## Introduction

The optical design of ACS is characterized by a large amount of geometric distortion. From the ACS Instrument Handbook Section 5.6.4: "The distortions render the pixels, as projected on the sky, trapezoidal in shape and their area varies over the field by about 19% and 3.5% in the WFC and HRC/SBC, respectively."

The AstroDrizzle software package transforms ACS images into a distortion-free frame  However, when photometry needs to be obtained on data that have not been processed by AstroDrizzle, a correction must be applied to account for the different on-sky pixel size across the field of view. A pixel area map (PAM), which is an image where each pixel value describes that pixel's area on the sky relative to the native plate scale, is used for this correction. For the ACS/WFC, the plate scale is 0.05 arcseconds/pixel, while for HRC and SBC it is set to 0.025 arcseconds/pixel.

To transform a distorted FLT/FLC image so that it is suitable for photometry, users must multiply the image by the PAM and divide the result by the exposure time so that the pixel values in the image are in units of electrons/second. After this transformation, the information on the ACS Zeropoints page can be used to convert flux measurements into physical units.

Originally, the ACS PAMs were provided as static FITS files available for download. However, these files did not include improvements in the distortion model made over the last several years.

## Creating PAMs with stsci.skypac.pamutils

The Python package pamutils, within stsci.skypac, is now available to create PAMs for a given FITS file. It supports all three of the ACS detectors, and it can generate PAMs for all dates since the ACS installation in March 2002. Additionally, PAMs generated with pamutils have the same shape and size as the input file, which is relevant for photometry of subarray FLT/FLC and CRJ/CRC files.

The input FITS file must have WCS keywords updated for time-dependent and some filter-dependent distortion effects contained within the IDCTAB to create the most accurate PAMs. The default WCS of FLT/FLC files downloaded from the MAST archive satisfy this requirement. FLT/FLC files processed from RAW by CALACS do not have properly updated WCS keywords - stwcs.updatewcs must be run on them. Note that non-polynomial distortion effects, tabulated in the NPOLFILE and D2IMFILE, are not included in PAMs made with pamutils.

In this example, we will create a PAM from observations of the galaxy cluster ABELL 1185 taken on February 3rd, 2004. We will use astroquery to download the required data and then use stsci.skypac module to create the PAM for the first science extension (chip 2 on the detector):

from astroquery.mast import Observations
from astropy.io import fits
from stsci.skypac import pamutils

import os
import glob
import shutil

# Query MAST for the data
obs_table = Observations.query_criteria(obs_id='J6ME13QHQ')

# Move the FLT to the top level directory
for f in files:
try:
shutil.move(f, '.')
except:
os.remove(f.split('/')[-1])
shutil.move(f, '.')

# Create the PAM using the 1st SCI extension (chip 2).
pamutils.pam_from_file('j6me13qhq_flt.fits', ('sci', 1), 'j6me13qhq_wfc2_pam.fits')

## Time-averaged PAMs for WFC

For WFC, comparison of the original static PAMs to a set of new PAMs generated with pamutils shows their relative precision. The new PAMs are for 20 F606W FLT files selected to span the 20-year ACS lifetime. The figure below shows the 20 ratios of new/original at three positions in the WFC field: the position of the photometric calibration reference point near pixel (3583, 3583), the position of the minimum of the ratios, and the position of the maximum of the ratios. To make this figure, the original PAM and this set of 20 new PAMs were smoothed by 2x2 pixels to better represent the effect of the PAMs on a stellar PSF. All three loci display the same relative trend with time. The ratios at the reference point range from 0.999–1.000, i.e. all within 0.1% precision.

Because the PAM is a multiplicative correction, the maximum change of 1.0007 near pixel (5, 2053) represents the region where photometric fluxes are 0.07% high for early observations. For observations after 2020, the ratios near pixel (4065, 4074) have the smallest values, which are as low as 0.9986, where photometry that uses the original static PAMs would be 0.14% low.

One way to simplify WFC photometric analyses while achieving errors that are <0.1% is to use an average of the 20 PAMs that have ratios from 0.9992 to 1.0000 with respect to the original static PAM. Thus, this new WFC PAM provides photometry with 0.1% precision, i.e. raising the maximum positive error from +0.07 to +0.11% and the minimum negative error from -0.14 to -0.10%.

## Static HRC PAM

With its much smaller geometric corrections and shorter operational lifetime of 2002–2007, the original HRC PAM retains adequate photometric precision.

LAST UPDATED: 03/24/2022