Analytical modeling of astronomical AO

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Analytical modeling ofastronomical AO

• New developments for
• active optics, laser guide star, MCAO

Laurent Jolissaint, HIA/NRC, Canada Rodolphe
Conan, University of Victoria, Canada CfAO Spring
Retreat 2005
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AO modelisation problem

• Matrices size
• Large mirror diameter, pixel scale 5 masec
• Atmospheric halo, large FoV 5 asec
• Segment gaps / mirror diameter 4 / 30'000
• gt 1'000 to 10'000 pixels for ELTs
• Needs huge CPU resources or ... be patient
• Solution split study
• 1. Explore AO parameter space with fast analytic
  tools
• 3. Select a few promising cases (best
  performances)
• 2. Run a Monte-Carlo analysis on a detailled
  End-to-End model to get second order effects
  e.g. DM/WFS misregistration, hidden modes...
• - B. Ellerbroek MC code M. Britton Arroyo c
  code, ...

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Basic principle of analytical method

• Total OTF OTF(TSC) x OTF(AO)
• OTF(AO)exp-1/2 SF(AO)
• SF(AO) an integral of phase power spectrum (PS)
• Classical AO system 5 terms in phase PS,
  (analytic)
• 1- High spatial frequencies - not corrected by DM
• 2- WFS Aliasing
• 3- WFS noise
• 4- Control System time-lag
• 5- Anisoplanatism
• Implemented in code PAOLA
• See Jolissaint, Veran, Conan (submitted to JOSA
  A, Feb. 2005)

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Other people codes

• Ellerbroek, B. CIBOLA code, includes correlation
  between phase components, modal (spatial
  frequency) gain optimisation, ...
• See Ellerbroek, SPIE 5490, 2004
• Verinaud, C. Spatial frequency analysis of
  pyramid sensor
• See Verinaud, C. in Optics Comm. 233, 2004
• Conan, R. et al. Development includes closed loop
  temporal transfer functions
• Internal note ONERA, Paris. To be published ...
• Gavel, D. - status ? reference ?

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New development active optics (aO)

• Step 1. It is possible to write an analytical
  expression for phase amplitude spectrum, for
  segmented hexagonal mirror
• Step 2. DM is a spatial filter, for which we do
  have an analytical expression derived from
  accurate measurement of real influence functions
  (ALTAIR's DM)
• Step 3. Filtered phase FT DM_filter x phase FT
  WFS aliasing
• Step 4. Go to focal plane phasor via FFT, as
  usual.
• Advantage no constraint on matrix and pixel size
  (segment gap/mirror diameter) because we are not
  in the pupil plane, gt much faster than MC codes
• See Jolissaint Lavigne, SPIE 5497, 2004

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New development active optics (aO)
Result analytic vs. wave-optics TMT mirror
static aberrations corrected by AO loop
feed-back to aO control (Troy Jolissaint, TMT,
2004)
Pyramid IF filter
Real IF filter
Realistic filter closer to ideal one than the
filter derived from a pyramid IF model
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New development LGS TT-NGS

• Basic idea for LGS TT-NGS
• Tip-tilt PS extracted from turbulent phase PS,
  and we apply classical AO filtering to it
  anisoplanatism, servo-lag noise only, DM
  filter1, no aliasing.
• Sasiela (JOSA A, vol 11, Jan 1994) gives the
  phase filter associated to focal anisoplanatism
  off-axis LGS on pistontip-tilt filtered phase.
• Development of phase power spectrum gives 8
  components (3)
• 1- High spatial frequencies (classical term)
• 2- WFS Aliasing (new term, includes LGS cone
  effect)
• 3- Focal anisoplanatism (new term, Sasiela's)
• 4- Control System time-lag (new term, includes
  LGS cone effect)
• 5- WFS noise (classical term)
• 6- Tilt anisoplanatism (new term)
• 7- Tilt servo-lag (new term)
• 8- Tilt sensing noise equivalent angle (new term)
• Calculation done, implementation into PAOLA in
  progress

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New development MCAO

• Fusco et al, ONERA, 2001 spatial filter
  associated to multiple-star LSE reconstructor for
  MCAO
• Can be implemented into PAOLA instead of single
  star LSE reconstructor spatial filter
• Works for LGS too (reconstructor independent of
  GS type)
• Implementation into PAOLA in progress

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Discussions...

• Open loop vs. closed loop modelisation limit of
  validity ?
• Neglecting correlations between phase components
  validity ? See Ellerbroek's approach
• Obliged to assume homogeneity of phase correction
  as if DM was infinite in extension but filtered
  by telescope OTF, though
• AO-LGS residual phase not corrected homogeneously
  into the pupil obliged to do an average effect
  ? do not know yet...
• Easy to get LSE reconstructors in a spatial
  filter. What about other reconstruction
  algorithms ? I'll be interested...
• Want the code ?
• laurent.jolissaint_at_nrc-cnrc.gc.ca