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AERI™ Atmospheric Patterns

Approach and Supporting Data

26 May 2006

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• 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

Approach

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• 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)

Approach cont’d

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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- expected variances calculated for = 633 nm

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RMS Phase (microns) Phase Variance (2)

RMS Phase and Phase Variance28 Zernike Terms – (D/r0)0.5 = 10 (tilt removed)

( 2 )Noll = 6.2

( 2 )=633 nm = 3.8 (D/r0 = 7.5)

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RMS Phase and Phase Variance30 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 Variance28 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 Variance30 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 Variance28 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 Variance30 Zernike Terms – (D/r0)0.5 = 30 (tilt included)

RMS Phase (microns) Phase Variance (2)

( 2 )Noll = 298

( 2 )=633 nm = 186 (D/r0 = 22.6)

• Large “DM Corrected” errors indicate poor DM fit to atmospheric phase• Error magnitude exceeds the limits of the DM design