4.1 ACS geometric distortions
ACS will produce the largest single images ever taken with HST to date. However, because the optics were designed with a minimum number of components, ACS focal surfaces are far from normal to the principal rays. This results in an image of the sky which is distorted in a large, but predictable manner. The distortion consists of two effects, discussed previously in section 1.1.3. The first is the elongation of the ACS apertures, causing the pixel scale to be smaller along the radial direction of the Optical Telescope Assembly (OTA) field of view than along the tangential direction. The second effect is the variation of pixel area across the detector.
The results presented in the discussion below are derived from the Ball optical and mechanical simulator which models the effect of the primary and secondary OTA mirrors (including aberrations) and supports the ACS, correctly aligned, in a model of the HST bay. The simulator was used to project a square array of point sources through the ACS optics. The received images therefore show what would be detected if there were a square grid of stars on the sky. The degree to which the image deviates from a square grid provides a measure of the total distortion. For the description of the reference file which quantifies the ACS geometric distortion model, see the section 4.2.
The general form of the optical distortions described should be quite representative of what we will see on orbit. The main changes to be expected are displacements from the calculated values of 5 to 10 arcseconds and rotations of the apertures of less than one degree.
WFC
The WFC detector is tilted at 22 degrees giving an elongation of 8% along the diagonal. The slightly non-square projected aperture shape is evident from figure 1.1 in chapter 1. This distortion is also illustrated in figure 4.1, a vector displacement diagram which shows the contribution of the non-linear part of a cubic fit to the data. The vectors represent the degree of distortion to be expected in the WFC beyond the directional dependence of the plate scale. For display, the vectors are magnified by a factor of 4 compared to the scale of the x and y axes. The largest displacement indicated at the top left corner of the figure is 82 pixels or about 4 arcseconds.
In the image frame, where the x axis is approximately in the V2 direction and the y axis is in the -V3 direction (see figure 1.1), the x and y pixel scales are 0.04921 and 0.04899 at the center of the WFC1 and 0.04980 and 0.05071 at the center of the WFC2. The average pixel scales of each chip are 0.04912 and 0.04987 for the WFC1 and 0.04971 and 0.05069 for the WFC2. This gives a total angular size of 201"x100" for the WFC1 and 204"x104" for the WFC2. These pixel scales and array sizes are summarized in table 4.1 for each ACS detector.
Table 4.1: X and Y Pixel scale (arcseconds/pixel) for each detector.
| Detector |
Pixel Scale at Center Xscale, Yscale |
Average Pixel Scale Xscale, Yscale |
Array size (pixels) |
Array size (arcsec) |
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The resulting variation of the projected pixel area on the sky requires corrections to the photometry of point sources. A contour plot of relative pixel size across the WFC normalized to the central pixel, is shown in figure 4.3. The range of area is from 0.89 to 1.08 times the central value.
HRC
The High Resolution Channel has its edges aligned approximately along the V2 and V3 axes. In this case, the center of the aperture lies on a line passing through the V2/V3 origin and making an angle of 20 degrees with the V3 axis. Because the aperture diagonal does not correspond to a radius of the HST field of view, the distortion has no particular symmetry with respect to the detector axes. Because the focal plane, and therefore the detector plane is 25 degrees away from the plane normal to the light path, the scales along the axes differ by ~16%. However, since the HRC is less than 30 arcsec across, the total variation in scale across the detector is much less than for the WFC, being only about 1%.
At the center the x and y scales derived from the simulator are 0.02855 and 0.02469 arcsec/pixel respectively. The average scales across the middle of the detector are 0.02855 and 0.02471 arcsec/pixel making the x and y widths ~29 by 25 arcsec.
A vector plot of the deviation from linearity is given in figure 4.2 in which the deviations have been magnified by a factor of 20 for illustrative purposes. The largest deviation is 4.9 pixels in the top left corner and corresponds to about 0.1 arcsec. The variation of pixel size across the HRC to be used for photometric correction of point sources in distorted, uncorrected images is shown in figure 4.4. The maximum deviation from the central value is just over 2%.
SBC
The Solar Blind Channel contains the MAMA detector. It is centered at the same place as the HRC in the V2/V3 plane and is slightly larger, about 35 by 30 arcsec. At the center the x and y scales derived from the simulator are 0.03399 and 0.02940 arcsec/pixel respectively. The average scales in the x and y directions are 0.03399 and 0.02942 arcsec/pixel, calculated by replacing the 21 micron HRC pixel by a 25 micron SBC pixel. The optical distortions will be identical to those displayed by the HRC. The only difference in their light paths is the presence of a plane M3 fold mirror which reflects light away from the SBC onto the HRC. The MAMA has a small amount of extra distortion in the detector itself, arising from irregularities in the multi-channel plate. The largest difference from a square pattern is 2 pixels, or 0.06 arcsec.
Figure 4.1: WFC Distortion: The longest vector corresponds to ~82 pixels. (This figure is similar to figure 4.2 but is projected onto a square grid.) 
Figure 4.2: HRC Distortion: The longest vector corresponds to ~5 pixels
Figure 4.3: Variation of WFC effective pixel area with position
Figure 4.4: Variation of HRC effective pixel area with position 
