Transcript power point presentation

AERI™ Atmospheric Patterns
Approach and Supporting Data
26 May 2006
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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
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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)
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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
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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
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- expected variances calculated for = 633 nm
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)
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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)
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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)
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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)
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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)
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RMS Phase and Phase Variance
30 Zernike Terms – (D/r0)0.5 = 30 (tilt included)
RMS Phase (microns)
• Large “DM Corrected” errors indicate
poor DM fit to atmospheric phase
• Error magnitude exceeds the limits
of the DM design
Phase Variance (2)
( 2 )Noll = 298
( 2 )=633 nm = 186 (D/r0 = 22.6)
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