FM-PE: A Robust Subaperture Tip/Tilt Errors Measurement Method for Spaceborne Segmented Telescopes Using Remote Sensing Imagery

The success of the James Webb Space Telescope (JWST) has instilled confidence in space-based segmented telescopes, which have emerged as one of the most promising avenues for achieving submeter resolution in geostationary orbits (GEOs) for Earth observation. Tip/tilt (T/T) error correction of subapertures is crucial for realizing the imaging capability of segmented telescopes, yet existing methods are inadequate to directly utilize remote sensing images for this purpose. We propose a novel frequency main-peak phase extraction (FM-PE) method for T/T error measurement of spaceborne segmented telescopes used in Earth observation. We derive the optical transfer function (OTF) formula of segmented telescopes with co-phasing errors and discover that only T/T errors, without piston errors, are contained in the OTF’s main peak. Consequently, we establish a theoretical model grounded in phase modulation, enabling the disentanglement of mutually intermixed T/T errors among subapertures within this main peak. Numerical simulations and experiments show that the proposed FM-PE method achieves subpixel-level T/T measurement by directly leveraging complex ground-scene images captured by cameras. This approach demonstrates high accuracy, and its calibration performance remains unaffected by piston errors, coherent conditions, and aperture layouts, showcasing remarkable robustness and noise resistance. As such, FM-PE presents an efficient and precise solution for T/T correction of segmented telescopes for Earth observation.