Configuring the Pan-STARRS Optics
From Simulations to Operational Control System
Nick Kaiser
Pan-STARRS, Institute for Astronomy, U. Hawaii
Following the Photons
Edinburgh, Oct 10, 2011
Pan-STARRS PS4 Observatory
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Haleakala Observatories, Maui, HI
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Introduction
• The Pan-STARRS telescope has to deliver sub-arcsecond images over a 3-degree diameter field of view
– It has 2 mirrors, 3 lenses (several highly aspheric
surfaces) and a focal plane
– alt-az design with L3 and the camera behind the
instrument rotator
– That gives 5x5 + 3 - 1= 27 degrees of freedom (tilts,
decenters and despaces)
– to be adjusted to get all of the elements collimated
and aligned with the rotator axis
– Required precision is ~tens of micron
– In addition, the primary mirror support system has 12
independently controllable pneumatic axial supports
– total of 39 d.o.f. to be controlled
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Pan-STARRS Opical Design
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Mirror Support Systems
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PS-1 Primary Mirror Support System
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How do we configure the PS optics?
• Advice from experts… not encouraging
– Too many parameters
– What about “degeneracies”?
– Won’t you get stuck in a local minimum?
• Or crawl along a valley?
– Discouraging lessons from megaprime…
– Try to “divide and conquer”?
• Problem: M1/M2 system alone does not deliver images even
on axis
• M1/M2 system has real-time control of all d.o.f
• Approach adopted (evolved)
– 1) Solve 8 d.o.f problem of M1, M2 relative to L1+L2
• L1+L2 assembled at UW on turntable quite accurately
– 2) Then fix any tilt of detector plane
• L3 (dewar window) is relatively weak
• Rotator allows this to be determined separately from any tilt
introduced by M1+M2+L1+L2 system
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Initial configuration:
• Plan: use auto-reflecting telescope
– Mounted on a jig on the back of the telescope
– Aligned with rotator axis
– Used to align other elements with targets (M2) and
fiducial marks (lenses)
• First light (07/2007) gave ~10” IQ
• Adjusting mirrors iteratively gave ~2” IQ
• Field curvature and field dependent astigmatism
diagnosed
– Attributed to L1, L2 de-space
• But still IQ was not adequate
• Exploring 8 parameter M1, M2 til + decenter parameter
space infeasible
• Needed a more methodical approach
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Aberration diagnosis techniques
• Traditional wave-front sensing approaches:
– Shack-Hartmann imaging
• Implemented in PS GPC1 as deployable probe
– Hartman mask imaging
– Knife-edge test
– Rotational beam-shearing interferometry
• Claude Roddier thesis
• Other probes
– Ghost image analysis
– Direct (e.g. laser) metrology
– Analysis of in-focus images
• Highly non-linear dependence on positional d.o.fs
• Too hard to explore big parameter space
• Technique adopted:
– Use M2 de-space to generate out-of-focus (a.k.a. donut) images
– Thousands of stars per exposure => huge amount of information
– At large enough defocus shapes become linearly dependent on
misconfiguration parameters (like weak-lensing)
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Wavefront Aberrations from Out-of-Focus Images
• Perfectly collimated (and designed) telescope gives donut images
when defocused that are
– Uniformly bright
– Circularly symmetric
• annular because of hole in primary
– At large-enough defocus these are well described by geometric
optics (images formed by “rays”)
• Any aberrations (displacement of elements or figure errors) deflect
rays and cause distortion of the shape of the out-of-focus image
– Crowding or dilution of the density of rays modulated brightness
a la Roddier (1990)
– Brightness proportional to curvature (Laplacian) of converging
wave-front aberration.
– Hence “curvature sensing”
– Pioneered by Roddier group at IfA for Adaptive Optics
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Illustration of the effect of a localized aberration on
out-of-focus images
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Advantages: Linearity and Multiplexing
• Donut shape statistics are a linear response to causes of
aberrations
– Linearity breaks down too close to focus.
– Shadowing and flat fielding etc. become problematic
too far from focus.
– `Sweet spot' seems to be around 3mm defocus
– may be possible to go closer for more sensitivity
• But may require `physical optics' modelling
• Solve a set of linear equations to find mirror
displacements and actuator commands to cancel
aberration
– No iteration (in principal) - one step solution
– No local minima - finds unique global minumum
– Massively multiplexed - thousands of stars per image
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Separating Seeing and Mirror Wobbling from Aberrations
• We want to obtain sub-seeing aberrations.
• But seeing causes wavefront errors of many radians of
phase
– Causes donuts to wobble around like jello.
– Averages out in long exposures
– But leads to smearing.
• Worse still, mirror oscillations will produce persistent
anisotropies
• Fortunately, such affects can be readily distinguished by
using both pre- and post-focus image pairs.
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Symmetries Between Pre- and Post-Focus Image Statistics
1) Focus aberration
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Symmetries Between Pre- and Post-Focus Image Statistics
2) Comatic (cos phi) aberration
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Symmetries Between Pre- and Post-Focus Image Statistics
3) Astigmatic (cos 2 phi) aberration
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Symmetries and anti-symmetries
• Even angular harmonic change sign passing through
focus, while the odd harmonics do not
• If we rotate the post focus images by 180 degrees the
sign always changes
• This is the characteristic of wave-front phase errors
• But wavefront amplitude errors have opposite symmetry
– Easily distinguished
– Can construct combinations of pre- and post focus
image statistics that are blind to effects of telescope
wobble, obscurations etc.
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What about “degeneracies”?
• `Degeneracy' here means combinations of displacements that
do not cause any measurable aberration
– Terminology is sloppy: Technically, `degeneracy' means
non-distinct eigenvalues
– Here all decenter/tilts are degenerate in the proper sense.
• `Quasi-degeneracy' arises if there are combinations that
produce almost zero measurable effect.
– These cause the linear equation solution (inversion of
matrix) to be singular or ill conditioned.
– Example: An exact degeneracy arises because IQ only
depends on relative positioning of optical elements
– But is easy to deal with
– Quasi-degeneracies are a little more tricky.
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Dealing with quasi-degeneracies
• Example: decenters and/or tilts of M1 nearly degenerate
with decenter of M2
• Similar degeneracies for L3/focal-plane system
• But quasi-degeneracies are not to be feared; they are
our friends
– Can be identified using elementary linear algebraic
techniques
– They allow one to correct for one misalignment that is
difficult to cure by moving another element or
combination of elements that are easier
– Fundamental to Pan-STARRS design
• real-time control over the configuration of the mirrors
• but not of the other elements -- which will surely
flex/expand etc
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Donut finding/analysis pipeline
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The goal is to obtain, from an out of focus gigapixel camera image, a grid of
donuts covering the focal plane.
– Step 1: Determine the size of the donuts
• Generate cleaned log-scaled image
• Compute the autocorrelation function
• Cross-correlate with theoretical model in log(r) space
– Step 2: Determine location of the donuts
• Generate an analytic model for the 2-D donut image.
• Construct a regularized deconvolution filter
• Apply to image to obtain the locations of candidate donuts
• Filter candidates catalog to obtain tens of good donuts per OTA
– Step 3: Generate robust (median) average
• Candidates include some overlaps, cell boundaries etc.
• Take median to get clean donut image
• Result is a grid of 60 donuts per focal plane
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Log-scaled image
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Donut model and regularised deconvolution filter
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Deconvolved OTA Image
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Donut locations - one OTA
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Donuts sample - 1 OTA
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Median donuts grid - full field - one per OTA
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Donut shape statistics
• We need to quantify the distortion of donuts and how this varies
across the field.
• What is a good set of statistics?
• It is traditional to use Zernike polynomials
– see Knoll, JOSA 66, p207
• We use something similar: angular Fourier expansion of radius,
width and brightness of donuts
– We first compute the centroid of the light in a postage stamp
containing the donut
– From the pixel locations, relative to the centroid, we define a
radius r and azimuthal angle
– Compute moments of donut radius, width and brightness
• Typically cos 2, cos 3, cos 4 theta modes
– Exploit symmetries in pre- and post-focus images to generate
combined statistic that is independent of actual focus
– Results in ~100 statistics for each of ~60 donuts across the focal
plane.
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M1, M2 tilts and decenters
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M1, M2 strongest eigenmodes
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Donuts - observed vs model
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PS1 Residual Aberration Analysis
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PS1 Residual Aberration Analysis
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PS1 Residual Aberration Analysis
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PS1 Residual Aberration Analysis
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PS1 Residual Aberration Analysis
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PS1 Residual Aberration Analysis
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PS1 IQ – Smallest Image Median FWHM to Date
NK FWHM = 0.69", JT FWHM = 0.63
q = measure of circularity of 2D PSF
UNIVERSITY OF HAWAII INSTITUTE FOR ASTRONOMY
Project Proprietary Data – For Internal Use Only
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PS1 y-band – first 1 micron image of
the sky
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PS1 z, i, r, g band coverage 2011-02-14
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PS1 3pi survey – 15 to 20 images in
five bands,
building astrometric catalog for reprocessing
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PS1+2
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