=================== 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: ``IDCTAB`` files which contain the coefficients for a polynomial correction and ``DGEO`` files which are images with the residual distortion. A new format for the residual distortion, called ``NPOL`` files (extension ``_npl.fits``), 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 ``IDCTAB`` files contain the polynomial distortion and the ``DGEO`` files contain the combined solution for the detector defect and the filter dependent fine scale residuals. 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 :math:`r_{j}` is the ``CRPIXj`` value in the distortion array which corresponds to the :math:`w_{j}` value in the image array, recorded as ``CRVALj`` in the ``WCSDVARR`` header. Elements in the distortion array are spaced by :math:`s_j` pixels in the image array, where :math:`s_j` is the ``CDELTj`` value in the distortion array header. In general :math:`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 look-up tables ---------------------------- 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 by Anderson [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 all edge effects due to extrapolation will be minimized. A Python script, `makesmall.py`, samples the large ``DGEO`` files and writes out the small NPOL files. This code has been included 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. `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 transformation methods distinguish between 0-based and 1-based input coordinates through the `origin` parameter. 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. 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.det2im()` method to account for the column correction reported in the ``D2IM`` reference file, then - to the `HSTWCS.p4_pix2foc()` method which applies bilinear interpolation to the WCSDVARR extension to the input grid. * The expanded NPOL file is compared to the original full size ``DGEO`` file and the difference images are (optionally) written to a file. This comparison allows us to verify that the ``NPOL`` files get interpolated to produce the exact same correction as provided by the ``DGEO`` files for the same pixel position. Any further comparisons based on the full coordinate transformation with and without these corrections get masked by the differences in how the input FLT image coordinates get transformed to pixel positions in the output image. Results ======= The best way to verify that the transformation from sub-sampled NPOLFILE into the full-frame represented by the full-size DGEOFILE was to use an artificial ``DGEOFILE``. This artificial ``DGEOFILE`` consisted of a strictly bilinear plane in the ``DX`` and ``DY`` arrays. This should be something that the bilinear interpolation routines in `STWCS/PyWCS` can exactly match when expanding the ``NPOLFILE``, which was created by sub-sampling the full-size ``DGEOFILE``. This also allows us to verify that we know how to specify the header for the ``NPOLFILE`` extensions as written out to the FLT images to insure that the proper expansion gets performed by `STWCS/PyWCS`. The residuals from this comparison came out to be within single-point floating point precision with the exception of the edge effects in the last few rows and columns of the expanded array as seen here: .. figure:: /images/fakedx.png :align: center :width: 90% :alt: artificial NPOL DX Residual image: mean = -3.75475e-08 +/- 2.0898e-07 .. figure:: /images/fakedy.png :align: center :width: 90% :alt: artificial NPOL Dy Residual image: mean = -1.87765e-08 +/- 3.66462e-07 This test confirmed that the interpolation routine implemented within `PYWCS` will correctly expand the ``NPOL`` file points to exactly recreate the ``DGEO`` file correction for any given pixel position, except at the far ends of the columns of rows. The variations at the ends of the rows and tops of the columns comes from edge effects of the interpolation as it interpolates over 1 less pixel at the edges, however, even these variations are well within numerical accuracy for the overall correction. The new ``NPOL`` reference files were then compared to actual DGEO files from CDBS for an ACS/WFC F606W image using this testing code. The test image was run through `STWCS.UPDATEWCS` to populate the headers and write the ``WCSDVAR`` extensions. Fig 3-6 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 :align: center :width: 90% .. figure:: /images/y1.png :alt: NPOLY-DGEOY for 'SCI,1' : mean = 6.1437e-07 +/- 1.2e-04 :align: center :width: 90% .. image:: /images/x2.png :alt: NPOLX-DGEOX for 'SCI,2' : mean = -1.3293e-06 +/- 9.38e-05 :align: center :width: 90% .. image:: /images/y2.png :alt: NPOLY-DGEOY for 'SCI,2' : mean = -1.53e-05 +/- 1.5e-04 :align: center :width: 90% 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 :align: center :width: 90% .. image:: /images/diffy1_256.png :alt: A line in the difference Y image for 'SCI,1' extension :align: center :width: 90% These results were used as the intial indication that the NPOL lookup tables accurately reproduce the same corrections as the original full-size DGEO reference images while avoiding the confusion of a full coordinate transformation. Further testing by the ACS Instrument Team will independently confirm whether or not the code and the new reference files accurately correct ACS images before these new reference files will be made available for general use or even for use in the pipeline. 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