  We describe a system being developed for measuring the shapes of the mirrors
of the Fred Young Submillimeter Telescope (FYST), now under construction for
the CCAT Observatory. "Holographic" antenna-measuring techniques are an
efficient and accurate way of measuring the surfaces of large millimeter-wave
telescopes and they have the advantage of measuring the wave-front errors of
the whole system under operational conditions, e.g. at night on an exposed
site. Applying this to FYST, however, presents significant challenges because
of the high accuracy needed, the fact that the telescope consists of two large
off-axis mirrors, and a requirement that measurements can be made without
personnel present. We use a high-frequency (~300GHz) source which is relatively
close to the telescope aperture (<1/100th of the Fresnel distance) to minimize
atmospheric effects. The main receiver is in the receiver cabin and can be
moved under remote control to different positions, so that the wave-front
errors in different parts of the focal plane can be measured. A second receiver
placed on the yoke provides a phase reference. The signals are combined in a
digital cross-correlation spectrometer. Scanning the telescope provides a map
of the complex beam pattern. The surface errors are found by inference, i.e. we
make models of the reflectors with errors and calculate the patterns expected,
and then iterate to find the best match to the data. To do this we have
developed a fast and accurate method for calculating the patterns using the
Kirchhoff-Fresnel formulation. This paper presents details of the design and
outlines the results from simulations of the measurement and inference process.
These indicate that a measurement accuracy of ~3 microns rms is achievable.
