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AERI™ Atmospheric Patterns Approach and Supporting Data 26 May 2006 1 Approach • Aeri™ pattern files representing atmospheric turbulence were created by simulating atmosphere phase and commanding the mirror to correct the phase aberration • The Kolmogorov spectrum is often used for constructing phase aberrations representative of those produced by atmospheric turbulence • Atmospheric phase realizations were constructed using a Zernike Polynomial representation of Kolmogorov turbulence - based on: R. J. Noll, “Zernike polynomials and atmospheric turbulence,” JOSA, Vol. 66, No. 3, March 1976 - Zernike term strength based on aperture size (D) and atmospheric coherence diameter (r0) - variance of Zernike terms are proportional to (D/r0)5/3 2 Approach cont’d • Wavefront slope measurements of atmospheric phase are used to drive DM correction - Control matrix derived from DM zonal influence functions for mirror design - Control provides least-squares fit of DM surface phase to phase aberrations - Correction is applied statically in simulation • Mirror Voltages obtained for each phase aberration correction define pattern file voltages • Residual phase after static correction determines DM performance in matching phase - Residual RMS phase variance (2) - Strehl Intensity can be estimated from phase variance (Istr = exp(-2)) - only valid for wavelength used in simulation (can scale to wavelength desired) 3 Supporting Data • Simulations were conducted using an optical wavelength () of 500 nm - the atmospheric coherence diameter (r0) is proportional to 6/5 - atmospheric strength (OPD) varies with the ratio D/r0 - D/r0 can be scaled to any wavelength using r0 for = 500 nm (r0 (500)) D/r0 () = D/r0 (500) (500 / (nm))6/5 - phase variance scales according to: ()2 = (500)2 (500 / (nm) )2 - OPD calculated for 500 nm simply represents a different D/r0 at a different • Atmospheric tilt is a large portion of the phase variance due to atmospheric turbulence - Adaptive Optics (AO) systems generally use tip/tilt mirrors to correct tilt errors - atmospheric phase with tilt removed is of general interest for AO systems - atmospheric phase with tilt included may be of interest for simulating the atmosphere - atmospheric pattern files produced for the Aeri™ may include tilt if desired - including tilt severely limits the range of atmospheric strengths adequately represented using a given Aeri™ design 4 Supporting Data cont’d • Ran simulations to produce pattern files for Aeri™ at 3 values of D/r0 for =500 nm - D/r0 = 10, 15, and 30 with both tilt removed and tilt included - at = 633 nm, D/r0 = 7.5, 11.3, and 22.6, respectively - used up to 30 Zernike aberration terms (from Noll) to define 150 uncorrelated phase realizations at each D/r0 - atmospheric coherence time is on the order of 1 msec - the delay between pattern realizations is totally controllable with Aeri™ • Statistics representative of the atmospheric realizations are given in the following slides - RMS phase and ensemble-mean of uncorrected RMS phase - RMS of Uncorrected phase, DM phase, and DM Corrected phase - RMS DM Phase is the expected spatial RMS phase due to each atmospheric phase pattern induced by the Aeri™ - DM Corrected phase represents residual error in DM match to each atmospheric phase realization - Phase Variance and ensemble-mean uncorrected Phase Variance - variance for Uncorrected phase, DM phase, and DM Corrected phase are given - calculated variances (from Noll, pg. 210) agree well with ensemble-mean values - expected variances calculated for = 633 nm 5 RMS Phase and Phase Variance 28 Zernike Terms – (D/r0)0.5 = 10 (tilt removed) RMS Phase (microns) Phase Variance (2) ( 2 )Noll = 6.2 ( 2 )=633 nm = 3.8 (D/r0 = 7.5) 6 RMS Phase and Phase Variance 30 Zernike Terms – (D/r0)0.5 = 10 (tilt included) RMS Phase (microns) Phase Variance (2) ( 2 )Noll = 47.8 ( 2 )=633 nm = 30 (D/r0 = 7.5) 7 RMS Phase and Phase Variance 28 Zernike Terms – (D/r0)0.5 = 15 (tilt removed) RMS Phase (microns) Phase Variance (2) ( 2 )Noll = 12.2 ( 2 )=633 nm = 7.6 (D/r0 = 11.3) 8 RMS Phase and Phase Variance 30 Zernike Terms – (D/r0)0.5 = 15 (tilt included) RMS Phase (microns) Phase Variance (2) ( 2 )Noll = 94 ( 2 )=633 nm = 59 (D/r0 = 11.3) 9 RMS Phase and Phase Variance 28 Zernike Terms – (D/r0)0.5 = 30 (tilt removed) RMS Phase (microns) Phase Variance (2) ( 2 )Noll = 38.8 ( 2 )=633 nm = 24 (D/r0 = 22.6) 10 RMS Phase and Phase Variance 30 Zernike Terms – (D/r0)0.5 = 30 (tilt included) RMS Phase (microns) Phase Variance (2) • Large “DM Corrected” errors indicate ( 2 )Noll = 298 poor DM fit to atmospheric phase • Error magnitude exceeds the limits ( 2 )=633 nm = 186 (D/r0 = 22.6) of the DM design 11
"Slide 1 - AgilOptics"