Linear astigmatism-free three-mirror system using spiral phase plate for lunar regolith grain 3D imaging

We present a microscopic spiral-phase-contrast (SPC) imaging system that incorporates a linear astigmatism-free three-mirror system (LAF-TMS), an unobscured reflective optical configuration designed to ensure high optical performance across a wide field of view by eliminating linear astigmatism through an off-axis optical design, based on a 4f system configuration. In this system, a spiral phase plate with a flattened central region is employed to enable spiral interferometry, which is a kind of SPC imaging. The spiral interferometry is a form of self-referencing interferometry that does not require a separate additional reference beam path. It arises from the interference between the higher-order diffracted and the undiffracted zero-order beam from the sample within a single optical arm path. The fringe pattern obtained from spiral interferometry enables quantitative three-dimensional structural analysis by deriving height variations of the observed object from the optical path difference gradient. The lunar surface microstructure known as the "fairy castle" is characterized by weak cohesive strength, which causes it to collapse during the sampling process. Therefore, in-situ observation is required, yet it has not been directly observed. As an optical system for observing and performing three-dimensional structural analysis of the "fairy castle," we designed an SPC imaging system based on the LAF-TMS optical design. We performed optical simulations to analyze its performance and assess its operational feasibility. Additionally, we carried out a tolerance analysis assuming actual manufacture and assembly to confirm the overall feasibility of the system.