Performance and Analysis of a Deployable DiffractiveOptical Element for Small Satellite Missions

Abstract

As space missions push toward smaller, lighter, and more deployable instrumentation, diffractive optical elements (DOEs) offer a compelling alternative to traditional optics. Their ability to focus light through engineered phase profiles rather than curved surfaces allows for large-aperture, flat optics that are far lighter and easier to package for launch. However, this benefit comes with trade-offs: DOEs are sensitive to wavelength mismatch, manufacturing errors, and environmental deformations—especially thermal gradients and membrane tensioning in space. This thesis develops a comprehensive framework for understanding and simulating the performance of DOEs under realistic operating conditions. Beginning from first principles, the work contrasts geometric and wave-optical models for Fresnel zone plates and multilevel diffractive lenses, leading to quantitative predictions of diffraction efficiency and PSF quality under non-idealities. A key contribution is the analytical and numerical analysis of how uniform thickness errors, wavelength mismatches, and thermal expansions degrade optical performance, both in efficiency and wavefront fidelity. To evaluate these effects in detail, a flexible simulation tool was developed in MATLAB, enabling both Fourier and integral-based propagation through arbitrarily deformed DOEs. These models are applied to a conceptual space-based LIDAR system—SPECIES—that uses a deployable DOE optic to demonstrate the feasibility and limitations of this approach. The results show that DOEs can tolerate some global deformations - for example, a 1 mm deformation results in a 38% performance loss in an F3 LiDAR system with a 1 mm detector diameter. However, they remain highly sensitive to fine-scale shape errors, posing significant challenges for high-precision applications like fiber coupling or imaging. The findings provide new insight into the tolerances, benefits, and trade-offs of DOEbased systems in space, and lay the groundwork for future missions seeking to leverage lightweight diffractive optics for remote sensing and optical communication.