Sloan Digital Sky Survey Telescope Technical Note 19990127
This document and the attached postscript figure document an analysis that I did to determine the optimum midpoint and required ranges for both the rotator and azimuth for the 2.5 M telescope. [Only the rotator is discussed here, since the azimuth wrap is already installed]. These quantities are constrained by the desire to conduct long drift scans on the sky without interruption.
I simulate a series of drift scans on the sky for tracks that cover the northern survey area. These tracks cover the range in survey latitude of -60 to +60 degrees, spaced by 10 degrees. Each track covers -90 to +90 degrees of survey latitude. This range extends up to the survey boundaries. For each survey latitude, tracks are computed for a range of starting times spaced by 1 hour. The start time is parameterized by the hour angle of the Survey Center (= NGP) at the start of the scan. Along each track the azimuth, elevation, and position angle of the CCD is computed at 1 minute intervals. Also computed is the hour angle of the Survey Center at that time and the distance from the Survey Center.
A few restrictions on tracks are made. First, tracks are not followed below an elevation of 30 degrees. Second, if the azimuth rotation rate or rotator rotation rate exceed a critical value, the track is also not followed. Third, if a track is broken into multiple segments due to the fact that a portion falls outside these allowed limits, then the track is divided into discontinuous segments, and limits are determined for each segment independently. I use a maximum tracking rate of 3 times the sidereal rate (or 45 degrees per hour). This limit is imposed to maintain astrometric accuracy, not because of any telescope physical limitations.
For good measure, a set of tracks are computed for ``retrograde'' scanning. Such scans have been proposed for QA purposes. I have not computed tracks for scans along other arbitrary great circles. We will likely observe along some tracks that cut perpendicular to the main survey pattern, but they will not be done frequently.
The conventions are documented in SDSS Telescope Technical Note 19981113, "Plug-plate coordinate system". For my calculations, I define position angle to be that of the +y axis on the camera (which points towards the leading edge of the camera). The sense of rotation is defined such that if the telescope is pointed to the horizon and one is looking at the back of the telescope, the position angle increases in the counterclockwise direction. If one looks at the projection of the y axis on the sky, then the conventional astronomical position angle (defined such that N is 0 degrees, E is 90 degrees) of this axis also increases. The zero point is defined such that at zero degrees, the projection of the +y axis onto the sky points towards the zenith. With this convention, the camera is oriented at zero degrees at the instrument change position. [The leading edge of the camera emerges first when the camera comes out of the doghouse].
The attached figure shows the range in rotator angles that are followed along a single continuous scan of one track. Values for which the elevation is lower than 30 degrees are excluded; we will likely not scan below that elevation. Each horizontal line corresponds to one survey latitude and one particular starting time. The vertical axis is just a label assigned to each track and had no other significance. Since the rotator has a range of more than 360 degrees, the starting position angle has been adjusted modulo 360 degrees so that the midpoint of the position range is centered around 90 degrees. The detailed rules for determining which side of the wrap one should put a scan were derived empirically.
It is seen that a range in rotator angle of -150 to +331 will accommodate all proposed tracks. This corresponds to a midpoint of 91 degrees with a range of +/-- 240 degrees. The prograde scans (which are the most common by far) are constrained to a smaller range: -140 to +270.
One could also center the wrap at other angles; in fact, centering it at 4.5 degrees reduces the range to +/- 234 degrees. The prograde scans use the full range of travel, however.
The rotator design is intended to provide a full range of +/- 270 degrees. If the range needs to be contrained, later, due to unforseen problems, the 90 degree centering is to be preferred.
Figure: Position angle range required for each of about 600 simulated tracks on the sky. The vertical axis is an arbitrary number. Track up to about 200 are prograde; the remainder are retrograde. The vertical lines give limits assuming that the rotator wrap is centered at 90 degrees.
Set the rotator to the instrument change position. Point the telescope to the horizon and face the back of the telescope. Rotate the rotator counterclockwise 90 degrees. Center the wrap there.
Date created: 1/27/99 Last modified: 1/27/99 Copyright © 1999, Steve Kent Steve Kent
