Interferogram-free adaptive wavefront interferometry: fourier spot analysis enhancing adaptive compensation performance

Over the past decades, adaptive wavefront interferometry (AWI) has been widely employed as a high-resolution and intelligent metrological technique for measuring freeform surfaces with substantial surface error deviations. However, conventional AWI approaches predominantly rely on the detection, reconstruction, and sparsification of incomplete interferograms-a process that inherently constrains the efficacy and directionality of the initial optimization phase due to the limited information provided by such interferograms. This study presents an improved AWI methodology that enhances directional optimization and efficient measurement for freeform surfaces with significant deviations by optimizing the Fourier spot (FS). Significantly, this approach eliminates the requirement for wavefront sensors or phase-shifting procedures throughout the optimization process, substantially simplifying the measurement process. Numerical simulations demonstrated that a freeform wavefront with a peak-to-valley (PV) value of 109.1<i>λ</i> (<i>λ</i> = 632.8 nm) and root-mean-square (RMS) of 13.49<i>λ</i> could be effectively compensated within tens of iterations. In experiments, a test of a freeform surface with a PV of 104.1<i>λ</i> and RMS of 24.89<i>λ</i>, which initially produced indistinguishable interference fringes, was successfully accomplished in 60 iterations, achieving a measurement error with PV of 0.89<i>λ</i> and RMS of 0.17<i>λ</i>. These findings confirm that the proposed IF-AWI method is capable of efficiently and accurately measuring freeform surfaces with substantial deviations.