A Simplified Theory of External Occulters for Solar Coronagraphs

Abstract

We present a first-principles analytic treatment of modern multivane occulters in circular (coronagraph) and linear (heliospheric imager) geometry, develop a simplified theory that is useful for designing and predicting their performance, explain certain visual artifacts, and explore the performance limits of multivane occulters. Multivane occulters are challenging to design in part because they violate the conditions for both the Fraunhofer and Fresnel approximations to diffraction theory, and new designs have therefore generally required explicit simulation, empirical measurement, "guesstimation," or all three. Starting from the Kirchoff diffraction integral, we develop a "successive plane-wave" approximate analytic theory that is suitable for predicting the performance of multivane occulters, and use it to derive closed-form expressions for the performance of new designs. We review the fundamental 2D system of an occulter edge, discuss how it applies to real 3D systems by extrusion or revolution, present the reason for observed bright quasi-achromatic fringing around coronagraph occulters, develop the successive plane wave approximation in 2D and explore its limits, describe the relevance of the 2D theory to practical 3D instruments, and discuss implications for multivane occulter design in current and future instruments.