Transcript y - The Royal Observatory, Edinburgh

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
2
3
Haleakala Observatories, Maui, HI
4
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
5
Pan-STARRS Opical Design
6
Mirror Support Systems
7
PS-1 Primary Mirror Support System
8
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
9
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
10
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)
11
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
12
Illustration of the effect of a localized aberration on
out-of-focus images
13
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
14
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.
15
Symmetries Between Pre- and Post-Focus Image Statistics
1) Focus aberration
16
Symmetries Between Pre- and Post-Focus Image Statistics
2) Comatic (cos phi) aberration
17
Symmetries Between Pre- and Post-Focus Image Statistics
3) Astigmatic (cos 2 phi) aberration
18
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.
19
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.
20
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
21
Donut finding/analysis pipeline
•
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
22
Log-scaled image
23
Donut model and regularised deconvolution filter
24
Deconvolved OTA Image
25
Donut locations - one OTA
26
Donuts sample - 1 OTA
27
Median donuts grid - full field - one per OTA
28
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.
29
M1, M2 tilts and decenters
30
M1, M2 strongest eigenmodes
31
Donuts - observed vs model
32
PS1 Residual Aberration Analysis
33
PS1 Residual Aberration Analysis
34
PS1 Residual Aberration Analysis
35
PS1 Residual Aberration Analysis
36
PS1 Residual Aberration Analysis
37
PS1 Residual Aberration Analysis
38
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
39
40
41
42
PS1 y-band – first 1 micron image of
the sky
43
PS1 z, i, r, g band coverage 2011-02-14
44
PS1 3pi survey – 15 to 20 images in
five bands,
building astrometric catalog for reprocessing
45
PS1+2
46
47