SPT

PSF analysis and plots

Anna gave me a data file of PSF analysis for a Megacam image. it's here: PSF analysis file

Here's the column description:

# 1 FIELD_POS
# 2 SeqNr
# 3 x
# 4 y
# 5 xbad
# 6 ybad
# 7 rg
# 8 nu
# 9 rnumax [pixel]
# 10 numax
# 11 rmax
# 12 flux [pixel]
# 13 mag
# 14 nbad
# 15 rh [pixel]
# 16 e1
# 17 deltae1
# 18 e2
# 19 deltae2
# 20 A
# 21 B
# 22 Theta [degree]
# 23 Xpos [pixel]
# 24 deltaXpos [pixel]
# 25 Ypos [pixel]
# 26 deltaYpos [pixel]
# 27 Psh11
# 28 Psh22
# 29 Psh12
# 30 Psh21
# 31 Psm11
# 32 Psm22
# 33 Psm12
# 34 Psm21
# 35 cl
# 36 q11
# 37 q22
# 38 q12
# 39 Xsh11
# 40 Xsh22
# 41 Xsh12
# 42 Xsm11
# 43 Xsm22
# 44 Xsm12
# 45 eh0
# 46 eh1
# 47 em0
# 48 em1
# 49 snratio
# 50 MAG_AUTO Kron-like elliptical aperture magnitude [mag]
# 51 MAGERR_AUTO RMS error for AUTO magnitude [mag]
# 52 Flag Extraction flags
# 53 IMAFLAGS_ISO FLAG-image flags OR'ed over the iso. profile
# 54 NIMAFLAGS_ISO Number of flagged pixels entering IMAFLAGS_ISO
# 55 ALPHA_J2000 Right ascension of barycenter (J2000) [deg]
# 56 DELTA_J2000 Declination of barycenter (J2000) [deg]
# 57 theta_al "" [""]
# 58 eps_abs
# 59 e1anisocorr anisotropy corrected e1
# 60 e2anisocorr anisotropy corrected e2
# 61 e1corrpol anisotropy polynomial e1
# 62 e2corrpol anisotropy polynomial e2
# 63 PshstPsmst Psh^*/Psm^* for isotropy correction

This is a combination of SourceExtractor output parameters and a subsequent analysis stage done with some other code. The A and B and Theta parameters are presumably standard SE PSF descriptors, namely the major and minor axis values, and position angle from 2-d elliptical fits. The derived second stage fitted parameters are e1 and e2, and their PSF-corrected cousins.

The A and B parameters seem fairly well behaved. FWHM=sqrt(A^2+B^2) vs magnitude:

Plot of e1 uncertainty vs. magnitude, clearly just an analytic Poisson approximation:

This implies it would be a good idea to only consider point sources that have FWHM < 2.5, since the bright sources obviously suffer from broadening in the SE catalog. If we restrict the e1 and e2 values to those obtained from FWHM<2.5, here is the position-dependence of e1 and e2:

For 5th order polynomial fits, here's what we get:

shape parameter	mean	rms residual
e1	-0.0504	0.0081
e2	-0.0301	0.0085
e2 < 18th	-0.0299	0.0038

How do the e2 residuals depend on magnitude?

So if we restrict this to sources brighter than 18th magnitude, that might help improve the fit. Also still need to cut out the bright ones as well, with FWHM cut.

Plot of e2 vs. position, and also fit residuals, for sources brighter than 18th and FWHM < 2.5:

Residual rms after position fit is a factor of 10 below the intrinsic value of 0.03, for these sources.

Aug 27 2013.

Note that e1 and e2 are 45 degrees apart, in the standard convention for WL shape analysis. From 2003 review paper:

So if we want to map (e1,e2) into ex, ey:

eta=0.5*atan2(e2,e1)

ex=|e|*cos(eta)

ey=|e|*sin(eta)

Aug 29 2013

A table of ellipticity systematics

Note that we need to be reporting image elongations in the context of some underlying PSF width, say 0.6 arc sec FWHM.

Physical Effect	Pattern	Amelioration and Fitting Parameterization
tracking errors in az or elevation	coherent linear pattern, aligned with az or el	Parameterize: e_x, e_y
radial optical distortion	radial or tangential shear about optical axis	think about whether it's better to run on raw or swarped images. parameterize: r*e_r
dual guiders pushing a rotation about arbitrary point can arise from stars of different color, with differential refraction	circular pattern about offset center	align the two guiders along parallactic angle use only one and decide which 2 of 3 DOF to correct parameterize: rotation about an offset center
focus travel not along optical axis, with focus adjustments during exposure	coherent linear pattern	test by running focus back and forth during a test image parameterize: e_x, e_y (I think?)
rotation tracking errors	swirl about center, with ellip proportional to R	look at dependence on exposure time. parameterize: r*e_theta
improper correction for refraction during exposure, while tracking	to first order, linear ellip aligned with parallactic angle at second order, see color-dependent effects	e_x, e_y
focal length changes in telescope	plate scale changes, radial pattern with ellip prop to R?	r*e_r
differential refraction during an exposure	elongation aligned with parallactic angle	e_x, e_y
ellipticity due to focal plane charge transport effects	fixed shape noise on detectors	fit surfaces of e_x and e_y in pixel coordinates (i,j), likely high spatial order
optical corrector anomalies, co-rotate with instrument	fixed shape noise on focal plane	fit surfaces of e_x and e_y in pixel coordinates (i,j),
optical anomalies that are upstream of rotator	shape noise fixed at telescope focus	fit to surfaces in unrotated coord's, except dynamic optics will make this complicated

Looking at differential refraction aspect:

from http://gtc-phase2.gtc.iac.es/science/astroweb/atmosRefraction.php for refraction calculation. R band goes from 550 nm to 700 nm.

Also agrees with Filippenko's PASP paper, 1982.

refraction in arcsec compared to 500nm

sec(z)	550	600nm	650nm	700nm	delta
0	0	0	0	0	0
1.05	0.06	0.11	0.14	0.17	0.11
1.1	0.09	0.15	0.20	0.24	0.15
1.2	0.13	0.23	0.30	0.35	0.22
1.5	0.21	0.37	0.50	0.60	0.39
1.75	0.27	0.48	0.64	0.77	0.50
2.0	0.33	0.58	0.77	0.92	0.61
2.5	0.44	0.77	1.02	1.38	0.94

SO if we imagine a source that is photon-SED -flat across the r band, each of these wavelengths makes a PSF in a different place, displaced along the parallactic angle direction.

The result is the PSF convolved with a 1-d stick of length given in the table above. It's a delta function in one direction, but does produce elongation in the other direction. So it should be fine to just take a 1-d Gaussian and convolve with a square wave, and measure the elongation in terms of a revised sigma, which is proportional to FWHM.

Wrote matlab code to do 1-d convolution with Gaussian PSF, made table of resulting ellipticity vs. airmass and FWHM

Ellipticity introduced by differential refraction across r band, assumes photon-flat SED. Green indicates cases where differential refraction introduces under 1% ellipticity.

Note definition of ellipticity used here is e=1-(b/a) where b is semi-minor axis and a is semi-major axis. This differs from that used in LSST science book chapter 14,

which is e_LSST=(1-b/a)/(1+b/a), almost a factor of two difference.

FWHM\airmass	1.05	1.1	1.2	1.5	1.75	2.0	2.5
0.4	0.0069	0.0136	0.033	0.09	0.153	0.216	0.378
0.5	0.0044	0.0088	0.022	0.062	0.104	0.151	0.286
0.6	0.0031	0.0061	0.015	0.044	0.074	0.110	0.220
0.7	0.0022	0.0045	0.011	0.033	0.056	0.083	0.172
0.8	0.0017	0.0034	0.009	0.025	0.043	0.065	0.137
0.9	0.0014	0.0027	0.007	0.020	0.034	0.052	0.112
1.0	0.0011	0.0022	0.006	0.016	0.028	0.042	0.093
1.2	0.0008	0.0015	0.004	0.011	0.020	0.030	0.066
1.5	0.0005	0.0010	0.002	0.007	0.013	0.019	0.043
2.0	0.0003	0.0006	0.001	0.004	0.007	0.011	0.025

note- doug's definition of ellipticity comes from P. Schneider. For a minor axis b and major axis a, and r=b/a, he uses

e=(1-r^2)/(1+r^2).

Aug 29 2013.

We are making slow progress towards characterizing Megacam ellipticities but still don't have it understood yet. Some observations:

Short (30 s) and long (600 s) exposures tend to all show the linear elongation at about the same level. Except for at least one case where it was absent.
- but this means there is little to gain by going to shorter exposures
After subtracting off a mean in both vector ellipticities, what's left over tends to be pretty consistent, even if SH wavefront correction is done in between.
- this suggests we might be able to co-add the post-subtraction ellipticity fields.
Dave Osip says that during an exposure, the focus adjustment moves the secondary, only. So effective plate scale is changing and this could produce radial displacements that are proportional to r.
There are clear instances of rotator guiding being off, with concentric circles with amplitude growing in r.
Need to extract ex and ey and make scatter plots against temperature, temperature gradients, rotator angles, etc.

made a merged data file for night of UT08292013, that includes relevant parameters. Top of file:

# Exposure MeanEllipMag StdEllipMag MedianMag MeanEllipTheta StdEllipTheta MedianTheta RA DEC HA Rotator texp UT focus temp
SPT-CLJ0212-4657.8283 0.147385 0.211310 0.058232 11.632927 51.667598 21.316130 +02:12:22.5675 -46:56:30.0318 -02:38:22 -073.852 30.000 05:46:58 -2039.00 17.06
SPT-CLJ0212-4657.8284 0.179838 0.144740 0.128764 9.932401 40.987813 17.093513 +02:12:19.6413 -46:57:00.0636 -02:36:34 -073.405 600.000 05:48:40 -2053.00 17.06

link to attached file: night1.merged.dat

version with no sexagesimal coordinates night1.merged2.dat

Did scatter plot matrix with

median ellipticity
median angle of orientation
instrument rotator angle
exposure time
focus setting
temperature

Observations:

There is an indication of the ellipticity depending on exposure time. Longer images are slightly more elongated
rotator angle is correlated with temperature, but only because both changed monotonically over the second half of the night
median ellipticity seems somewhat correlated with angle of ellipse.
There is some evidence that the PA of the ellipticity does rotate in proportion to rotator angle. This is what we'd expect if the aberration is locked to the telescope.