  Rotating modulation is a technique for indirect imaging in the hard x-ray and
soft gamma-ray energy bands, which may offer an advantage over coded aperture
imaging at high energies. A rotating modulator (RM) consists of a single mask
of co-planar parallel slats typically spaced equidistance apart, suspended
above an array of circular non-imaging detectors. The mask rotates, temporally
modulating the transmitted image of the object scene. The measured count rate
profiles of each detector are folded modulo the mask rotational period, and the
object scene is reconstructed using pre-determined characteristic modulation
profiles. The use of Monte Carlo simulation to derive the characteristic count
rate profiles is accurate but computationally expensive; an analytic approach
is preferred for its speed of computation. We present both the standard and a
new advanced characteristic formula describing the modulation pattern of the
RM; the latter is a more robust description of the instrument response
developed as part of the design of a wide-field high-resolution telescope for
gamma-ray astronomy. We examine an approximation to the advanced formula to
simplify reconstruction software and increase computational speed, and comment
on both the inherent limitations and usefulness of the approach. Finally, we
show comparisons to the standard formula and demonstrate image reconstructions
from Monte Carlo simulations.
