Scalability in Simulating a Large-Aperture, Fresnel Zone Plate Lens for a Conceptual Space Telescope

Abstract

As ambitious space telescope concepts such as ultra-lightweight planar diffractive optical elements (DOEs) emerge, validating the performance remains a major computational challenge. Conventional Fourier propagation algorithms were observed to fail at meter-class apertures due to severe memory limits caused by rigid grid-sampling requirements, and the scaled-down proxy models used for reflector telescopes cannot be applied, since scaling compresses the outermost zones that govern resolution. We benchmarked five Fourier-based propagators against a common Fresnel diffraction integral and found that only those decoupling the focal-plane grid from the input aperture converge within a 1% error threshold. With these findings, we implemented an optimized, stripe-processed Chirp Z-Transform (CZT) framework, evaluating the focal spot strictly within a fixed region of interest to reduce peak memory usage. Applied to five full-aperture configurations from 1.0 m to 5.0 m at f/# = 5, the framework predicted spatial resolution and diffraction efficiency to within 0.001% and 0.16% of analytical references, with modulation transfer function results cross-checked by two analytical extraction methods, all within 6.4 GB of memory on a single consumer-grade GPU. This simulation study represents first steps toward quantifying the expected results of ambitious space telescope concepts and aids the mission development (or selection) phase. With a highly accurate, memory-efficient validation tool, the findings obtained will be used to guide the fabrication decisions of future hardware, optical testing, and physical deployment mechanisms of large-scale diffractive telescopes.