Transcript Document
In Search of Q
David Johnston
(JPL)
Jason Rhodes (JPL)
Gary Bernstein (U Penn)
Håkon Dahle (Marseille)
and others from the
SNAP Collaboration
Goal: to determine the error on the mean shear
as a function of noise level and PSF size
Q - defined as the inverse variance on the shear
that you get with 1 square arcminute of data
•
Q is a function of the survey instrument but
not a function of survey area
•
The main dependence of Q should be
Noise level
PSF size
We want to calibrate Q as a function of these two parameters
So that we can compare different surveys and different
Strategies.
Plan of attack
Make a set of simulated images on a 2D grid of
Parameters in noise level and PSF size
Analyze these with various weak lensing codes
To see if we can all agree and try to come up with a
Universal function for Q (or close enough)
PSF Size
As a measure of PSF size we use:
The half light radius aka EE50
EE50 is affected more by the tails of the profile than FWHM
However can be somewhat tricky to measure with
pixelated data
Grid of EE50 :
PSF half-light radius
in pixels:
2.1
3.0
in arcsec:
0.063 0.090
2.3
0.138
2.15
0.194
2.25
0.270
2.15
0.39
2.25
0.54
Noise level
Noise level can be described by a “noise magnitude”
Which is defined by N_mag = Z_AB - 2.5* log()
Where is the noise level of the sky background
Depends on :
• Background noise spectrum
F() (either atmosphere or zodiacal)
• Total filter throughput curves T()
• Collecting area of telescope A
• Exposure time t
Grid of Noise mags:
29.30 29.05 28.80 28.55 28.30 28.05
These are SNAP-like levels
Sets of Simulated images
Simulated shapelet images similar to those made for
Space STEP (Johnston, Rhodes, Massey, Ferry, High et al.)
Use Hubble UDF data as training set to build
Shapelet catalog
Filters and PSF is taken from SNAP configuration.
Charge diffusion included in PSF.
The sampling is constant for all PSF sizes so
PSF is identical in pixels but not in arcseconds because the
pixel scale changes
Degraded Hubble UDF images as sanity check (Gary B.)
Noise is added, image is convolved and rebinned as needed
to simulate a degraded image
Weak Lensing Codes
Jason - using RRG
Gary - using Bernstein & Jarvis
Håkon Dahle - using modified
KSB
Each was asked to measure galaxy positions,
Measure moments of galaxies and stars and
Determine the number of usable galaxies and
Also their estimate of the error on the mean shear
For each image
Q
Gary’s plot
Also shows the effect
Of size cuts
>1.1 PSF size (solid)
>1.25 PSF size (dashed)
The 2D surface can be well fit by a 4 parameter model
Gary’s was between the
other Two and was the
least noisy so we use his
p[0] = 5.64680
p[1] = -0.434010
p[2] = 0.168388
p[3] = -0.178452
ln(Q) = p[0]+p[1]*x+p[2]*y+p[3]*x*y+p[4]*x^2+p[5]*y^2
where x=ln(EE50) and y=n_mag-28
"It's time to put an end to your trek through the stars" -- Q
Conclusions:
• We have a decent function for the expected mean
shear error as a function of noise level and PSF size.
• We can use this formulation to compare surveys and
survey configurations.
• We still have some room for convergence between
methods.