Transcript f 2 (x)

Maintaining JWST PSF
quality
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
Anand Sivaramakrishnan
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JWST Lite
it’s iTar Free!
Newton Huygens Fourier Fraunhofer Sommerfeld Rayleigh Airy
Fresnel Kirchoff Fabry Perot de Broglie Heisenberg Poisson Fermat
Lagrange Bessel Parseval
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
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Math & pictures
If the math goes over your head…
don’t worry: pictures will follow
If the pictures bore you…
don’t worry, math will follow
There is still scope for physical intuition
amongst all the equations of optical theory!!!
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
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The telescope
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
•
•
Primary ~ f/1.5 (by eye from the figure)
‘Cass’ f/16.7 (from the web)
•
The Wavefront Sensor Camera
– NIRCam short wave arm ~1-2.5 mm
– 18 mm pixel H2RG
– 32 mas/pixel
– Some special optics & software
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PI M-840
Hexapods, radius of curvature
actuation
(sold with PC and
Hexapod.py control code)
Physik Instrumente
X
Y
6 actuators control 6 rigid body
degrees of freedom
Custom secondary mirror control
Ultra-precise brain surgery
ROC: rigid tripod fixed to back
Physik Instrumente
PM Segments: Hexapod + ROC
SM: Hexapod only
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
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PI M-840
Hexapods, radius of curvature
actuation
(sold with PC and
Hexapod.py control code)
Physik Instrumente
X
Y
6 actuators control 6 rigid body
degrees of freedom
Custom secondary mirror control
Ultra-precise brain surgery
ROC: rigid tripod fixed to back
Push/pull between X and Y with actuator
Physik Instrumente
PM Segments: Hexapod + ROC
SM: Hexapod only
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
6
65k mas
2040 pixels
NIRCam
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Two wheels: “Pupil” & “Filter”
Weak Lenses to add defocus
Bandpass: few % dl/l filter ~2mm
K ~ 15 (TBD)
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
7
Barely OK co-phased PSF
log
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
SR 78%
Strehl Ratio: Peak intensity (actual aberration) / Peak intensity (perfect wavefront)
(on the same pupil with secondary obstructions/gaps/transmission)
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
8
Perfectly co-phased PSF
log
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
SR 78%
SR 100%
Strehl Ratio: Peak intensity (actual aberration) / Peak intensity (perfect wavefront)
(on the same pupil with secondary obstructions/gaps/transmission)
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
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Typical WFS data
+/- 3 waves
+/- 6 waves
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Median filter CRs
Dark-subtract
1-5 minute CR splits without dithering
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
WFSC EXEC @ STScI
(JPL-written)
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Subtract ‘0th read’
(DCS) or fit up-the-ramp
Limits on routine wavefront sensing with NIRCam on JWST
A. Sivaramakrishnan, E. C. Morse, R. B. Makidon, L. E. Bergeron,
S. Casertano, D. F. Figer, D. S. Acton, P. D. Atcheson, and M. J. Rieke
SPIE 5487-149 2004 (Glasgow)
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
Flatten - fix bad pixels
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WFS data to WFC commands
Visits being executed
By JWST Observing
Plan Executive (OPE)
WFSC
EXEC
R. Makidon
WFSC WG
24 Feb 2005
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
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Part II - PSF theory
Optical Path Difference
This is the deviation of the wavefront from ‘perfect’… when talking of an image being formed
by a converging wavefront,
THE DEVIATION OF THE WAVEFRONT FROM THE
PERFECT SPHERICAL CONVERGING WAVE
is the optical path difference.
In a collimated beam such as an interferometer, the deviation of a wavefront from the
perfect, flat wavefront is the OPD.
OPD(x,y) is a real function in ‘pupil space’, dimensions of LENGTH usually
At wavelength it is expressed in RADIANS of PHASE: fx,y) = (2 p / l)OPD(x,y)
Ray optics
Sivaramakrishnan
converging spherical
JWSTRoutine WFSC
STScI June 9 2005
plane wavefronts
diverging spherical
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Wave optics (scalar field, Fraunhofer approximation)
PSF theory (cont’d)
Monochromatic plane wave propagating in z direction
Aperture A(x,y): real function
Phase f(x,y): real function
Electric field over aperture: E(x,y) = A exp(i f(x,y)) (complex number, encodes
phase lag with the ‘angle’ part of the complex number) - useful fiction
Intensity I = E E* (real positive) - measurable
If phase is constant over aperture: perfect wavefront resulting in perfect PSF
Image field strength = a(k) = FT(E(x)). k is 2-d vector in angle space (radians)
John Krist calls a(k) the “Amplitude Spread Function”. PSF(k) = a a* - real positive
Ray optics
Sivaramakrishnan
converging spherical
JWSTRoutine WFSC
STScI June 9 2005
plane wavefronts
diverging spherical
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Phase aberrations in cycles per diameter
Think Fourier
Sine wave aberration is a
pair of delta functions
in its ‘Fourier transform
domain’
At small amplitudes this
corresponds to pair of
bright spots in the PSF:
pupil: exp(if) ~ 1 + if
image: d(0) + FT(sine)
As size of aberration
increases, exp(if)
expansion gets higher
order terms. Quadratic
terms produce spots at
twice the separation...
Sivaramakrishnan
JWSTRoutine WFSC
sf2 = 0.01
sf2 = 0.03
sf2 = 0.10
sf2 = 0.30
sf2 = 1.0
sf2 = 3.0
STScI June 9 2005
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What is a PSF?
Sivaramakrishnan, Lloyd, Hodge and Macintosh (2002) ApJL
Aperture A(x,y): real function
Phase f(x,y): real function
Electric field over aperture: A exp(if)
For f < 1 truncate expansion of exp(i f) at second order in f:
FT this to get image plane electric field
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
15
What is a PSF?
Sivaramakrishnan, Lloyd, Hodge and Macintosh (2002) ApJL
A, a are FT pairs
Sivaramakrishnan
JWSTRoutine WFSC
F, f are FT pairs
STScI June 9 2005
star is convolution
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Sivaramakrishnan (2005)
What is a PSF?
Perrin, Sivaramakrishnan, Makidon,
Oppenheimer, Graham (Oct 2003) ApJ
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
Python/Numarray/pyfits/matplotlib
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So what?
Extra
curvature
Brighter
Dimmer
Calculate the phase in the pupil
plane from imaging data “Image-based phase retrieval”
Curvature Sensing
Roddier
Early focus
Regular focus
Focus-diverse
phase retrieval
“Phase diversity”
Extra-focal images
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
Paxman, Fienup, Gonsalves
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Choosing the amount of defocus
2 across D
Numerical experiment
Place a sinusoidal phase
aberration over the pupil and try
three different amounts of
defocus.
4 across D
pre-focus image
rotated post-focus image
=
signal
7 across D
10 across D
2 waves
Sivaramakrishnan
JWSTRoutine WFSC
4 waves
STScI June 9 2005
6 waves
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What is the best defocus to use?
Signal strength for given spatial frequency of
aberration (number of ripples across mirror)
is periodic in 1/defocus
good contrast
poor contrast
B. Dean, C. Bowers, “Diversity Selection for Phase-Diverse-Phase-Retrieval,” JOSA, 20(8), 2003, pp. 1490-1504
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
20
PSF examples
Aberrations - linear stretch +/- 1 micron rms segment error (wavefront)
1
1 reduced tilts
1
1 reduced tilts
1/2
end of DHS?
140nm (RQ)
SR ~80%
50nm (~perfect)
SR ~97%
2 micron monochromatic PSFs (simple FFTs at Nyquist sampling)
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
21
Misell-Gerchberg-Saxton (MGS) algorithm
MGS in this case - a mapping from one guess at the phase, f1(x)
to a better estimate, f2(x), using a known pupil function and image data
•
•
•
•
•
•
Assume a pupil function A(x) and a first-guess phase f1(x)
Calculate a(k) = F[(A(x) exp {i f1(x)}] = b(k) exp {i g(k)} (b is real)
Use measured data for intensity I(k) - replace b(k) with sqrt(I(k))
Now we have sqrt(I(k)) exp {i g(k)}
Back-transform it - we write this as C(x) exp{i f2(x)}
This gives us our revised estimate of the phase, f2(x)
•
•
Now write the pupil field using known pupil A instead of C: A(x) exp {i f2(x)}
And do the same operations to get the next estimate, f3(x), for the phase
TPF cottage
industry
Keep going till you are happy. It WILL converge but not necessarily to the right phase •
Incorrect A(x)
•
Improperly reduced data I(k) (CR, flats, photon noise, real pixel response,…)
•
Difference between FFT samples and physical pixels, etc.
Misell, D. L. 1972, J. Phys. D, 6, L6
Gerchberg, R. H. & Saxton, H. O. 1972, Optik, 35(2), 237
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
22
Developing MGS intuition - I
SR 78% - below par by 2%
Crank up the defocus…
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.
OPD from “Limits on routine wavefront sensing with NIRCam on JWST” A. Sivaramakrishnan, E. C. Morse,
R. B. Makidon, L. E. Bergeron, S. Casertano, D. F. Figer, D. S. Acton, P. D. Atcheson, and M. J. Rieke SPIE 5487149 2004 (Glasgow)
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
23
Developing MGS intuition - II
Gaussian bump on mirror
Same height bump,
different widths of bump
Aperture is 192 pixels dia
Bump at half a radius out
Bump height 1 radian at 2um
+/- defocus amount in waves
Sivaramakrishnan
JWSTRoutine WFSC
STScI June 9 2005
Python/Numarray/pyfits/matplotlib
24
Rules of thumb, definitions
•
•
•
•
•
•
Sivaramakrishnan
Resolution element (Res Elt) l/D radians
– 0.2 l(in microns) / D (in meters) in arcseconds
Nyquist sampling
– Astronomer’s version - 2 pixels across 1.22 Res Elts
– Nyquist’s version: 2 samples per Res Elt
Effective focal length
– F = f D (where f = focal ratio)
Pixel size p
– Angular size on sky = p / F radians
– 0.2 p (in microns) / (f D (in meters))
Strehl ratio
– Peak intensity (actual aberration) / Peak intensity (perfect wavefront)
– Marechal approximation: SR ~ exp - (phase variance) = 1 - sf2
Diameter of a defocussed image:
– ~8 (peak-to-valley defocus in waves) Res Elts
JWSTRoutine WFSC
STScI June 9 2005
25
Rough photometric zero points
From "Allen's Astrophysical Quantities" 4th ed (2000)
band
J
H
Ks
K
L
L'
M
8.7
N
11.7
Q
Sivaramakrishnan
l/um
1.215
1.654
2.157
2.179
3.547
3.761
4.769
8.756
10.472
11.653
20.13
JWSTRoutine WFSC
dl/um
0.26
0.29
0.32
0.41
0.57
0.65
0.45
1.2
5.19
1.2
7.8
W m-2
um-1
3.31E-09
1.15E-09
4.30E-10
4.14E-10
6.59E-11
5.26E-11
2.11E-11
1.96E-12
9.63E-13
6.31E-13
7.18E-14
STScI June 9 2005
Jy
photons s-1
m-2 um-1
1630
1050
667
655
276
248
160
50
35.2
28.6
9.7
2.02E+10
9.56E+09
4.66E+09
4.53E+09
1.17E+09
9.94E+08
5.06E+08
8.62E+07
5.07E+07
3.69E+07
7.26E+06
R
4.67
5.7
6.74
5.31
6.22
5.79
10.6
7.3
2.02
9.71
2.58
zero mag countrate
photons m-2 s-1
5.25E+09
2.77E+09
1.49E+09
1.86E+09
6.67E+08
6.46E+08
2.28E+08
1.03E+08
2.63E+08
4.43E+07
5.66E+07
26