  Stereoscopic spectral imaging is an observing technique that affords rapid
acquisition of limited spectral information over an entire image plane
simultaneously. Light from a telescope is dispersed into multiple spectral
orders, which are imaged separately, and two or more of the dispersed images
are combined using an analogy between the (x,y,\lambda) spectral data space and
conventional (x,y,z) three-space. Because no photons are deliberately destroyed
during image acquisition, the technique is much more photon-efficient in some
observing regimes than existing techniques such as scanned-filtergraph or
scanned-slit spectral imaging. Hybrid differential stereoscopy, which uses a
combination of conventional cross-correlation stereoscopy and linear
approximation theory to extract the central wavelength of a spectral line, has
been used to produce solar Stokes-V (line-of-sight) magnetograms in the 617.34
nm Fe I line, and more sophisticated inversion techniques are currently being
used to derive Doppler and line separation data from EUV images of the solar
corona collected in the neighboring lines of He-II and Si-XI at 30.4 nm. In
this paper we develop an analytic a priori treatment of noise in the line shift
signal derived from hybrid differential stereoscopy. We use the analysis to
estimate the noise level and measurement precision in a high resolution solar
magnetograph based on stereoscopic spectral imaging, compare those estimates to
a test observation made in 2003, and discuss implications for future
instruments.
