The Basics

After various focus tests, we determined that the telescope focus depends on the temperature and the elevation. There does not appear to be a focus dependence on azimuth, and hence all focus data is taken pointing south or north. The final ``focus model'' is the term used for the parameters for a bilinear fit of the best focus as a function of temperature and elevation.

During a focus run, (see Section 4.3.3 and Section 6.4), images are taken of a single field at regular focus intervals. With a typical focus run, images are taken at a fixed azimuth and elevation several times during the night.^6.1It is important to make sure the configured focus motor range covers both sides of focus for the entire night. Also, any focus images taken while the motor has not yet engaged the diaphragm are not useful.

The quality of the focus is determined by the median of the central subregion full-width-half-maximum (FWHM) measurements of the PSF made by SExtractor. For a given focus run, a parabola is fit to the plot of FWHM as a function of focus position, as in Figure 6.1. The best focus is determined to be the minimum of the parabolic curve. The error is determined to be the width at which the parabolic fit changes by 10% from the minumum value.

Figure 6.1: Plot of FWHM (pixels) vs. Focus Position (mm) for a sample focus run. The stars are the points used to fit the parabola.

When enough focus values have been tabulated for a range of temperatures and elevations, we can begin a focus model fit. The model can be improved with more than one night of focus data to cover a wide temperature range.

The focus model is created with a least-squares fit to the best focus as a function of temperature, elevation, elevation squared, and the various cross terms. The idl program that performs this task is described in Section 6.5.

The focus model implemented as described in Section 3.8.1 is flexible, and can handle any polynomial combination of temperature, elevation, and azimuth, if such fits become desirable in the future.