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We present a first-principles analytic treatment of modern multi-vane 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 multi-vane occulters. Multi-vane 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 "sequential plane wave" approximate analytic theory that is suitable for predicting performance of multi-vane occulters, and use it to derive closed-form expressions for the performance of new designs. We review the fundamental 2-D system of an occulter edge, discuss how it applies to real 3-D systems by extrusion or revolution, present the reason for observed bright quasi-achromatic fringing around coronagraph occulters, develop the sequential plane wave approximation in 2-D and explore its limits, describe the relevance of the 2-D theory to practical 3-D instruments, and discuss implications for multi-vane occulter design in current and future instruments., Comment: 20 pp., 9 figures, 59 equations. As accepted by Astrophysical Journal (pre proof)

We present the design of a portable coronagraph, CATEcor, that incorporates a novel "shaded truss" style of external occultation and serves as a proof-of-concept for that family of coronagraphs. The shaded truss design style has the potential for broad application in various scientific settings. We conceived CATEcor itself as a simple instrument to observe the corona during the darker skies available during a partial solar eclipse, or for students or interested amateurs to detect the corona under ideal non-eclipsed conditions. CATEcor is therefore optimized for simplicity and accessibility to the public. It is implemented using an existing dioptric telescope and an adapter rig that mounts in front of the objective lens, restricting the telescope aperture and providing external occultation. The adapter rig, including occulter, is fabricated using fusion deposition modeling (FDM; colloquially "3D printing"), greatly reducing cost. The structure is designed to be integrated with moderate care and may be replicated in a university or amateur setting. While CATEcor is a simple demonstration unit, the design concept, process, and trades are useful for other more sophisticated coronagraphs in the same general family, which might operate under normal daytime skies outside the annular-eclipse conditions used for CATEcor., Comment: 27pp; 12 figures; accepted to Solar Physics

We present results of a dual eclipse expedition to observe the solar corona from two sites during the annular solar eclipse of 2023 October 14, using a novel coronagraph designed to be accessible for amateurs and students to build and deploy. The coronagraph "CATEcor" builds on the standardized eclipse observing equipment developed for the Citizen CATE 2024 experiment. The observing sites were selected for likelihood of clear observations, for historic relevance (near the Climax site in the Colorado Rocky Mountains), and for centrality to the annular eclipse path (atop Sandia Peak above Albuquerque, New Mexico). The novel portion of CATEcor is an external occulter assembly that slips over the front of a conventional dioptric telescope, forming a "shaded-truss" externally occulted coronagraph. CATEcor is specifically designed to be easily constructed in a garage or "makerspace" environment. We successfully observed some bright features in the solar corona to an altitude of approximately 2.25 R$_\odot$ during the annular phases of the eclipse. Future improvements to the design, in progress now, will reduce both stray light and image artifacts; our objective is to develop a design that can be operated successfully by amateur astronomers at sufficient altitude even without the darkened skies of a partial or annular eclipse., Comment: Accepted by Solar Physics