Linear-Complexity Pixelated Absolute Testing Using Iteration for Laser Fizeau Interferometry

Absolute testing separates the reference surface error from the test surface error in Fizeau interferometry. To resolve high-spatial-frequency components in absolute surface errors at pixel-level resolution, a pixelated modeling approach is required to separate form errors. Conventional pixelated absolute testing, however, suffers from computational bottlenecks due to large-scale data processing. To address this limitation, we propose a linear-complexity pixelated (LCP) method for absolute testing through iterative processes. It establishes an absolute testing model by rotating and translating the test surface. The reference surface's form error is then computed with linear complexity via iteration. Simulations compare the proposed method with two alternative absolute testing methods. The results demonstrate significantly reduced computational complexity with high resolution at the pixel level. Experimental validation using flat and spherical reference mirrors confirms the method's capability to decouple surface errors containing mid-to-high-spatial-frequency components, including mounting-induced edge artifacts and localized defect signatures, demonstrating its superior absolute testing performance compared with the Zernike-fitting method.