Data fusion of full-band errors in optical surfaces

Maximum a posteriori estimation combines current measurements, a statistical prior derived from historical power spectral density data, and physical spectral constraints to estimate a continuous full-band power spectral density. Experiments using a laser interferometer and a white-light interferometer yield root mean square errors of 0.84 and 0.37 nm for low- and mid-frequency error extraction, respectively, and relative accuracies of 95.71%–99.73% for the four continuous representations.

Without full-aperture high-resolution observations, fusion produces a continuous full-band error power spectral density, full-aperture low- and mid-frequency error topography, and full-band error topography within locally measured regions. By integrating topographic and spectral information across measurement scales, the method supports full-band optical surface evaluation under limited observations. The overall workflow is independent of specific instruments and can be extended to other instrument combinations with complementary measurement capabilities.</p>