLAS-2D mnufctured by Wvefront Sciences.5 A discussion of the theoreticl opertion nd dt reduction process cn be found in vrious ppers.5'6'7 A brief summry is presented here. 2.1 Theory of Opertion Shck-Hrtmnn wvefront sensors were developed originlly for dptive optics pplictions.8'9 However, with the development of micro-optics bsed lenslet rrys nd highresolution CCD cmers, their use hs been extended to wide vriety of pplictions.5'6'10 The sensor is compct, robust nd inherently simple. It is bsed on the simple principle tht light propgtes norml to the wvefront surfce. Thus chnges in focl spot position on the CCD rry provides direct mesure of wvefront slope, nd through sptil integrtion process, the wvefront cn be determined. The Shck-Hrtmnn sensor consists of micro-optic lenslet rry tht is rigidly mounted Figure 1- A wvefront incident on the lenslet rry will produce in front of CCD detector s shown in Figure distinct focl spots on the CCD. The loction of these focl fused silic lenslet rry is mde using spots reltive to reference is mesure of the locl wvefront 1. The photo-lithogrphy nd etching processes, with 1 tilt t the lenslet rry. edor Lens y tm resolution feture sizes. Ech of the lenslets is precision sphere rrnged in rectngulr rry with 100% fill fctor. The wvefront sensor used here consists of 10 bit CCD cmer with 33 x 44 lenslet rry cross 4.8 x 6.4 mm perture. The lenslet rry cretes series of focl spots on the detector rry. With pproprite synchroniztion between the scn mirror, diode lser source nd cmer electronics, the CCD records the loction of the focl spots nd trnsfers them to the computer memory. This informtion is processed using the procedure shown schemticlly in Figure 2. First the CCD imge is generted representing the distribution of power cross the detector. Ech focl spot is then locted nd the loction of the centroid corresponding to ech lenslet is clculted. The wvefront slopes cn then be clculted from the difference between these centroid loctions nd those of reference wvefront. The wvefront is then reconstructed from the wvefront slopes. The use of the reference file llows for the minimiztion of effects from imperfections in the CCD rry, lenslet rry, mounting system, imging systems nd electronics. The reference file is determined by recording the position ofthe focl spots t known condition. The Shck-Hrtmnn wvefront sensor hs both lrge dynmic rnge (4-5 mrd/lenslet) nd high sensitivity (<2J20 Pek to Vlley), tht llow cpture of wvefront mesurements over wide rnge of mirror ngles, since mesurements of the scnning mirror cn be mde when there is reltively lrge residul tilt in the wvefront. Proc. SPIE Vol

3 3. FINITE ELEMENT ANALYSIS OF MIRROR DEFORMATION The bsic structure of the scnning mirror is illustrted in the left pnel of Figure 3. The mirror is rotted by twisting t the torsion brs, shown here t the top nd bottom of the mirror. Previous ttempts to model the mirror deformtion were performed using 2-D models2 tht clculted the deformtion t the centerline of the mirror nd then extrpolted this into 3-D spce. However, using this centerline pproximtion, it ws impossible to see the effects of the dominnt deformtion mechnism due to twisting t the torsion brs on the mirror. Lenslet Arry & CCD Cmer Figure 2- Schemtic showing the dt reduction process used for the Shck-Hrtmnn device. FEA llowed us to model the chrcteristic deformtion t the torsion bem nd the "flpping" of the corners of the mirror. The FEA progrm used to model nd nlyze the mirror deformtion is Cosmos/M. The FEA predicted surfce deformtion ws multiplied by fctor of 2 to obtin the wvefront deformtion nd is plotted here in the right pnel of Figure 3. For 1.27 degree mximum scn ngle, the predicted pek to pek wvefront deformtion is 0.44 X with n RMS error of X. This dt is compred with mesurements of the sme mirror, summrized in subsequent sections of this pper, nd found to be bout 25% lrger thn the mesured deformtion. We believe this is due to uncertinty in the dmping coefficient used in the FEA. Mesurements confirm the dominnt deformtion mechnisms to be the stress t the torsion bem nd the flpping t the corners TORSION SEAM Wvefront Deformtion Predicted Using FEA Scn Angle = I.27 degrees Pek to Pek Deformtion = RMS Wvefront Error = X Figure 3-The left pnel shows the bsic mirror structure. Rottion occurs bout n xis prllel to nd running through the torsion bems. The right pnel shows the results of the FEA. Deformtion is dominted by twisting stress t the torsion bems. 482 Proc. SPIE Vol. 4451

4 5.1 EXPERIMENTAL DESIGNS 4.1 Stroboscopic Interferometer A schemtic of the stroboscopic mterferometer is shown in Figure 4. A Twymn-Green interferometer is formed using bem splitter, reference mirror nd the scnning mirror. A fiber coupled 635 nm lser diode is used s the light source nd rely imging system is used to imge the fringe pttern onto the CCD cmer. Fiber coupling is used here to provide diffrction limited opticl bem. A mximum of 2 mw of power is delivered from the fiber. The scnning mirror is driven in sinusoidl oscilltion t between 1 5 nd 20 khz nd t mximum ngles rnging from 0 to over 5 degrees. To fcilitte the mesurement of the dynmic mirror deformtion t n rbitrry scn ngle, signl is synchronized to the phse of the scnning mirror nd is delivered to dely genertor, which in turn delivers pulse to the lser diode driver t the frequency t which the scnning mirror is oscillting. Adjustment of the dely tunes the strobe to be incident on the scnning mirror t specific scn ngle. The rottion stge then redirects the bem tht is reflected t the scnning mirror down the opticl xis of the interferometer on into the CCD cmer. The durtion of the lser pulse determines the temporl resolution of the mesurement. Minimizing the pulse length increses the temporl resolution of the mesurement. However, this reduces the power incident on the CCD cmer resulting in poor contrst nd low signl to noise rtio. The mesurement presented here used pulse durtions between nsec. Fiber 8-20 nsec Pulse Delyed Reltive to Sync Sync Signl Figure 4 Experimentl set-up of stroboscopic interferometer. A sptil liner crrier nlysis'3 reduces the interferogrm nd the surfce deformtion of the mirror is infened. A crrier frequency is introduced by tilting the reference wvefront reltive to the smpling wvefront, introducing high sptil frequency fringes into the interferogrm. The typicl frequency of the sptil crrier for the dt tken is 10 (mm1). High frequency noise is removed using low pss filter Proc. SPIE Vol

5 with cut-off frequency set to.75 times the cnier frequency. A typicl interferogrm tken from MEMs scnning minor is shown in the upper left corner offigure Shck-Hrtmnn Wvefront Sensor The experimentl set-up for the Shck-Hrtmnn is similr to the interferometer. Figure 5 shows schemtic of the test bed. The Shck-Hrtmnn test bed uses the sme lser diode nd electronics with the sme dely nd triggering schemes used in the interferometer. Here we hve not fiber coupled the lser diode. This llows us to deliver more power to the Shck-Hrtmnn sensor, reducing the integrtion time on the CCD cmer nd incresing the temporl resolution. Becuse the Shck-Hrtmnn dt reduction softwre cn remove wvefront enors on the reference bem, perfect diffrction limited bem ws not required. The rottion stge, enbles smpling the dynmic mirror deformtion t rbitrry scn ngles. The mesurement procedure requires tht the Shck-Hrtmnn wvefront sensor be locted t the imge plne of the imging system nd tht the scnning mirror be locted t the object plne. With this condition met, rottion of the mirror will not result in lterl trnsltion of the imge plne. The lignment procedure begins with the scnning mirror in sttic position. The surfce of the mirror is mounted such tht is locted directly bove the center of rottion of the rottion stge. A trnsltion stge enbles fine djustment of the mirror surfce reltive to the center of rottion. Alignment of the reflected bem is such tht it is coincident with the opticl xis of the imging system nd directed onto the center of the sensor. The longitudinl position of the sensor is djusted using trnsltion stge such tht the imge of the scnning mirror remins sttionry s sttic mirror is rotted. The position of the object plne is then verified by rotting the sttic mirror. If the cmer is locted t the imge plne nd the scnning mirror is locted t the object plne, there will be no lterl trnsltion of the imge s the mirror is rotted. Some itertion is required to minimize the trnsltion. Figure 5- Experimentl set-up used for Shck-Hrtmnn wvefront sensor mesurements. To crete reference wvefront dt, the scnning mirror is returned to its sttic position with the reflected bem directed down the opticl xis of the imging system nd reference bem is recorded. Typicl noise floors, chieved in this wy, re less thn 0.05?. Note here tht the cretion of the reference file in this wy, removes ny sttic surfce deformtion from the mirror. To check the repetbility of this noise floor, the scnner ws turned on nd off severl times, nd the noise floor mesured. We found tht the noise floor returned to less thn The next step in the mesurement procedure is to turn the scnner on nd djust the dely on the lser diode pulse until the mesured wvefront tilt is minimized. This results in the condition tht the lser pulse 484 Proc. SPIE Vol. 4451

6 smples the mirror t zero scn ngle. The dt cquisition nd reduction softwre opertes rpidly nd is ble to provide effectively "rel time" mesurements of the wvefront tilt s the dely is tuned. After determining the dely t the center of the scn, incrementl chnges in the dely re mde. Chnging the dely results in the introduction of wvefront tilt. The softwre displys the mgnitude of this tilt. The rottion stge is now used to remove the tilt. As the tilt of the minor is removed, the dynmic surfce deformtion of the mirror is displyed. Complete removl of the tilt is not necessry, s the softwre will subtrct tilt (if it does not exceed the dynmic rnge of the instrument). In this wy, surfce deformtion mp of the mirror surfce is mesured t known ngle of the scnner oscilltion. 5.1 RESULTS In this section, we present wvefront deformtion mesurements for MEMS mirror. Mesurements re tken of the sme mirror using both the interferometer nd the Shck-Hrtmn. Results show good greement with the FEA results, confirming the dominnt deformtion mechnism. Further, the results obtined using the interferometer re in excellent greement with those obtined using the Shck-Hrtmnn wvefront sensor. Interferogrm of MEMS Mirror Scn Angle 1.27 deg Mesured Mirror Deformtion t Scn Angle 1.27 deg Pek to Pek Wvefront Deformtion = 0.35 RMS Wvefront Error = ) C ) ) > c C E.2 0 ) C ) > Interferogrm of MEMS Mirror Scn Angle-ner 0 degrees Mesured Mirror Deformtion t Scn Angle Ner 0 Degrees Pek to Pek Wvefront Deformtion.12 X RMS Wvefront Error =0.02 X Figure 6- Mesurement results obtined using the stroboscopic interferometer. Results re shown for scn ngles t 0 nd 1.27 degrees. Proc. SPIE Vol

7 5.1 Interferometric Mesurements The MEMS mirror is mounted s described previously onto the rottion stge of the interferometer test bed. Two mterferogrms re tken, one with the dely set t the pek voltge of the drive electronics nd one with the dely set t zero crossing of the drive electronics. There is some dely between the pek voltge nd the scn ngle due opertion t resonnce nd delys in the electronics. The left pnel of Figure 6 show these dt. The wvefront deformtion mps, infened from the interferogrms, re shown on the right pnels. Pek to pek wvefront deformtion t scn ngle estimted to be 1.27 degrees, is clculted to be 0.35 X with n RMS wvefront enor of X. The deformtion mp shows the chrcteristic wrping due to stress t the mirror flexures predicted by the FEA. The lower pnels show the results for scn ngle ner zero. At zero scn ngle the mirror ccelertion is zero nd the mechnicl stresses re zero. In this cse, the wvefront deformtion should indicte no wrping t the flexures. However, this deformtion mp shows cler wrping due to stresses, from which we conclude tht the scn ngle is not t precisely zero. Given the cler indiction of this chrcteristic pek to pek deformtion, we conclude tht the interferometer is cpble of resolving fetures with sensitivity greter thn 0.05 A. 5.2 Shck Hrtmnn Wvefront Sensor Mesurements The sme scnning mirror is mesured using the Shck-Hrtmnn device nd using the procedure described bove. The left pnel of Figure 7 shows the results for scn ngle of 1.27 degrees. The surfce mp shows the chrcteristic dynmic deformtion of the torsion bems. The mgnitude of the pek to pek wvefront deformtion is mesured to be 0.32? with RMS wvefront enor of Both of which re in good greement with the interferometer mesurements. The results in the right pnel show the mirror deformtion t scn ngle of 6.5 deg. The mesured pek to pek wvefront deformtion is 1.34? with RMS error ofo.19 X. Mesured Mirror Deformtion using Shck- Hrtmnn t Scn AngIe =1.27 deg Pek to Pek Wvefront Deformtion RMS Wvefront Error = X Mesured Mirror Deformtion using Shck- Hrtmnn t Scn AngIe =6.5 deg Pek to Pek Wvefront Deformtion= RMS Wvefront Error = 0.19 X S ) S ) ) Figure 7-Wvefront deformtion dt obtined using the Shck-Hrtmnn wvefront sensor. 6.0 Conclusions The dynmic deformtion of high frequency MEMS scnning mirror hs been modeled using FEA nd mesured using n interferometer nd Shck-Hrtmnn wvefront sensor. Mesurements using the interferometer nd Shck-Hrtmnn re in excellent greement. Mesurements confirm tht the dominnt deformtion mechnism is twisting t the mirror torsion bems. Mesurements re bout 25% less thn 486 Proc. SPIE Vol. 4451

8 tht predicted by the FEA. We believe this is due to uncertinty in the dmping coefficients used in the FEA. Both the Shck-Hrtmn sensor nd the stroboscopic mterferometer hve been shown to be cpble of mesuring high frequency mirror deformtions with sensitivity of less thn.05 X. Advntges of the Shck-Hrtmnn device include; 1) robust production redy mesurement pckge; 2) the ner rel time dt reduction softwre enbling rpid mesurements; 3) the use of reference file enbling the removl of bentions in the probe bem nd imging optics; nd 4) lrge dynmic rnge llowing for ccurte loction ofthe mirror ngle. Improvements tht will be mde to the test bed using the Shck-Hrtmnn wvefront sensor include incresing the lser diode power. A 200 mw 830 nm lser diode hs recently been instlled on the test bed. This will llow for shorter integrtion times nd higher temporl resolution, with the possibility of performing single shot mesurements. The resolution of the rottion stge will be incresed llowing for the djustment nd mesurement of the scn ngle with higher precision. REFERENCES 1. Urey, H.; Wine, D.; Osborn, T. Opticl performnce for MEMS-scnner bsed microdisplys. In MOEMS nd Miniturized Systems, Proc. SPIE vol , Snt Clr, CA, Sep 2000, Urey, H.; Wine, D.W.; Lewis, J. R. Scnner design nd resolution trdeoffs for miniture scnning displys. In Flt Pnel Disply Technology nd Disply Metrology, Proc. SPIE vol. 3636, Sn Jose, CA, Jn. 1998; R. Connt, J. Nee, K. Lu, R. Muller, "Dynmic Deformtion of Scnning Micromirrors," IEEE/LEOS Opticl MEMS 2000, Kui, Hwii, pgs J.S. Hrris, R.L. Fusek nd J.S. Mrcheski, "Stroboscopic interferometer", Applied Optics, 1 8, , D. R. Nel, D. J. Armstrong nd W. T. Turner, "Wvefront sensors for control nd process monitoring in optics mnufcture," SPIE 2993 (1997) 6. D. R. Nel, W. J. Alford, nd J. K. Gruetzner, "Amplitude nd phse bem chrcteriztion using two-dimensionl wvefront sensor," SPIE Vol. 2870, pp (1996). 7. W. H. Southwell, "Wve-front estimtion from wve-front slope mesurements," J. Opt. Soc. Am., Vol. 70, No. 8 (August 1980). 8. R. Q. Fugte, "Observtions of fint objects with lser becon dptive optics," SPIE Vol. 2201, pp (1994). 9. D. R. Nel, T.J. O'Hern, JR. Torczynski, ME. Wnen, nd R. Shul, "Wvefront sensors for opticl dignostics in fluid mechnics: ppliction to heted flow, turbulence nd droplet evportion," SPIE Vol. 2005, pp (1993). 10. D. R. Nel, W. J. Alford, nd J. K. Gruetzner, "Amplitude nd phse bem chrcteriztion using two-dimensionl wvefront sensor," SPIE Vol. 2870, pp (1996). 11. D. R. Nel, D. J. Armstrong, E. Hedlund, M. Lederer, A. Collier, C. Spring, J. Gruetzner, G. Hebner nd J. Mnsell, "Wvefront sensor testing in hypersonic flows using lser-sprk guide str," SPIE Vol (1997). Proc. SPIE Vol

9 12. D. R. Nel, D. J. Armstrong nd W. T. Turner, "Wvefront sensors for control nd process monitoring in optics mnufcture," SPIE 2993 (1997) 13. D. Mlcr, M. Servin, nd Z. Mlcr, "Interferogrm nlysis for opticl testing", pg Mrcel Dekker, mc, New York, NY, Proc. SPIE Vol. 4451