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AERI ™ Atmospheric Patterns

AERI ™ Atmospheric Patterns. Approach and Supporting Data 26 May 2006. Approach. Aeri ™ pattern files representing atmospheric turbulence were created by simulating atmosphere phase and commanding the mirror to correct the phase aberration

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AERI ™ Atmospheric Patterns

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  1. AERI™ Atmospheric Patterns Approach and Supporting Data 26 May 2006

  2. 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

  3. 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)

  4. 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

  5. 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

  6. 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)

  7. 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)

  8. 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)

  9. 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)

  10. 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)

  11. RMS Phase and Phase Variance 30 Zernike Terms – (D/r0)0.5 = 30 (tilt included) RMS Phase (microns) Phase Variance (2) ( 2 )Noll = 298 • Large “DM Corrected” errors indicate • poor DM fit to atmospheric phase • Error magnitude exceeds the limits • of the DM design ( 2 )=633 nm = 186 (D/r0 = 22.6)

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