Double blind Fourier holography for high-precision wavefront sensing in segmented mirror telescopes

Segmented primary mirror (PM) telescopes offer significant advantages over monolithic mirrors: scalability, modularity, ease of fairing, serviceability, and segment-level wavefront control. Achieving the scientific objectives of such observatories requires accurate wavefront sensing to support fine alignment, calibration, and long-term wavefront control. In this work, we explore double blind Fourier holography (DBFH) as a high-precision wavefront sensing scheme and its relevance for future space observatory flagship missions such as the Habitable Worlds Observatory (HWO). DBFH has previously been applied successfully to challenging phase retrieval problems, including electron diffraction in crystallography and attosecond pulse characterization. Using DBFH, we numerically demonstrate full wavefront reconstruction for a segmented aperture consistent with HWO geometry from as few as four carefully selected focal-plane captures, achieving estimation precision approaching the picometer regime, with segment piston errors as low as 13 picometers in the presence of measurement noise. Finally, DBFH is algebraically linear, and as such, has the potential to reduce computational costs and avoid convergence pathologies common to nonlinear, iterative phase-retrieval (PR) methods. While demonstrated in the context of the HWO, this scheme is broadly applicable to high-precision wavefront sensing in any segmented PM telescope.