Diffraction-based analysis of tunnel size for a scaled external occulter testbed

For performance verification of an external occulter mask (also called a starshade), scaled testbeds have been developed to measure the suppression of the occulter shadow in the pupil plane and contrast in the image plane. For occulter experiments the scaling is typically performed by maintaining an equivalent Fresnel number. The original Princeton occulter testbed was oversized with respect to both input beam and shadow propagation to limit any diffraction effects due to finite testbed enclosure edges; however, to operate at realistic space-mission equivalent Fresnel numbers an extended testbed is currently under construction. With the longer propagation distances involved, diffraction effects due to the edge of the tunnel must now be considered in the experiment design. Here, we present a diffraction-based model of two separate tunnel effects. First, we consider the effect of tunnel-edge induced diffraction ringing upstream from the occulter mask. Second, we consider the diffraction effect due to clipping of the output shadow by the tunnel downstream from the occulter mask. These calculations are performed for a representative point design relevant to the new Princeton occulter experiment, but we also present an analytical relation that can be used for other propagation distances.