  Future NASA X-ray Observatories will shed light on a variety of high-energy
astrophysical phenomena. Off-plane reflection gratings can be used to provide
high throughput and spectral resolution in the 0.3--1.5 keV band, allowing for
unprecedented diagnostics of energetic astrophysical processes. A grating
spectrometer consists of multiple aligned gratings intersecting the converging
beam of a Wolter-I telescope. Each grating will be aligned such that the
diffracted spectra overlap at the focal plane. Misalignments will degrade both
spectral resolution and effective area. In this paper we present an analytical
formulation of alignment tolerances that define grating orientations in all six
degrees of freedom. We verify our analytical results with raytrace simulations
to fully explore the alignment parameter space. We also investigate the effect
of misalignments on diffraction efficiency.
