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Slide 1 - AgilOptics

VIEWS: 0 PAGES: 11

									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

								
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