Phasing segmented telescopes via deep learning methods: application to a deployable CubeSat

Capturing high-resolution imagery of the Earth's surface often calls for a telescope of considerable size, even from low Earth orbits (LEOs). A large aperture often requires large and expensive platforms. For instance, achieving a resolution of 1 m at visible wavelengths from LEO typically requires an aperture diameter of at least 30 cm. Additionally, ensuring high revisit times often prompts the use of multiple satellites. In light of these challenges, a small, segmented, deployable CubeSat telescope was recently proposed creating the additional need of phasing the telescope's mirrors. Phasing methods on compact platforms are constrained by the limited volume and power available, excluding solutions that rely on dedicated hardware or demand substantial computational resources. Neural networks (NNs) are known for their computationally efficient inference and reduced onboard requirements. Therefore, we developed a NN-based method to measure co-phasing errors inherent to a deployable telescope. The proposed technique demonstrates its ability to detect phasing errors at the targeted performance level [typically a wavefront error (WFE) below 15 nm RMS for a visible imager operating at the diffraction limit] using a point source. The robustness of the NN method is verified in presence of high-order aberrations or noise and the results are compared against existing state-of-the-art techniques. The developed NN model ensures its feasibility and provides a realistic pathway towards achieving diffraction-limited images.