The Rigel Telescope Calibration Tests - Focus Position with Temperature

The Rigel Telescope Installation and Calibration Tests:

Establishing the Relationship between Focus Position and Temperature

At Left: The Rigel Telescope

It is obviously important that Rigel be properly focused. One can easily imagine that it is necessary to adjust the position of the secondary mirror in order to do this. It is necessary to always have the secondary mirror in the same position in order for the telescope to be correctly focused at all times. This sounds very straight forward, but there is a catch. The struts that hold the secondary mirror are actually made of aluminum and therefore they expand in increasing temperatures. This effect causes the secondary mirror to effectively be pushed away from the primary mirror, causing the image to go out of focus. The same is true if the secondary mirror is effectively being pulled toward the primary mirror in cooling temperatures.

There is a tiny motor that adjusts the secondary mirror in order to account for the change in position due to temperature. The Rigel observatory is also equipped with a weather station. So, once a relationship between the focus position and the temperature is established and inserted in the configuration file the telescope will adjust itself automatically. This was the central goal of this part of the calibration tests. It was done by first plotting the full width half maximum (FWHM) of an average star against the focus position for a series of images taken at roughly the same temperature, but with the focus position altered for each image. The FWHM is effectively a measure of the size of the image, it is defined as the width of the Gaussian fit at half the maximum value (see below). Since stars are point-like objects, the FWHM is minimized. That is, the star is closest to a point-like object when the telescope is optimally focused. The diagrams below show that when the secondary is too far away, and when it is too close the star light will be distributed in a ring like structure. When the secondary is in the correct position the star will be point-like, which means the FWHM is minimized.

Ray-trace diagram displaying how a point source appears ring shaped with incorrect focus.

FWHM for different focus postions

Far left, Gaussian fit of larger image; Far right, Gaussian fit of smaller image. They are both the same star, just different focus positions. The larger image is at a farther focus position. Note the difference in FWHM's
When the FWHM is plotted against the focus position for a series of images at the same temperature the minimum of the graph corresponds to the ideal focus position at that temperature. The second order polynomial was fit to the data points and the minimum was evaluated by setting the derivative equal to zero and solving for the focus position. About ten of these plots were completed in North Liberty, IA before the telescope was moved to the Winer Observatory in Sonoita, AZ. These graphs, when evaluated for their ideal focus positions were used to create a plot of ideal focus position versus temperature. The slope of this plot was the rate at which the secondary mirror needed to be adjusted per degree Celsius. The plot suggested that the mirror needed to be adjusted at 45 motor steps per degree Celsius. (This corresponds to 22.5 microns/°C.) This is about what was expected because the expansion rate of aluminum is 24 microns/°C. The error bars on the graph correspond to a change in the focus position that corresponds to an imperceptible change in the FWHM. This was found by solving for the change in focus position for a change in the FWHM of 0.3" (known to be nearly unmeasurable) in each plot of FWHM versus focus position. Click here for the plots above.

All of the data from North Liberty was just as expected however, during the process of creating these plots it became obvious that the camera needed to be moved out in order for the telescope to be correctly focused for all temperatures between +20 °C and -10 °C, outside of these temperatures the secondary mirror was not expected to be able to move enough to compensate for the displacement due to the aluminum. This was the specification from Torus optics for all the temperatures that the telescope should focus at. To solve this problem the camera was moved 1/8 of an inch. This meant that the focus position versus temperature tests would need to be done again in Sonoita, however there was no reason that the slope should change. So, in theory it was only necessary to solve for one position and then program the focus configuration file to use that point and the previous slope. But, because we wanted to check for consistency the procedure was repeated for several different temperatures in the hopes that the slope would be the same as it was in North Liberty, further verifying the previous result. When this was done it was found that the two results were actually inconsistent with each other. At first this was exceptionally puzzling as the new information appeared to have a negative slope, which would mean that the aluminum was contracting in expanding temperatures, which is impossible! After analyzing this data very carefully it was determined that at some point the motor that controls the position of the secondary mirror had become disoriented. As a result of the motor not knowing where it was all of the positions that the motor thought it was at were shifted by approximately 400 microns. This is a serious problem, and we’re currently in the process of attempting to isolate the cause of the problem. We suspect that the telescope had problems finding its homes on that evening. The homes are positions that are triggered by a switch and then all other positions are counted in motor steps from the home switch. The motor has since been programmed to not move beyond a maximum acceleration. This was done in the hopes that if the motor didn’t accelerate as fast, then perhaps it wouldn’t lose its place as easily. Another option would be to set a maximum velocity of the motor.

As a result of these problems this procedure will be repeated remotely in the near future from Iowa City in order to determine for certain the exact focus position versus temperature relationship.