calibration results by item geometry AUTHORS : D. Lindler, G. Hartig, A.R. Martel.
LOCATION AND DATE : BATC : Jun 19, 2000
PURPOSE :
To map the geometric distortions of the HRC Build#1 and WFC Build#3 detectors and calculate the plate scale differences between orthogonal axes.
DATA :
All the images were acquired at BATC on June 19, 2000 with the detectors HRC#1 and WFC#3. For the HRC, the dataset consists of images 16454, 16461, 16464, and 16466 and for WFC, images 16463, 16465, and 16467. Examples are shown in Figures 1 and 2.
METHOD :
1. Instrument Configuration
The checkerboard Ronchi ruling is positioned at the location of the RAS source plate with three layers of Mylar transmissive diffuser and short exposures (5 sec for HRC and 0.5 sec for WFC) are taken through the F606W (HRC) and F625W (WFC) filters at the HeNe wavelength of RAS/HOMS (6328 Ang). The source plate is then offset by one grid pattern and another set of HRC and WFC images is acquired. In total, three and four sets of WFC and HRC images were acquired, respectively.
2. Distortion Analysis
The distortion analysis uses an image of a grid of squares tilted approximately 45 degrees with respect to the image's x and y axes. Differences in plate scales cause the squares to appear as diamonds in the images.
The first step in the analysis is to number the squares with a grid of rows and columns (m,n) where m is the number of the square along a row running in the +x and +y direction. n is the row number for the squares running in the -x and +y direction.
(x,y) = pixel
number (m,n) =
diamond number
n +y m
\ | /
\ | /
\ | /
\ | /
\|/
---------+x
The numbering is accomplished by the IDL routine DIAMOND_SETUP. The user is asked to select the center of a square in the lower left corner which is defined as square n=0, m=0. The user is then asked to select the approximate center for square (m=3,n=0) and (m=3,n=3) (see Fig. 3) This information is then used compute the origin of the (n,m) grid and to compute the approximate offsets between the squares.
DIAMOND_FIND will use the output of DIAMOND_SETUP to attempt to find the centers of all squares in the image and assign a (m,n) grid location. DIAMOND_FIND uses cross correlation of a template square to find the center of each square. The center is then refined by extracting cross section profiles in the m and n directions and finding the positions of the valleys between the squares. The refined position of the square is then the halfway point between the valleys at each sides the square.
Once DIAMOND_FIND is completed, we have a table of (x,y,n,m) for all squares found where x and y is the computed center of the square.
For the WFC, DIAMOND_SETUP and DIAMOND_FIND are run separately on each of the two chips. The results of the two chips are combined by adding 2048 to the y positions of the second chip and adding the appropriate n and m offsets to the second chip.
The next step is to compute a distortion map based on the assumption that all of the observed diamonds were originally squares on an equally spaced grid in the n and m directions. Routine DISTORTION_FIT2 performs a least-squares fit to the equations :
xfit = c0 + c2*m - c3*n
yfit = c1 + c3*m + c2*n + c4*(chip-1)
where chip equals the chip number (1 or 2) and c0, c1, c2, c3, and c4 are the coefficients of the fit. c0 and c1 are zero point terms for the grid, c4 is the offset in the y-position between the two WFC chips, and c2 and c3 take into account the rotation of the grid with respect to the x and y axes and a single plate scale difference between the (n, m) and (x, y). The residuals x-xfit and y-yfit provide a measurement of the total distortion.
The residuals of the fit from DISTORTION_FIT2 can be used as a distortion map to correct the raw input images (IDL routine UNDISTORT). After running UNDISTORT, the diamonds will become square and will be equally spaced in both directions. The distortion as computed by DISTORTION_FIT2 can be plotted with the routine DISTORTION_PLOT.
Most of the distortion in the residuals calculated with DISTORTION_FIT2 are due to a plate scale variation in orthogonal directions in the image. Routine DISTORTION_FIT3 performs a least-squares fit to determine the ratio of this plate scale variation and the direction of the axes for the different plate scales. The routine returns the angle, plate scale ratio, and a revised fit, XFIT2 and YFIT2, which has the plate scale variation removed. The residuals X-XFIT2 and Y-YFIT2 now give the residual distortions after removing a plate scale difference in orthogonal directions.
RESULTS :
The results of the analysis are shown below. In Figs 4-7, the distortion plots calculated with DISTORTION_FIT2 are shown for the HRC and in Figs 8-10, for the WFC.
In Figs 11-14, the residual distortion maps are plotted for the HRC and in Figs 15-17, for the WFC. The plate scale variation between orthogonal directions, as computed with DISTORTION_FIT3, was removed.
The plate scale ratio between orthogonal axes and the direction of the axes for the different plate scales are tabulated in Table 1.
Table 1 : HRC#1 and WFC#3 Plate Scale Ratios and Angles
| ID | DETECTOR | SCALE RATIO | ANGLE |
|---|---|---|---|
| 16454 | HRC | 0.85273 | 19.56 |
| 16461 | HRC | 0.85272 | 19.55 |
| 16464 | HRC | 0.85273 | 19.56 |
| 16466 | HRC | 0.85261 | 19.57 |
| 16463 | WFC | 0.92482 | 46.08 |
| 16465 | WFC | 0.92479 | 46.09 |
| 16467 | WFC | 0.92483 | 46.08 |
CEI SPECIFICATIONS :
To be determined.
CONCLUSION :
The field distortions and plate scale variations for HRC and WFC were measured.
REFERENCES :
