Wavefront Sensing for the LSST

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Wave-front Sensing for the LSST

• K.L. Baker

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Outline

• I. Overview
• II. Wave-front sensing techniques using the sky
• Curvature sensing
• Phase Retrieval
• Phase Diversity
• III. Active probing possibilities
• Shack-Hartmann Sensing
• Shear Interferometry
• IV. Wave-front tomography

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Overview

• The LSST will have three actively controlled
  mirrors, three lenses and a filter.
• These optics will have to be set initially and
  the mirrors will have to be continually actuated
  to counteract gravitational and thermal bending
  modes.
• Wave-front sensing techniques are required to
  sense the aberrations induced by the optics,
  thereby allowing their correction.
• The FPAs dedicated to wave-front sensing might
  need to be recessed, have a smaller pixel size,
  lower band gap energy than silicon, require
  additional optics or coatings.

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Curvature Sensing

• A curvature sensor measures the spatial intensity
  distribution equal distances on either side of
  focus.
• The difference in the intensity is proportional
  to the Laplacian of the phase.

Transport of Intensity Equation
References FFT - F. Roddier and C. Roddier, J.
Opt. Soc. Am. A. 10, 2277 (1993). Zernike - T.E.
Gureyev and K.A. Nugent, J. Opt. Soc. Am. A 13,
1670 (1996). Alt. Approach - M.A. Van Dam and
R.G. Lane, Appl. Opt. 41, 5497 (2002).
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Phase Retrieval/Phase Diversity (Measurement in
one plane)

• Simplest approach would be to use phase retrieval
  in a single plane.
• Phase retrieval (Gershberg-Saxton)
• Measure intensity far-field
• Assume intensity at pupil
• Guess a phase and iteratively transform between
  the two planes replacing the calculated intensity
  with the known intensity on each iteration
• Works well at small D/ro
• Next step is to deconvolve far-field with the
  long term Kolmogorov atmospheric psf

• Evaluate the effect of undersampling (20x for
  400 nm)
• Might require wfs pixel recession and additional
  optics to extend f/ and increase sampling

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Phase Diversity (Measurement in two planes)

• Phase diversity involves the measurement of the
  intensity in two planes.
• Typically at focus and a wave out of focus.
• Could potentially be accomplished by putting an
  additional transparent film on top of a portion
  of the WFS pixels in combination with additional
  optics such as a Wollaston prism.
• Different phase retrieval/phase diversity
  algorithms
• Gershberg-Saxton iteration/error reduction
• Gradient search method
• Least squares fitting of Zernike modes

Ref C. Carrano et al.,Phase retrieval
techniques for adaptive optics, Proc. SPIE. Vol.
3353, 658 (1998) R.G Paxman et al.,
Evaluation of Phase-Diversity Techniques for
solar-Image Restoration, Astr. Journal
466, 1087 (1996)
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Action Items for Phase Retrieval/Diversity

• Deconvolve the psf with the long-term Kolmogorov
  psf and average multiple shots to determine
  telescope aberrations using phase retrieval in a
  single plane.
• Begin simulations on phase diversity techniques
  using two measurement planes.
• Investigate performance of different algorithms
  for point sources, extended sources and general
  scenes under different atmospheric turbulence
  levels.
• Examine undersampling effects on achievable
  performance.

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Active Probing Possibilities

• Place fiber laser sources within the spider
  structure supporting the secondary mirror.
• Light reaching the FPA would be in the near
  field.
• Would allow the use of Shack-Hartmann sensors,
  shear interferometry or curvature sensors.
  Potentially phase diversity or correlation
  sensors with additional optics.
• Advantages
• Avoid most time-dependent atmospheric effects
• Probe from fixed locations allowing matrix
  inversion to be done outside of control loops
• Requirements to run concurrently with science
  data collection (First two were discussed to
  reduce atmospheric effects)
• WFS pixels lower bandgap energy (InGaAs-typically
  larger size 30 microns and non-uniformities)
• Coatings on lenses and filters pass wavelength
• Fiber lasers operate beyond Silicon Bandgap
• Different field points collected separately(SH,SI
  and C).
• Active probe dominate sky emission and collected
  at a rate of ltlt10 sec

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Wave-front Tomography via Zernike Decomposition

• Wave-front data from different field angles
  enables a tomographic reconstruction.
• Performing Zernike Decomposition at each of the
  axial planes greatly reduces the problem size.
• BHA where B is an array of optical path
  differences for each ray, H is the array of
  Zernike polynomial values for each ray and A is
  the array of Zernike coefficients describing the
  phase profile at each axial plane.
• A is determined by inverting the matrix H via
  singular value decomposition.

Tomography geometry
Applied Phase
Reconstructed Phase
Ref George N. Lawrence and Weng W. Chow, Opt.
Lett. 9 267 (1984).
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Summary

• We are investigating a number of techniques for
  wave-front sensing on the LSST.
• This also includes active probing of the
  telescope to avoid atmospheric effects. The
  transmission through the filters will likely
  determine the feasibility of this approach.
• In the near term we will primarily be looking at
  phase retrieval and phase diversity techniques
  applied to sky images.