=================== NPOL Reference File =================== .. abstract:: :author: Nadezhda Dencheva, Warren Hack :date: 12 Oct 2010 The HST pipeline uses two types of reference files to correct for distortion – the IDCTAB files contain the coefficients for a polynomial correction and the DGEO files are images with the residual distortion. A new format for the residual distortion, called NPOL files, is presented in this document. The conversion from DGEO files to NPOL files is described and an example of the format is given using ACS/WFC F606W filter. Tests of the conversion procedure show that the differences between the DGEO files and NPOL files are of the order of :math: 10^{-4} pixels. Introduction ============ HST images can exhibit significant distortion, one of the severe cases being ACS/WFC where it can reach 50 pixels. Anderson [1]_ describes the total distortion solution for ACS/WFC as consisting of a polynomial part which provides position accuracy of 0.1-0.2 pixels, a filter dependent fine scale solution which brings the accuracy of the positions to 0.01 pixels and a detector defect correction with a maximum amplitude of 0.008 pixels. Currently these distortion solutions are implemented in the ACS pipeline as reference files. The polynomial distortion is in the IDCTAB files and the combined solution for the detector defect and the filter dependent fine scale residuals is in the DGEO files. This document describes how the DGEO files are converted to the new format, called NPOL files, and how they will be distributed and used. It also describes the testing procedure of the NPOL files and provides an example of converting and testing an ACS/WFC F606W DGEO file. New representation - look-up tables =================================== The fine scale distortions represented in the DGEO images can be stored in smaller look-up tables without significant loss of information. These look-up tables follow the conventions in WCS Paper IV [2]_. 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 [2]_. 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 the last section. The look-up tables are saved as separate FITS image extensions in the science files with EXTNAME set to 'WCSDVARR'. EXTVER is used when more than one look-up table is present in a single science file. Software which performs coordinate transformation will use bilinear interpolation to get the value of the distortion at a certain location in the image array. To fully map the image array to the distortion array the standard WCS keywords `CRPIXj`, `CRVALj` and `CDELTj` are used. The mapping follows the transformation ..math:: p_j = s_j(p_j-r_j) + w_j , where r_j is the `CRPIXj` value in the distortion array which corresponds to the w_j value in the image array, recorded as `CRVALj` in the WCSDVARR header. Element in the distortion array are spaced by s_j pixels in the image array, where s_j is the `CDELTj` value in the distortion array header. In general s_j can have a non-integer value but cannot be zero. However, if the distortion array was obtained as a subimage of a larger array having a non-integer step size can produce undesirable results during interpolation. An example header for ACS/WFC F606W WCSDVARR extension header is given in the last section. A note about NPOL files ======================= It is essential that the look-up tables meet two restrictions: * Every point in the corrected image is mapped to by not more than one point in the uncorrected image. * Every point in the corrected image is mapped to by at least one point on the corrected image. This one-to-one (non-extrapolation) requirement can have implications on the geometry of the distortion array. If the distortion array is obtained as a subimage or subsample of a larger array, it is important that the edges of the distortion array coincide with the edges of the image. Creating an NPOL file from a DGEO file ====================================== The DGEO files are FITS files with four image extensions with full chip size 4096x2048 pixels representing the residuals of the distortion in X and Y for the two ACS/WFC chips. As described in [1]_ the original tables, from which the full size DGEO images were created, were sampled every 64 pixels to a size of 65x33 pixels. Because of the coordinate transformations and many steps involved in creating the DGEO files it was not possible to start with the original tables. Our purpose was to sample the full size DGEO files in such a way that after interpolating them again the newly expanded images would match the original images as close as possible. This is why we chose a step size of 64 pixels for the sampling. Given the non-extrapolation restriction and the requirement to have an integer step size we needed to sample an image of a size 4097x2049. We copied the last row/column of the DGEO images to the extra row/column before sampling. This padding ensures that after bilinear interpolation there won't be any edge effects due to extrapolation. A Python script (makesmall.py) to sample the large DGEO files and write out the small NPOL files was written and made available in the REFTOOLS package in IRAFDEV. The script also writes the sampling step size in each direction to the headers of the NPOL file extensions. The step size is later stored in the header of each WCSDVAR extension as the value of CDELT keywords to be used by the software which does the coordinate transformation and interpolation. Since the original DGEO files include the combined fine scale distortion and the detector defect, it is imperative that the detector defect is removed from the DGEO files before they are sampled. (The detector defect correction is stored also as a WCSDVARR extension and applied separately.) Using NPOL files ================ STWCS.UPDATEWCS is used to incorporate all available distortion information for a given observation in the science file. The name of the NPOL file which stores the residual distortion for a specific science observation is written in the 'NPOLFILE' keyword in the primary header. UPDATEWCS copies the NPOL file extensions as WCSDVARR extensions in the science file. The header of each WCSDVARR extension is also created at this time following the rules in section 2 and the necessary record-valued keywords are inserted in the science extension header so that the axes in the science image are mapped to the correct WCSDVARR extension. A note about the fine scale distortion: The original fine scale distortion was meant to be applied after the polynomial IDCTAB distortion. In the new coordinate transformation pipeline the polynomial distortion follows the SIP convention and the first order coefficients are incorporated in the CD matrix which is used last in the pipeline to transform from distortion corrected coordinates to sky coordinates. As a consequence residual distortion arrays must be corrected with the inverse of the CD matrix since they will be applied before the first order coefficients. UPDATEWCS performs this correction for each extension of the NPOL file. However, when we test the NPOL files this correction is omitted because the test does not require performing the entire coordinate transformation pipeline from detector to sky coordinates. STWCS.WCSUTIL and its main class HSTWCS, as well as its base class PyWCS.WCS, can read and interpret FITS files with WCSDVARR extensions. The method which performs the bilinear interpolation and corrects the coordinates is `p4_pix2foc`. All coordinate transformations methods distinguish between 0-based and 1-based input coordinates through the 'origin' parameter. Testing NPOL files ================== A Python script (REFTOOLS.test_small_dgeo.py) was written and made available for testing of the NPOL files. The following procedure is implemented in the test script: * A science observation is run through `STWCS.UPDATEWCS` to update the headers and create the WCSDVAR extensions. * An HSTWCS object is created from a 'SCI' extension * A regular grid with the size of the image is created and is passed as input to the `HSTWCS.p4_pix2foc` method which applies bilinear interpolation to the WCSDVARR extension to the input grid. * The so expanded NPOL file is compared to the original full size DGEO file and the difference images are (optionally) written to a file. Results ======= Following this procedure an ACS/WFC F606W observation was run through STWCS.UPDATEWCS to populate the headers and write the WCSDVAR extensions. Fig 1-4 show the difference between the DGEO files and the expanded NPOL files for the two ACS/WFC chips in X and Y. .. figure:: /images/x1.png :alt: NPOLX-DGEOX for 'SCI,1' : mean = -3.2421e-05 +/- 8.69522e-05 .. figure:: /images/y1.png :alt: NPOLY-DGEOY for 'SCI,1' : mean = 6.1437e-07 +/- 1.2e-04 .. image:: /images/x2.png :alt: NPOLX-DGEOX for 'SCI,2' : mean = -1.3293e-06 +/- 9.38e-05 .. image:: /images/y2.png :alt: NPOLY-DGEOY for 'SCI,2' : mean = -1.53e-05 +/- 1.5e-04 A random line from the difference image in X and Y is shown in the next two plots. .. image:: /images/diffx1_256.png :alt: A line in the difference X image for 'SCI,1' extension .. image:: /images/diffy1_256.png :alt: A line in the difference Y image for 'SCI,1' extension References ========== .. [1] Anderson, J. 2002, in the Proceedings of the 2002 HST Calibration Workshop, S. Arribas, A. Koekemoer, and B. Whitmore, eds .. [2] Calabretta, M. et al. 2004, draft WCS paper IV