First-order finite element model for modeling of a continuous facesheet deformable mirror

Evaluationoftheusea rstorder niteelementmo delformo delingofacontinuousfacesheetdeformablemirrorKelsey L. Rogers,Air Force Research Lab oratory, Directed Energy Directorate, Star re Optical Range3550 Ab erdeen Ave SE, Kirtland AFB, NM 87117-5776Je rey D. BarchersScience Applications International Corp orationAir Force Research Lab oratory, Directed Energy Directorate, Star re Optical Range3550 Ab erdeen Ave SE, Kirtland AFB, NM 87117-5776ABSTRACTA calibration pro cedure is describ ed for improved mo deling of a continuous facesheet deformable mirror.Aresistiveforceofeachactuatorasitattemptstomovitscommandedp ositionismo deledalinearspringforce.Aforceasso ciatedwiththeresistanceoffacesheettob endingismo deledasamomentthatexertsforceontheactuators.Theresultan rstorder niteelemenmo delisparameterized by a gain on each actuator channel and a ratio relating the average actuator spring constantand the facesheet b ending momentcoecient.Example exp erimental results are presented indicating thatmo deling accuracy is improved by use of the rst order nite element mo del.Keywords:adaptive optics, deformable mirrors1INTRODUCTIONManyadaptiveopticalsystemsinuseto daemplowhatiscommonlyknownasa\conventional",continuousfacesheet deformable mirror (DM).1Conventional DMs utilize electrostrictive actuators that elongate when voltageis applied.The actuators are attached to the back of a thin reective facesheet that deforms according to the p ositionsof the actuators.The p ositions of the actuators are controlled by measurements fromawavefront sensor.The typicalsensor in use to dayisa Hartmannsensor in the Fried-geometry.TheHartmann wavefront sensor measures phasegradients and a reconstructor is then used to estimate the phase function.The reconstructor is typically computedbased on an assumption that the resp onse of the DM to changes in the actuator voltage is linear and that the motionof one actuator do es not e ect the motion of the other actuators.This is not in fact true.Pushing up on one actuator causes an \inuence" on the neighb oring actuators b ecauseofthesti nessDMfacesheet.Further,ab endingmomentisoftenobserved ab outnearest neighboringactuators that causes the actuators two spacings aay to exp erience a downard pushing force.In general, one do esnot have to b e concerned with suchtypically small magnitude e ects:By allowing the waefront sensor to observethewavefrontaftercorrectionbyDM,thereisfeedbackregardingerrorsthato ccurduetomo deluncertainties and there is a minimal impact on p erformance.However, there are at least to instances known to theauthors in whichsuch mo deling errors can b e signi cant.If one wishes to utilize knowledge of the DM commandscombinedwithmeasurementsoftheresidualwavefronttoformanestimateinputdisturbance(turbulenceinduced wavefront distortions), then mo del uncertainties directly cause an estimation error.This is, in a sense, anop en lo op use of the data.Op en lo op applications are typically highly sensitive to mo del uncertainties.The second situation in which mo deling errors can b ecome imp ortant is when one considers advanced adaptiveopticalsystems designed to comp ensate forbranchpoints inthephase function.It has b eenshown thatthe p er-formanceofaHartmannsensorcanbeseverelylimitedinstrongscintillationduetobranchpointsthephasefunction | even when a reconstructor capable of estimating the branchpointcontribution to the phase function is