Grid Optimization for Wide Field Modulation Collimators

Wide-field localization of transient sources such as gamma-ray bursts (GRBs) places new demands on the grid design of modulation collimators, whose usable field of view (FOV) is normally limited by self-vignetting. A grid slat thick enough to be opaque at the energies of interest also clips off-axis rays, shrinking the effective slit width and ultimately defining the FOV itself. Historical bigrid or rotating-modulation-collimator (RMC) designs have been designed with this trade-off as an unavoidable consequence of geometric optics. We explore whether the cross-sectional shape of the grid slats can be optimized for wide FOV applications. We derive a general transmission-function framework for a bigrid pair in terms of an effective slit width that depends on slat geometry and use it to compare four slat cross sections: the conventional rectangular slat, an idealized diamond profile, a hexagonal profile that approximates photochemical etching, and the circular wire grids of early X-ray astronomy. We show that for the same bigrid pitch and thickness, a diamond profile extends the FOV and eliminates clipping throughout most of the field. We also demonstrate that a hexagonal profile achievable with standard tungsten etching factors captures many of the benefits of the idealized diamond profile. Extending the analysis to the four-phase demodulation, we show that slat shape directly sets the extent of the resulting phase-space blind spots, and that the diamond profile removes them entirely across a target FOV where the rectangular baseline cannot. We further show that finite grid opacity is a largely separable effect. Leakage through the grid leaves the geometric blind-spot boundaries unchanged. These results identify slat cross-sectional shape as a design parameter that can substantially increase throughput and widen the blind-spot-free field of view of a wide-field modulation collimator.