The Joint Dark Energy Mission (JDEM)1,2 is a proposed dark energy space mission that will measure the
expansion history of the universe and the growth of its large scale structure. It is intended to provide tight
constraints on the equation of state of the universe and test the validity of general relativity. Three
complementary observational analyses will be employed: Baryon Acoustic Oscillations, Type 1a Supernovae
and Gravitational Weak Lensing. An observatory designed for efficient accommodation of these techniques
combines wide-field, diffraction-limited observations, ultra-stable point spread function, and spectroscopy.
In this paper we discuss optical configurations capable of simultaneous wide-field imaging and spectroscopy,
using either afocal or focal telescope configurations. Spectroscopy may be performed by an integral field unit
(IFU), grism or prism spectrometer. We present a flowdown of weak lensing image stability requirements
(the most demanding technique optically) to telescope thermo-mechanical stability limits, based on variations
in the optical transfer function of combinations of Zernike modes, and the sensitivity of these mode
combinations to thermo-mechanical drift of the telescope. We apply our formalism to a representative threemirror
anastigmat telescope and find quantitative relations between the second moments of the image and the
required stability of the telescope over a typical weak lensing observation.