Non-polynomial Residual Correction

ACS and WFPC2 images used the DGEOFILE reference file to specify the residual correction in X and Y for each and every pixel in each chip of the observation. These DGEOFILE reference fiels required up to 168Mb each to cover all chips of each camera for ACS/WFC images. Distortion residuals have been always been calibrated for ACS by looking at the average correction that needs to be applied over each 64x64 pixel section of each chip after applying the polynomial coefficients correction. This would normally result in a 64 x 32 array of residuals for each 4096 x 2048 chip. These arrays get expanded by one value in each dimension to support interpolation all the way to the edge of each chip resulting in 65 x 33 arrays of distortion correction data.

This figure illustrates the corrections included in the ACS/WFC F475W non-polynomial distortion correction included in the new NPOLFILE reference file. Each vector represents the correction for a 64x64 pixel section of each chip.

These look-up tables follow the conventions in the WCS FITS Distortion Paper [DistortionPaper]. Record-valued keywords are used to map an image in the science extension to a distortion array in the WCSDVAR extension. This new type of FITS keywords has been implemented in PyFITS and is fully described in [DistortionPaper]. Specifically, DPj.EXTVER in the science extension header maps the science image to the correct WCSDVAR extension. The dimensionality of the distortion array is defined by DPj.NAXES. Keywords DPj.AXIS.j in the SCI extension header are used for mapping image array axis to distortion array axis. In the keywords above j is an integer and denotes the axis number. For example, if distortion array axis 1 corresponds to image array axis 1 of a SCI extension, then DP.1.AXIS.1 = 1. A full example of the keywords added to a SCI extension header is presented in Appendix 1: Headerlet API.

A complete description of the conversion of the DGEOFILE reference data into NPOLFILE reference files can be found in the report on the npolfile-tsr.

NPOLFILE reference File Format

With the goal of including all distortion reference information directly in the science image’s FITS file, including the full 168Mb DGEOFILE for ACS/WFC images would more than double the size of each input image. A new reference file based on the sub-sampled calibrations, though, would be small enough to serve as the basis for a new reference file while also being a more direct use of the calibration data. This new reference file has been called NPOLFILE in the FITS image header, so that any original DGEOFILE reference filename can be retained in parallel for backwards compatibility with the current software. This reference file also has a unique suffix, _npl.fits, as another means of identifying it as a new reference file separate from the current DGEOFILE files. The header for this new reference file also remains very simple, as illustrated in Appendix 2 - NPOLFILE Example.

Applying these corrections starts by reading the two 65 x 33 arrays into memory with each input ACS/WFC chip WCS (one for X offsets and one for Y offsets). Bi-linear interpolation based on the input pixel position then gets used on-the-fly to extract the final offset from this reference file. Initial versions of these sub-sampled NPOLFILE reference files for ACS have been derived from the current full-size DGEOFILEs, and testing indicates residuals only on the order of 0.02 pixels or less remain when compared to the original calibration.