W

1997 DEC 02 22:04:03 Figure 9.3

On November 30, 1997 while making astrometric images of 1997 AH1, Brian Manning discovered 1997 WL23. Pursuing that find two nights later, he captured yet another asteroid, A0054, which (unfortunately) he did not notice until April 1998. Five-minute integration; 10-inch reflector; Cookbook CCD.

er before an astrometric session.

Correct Exposures. For stationary target objects, integrations can be as long as necessary to record a clear image, and may consist of multiple integrations that are track-and-stacked in software. However, images of the brightest reference stars must lie in the linear portion of the CCD's response curve. For moving objects, the practical upper limit on the integration time depends on how rapidly they are moving. For top-notch results, the object should not trail more than about half of the full-width half-maximum of the image object; that is, the trail should not exceed one second of arc. In a pinch, however, astrometry from trailed target images usually gives acceptable results.

Calibration. Astrometric images must be dark-subtracted to eliminate hot pixels that might distort star centroids, but for images that are free of vignetting, flat-fielding is usually unnecessary because the centroid algorithm operates over a small region around each star image and is not strongly affected by the sky background. Images with vignetting should not be used for high-precision astrometry because vignetting may slightly distort the stars' intensity profiles and degrade the accuracy of the centroids.

High Elevation. Differential refraction by Earth's atmosphere shifts the apparent places of stars, reducing the accuracy of the plate constants determined from the reference stars. If the field is above 45° elevation, the effects of differential refraction become negligible. Because astrometry has built-in quality control in the form of the residuals, however, a practical approach to reporting the positions of low-sky objects is to take the image, make the measurements, and report the residuals with the derived position.

Proper Sampling. For accurate astrometry, you need sharply focused star images that have a full-width half-maximum of at least two pixels. Very small images do not produce high-quality centroids. Depending on the telescope optics, the atmospheric seeing, and pixel size of the CCD camera, this implies a focal length between 1 and 3 meters (40 to 120 inches). However, acceptable astrometric images may be obtained with any optical system from a 200-mm telephoto lens to a Cassegrain telescope with a 10-meter focal length, providing the star images are well sampled.

Take Images with North at Top. Technically speaking, the orientation of the image does not matter—but it is much easier to identify reference stars if they are oriented the same way that most finder maps and charts are. By allowing a bright star to trail, the camera can be set within a few degrees of north at the top in two or three minutes at the beginning of the observing session.

Enough Reference Stars. At least three reference stars are required for astrometry—between six and ten are desirable. This places significant constraints on the size of the field of view, the limiting magnitude of the image, and the reference star catalog that you use. A quick check of the field of view using star-chart software (such as MegaStar) will show how many potential reference stars will be available. If the field of view is very small and includes only one or two reference stars, either a shorter focal length telescope, a larger CCD camera, or an astrometric catalog with more reference stars is necessary.

Calibration Only, Please! The Golden Rule of CCD Astrometry is "calibrate and then analyze." Brightness scaling, sharpening, and resampling seriously degrade the value of an image for astrometry. There is no need to process any astrometric or photometric images beyond calibration—the image is ready for analysis immediately after dark current subtraction and flat-field correction.

9.3.2 Scanned Photographs for Astrometry

It is possible to carry out astrometric measurements on digitally scanned photographs, although the accuracy of the positions obtained is often limited by the quality of the scan. Three problems plague scanned photographs: the initial nonlinear image storage in film, the danger of saturated data in scanning, and poor scanner characteristics.

In digital images from CCDs, the pixel values are proportional to the intensity of the light that fell on the CCD. This is not true of scanned photographic images; intensity is lost at both the low end and the high end of the intensity scale. At the low end, the outer parts of the star images are lost in the "toe" portion of the photographic response curve; and at the high end, the density of the aggregated

Figure 9.4 Brian Manning made this image 22 minutes after the one in Figure 9.3.

Compare carefully: you will see that all three asteroids have moved noticeably. The field is in Taurus at 4h 00m 19s; +20° 20' 20". Five-minute integration; 10-inch reflector; Cookbook CCD.

silver grains hides the peak intensity in the center of the star image. Even with a high-quality scan, star centroids derived from photographs depend on the shoulders of the star image rather than its bright core.

The second problem is that few scanners capture the full dynamic range between the sky and well-exposed stars images. The internal algorithms that determine how the data will be saved in the scanner software allow star images to become saturated at pixel values of 255, 1023, or 4095 in order to preserve the sky background. The centroid routine must therefore operate on a star image consisting of a rough circle of saturated pixels surrounded by an apron of pixels representing only the outer edge of the star image.

Finally, the x and y axes in the scanner may depart slightly from the orthogonal (i.e., they may not be perfectly perpendicular) and not be at the same scale. In themselves, these are not problems because the plate constants compensate for non-orthogonality and differing scales in the two axes—but if the scales vary and the angle between the axes varies across the image, the astrometric solution will be degraded.

Despite these problems, astrometric measurements work reasonably well on scanned photographs. In a test, Kodak PhotoCD scans from 35-mm film yielded residuals of 5 arcseconds r.m.s., and desktop scanner scans from color enlarge-

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