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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., Comment: Proceedings Volume 11445, Ground-based and Airborne Telescopes VIII SPIE Astronomical Telescopes + Instrumentation, 2020, Online Only Conference