The PSF Library of The Advanced Camera for Surveys

based on

M.J. JEE, J.P. BLAKESLEE, M. SIRIANNI, A.R. MARTEL, R.L. WHITE, AND H.C. FORD "Principal Component Analysis of the Time- and Position-dependent Point-Spread-Function of the Advanced Camera for Surveys" 2007, PASP, December Issue

We describe the time- and position-dependent point spread function (PSF) variation of the Wide Field Channel (WFC) of the Advanced Camera for Surveys (ACS) with the principal component analysis (PCA) technique. The time-dependent change is caused by the temporal variation of the HST focus whereas the position-dependent PSF variation in ACS/WFC at a given focus is mainly the result of changes in aberrations and charge diffusion across the detector, which appear as position-dependent changes in elongation of the astigmatic core and blurring of the PSF, respectively. Using ~400 archival images of star cluster fields, we construct a ACS PSF library spanning a wide range of HST focus values. We find that interpolation of a small number ~20 of principal components or "eigen-PSFs'' per exposure (or focus) can robustly reproduce the observed variation of the ellipticity and size of the PSF. Our primary interest in this investigation is the application of this PSF library to weak-lensing analyses, where precise knowledge of the instrument's PSF is crucial. However, the nice agreement between the model and observed PSFs suggests that the model is potentially also useful in other applications such as crowded field stellar photometry, galaxy profile fitting, AGN studies, etc., which similarly demand a fair knowledge of the PSFs at objects' locations.

The Quality of PSF Representation



Representation of a ACS/WFC F814W PSF with different basis functions. (a) The original 31x31 stellar image used for the analyses. (b) Wavelet decomposition with ~150 Haar wavelet basis functions. (c) Shapelet decomposition with 78 basis functions (n=12). (d) Representation with 20 basis functions that are obtained from the PCA of ~800 stars. The PSF images in (b) and (c) describe the PSF core well. However, it is obvious that many features in the PSF wing are lost in these schemes. Although only 20 basis functions are used, the PCA method (d) captures many detailed features in the wing outside the second-diffraction ring, as well as the cuspiness in the PSF core.



Access to our PSF Library

We make our PSF library publicly available via this web page. Please click the following links to access the
PSF library for each filter.

F435W F475W F555W F606W F625W F775W F814W F850LP

Useful IDL Routines

The following IDL sources are needed to obtain a PSF in an arbitrary (x,y) position in the ACS/WFC detector.

fit_psf_pca.pro

pick_psf_pca.pro

The above two IDL programs are sufficient to load PCA coefficients from a PCA file and to obtain a PSF at any arbitrary position (x,y). For example, if the PCA file name you just downloaded is F850LP_2002-04-18_07:59:28.pca.fits and you want to obtain the PSF at (x,y)=(105,2002), you run the following two commands at the IDL prompt.

IDL>fit=fit_psf_pca('F850LP_2002-04-18_07:59:28.pca.fits',5,basis=basis,mean_psf=mean_psf)
IDL>psf=pick_psf_pca(fit,basis,105,2002,mean_psf)

To display the psf, type

IDL>tvscl,congrid(psf^0.2,310,310)

which shows the following image.


How to find a matching PSF template

We propose to use both ellipticity and size of stars to find a matching PSF template, which can be implemented by fitting all the three quadrupole moments of stars. We provide a step-by-step description here.

Caveats

Although we do our best to provide the community with the PSF models that closely resemble the real environment PSFs, it is possible that our PSF models may not become optimal in certain situations.

1. Use your discretion when the number of stars used for PCA is less than 300. Some stellar fields do not provide more than 300 stars that meet our criteria for "good" stars. In general, many PSF models taken from these exposures look still OK and do not possess artifacts. However, we advise users to examine these PSF models carefully because in some unfortunate cases it is possible that relatively poor statistics can create measurable artifacts.

2. Although PCA by construction provides the optimal basis functions, it still fits noise in the outskirts of the PSF, which can result in occasional, small negative pixel values. The IDL program pick_psf_pca.pro artificially prevents it from happening by returning the absolute values of the pixels.

3. Use caution when you apply the PSF models here to stellar photometry. We normalize the flux of a star so that it becomes unity in the 31x31 array.

4. Our PSF models are valid for ACS/WFC images that are drizzled with the Lanczos3 kernel and an output scale of 0.05".

5. We constantly add newer data sets to our library and improve existing PSF models with different star selection algorithms. Therefore, the content on this site is subject to change without prior warning.

Acknowledgements

ACS was developed under NASA contract NAS5-32865, and this research was supported by NASA grant NAG5-7697.