Breaking the mid-spatial-frequency noise floor to sub-nanometer in Fizeau interferometry via anisotropic spatial-coherence engineering

Anisotropic spatial-coherence engineering via illumination modulation is demonstrated to selectively suppress the mid-spatial-frequency (MSF) noise in interferometry. Using a 3D spatial-coherence model, we prove the superiority of a synthetic ring source with anisotropic spatial-coherence function in Fizeau systems and reveal characteristic residual noise patterns of a zero-order Bessel function. A noise transfer function (NTF) is proposed as an essential complement to the instrument transfer function (ITF) framework, enabling quantitative assessment of noise suppression across all spatial frequencies. With the proposed method, NTF < 0.4 and ITF > 0.8 within 9.1 lp/mm are achieved in a 632.8-nm, 4-in. Fizeau interferometer, breaking the MSF noise floor to sub-1 nm. This work provides a rapid, full-aperture measurement solution for MSF errors on high-precision optical surfaces.