Adapive Opics PSF reconsrucion a ALFA Sebasian Egner Max-Planck Insiue for Asronomy, Heidelberg Vicoria, 10. 12. May 2004 Adapive Opics PSF reconsrucion workshop
Layou of he alk ALFA sysem relevan parameers on-axis PSF reconsrucion conrol loop AO loop daa AO loop daa PSF off-axis PSF reconsrucion his afernoon firs resuls Srehl raio, shape of PSF fuure plans pyramir,, ESO
The ALFA sysem ALFA = Adapive opics wih a Laser For Asronomy Calar Alo, Spain
ALFA General 3.5 m elescope, Calar Alo / Spain SHS, 28 subaperures,, Keysone design Xineics DM, 97 acuaors,, 7cm CCD deecor, Lincoln Labs, LLCCD, 64x64 pixel RON 4 e - mos sensiive in he visible (500nm) Up o 1000Hz frame rae
ALFA Loop Conrol DSP compuer: 5 DSP boards, each 4 DSP chips, 12 MHz, VxWorks Loop frequency: : 100 300 Hz used Modal conrol: Zernike modes, Karhunen-Loeve funcions, 32 modes Leas-Squares algorihm o calculae reconsrucion marix (MAP, WLS in preparaion)
ALFA Opical Seup FISBA inerferomeer: measure response of DM Fiber can be placed a focus poin: calibraion of AO saic aberraions for PSF reconsrucion OmegaCass in K-band science camera, Hawaii deecor, 0.04 /pixel
ALFA Opical Seup II
PSF reconsrucion @ ALFA Markus Kasper: now a ESO basic algorihms, ALFA opimizaion Rober Weiss: now a FGAN / FOM implemenaion of PSF reconsrucion, es of principle
PSF from OTF Calculae OTF: (Veran Veran 1997) PSF = FFT(OTF) OTF (ñ) = OTF (ñ) OTF (ñ) OTF (ñ) o sa ε Saic aberraions: fiber image Conrolled modes: modal covariance marix OTF / Phase Srucure Funcion D: Un-conrolled modes: Kolmogorov covariance marix [ ] D ) OTF ( ρ) = exp (ñ x x
OTF from loop daa Conrolled modes: residual modal covariance D φ ε (ñ) = εε U Un-conrolled modes: heoreical higher order modal covariance D φ (ñ) = m i, j i, j > m i, j a a ij ij ij U ( ρ) ij ( ρ)
U funcions ij U ij U ij funcions: ( ) ( ) [ ( ) ( )] [ ( ) ( )] ( ) P r P r + ρ Fi r Fi r + ρ Fi r Fi r + ρ ij ρ = 2 P( r) P( r + ρ) d r Calculaed numerically for given elescope P(r) and conrol modes F i (r) Conrol modes F i (r) : Theoreical modes (Karhunen( Karhunen-Loeve / Zernike) Measured wih FISBA inerferomeer d 2 r
Modal covariance marix True residual modal covariance marix: εε εε ˆˆ + C a a C R R ˆ ε ˆ ε a a R Measured residual modal covariance marix Noise covariance marix Higher order modal covariance marix Reconsrucion Marix (LS)
Residual modal covariance εε εε ˆˆ + C a a C R R Deermined direcly from measured residual modes Sop loop and save residual modes 12 000 modal ses 40s @ 300Hz Calculaed off-line
High order modal covariance εε εε ˆˆ + C a a C R R Theoreical modal covariance marix for Kolmogorov urbulence and Karhunen-Loeve funcions (diagonal) Calculaed numerically for given elescope Consider ~250 modes Scale wih r 0 Aliasing / Crossalk marix: C + = D D
Crossalk marix Crossalk marix: + D : reconsrucion marix from measured ineracion marix by Leas- squares algorihm (SVD) : Simulaed ineracion marix D C Use numerical model of SHS Consider ~250 KL-modes + = D D
Fried-parameer For scaling of higher-order modal covariance marix for alias calculaion: Fried-parameer r 0 needed Calculae r 0 from AO loop daa Idea: Low-order (measured) modal covariance marix in open-loop scales wih r 0 Calculae his modal covariance marix from measured closed-loop daa Fi measured o heoreical one o ge scaling facor (r( 0 )
Fried-parameer II True modal covariance marix closed loop: 2 aa mm C a a C R R h ( f ) df mm : Measured modal covariance (mirror modes) 2 h n ( f ) df : Noise ransfer funcion analyically Noise and aliasing like above n
Mirror Modes aa 2 mm C aa C R R hn ( f ) In ALFA no possible o: Save applied /mirror modes Calculae mm online Simulaion saring from residual gradiens ALFA conrol sysem digial, use same parameers Assume perfec DM Calculae applied / mirror modes df
Fried-parameer - Ieraion aa 2 mm C aa C R R hn ( f ) Diagonal of aa scales wih r 0 Aliasing also scales wih r 0 Ieraion o deermine r 0 (Kasper, 2000) Saring from r 0 = Convergence wihin ~3 10 ieraions df
Fried-parameer - Ieraion aa 2 mm C aa C R R hn ( f ) Diagonal of aa scales wih r 0 Aliasing also scales wih r 0 Ieraion o deermine r 0 (Kasper, 2000) Saring from r 0 = Convergence wihin ~3 10 ieraions df
Fried-parameer Accuracy Compare wih SCIDAR measuremens Accuracy of r 0 deerminaion: Closed-loop: simulaions, excellen agreemen, very small underesimaion (differen viewing direcions) Open-loop: sligh over-esimaion, consan il in SHS measuremens
Fried-parameer Accuracy Compare wih SCIDAR measuremens Accuracy of r 0 deerminaion: Closed-loop: simulaions, excellen agreemen, very small underesimaion (differen viewing direcions) Open-loop: sligh over-esimaion, consan il in SHS measuremens
Noise covariance marix εε εε ˆˆ SHS: CCD read-ou noise (~4 e - ) Noise deerminaion: auocovariance for each of he gradien ime-series: (Gendron & Lena, 1995) V ( L) = noise in differen subaperures uncorrelaed (diagonal marix) + C a a C 1 N N R ( x )( ) i x xi L x i= L R
Noise covariance marix II Amospheric Signal emporal correlaed, noise uncorrelaed Open-loop: difference / quadraic fi o origin hen difference: Closed-loop: = n = [ V (0) V (1) ] V ( 0) V V ( d loop 2V ( d (1) less correlaed (because of parial correcion) correcion o his formula (Hamilon, 1994): n 1) + V loop ( d 1) loop )
Noise covariance marix II Amospheric Signal emporal correlaed, noise uncorrelaed Open-loop: Open-loop difference / quadraic fi o origin hen difference: Closed-loop: n = n = [ V (0) V (1) ] V ( 0) V V ( d loop 2V ( d (1) less correlaed (because of parial correcion) correcion o his formula (Hamilon, 1994): 1) + V loop ( d 1) loop )
Noise covariance marix II Amospheric Signal emporal correlaed, noise uncorrelaed noise esimaion Open-loop: Closed-loop Open-loop difference / quadraic fi o origin hen difference: Closed-loop: n = n = [ V (0) V (1) ] V ( 0) V V ( d loop 2V ( d (1) less correlaed (because of parial correcion) correcion o his formula (Hamilon, 1994): 1) + V loop ( d 1) loop )
Noise covariance marix III Accuracy of noise deerminaion in closed-loop operaion for LS algorihm (does no work for WLS, MAP) Simulaion: addiional noise on measured gradiens, deermine oal noise Scaer around han 10% Sligh underesimaion: : ~1%
Noise covariance marix III Noise esimaion on Accuracy of noise deerminaion in closed-loop closed operaion loop residual for LS gradiens algorihm (does no work for WLS, MAP) Simulaion: addiional noise on measured gradiens, deermine oal noise Scaer around han 10% Sligh underesimaion: : ~1%
Implemenaion IDL code o generae needed funcions U ij IDL code o calculae he noise and residual modal covariance marix off-line from measured residual gradiens IDL simulaion for ALFA conrol sysem o calculae mirror modes from measured residual gradiens IDL code o calculae he PSF
Implemenaion II Gradiens g MEASUREMENTS Calibraion PSF SIMULATION Loop simulaion SHS simulaion m C n r 0 D ε D sa D a U ij NUMERICAL
Firs resuls brigh guide sar Brigh guide sar (7.14 mag) Median seeing (0.9 in V-band) Loop frequency 300 Hz Good correcion (Srehl( 46% on-axis) Deviaion (measured/reconsruced) smaller han 10% firs Airy-ring: fiber image? Undersampling of fiber PSF Problems wih OmegaCass: Coma (il / decenering) Srehl (%) FWHM ( )( Measuremen 45.7 ± 2.0 0.14 ± 0.01 Reconsruced 47.6 0.13
Firs resuls brigh guide sar Brigh guide sar (7.14 mag) Median seeing (0.9 in V-band) Loop frequency 300 Hz Good correcion (Srehl( 46% on-axis) Deviaion (measured/reconsruced) smaller han 10% firs Airy-ring: fiber image? Undersampling of fiber PSF Problems wih OmegaCass: Coma (il / decenering) Srehl (%) FWHM ( )( Measuremen 45.7 ± 2.0 0.14 ± 0.01 Reconsruced 47.6 0.13
Firs resuls fain guide sar Fain guide sar (13 mag) Median seeing (1.1 in V-band) Loop frequency 75 Hz Low correcion (Srehl( 13%) Srehl (%) FWHM ( )( Measuremen 13.2 ± 1.9 0.24 ± 0.02 Reconsruced 13.3 0.22
Firs resuls fain guide sar Very sensiive o he correc noise esimaion Wih oher mehods for noise deerminaion PSF reconsrucion no possible Deerminaion of r 0 gives wrong resuls Correcion for noise in conrolled modal covariance no correc Deviaion (measured/reconsruced) in x-cu direcion Coma: decener / il of OmegaCass (field-independen) Fiber image undersampled Cu y-direcion / radially averaged: accepable agreemen beween measured and reconsruced OTF deviaion: : lower SNR
Firs resuls fain guide sar Very sensiive o he correc noise esimaion Wih oher mehods for noise deerminaion PSF reconsrucion no possible Deerminaion of r 0 gives wrong resuls Correcion for noise in conrolled modal covariance no correc Deviaion (measured/reconsruced) in x-cu direcion Coma: decener / il of OmegaCass (field-independen) Fiber image undersampled Cu y-direcion / radially averaged: accepable agreemen beween measured and reconsruced OTF deviaion: : lower SNR
Fuure plans Adap sofware o ESO (NACO) daa: Ya Clene (ESO) PyramIR (PYRAMid InfraRed wavefron sensor) a ALFA: complemen SHS sysem plaed comissioning: : Nov 2004 new conrol compuer (4 Xeon off-he-shelf) also applied modes / covariance marix & r 0 online in closed-loop operaion PSF reconsrucion as service wih science images
Summary Principle is working for ALFA sysem No ye service for observaion (PyramIR) Problems: No all parameers direcly accessible (Fried prameer,, noise, modal covariance, ) Saic aberraions (Coma / Trefoil of OmegaCass, undersampled images) Firs resuls on-axis promising: Srehl raio & FWHM: very good Overall shape of PSF: saic aberraions