=============================================== Distortion Correction in HST FITS Files - DRAFT =============================================== .. abstract:: :author: Warren Hack, Nadezhda Dencheva, Andy Fruchter, Perry Greenfield :date: 18 Sept 2012 A convention for storing distortion information in HST images was developed and implemented in two software packages - PyWCS and STWCS. These changes allow the development of a WCS based version of Multidrizzle and image alignment software. The distribution of WCS solutions is discussed. Introduction ============ Calibration of the HST Advanced Camera for Surveys (HST/ACS) distortion requires the use of several components to the distortion correction; namely, polynomial coefficients, a correction for velocity aberration, a time-dependent skew, a lookup table for non-polynomial terms, and a detector defect correction. Each of these terms has been derived as part of the calibration effort to address separate aspects of the distortion that affects ACS observations. Ideally, each would be applied independently in the same manner used for deriving the original calibration reference information, with the time-dependent skew being folded into the other terms. However, the software for applying the distortion models does not support this option. In fact, there is no clear accepted standard for specifying distortion corrections in FITS headers. Instead, there are several separate proposals for specifying aspects of the distortion, but none by themselves allows us to fully specify the distortion already calibrated for ACS, let alone in a modular, efficient manner. This paper describes a composite implementation of a select set of proposed standards which supports all aspects of the distortion models for HST instruments without breaking any of the conventions/standards. The rules for merging the proposed standards allow software to be defined to apply each aspect of this proposal as a separate option while defining the requirements necessary to allow them to work together when specified in the header. As a result, the separate components essentially become tools where only those conventions appropriate to the observation can be used as needed. Problems Introduced by the HST/ACS Distortion ============================================= All calibrations for HST observations get recorded and applied through the use of reference files, separate files which describe some calibration. The geometric distortion typically applied to HST images gets recorded as a polynomial component in one reference file, and a pixel-by-pixel correction to the polynomial solution in a separate reference file. This method allows the distortion to be corrected to an accuracy of better than 0.1 pixels. However, this method requires the user to obtain the reference files themselves anytime they want to reprocess the data. The size of these reference files (up to 200Mb) makes this an expensive requirement for the end user. The alternative would be to include the necessary specification of the distortion model in the header of the image itself, as long as it can be done in a manner that does not dramatically increase the size of the image itself. For reference, a typical calibrated ACS/WFC image requires a 168Mb file. Thus, we needed an alternative to separate reference files which can be implemented in a very efficient manner within the image's FITS headers. The calibrations also represent separate aspects of the detector and the distortion, aspects which logically should remain as separate descriptions in the header. The pixels for each CCD do not have the same size across the entire chip. The ACS/WFC CCDs manufacturing process resulted in the pixels having different sizes every 68.3 columns, and can be represented most efficiently and accurately by a 1-D correction that gets applied to every row in the chip. This detector level characterization affects all images readout from the CCD regardless of any additional distortion applied to the field of view. Logically, this effect should be kept as a separate component of the distortion model that gets applied prior to correcting for any other distortion. This represents an example of an effect that is best applied sequentially to the image data. Additional distortions come as a result of the effect of the optics on the field of view. These are generally described by low-order polynomials for most instruments, although for ACS, an additional non-polynomial correction needed to be taken into account as well. Fortunately, the non-polynomial correction can sub-sampled enough to make it practical to include in the image headers directly, a correction of up to a quarter of a pixel in some areas of the detector. Both components need to be applied to the data in order to align images well enough for subsequent data analysis or cosmic-ray rejection. These corrections could be combined into a single look-up table, yet it would come at the cost of additional errors which may not allow the remaining data analysis or cosmic-ray rejection to actually succeed. We also have some instruments where there is only a polynomial component, requiring the development of support for a polynomial correction and a look-up table anyway. These requirements on the application of the calibrations to HST data leave us with no alternative within current FITS standards. As a result, we developed this set of rules which allow us to take advantage of the most appropriate conventions for each separate component of the distortion model and combine them in an efficient manner which eliminates the need for external reference data. SIP Convention ============== Current implementations of distortion models in FITS headers have been limited to simply describing polynomial models. The prime example of this would be the implementation of SIP in WCSTOOLS and DS9 as used for Spitzer data [SIPConvention]_. The new keywords defined by the SIP standard and used by PyWCS are:: A_ORDER = n / polynomial order, axis 1, detector to sky A_i_j / High order coefficients for X axis B_ORDER = m / polynomial order, axis 2, detector to sky B_i_j / High order coefficients for axis 2 These SIP keywords get used in conjunction with the linear WCS keywords defined with these values:: CTYPE1 = 'RA---TAN-SIP' CTYPE2 = 'DEC--TAN-SIP' CDi_j / Linear terms of distortion plus scale and orientation The SIP convention retains the use of the current definition of the CD matrix where the linear terms of the distortion model are folded in with the orientation and scale at the reference point for each chip to provide the best linear approximation to the distortion available. The SIP convention gets applied to the input pixel positions by applying the higher-order coefficients A_i_j, B_i_j, then by applying the CD matrix and adding the CRVAL position to get the final world coordinates. This convention was created from the original form of the FITS Distortion Paper standards, but the FITS Distortion Paper proposal since changed to use a different set of keywords and conventions. A sample ACS/WFC SCI header can be found in :ref:`Appendix1` to illustrate how these keywords actually get populated for an image. The current implementation does not take advantage of the A_DMAX, B_DMAX, SIPREFi or SIPSCLi keywords, so these keywords are not written out to the SCI header. Velocity Aberration Correction ------------------------------ This correction simply serves as a correction to the overall linear scale of the field of view due to velocity aberration observed due to the motion of HST in orbit. The typical plate scale for HST cameras results in a measurable velocity aberration with variations from the center of the field of view to the edge on the order of 0.1 pixels. More details about this correction can be found in `Appendix A.3 of the DrizzlePac Handbook `_. This scale factor gets computed by the HST ground systems for start of each exposure and recorded as the VAFACTOR keyword in each image's science extension header. This term, though, does not get included in the default CD matrix computed by the ground systems. As a result, it needs to be accounted for when reading in the distortion model polynomial coefficients from the IDCTAB reference table. Folding in the VAFACTOR into the polynomial enables the computation of new values for the CD matrix and SIP keywords applicable to this specific exposure without requiring any further use of the VAFACTOR keyword when applying this distortion model to the image. Time-Dependent Distortion ------------------------- Calibration of HST/ACS imaging data required the addition of a time dependent skew in addition to the other distortion terms. This skew represented a linear correction to the polynomial model and its residuals. This correction gets applied to the polynomial coefficients and the residuals from the polynomial model when they are evaluated for each image. As a result, the SIP keywords as written out to each HST/ACS image header reflects this time-dependent correction without the need for any further evaluation of this skew. FITS Distortion Proposal ========================= The current FITS Distortion Paper conventions [DistortionPaper]_ provide a mechanism for specifying either a lookup table or polynomial model for the distortion of each axis. The standard states in Section 2.1: ``Note that the prior distortion functions,, operate on pixel coordinates (i.e. p rather than p− r ), and that the independent variables of the distortion functions are the uncorrected pixel or intermediate pixel coordinates. That is, for example, we do not allow the possibility of`` .. math:: q'_{3} = q_{3} + \delta_{q_{3}}(q'_{1},q'_{2}) The keywords used for describing these corrections use the syntax given in Table 2 of the FITS Distortion Paper. For our purposes, the keywords of interest are those related to lookup tables; namely, :: CPDISja string 2.4.1 distortion code new Prior distortion function type. DPja record 2.4.2 distortion parameter new Parameter for a prior distortion function, for use in an image header This syntax only provides the option to specify one correction at a time for each axis of the image. This precludes being able to use this convention to specify both a lookup table and a polynomial model at the same time for the same axis. It does not state what should be done if the polynomial has been specified using a different convention, for example, the SIP convention. Thus, SIP and FITS Distortion Paper should not be seen as mutually exclusive. In fact, they may work together rather naturally since the SIP and FITS Distortion Paper conventions both assume the corrections will work on the input pixel and add to the output frame. The sample header in :ref:`Appendix1` shows how these keywords get populated for an actual reference file; specifically, an NPOLFILE as described in the next section. 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. .. _figure1: .. figure:: /images/npol_vector_text.png :width: 95 % :alt: ACS/WFC F475W NPOLFILE corrections :align: center 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. 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 r eference file separate from the current DGEOFILE files. The header for this new reference file also remains very simple, as illustrated in :ref:`Appendix2`. 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. Detector To Image Correction ============================ The last element of the distortion which remains to be described is the fixed column (or row) width correction. This needs to be applied as a correction to the input pixel position and the output of this correction is to be used as input to the polynomial and non-polynomial distortion corrections. The adopted implementation is based on the FITS Distortion Paper lookup table convention. It is assumed that the detector to image correction is the same for all chips but it can be extended to arbitrary number of chips and extensions if necessary. For ACS the correction is stored as an image extension with one row. Each element in the row specifies the correction in pixels for every pixel in the column (or row) in the science extension as predetermined by the calibration teams who would be responsible for creating the reference files. For ACS the correction is in the X direction and for WFPC2 - in the Y direction. The following new keywords are added to the header of each science extension of a science file: :: 'D2IMFILE' = "string - name of reference file to be used for creating the lookup table" 'AXISCORR' = "integer (1 or 2) - axis to which the det2im correction is applied" 'D2IMEXT' = "string - name of reference file which was last used to create the lookup table" 'D2IMERR' = (optional)" float - maximum value of the correction" 'D2IMFILE' is used by UPDATEWCS as a flag that a reference file with this correction exists and an extension should be created. UPDATEWCS records the name of the reference file used for the lookup table extension to a keyword D2IMEXT in the primary header. It also populates keyword 'AXISCORR' based on whether this is a row or column correction. The lookup table extension has an 'EXTNAME' value of 'D2IMARR'. 'AXISCORR' is used as an indication of the axis to which the correction should be applied (1 - 'X' Axis, 2- 'Y' axis). 'D2IMEXT' stores the name of the reference file used by UPDATEWCS to create a D2IMARR extension. If 'D2IMEXT' is present in the 'SCI' extension header and is different from the current value of D2IMFILe in the primary header, the correction array in D2IMARR is updated. The optional keyword 'D2IMERR' allows a user to ignore this correction without modifying other header keywords by passing a parameter to the software. The HSTWCS class accepts a parameter 'minerr' which specifies the minimum value a distortion correction must have in order to be applied. If 'minerr' is larger than 'D2IMERR' the correction is not applied. Detector To Image Reference File -------------------------------- An entirely new reference file, the D2IMFILE reference table, serves as the source of this 1-D correction for each affected instrument. This reference file only contains a single array of offsets corresponding to the 1-D correction to be applied. Header keywords in the reference file specify which axis needs this correction. As a result, this new reference file remains small enough to easily be added to an input image without significant change in size. An initial **D2IMFILE** for ACS has been generated for testing with a sample header provided in :ref:`Appendix3`. .. _figure2: .. figure:: /images/d2im_bar.png :width: 95 % :alt: ACS/WFC F475W D2IMFILE corrections :align: center This figure illustrates the corrections included in the first 246 columns of the ACS/WFC F475W D2IMFILE. The WCS for this correction describes the extension as a 1-D image, even though it gets applied to a 2-D image. This keeps it clear that the same correction gets applied to all rows(columns) without interpolation. The header specifies which axis this correction applies to through the use of the AXISCORR keyword. The WCS keywords in the header of the D2IMARR extension specifies the transformation between pixel coordinates and lookup table position as if the lookup table were an image itself with 1-based positions (starting pixel is at a position of (1,1)). The value at that lookup table position then gets used to correct the original input pixel position. Merging Of The Conventions ========================== The full implementation of all these elements ends up merging the SIP, DET2IM and FITS Distortion Paper conventions to create a new version of the figure from the FITS Distortion Paper which illustrates the conversion of detector coordinates to world coordinates. This implementation works in the following way: #. Apply detector to image correction (DET2IM) to input pixel values #. Apply SIP coefficients to DET2IM-corrected pixel values #. Apply lookup table correction to DET2IM-corrected pixel values #. Add the results of the SIP and lookup table corrections #. Apply the WCS transformation in the CD matrix to the summed results to get the intermediate world coordinates #. Add the CRVAL keyword values to the transformed positions to get the final world coordinates The computations to perform these steps can be described approximately using: .. math:: (x',y') &= DET2IM(x,y) .. math:: \binom{u'}{v'} &= \binom{x' - CRPIX1}{y' - CRPIX2} .. math:: \left( \begin{array}{ll} \alpha \\ \delta \\ \end{array} \right) &= \left( \begin{array}{ll} CRVAL1 \\ CRVAL2\\ \end{array} \right) + \left( \begin{array}{cc} CD11 & CD12 \\ CD21 & CD22\\ \end{array} \right) \left( \begin{array}{ll} u' + f(u',v') + LT_x(x',y') \\ v' + g(u',v') + LT_y(x',y') \\ \end{array} \right) where f(u',v') and g(u',v') represent the polynomial distortion correction specified as .. math:: f(u',v') = \sum_{p+q=2}^{AORDER} A_{pq} {u'}^{p} {v'}^{q} \\ g(u',v') = \sum_{p+q=2}^{BORDER} B_{pq} {u'}^{p} {v'}^{q} where * x', y' are the initial coordinates x,y with the 68th column correction applied through the DET2IM convention * u',v' are the DET2IM-corrected coordinates relative to CRPIX1,CRPIX2 * :math:`LT_{x}, LT_{y}` is the residual distortion in the lookup tables written to the header using the FITS Distortion Paper lookup table convention * A, B are the SIP coefficients specified using the SIP convention These equations do not take into account the deprojection from the tangent plane to sky coordinates. The complete Detector To Sky Coordinate Transformation is based on the CTYPE keyword. .. _figure3: .. figure:: /images/pipeline.png Coordinate Transformation Pipeline Updating the FITS File ====================== Updating each science image with the distortion model using this merged convention requires integrating these new reference files directly into the FITS file. This update gets performed using the following steps: * determining what reference files should be applied to the science image * read in distortion coefficients from IDCTAB reference file * [for ACS data only] compute time-dependent (TDD) skew terms from model described in IDCTAB file * read in velocity aberration correction factor (VAFACTOR) keyword * apply velocity aberration, and the TDD terms for ACS data as well, to the distortion coefficients * write time-corrected distortion coefficients as the SIP keywords * [if d2imfile is to be applied] read in D2IMFILE reference table * update D2IMEXT with name of reference table and AXISCORR keyword with axis to be corrected * append D2IMFILE array as a new D2IMARR extension * [if NPOLFILE is to be applied] divide the NPOLFILE arrays by the linear distortion coefficients * write out normalized NPOLFILE arrays as new WCSDVARR extensions * update each SCI extension in the science image with the record-value keywords to point to the 2 WCSDVARR extensions (one for X corrections, one for Y corrections) associated with the SCI extension's chip The STWCS task **updatewcs** applies these steps to update a science image's FITS file to incorporate the distortion model components using this convention. References ========== .. [DistortionPaper] Calabretta M. R., Valdes F. G., Greisen E. W., and Allen S. L., 2004, "Representations of distortions in FITS world coordinate systems",[cited 2012 Sept 18], Available from: http://www.atnf.csiro.au/people/mcalabre/WCS/dcs_20040422.pdf .. [SIPConvention] Shupe D.L., Hook R.N., 2008, "The SIP Convention for Representing Distortion in FITS Image Headers", [cited 2012 Sept 18], Available from: http://fits.gsfc.nasa.gov/registry/sip.html .. _Appendix1: ================================== Appendix 1 - Sample ACS/WFC Image ================================== The WCS of a single chip from an ACS/WFC exposure illustrates how the SIP keywords are populated based on the coefficients from the external IDCTAB reference file. In addition, this header includes the keywords referring to additional distortion corrections related to non-polynomial corrections from the NPOLFILE and to column-width corrections from the D2IMFILE. This sample illustrates how all three corrections can be specified at the same time in a FITS header using our rules for combining the SIP WCS convention and FITS Distortion Paper proposed syntax, while also using FITS WCS Paper I alternate WCS standards to maintain a record of the WCS information prior to being updated/recomputed to use the new reference information. The old WCS gets stored using WCS key 'O' and 'WCSNAMEO' = 'OPUS' to indicate it was originally computed by OPUS, the HST pipeline system. FITS File extensions ================================== The FITS file for this ACS/WFC image now contains extra extensions for the NPOLFILE and D2IMFILE corrections. :: Filename: jbf401p8q_flc.fits No. Name Type Cards Dimensions Format 0 PRIMARY PrimaryHDU 261 () int16 1 SCI ImageHDU 184 (4096, 2048) float32 2 ERR ImageHDU 55 (4096, 2048) float32 3 DQ ImageHDU 47 (4096, 2048) int16 4 SCI ImageHDU 183 (4096, 2048) float32 5 ERR ImageHDU 55 (4096, 2048) float32 6 DQ ImageHDU 47 (4096, 2048) int16 7 D2IMARR ImageHDU 12 (4096,) float32 8 WCSDVARR ImageHDU 37 (65, 33) float32 9 WCSDVARR ImageHDU 37 (65, 33) float32 10 WCSDVARR ImageHDU 37 (65, 33) float32 11 WCSDVARR ImageHDU 37 (65, 33) float32 12 WCSCORR BinTableHDU 59 14R x 24C [40A, I, 1A, 24A, 24A, 24A, 24A, D, D, D, D, D, D, D, D, 24A, 24A, D, D, D, D, J, 40A, 128A] The last extension, named WCSCORR, contains a binary table providing a summary of all the WCS solutions that have been applied to this file and does not act as an active part of the WCS or its interpretation. Primary Header ================================== The PRIMARY header of HST data contains keywords specifying information general to the entire file, such as what calibration steps were applied and what reference files should be used. No active WCS keywords (keywords interpreted for coordinate transformations) are present in the PRIMARY header, but keywords specifying the applicable distortion reference files can be found in the PRIMARY header. Some keywords describing the distortion model and when the WCS was updated with the distortion information from the reference files can also be found in the PRIMARY header. These distortion and WCS related keywords from the PRIMARY header are:: / CALIBRATION REFERENCE FILES IDCTAB = 'jref$v8q1444sj_idc.fits' / image distortion correction table DGEOFILE= 'jref$qbu16420j_dxy.fits' / Distortion correction image D2IMFILE= 'jref$v971826mj_d2i.fits' / Column Correction Reference File NPOLFILE= 'jref$v971826aj_npl.fits' / Non-polynomial Offsets Reference File UPWCSVER= '1.0.0 ' / Version of STWCS used to updated the WCS PYWCSVER= '1.11-4.10' / Version of PYWCS used to updated the WCS DISTNAME= 'jbf401p8q_v8q1444sj-v971826aj-v971826mj' SIPNAME = 'jbf401p8q_v8q1444sj' The remainder of the PRIMARY header specifies the general characteristics of the image. SCI Header Keywords ================================== The following keywords only represent the WCS keywords from a sample ACS/WFC SCI header with 4-th order polynomial distortion correction from the IDCTAB reference file, along with NPOLFILE and D2IMFILE corrections from the specific reference files used as examples in :ref:`Appendix2` :ref:`Appendix3`. :: XTENSION= 'IMAGE ' / IMAGE extension BITPIX = -32 NAXIS = 2 NAXIS1 = 4096 NAXIS2 = 2048 PCOUNT = 0 / required keyword; must = 0 GCOUNT = 1 / required keyword; must = 1 ORIGIN = 'HSTIO/CFITSIO March 2010' DATE = '2012-06-13' / date this file was written (yyyy-mm-dd) INHERIT = T / inherit the primary header EXTNAME = 'SCI ' / extension name EXTVER = 1 / extension version number ROOTNAME= 'jbf401p8q ' / rootname of the observation set EXPNAME = 'jbf401p8q ' / exposure identifier BUNIT = 'ELECTRONS' / brightness units / WFC CCD CHIP IDENTIFICATION CCDCHIP = 2 / CCD chip (1 or 2) / World Coordinate System and Related Parameters WCSAXES = 2 / number of World Coordinate System axes CRPIX1 = 2048 / x-coordinate of reference pixel CRPIX2 = 1024 / y-coordinate of reference pixel CRVAL1 = 11.3139376926 / first axis value at reference pixel CRVAL2 = 42.0159325283 / second axis value at reference pixel CTYPE1 = 'RA---TAN-SIP' / the coordinate type for the first axis CTYPE2 = 'DEC--TAN-SIP' / the coordinate type for the second axis CD1_1 = -7.8194868997837E-06 / partial of first axis coordinate w.r.t. x CD1_2 = 1.09620231564470E-05 / partial of first axis coordinate w.r.t. y CD2_1 = 1.14279318521882E-05 / partial of second axis coordinate w.r.t. x CD2_2 = 8.66885775536641E-06 / partial of second axis coordinate w.r.t. y LTV1 = 0.0000000E+00 / offset in X to subsection start LTV2 = 0.0000000E+00 / offset in Y to subsection start LTM1_1 = 1.0 / reciprocal of sampling rate in X LTM2_2 = 1.0 / reciprocal of sampling rate in Y ORIENTAT= 51.66276166150634 / position angle of image y axis (deg. e of n) RA_APER = 1.133205840898E+01 / RA of aperture reference position DEC_APER= 4.202747924810E+01 / Declination of aperture reference position PA_APER = 51.4653 / Position Angle of reference aperture center (de VAFACTOR= 9.999374411935E-01 / velocity aberration plate scale factor WCSCDATE= '18:41:12 (13/06/2012)' / Time WCS keywords were copied. A_0_2 = 2.18045745103211E-06 B_0_2 = -7.2266555836441E-06 A_1_1 = -5.2225148886672E-06 B_1_1 = 6.20296011911662E-06 A_2_0 = 8.54842918202735E-06 B_2_0 = -1.7551668097547E-06 A_0_3 = 8.09354090167772E-12 B_0_3 = -4.2488740853874E-10 A_1_2 = -5.2903025382457E-10 B_1_2 = -7.6098727022982E-11 A_2_1 = -4.4821374838034E-11 B_2_1 = -5.1244088812978E-10 A_3_0 = -4.6755353102513E-10 B_3_0 = 8.48145748580355E-11 A_0_4 = -8.3665541956904E-17 B_0_4 = -2.1662072760964E-14 A_1_3 = -1.5108585176304E-14 B_1_3 = -1.5686763638364E-14 A_2_2 = 3.61252682019403E-14 B_2_2 = -2.6194214315839E-14 A_3_1 = 1.03502537140899E-14 B_3_1 = -2.6915637616404E-15 A_4_0 = 2.32643027828425E-14 B_4_0 = -1.5701287138447E-14 A_ORDER = 4 B_ORDER = 4 IDCSCALE= 0.05 IDCV2REF= 256.6019897460938 IDCV3REF= 302.2520141601562 IDCTHETA= 0.0 OCX10 = 0.001965125839177266 OCX11 = 0.04983026381230307 OCY10 = 0.0502766128737329 OCY11 = 0.001493971240339153 TDDALPHA= 0.246034678162242 TDDBETA = -0.07934489272074734 IDCXREF = 2048.0 IDCYREF = 1024.0 AXISCORR= 1 D2IMEXT = '/grp/hst/cdbs/jref/v971826mj_d2i.fits' D2IMERR = 0.002770500956103206 WCSNAMEO= 'OPUS ' WCSAXESO= 2 CRPIX1O = 2048 CRPIX2O = 1024 CDELT1O = 1 CDELT2O = 1 CUNIT1O = 'deg ' CUNIT2O = 'deg ' CTYPE1O = 'RA---TAN-SIP' CTYPE2O = 'DEC--TAN-SIP' CRVAL1O = 11.3139376926 CRVAL2O = 42.0159325283 LONPOLEO= 180 LATPOLEO= 42.0159325283 RESTFRQO= 0 RESTWAVO= 0 CD1_1O = -7.81948731152E-06 CD1_2O = 1.09620228331E-05 CD2_1O = 1.14279315609E-05 CD2_2O = 8.66885813904E-06 WCSNAME = 'IDC_v8q1444sj' CPERR1 = 0.0 / Maximum error of NPOL correction for axis 1 CPDIS1 = 'Lookup ' / Prior distortion funcion type DP1 = 'EXTVER: 1' / Version number of WCSDVARR extension containing lookup d DP1 = 'NAXES: 2' / Number of independent variables in distortion function DP1 = 'AXIS.1: 1' / Axis number of the jth independent variable in a distort DP1 = 'AXIS.2: 2' / Axis number of the jth independent variable in a distort CPERR2 = 0.0 / Maximum error of NPOL correction for axis 2 CPDIS2 = 'Lookup ' / Prior distortion funcion type DP2 = 'EXTVER: 2' / Version number of WCSDVARR extension containing lookup d DP2 = 'NAXES: 2' / Number of independent variables in distortion function DP2 = 'AXIS.1: 1' / Axis number of the jth independent variable in a distort DP2 = 'AXIS.2: 2' / Axis number of the jth independent variable in a distort NPOLEXT = 'jref$v971826aj_npl.fits' All keywords related to the exposure itself, such as readout pattern, have been deleted from this SCI header listing for the sake of brevity. .. _Appendix2: ================================== Appendix 2 - NPOLFILE Example ================================== The NPOLFILE reference file format includes a PRIMARY header describing what kind of image should be corrected by this file, along with extensions containing the corrections for each chip. FITS File Extensions ================================== A sample NPOLFILE applicable to ACS/WFC F475W images has the FITS extensions:: Filename: /grp/hst/cdbs/jref/v971826aj_npl.fits No. Name Type Cards Dimensions Format 0 PRIMARY PrimaryHDU 35 () int16 1 DX ImageHDU 180 (65, 33) float32 2 DY ImageHDU 215 (65, 33) float32 3 DX ImageHDU 215 (65, 33) float32 4 DY ImageHDU 215 (65, 33) float32 The extensions with the name 'DX' provide the corrections in X for each of the ACS/WFC's 2 chips, while the 'DY' extensions provide the corrections in Y for each chip. Primary Header ================================== The PRIMARY header of this file only includes the minimum information necessary to describe what exposures should be corrected by this reference file and how it was generated. A full listing of the PRIMARY header includes:: SIMPLE = T / Fits standard BITPIX = 16 / Bits per pixel NAXIS = 0 / Number of axes EXTEND = T / File may contain extensions ORIGIN = 'NOAO-IRAF FITS Image Kernel July 2003' / FITS file originator IRAF-TLM= '2011-09-09T13:24:40' NEXTEND = 4 / Number of standard extensions DATE = '2010-04-02T19:53:08' FILENAME= 'v971826aj_npl.fits' / name of file FILETYPE= 'DXY GRID' / type of data found in data file OBSTYPE = 'IMAGING ' / type of observation TELESCOP= 'HST' / telescope used to acquire data INSTRUME= 'ACS ' / identifier for instrument used to acquire data DETECTOR= 'WFC' / detector in use: WFC, HRC, or SBC FILTER1 = 'F475W ' / element selected from filter wheel 1 FILTER2 = 'CLEAR2L ' / element selected from filter wheel 2 USEAFTER= 'Mar 01 2002 00:00:00' COMMENT = 'NPOL calibration file created by Ray A. Lucas 29 APR 2010' DESCRIP = 'Residual geometric distortion file for use with astrodrizzle-------' PEDIGREE= 'INFLIGHT 11/11/2002 11/11/2002' HISTORY Non-polynomial offset file generated from qbu16420j_dxy.fits HISTORY Only added to the flt.fits file and used in coordinate HISTORY transformations if the npol reference filename is specified in HISTORY the header. The offsets are copied from the reference file into HISTORY two arrays for each chip. Each array is stored as a 65x33 pixel HISTORY image that gets interpolated up to the full chip size. Two new HISTORY extensions for each chip are also appended to the flt file HISTORY (WCSDVARR). HISTORY qbu16420j_npl.fits renamed to v9615069j_npl.fits on Sep 6 2011 HISTORY v9615069j_npl.fits renamed to v971826aj_npl.fits on Sep 7 2011 Data Extension Header ================================== Each ACS/WFC chip has a shape of 4096 x 2048 pixels, yet the data arrays in this specific reference file only have 65x33 values. Each data extension ('DX' and 'DY') contains only those keywords necessary to properly interpolate the sub-sampled values from the arrays to apply to each individual pixel in the full ACS/WFC exposure. The full header for the ['DX',1] extension contains:: XTENSION= 'IMAGE ' / Image extension BITPIX = -32 / Bits per pixel NAXIS = 2 / Number of axes NAXIS1 = 65 / Axis length NAXIS2 = 33 / Axis length PCOUNT = 0 / No 'random' parameters GCOUNT = 1 / Only one group EXTNAME = 'DX ' / Extension name EXTVER = 1 / Extension version ORIGIN = 'NOAO-IRAF FITS Image Kernel July 2003' / FITS file originator INHERIT = F / Inherits global header DATE = '2004-04-28T16:44:21' IRAF-TLM= '16:42:00 (30/11/2006)' WCSDIM = 2 LTM1_1 = 1. LTM2_2 = 1. WAT0_001= 'system=physical' WAT1_001= 'wtype=linear' WAT2_001= 'wtype=linear' CCDCHIP = 2 / CCDCHIP from full size dgeo file LTV1 = 0 LTV2 = 0 ONAXIS1 = 4096 / NAXIS1 of full size dgeo file ONAXIS2 = 2048 / NAXIS2 of full size dgeo file CDELT1 = 64 / Coordinate increment along axis CDELT2 = 64 / Coordinate increment along axis .. _Appendix3: ================================== Appendix 3 - D2IMFILE Example ================================== The D2IMFILE reference file only contains a single 1-D array that should correct the column (row) values based on the value of the 'AXISCORR' keyword in the SCI header. FITS File Extensions ================================== This simple reference file, therefore, contains only 2 extensions; namely, :: Filename: /grp/hst/cdbs/jref/v971826mj_d2i.fits No. Name Type Cards Dimensions Format 0 PRIMARY PrimaryHDU 35 () int16 1 DX ImageHDU 18 (4096,) float32 PRIMARY Header ================================== The PRIMARY header only needs to contain information on what detector this file corrects, along with any available information on how this file was generated. The ACS/WFC D2IMFILE PRIMARY header only includes:: SIMPLE = T / Fits standard BITPIX = 16 / Bits per pixel NAXIS = 0 / Number of axes EXTEND = T / File may contain extensions ORIGIN = 'NOAO-IRAF FITS Image Kernel July 2003' / FITS file originator DATE = '2010-02-01T20:19:11' / Date FITS file was generated IRAF-TLM= '2011-09-02T13:04:07' / Time of last modification NEXTEND = 1 / number of extensions in file FILENAME= 'v971826mj_d2i.fits' / name of file FILETYPE= 'WFC D2I FILE' / type of data found in data file OBSTYPE = 'IMAGING ' / type of observation TELESCOP= 'HST' / telescope used to acquire data INSTRUME= 'ACS ' / identifier for instrument used to acquire data DETECTOR= 'WFC ' USEAFTER= 'Mar 01 2002 00:00:00' COMMENT = 'D2I calibration file created by Warren Hack 29 APR 2010' DESCRIP = 'Column-width correction file for WFC images------------------------' PEDIGREE= 'INFLIGHT 11/11/2002 11/11/2002' HISTORY HISTORY Fixed column (or row) width correction file. This is applied HISTORY as a correction to the input pixel position and the output of HISTORY this correction is to be used as input to the polynomial and HISTORY non-polynomial distortion corrections. HISTORY HISTORY For ACS WFC data, the correction is stored as an image extension HISTORY (D2IMARR) with one row. Each element in the row specifies the HISTORY correction in pixels for every pixel in the column (or row) in HISTORY the science extension; for ACS WFC, the correction is in the X HISTORY direction. HISTORY HISTORY For a more in-depth explanation of this file, please see the HISTORY draft writeup at: HISTORY http://stsdas.stsci.edu/stsci_python_epydoc/stwcs/fits_conventions.html HISTORY wfc_ref68col_d2i.fits renamed to v961506lj_d2i.fits on Sep 6 2011 HISTORY v961506lj_d2i.fits renamed to v971826mj_d2i.fits on Sep 7 2011 In this case, most of the keywords not required by FITS describe how this file was computed while also describing how it should be applied. Data Extension Header ================================== The header keywords for the actual DX array simply needs to provide the information necessary to apply the values to the data; namely, :: XTENSION= 'IMAGE ' / Image extension BITPIX = -32 / Bits per pixel NAXIS = 1 / Number of axes NAXIS1 = 4096 / Axis length PCOUNT = 0 / No 'random' parameters GCOUNT = 1 / Only one group EXTNAME = 'DX ' / Extension name EXTVER = 11 / Extension version ORIGIN = 'NOAO-IRAF FITS Image Kernel July 2003' / FITS file originator INHERIT = F / Inherits global header DATE = '2009-03-18T19:28:09' / Date FITS file was generated IRAF-TLM= '16:05:02 (18/03/2009)' / Time of last modification CRPIX1 = 0 / Distortion array reference pixel CDELT1 = 0 / Grid step size in first coordinate CRVAL1 = 0 / Image array pixel coordinate CRPIX2 = 0 / Distortion array reference pixel CDELT2 = 0 / Grid step size in second coordinate CRVAL2 = 0 / Image array pixel coordinate The fact that these values get applied without interpolation to each pixel in a row, in this case, means that no translation terms are needed in the header, making for a very simple header and very simple application to the data.