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DrizzlePac 2012 Handbook
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The DrizzlePac Handbook > Appendix A: Plate Scales and Polynomial Distortions > A.2 Detector Plate Scales

A.2 Detector Plate Scales
HST instruments have multiple folds in the light path to direct light to selected optical elements, and to the detector(s), in a way that achieves the desired focal ratios within the confines of the optical bench envelope, while minimizing throughput loss and image degradation.
In some instruments, the focal surfaces are far from being normal to the principal rays. This results in an image of the sky that’s distorted in a large, but predictable manner, depending on the tilt of the detector plane and curvature of the folding optics. To first order, the tilt causes a square pixel on the detector to be projected as a rectangle (for rotation of the detector about one of its axes), as a rhombus (for rotation of a square detector about one of its diagonals), or more generally as a parallelogram. The curvature of the folding optics introduces higher order terms in the distortion, causing the projected dimensions of a pixel to vary somewhat with location on the detector.
The current best-determined values of the projected pixel dimensions are stored in the Science Instrument Aperture File (SIAF), specifically defined for a single pixel at specified reference locations on the detector. The geometric distortion model appropriate to a given detector then allows the calculation of projected pixel dimensions at other locations on the detector.
The Instrument Aperture tables contain parameters relating the instrument coordinates, pixels, or deflection offsets to the telescope coordinate frame. This frame, designated V2, V3, represents the projected position on the sky. If the telescope roll is zero, then V3 points North, and V2 points East. The reason for the unconventional axis order is that V2 and V3 are part of a three-dimensional coordinate system with V1 being approximately along the optical axis. The x,y coordinate system relates to each instrument aperture and the angles and are measured counter-clockwise from the V3 axis, to the x and y axes. A reference point is chosen near the center of the aperture, which has the coordinates (xr, yr) in the instrument frame, and V2r, V3r in the telescope frame. The reference point is the fiducial in the focal plane on which, HST will endeavor to position the target specified in the proposal. The scales sx and sy, in x and y directions, are not necessarily equal, but are each tabulated. For most HST imaging instruments, the x and y axes are flipped with respect to the V2 and V3 axes , as shown in Figure A.1, such that their projection onto the V2, V3 frame may not be orthogonal. This can be expressed by the and angles, such that the transformation formula remain valid. The transformation from any point (x, y), to V2, V3, is determined to first order by:
 
 
 
Figure A.1: Visual Representation of the Frame of Reference for Angles in the SIAF Instrument File for ACS, NICMOS, STIS, WFC3, WFPC, and WFPC2
The x and y dimensions of the reference pixels in the V3 coordinate system for each of the commonly used imaging detectors are tabulated in Table A.1. Also listed in the table are the angles of the x and y axes for each detector, corresponding to the CCD rows and columns, measured counter-clockwise from the +V3 axis of the spacecraft, ( and ). These dimensions are measured for the reference pixel. The orientation and scale of the pixel axes may change somewhat across the detector as a result of geometric distortion. The last column in the table lists the approximate, maximum change in scale from the center pixel to any other position on the detector (the largest changes are generally seen between the centers of the chips and the corners). While the values in this table are intended to be current, the latest positional information can always be obtained directly through the Observatory Support Group’s webpages on apertures and pointing.
All of the numbers detailed in the table below are a snapshot of the current SIAF information as of the printing of this handbook, or values from the latest calibrations reported in Instrument Science Reports. The SIAF file itself is an internal table, which is used in the operational science database at STScI. Information that users would be the most interested in is available from the SIAF Aperture file. If this information is insufficient to meet your needs, please contact the Space Telescope Science Institute help desk.
Table A.1: Pixel Scales of the Primary HST Instruments
Distortion Center- corner

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