A New Methodology to Assess Spatial Response Models for Satellite Imagers Using the Optical Design Parameters of a Generic Sensor as Independent Variables

Abstract

Several types of analytic models are currently used to estimate the spatial response of satellite imagers, the accuracy of these models being critical for applications requiring precise knowledge about the spatial response of a given imager. The assessment of these models is complicated because the actual spatial response of an imager depends on its optical design, so evaluations based on a single kind of design are inherently biased. To reduce this bias, a new assessment methodology based on a generic imaging sensor is proposed; the key optical design’s parameters of this sensor are selected as independent variables, so the error of any spatial response model can be computed within a broad domain of possible optical designs. Assuming a generic sensor with annular optical aperture and square detector elements, the optical factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and the aperture obstruction ratio ε are selected as key design parameters, allowing the error of spatial response models to be computed in the ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , ε) plane. This approach is used to assess the separable Point Spread Function ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSF</i> ) model, which assumes that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSF</i> is equal to the product of two perpendicular line spread functions, concluding that it is only valid when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ≤ 0.35 for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSF</i> ≥ 0.1. This methodology can be used to assess other types of spatial response models for different shapes of optical apertures and detect or elements. We contend that our approach provides a standard assessment procedure that will help end users select the correct model for their specific application.