Pixel scale in the Stardust images
A crude analysis by Tony Farnham
As part of a project utilizing the Stardust Wild 2 images, there arose
a question about how much the image might be distorted across the
field of view. To get a feel for this, I did a couple crude analyses
of some of the calibration data.
In the first analysis, I made used of the Stardust early cruise data
(safed data set STARDUST-C/E/L-NC-2-EDR-V1.0), in which there are 16
images taken of the Pleiades star cluster (frames 175-190). The
viewpoint was shifted between frames to position the cluster at a
different location in the field of view in each image. Using the
bright stars around the center of the cluster, I did a linear plate
solution to fit the brightest stars in the cluster (typically 10-12).
The result of the fit gives a measure of the pixel scale and the
rotation angle for a local region of the CCD in the vicinity of the
center of the cluster. With multiple measurements, different portions
of the CCD can be compared.
The fits were generally very good, and with a couple exceptions, the
pixel scale consistently converged to within a value of 0.1
arcsec/pix. Figure PIXSCL.PNG illustrates the results. Each
measurement is plotted in the figure as a circle whose size reflects
the derived pixel scale and whose color represents the rotation angle.
(The very smallest circle (at 159, 981) represents a pixel scale of
12.15 arcsec/pixel, while the largest circles represent 12.30
arcsec/pix. and the color bar at the top defines the rotation angle.)
The position of the circle gives the pixel location of the brightest
star near the center of the cluster, which shows the approximate
center of the local region being fit. The results from these
measurements indicate that the pixel scale is pretty much constant
across the frame.
There are two notable exceptions that deviate from the nearly constant
pixel scale: the smallest circle in the upper left (12.15"/pix), is in
a position where most of the stars are off the edge of the frame,
significantly affecting the fit; the next smallest circle at pixel
200,550 (12.22"/pix) is from an image where the stars that are
somewhat streaked, producing large residuals in the fit. The rest of
the measurements are around 12.27-12.30"/pix, with an average of
12.29.
On the other hand, there is a notable difference in the field rotation
in the different images. When the stars are in the upper right part
of the frame, the rotation of the North direction is -10 degrees, but
when the stars are in the lower left, the rotation is only about -3
degrees (with a reasonable gradient in between). This difference
could be a fundamental distortion in the field of view at the focal
plane, or it could be due to the rotation introduced by the camera's
mirror when it turns to change the pointing. Given the magnitude of
the variation, it is likely a combination of both.
As a check on this, and to double check the pixel scale, I performed a
second test, using frame #296, a long exposure of the star background
where the comet would be located around the time of encounter. This
field shows relatively faint stars distributed across the field of
view. Using this image, I performed both a linear solution and a
full, non-linear astrometric solution of the field. The linear
solution gave an average pixel scale of 12.29 arcsec/pix.
In the full solution, the IRAF HST astrometry routines fit a warped
surface to the position measurements. The result from this fit
produced better residuals than the linear fit, suggesting that there
is indeed some distortion of the field of view. For this solution I
got an average pixel value of about 12.31 arcsec/pix.
To estimate the field distortion, I used the linear fit of the
brightest stars in the frame, and computed the positions of grid
points at intervals of 10 arcmin (which represents an undistorted
solution). Then I did the same computation using the positions
derived from the full solution to determine how much the grid was
warped. Figure FIELD_DISTORT.PNG shows the difference between these
two grids (normalized to the central pixel). Each square represents
the grid point in the linear fit, and the arrows represent the
direction and (scaled) magnitude of the corresponding shift of that
point as found in the warped surface. The magnitude of the shift has
been magnified by a factor of 25 to better show the result. Typical
shifts are on the order of about half a pixel.
This confirms that, at least for this observation there is a slight
amount of distortion, though it is not enough to cause any significant
problems in the astrometry or photometry measurements.