Lenses for staring-array point-source detection sensors must maintain good signal-to-noise ratio (SNR) over fields of view often exceeding 100 degrees. Such lenses typically have f-θ distortion to provide constant solid angle sampling in object space. While the relative illumination calculation is often used to describe flux transfer from a Lambertian extended object for imaging applications, maximizing SNR for point-source detection depends primarily on maximizing collected irradiance at the entrance pupil, the shape of which can vary dramatically over field. We illustrate this field-dependent SNR calculation with an example lens and outline the calculations needed to derive a simple aberration-based expression for the field dependence of point-source SNR.
S. Craig Olson, Andrew W. Sparks, Robert A. Cline, and Timothy D. Goodman, "A system perspective on designing for field-dependent SNR in wide-angle point-source detection lenses," Proc. SPIE 10181, Advanced Optics for Defense Applications: UV through LWIR II, 101810G (Presented at SPIE Defense + Security: April 09, 2017; Published: 11 May 2017); https://doi.org/10.1117/12.2262684.
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