Performance and modelling of a deployed diffractive optical element for space-based LiDAR

SPECIES (Smart Polyimide Expandable Collector to enable Investigations for Earth Science) is a NASA Earth Science Technology Office (ESTO) project that explores the use of a deployable diffractive optical element (DOE) in a space-based LiDAR instrument for a 12–24U small satellite operating in low Earth orbit (LEO). The DOE is a 0.6-meter hybrid multi-level Fresnel zone plate (MLFZP), constructed from a tessellation of hexagonal polyimide membranes, each with a distinct number of diffractive levels. It is stowed for launch and deployed on orbit using a 3-meter-long extendible boom, which positions the optic at the correct distance from the spacecraft, while guy wires provide tensioning to maintain a flat profile. This architecture enables the DOE to achieve high diffractive efficiency and optical performance while significantly reducing mass and cost compared to traditional refractive or reflective optics of comparable size. This work presents methods and results to model the performance of a deformed DOE. A custom optical model is employed to propagate the beam through the deformed DOE and characterize the optical response and system performance. Using deformation inputs from mechanical stresses due to packing and deployment and thermal variations in orbit, the model evaluates key optical performance parameters, including the focal point spread function, beam quality, diffraction efficiency, and wavefront aberrations. The model extends traditional Fourier optics principles to enable field propagation from a non-planar diffractive optic, maintaining computational efficiency through Fourier transforms. These results are then used to assess the effects on LiDAR performance, including measurement uncertainties and overall system efficiency. We present the implementation of this model, including numerical wave propagation techniques for deformed diffractive optical elements. By addressing these challenges, SPECIES demonstrates the viability of large-format, lightweight DOEs for high-performance, space-based LiDAR applications. The findings offer broader insights into the practical implementation of diffractive optics for compact, deployable, and cost-effective optical systems, with potential applications in Earth observation and beyond.