Fast, intelligent and high-precision adaptive null interferometry for optical freeform surfaces by backpropagation

In the past 10 years, adaptive wavefront interferometry (AWI) has been employed for measuring freeform surface profiles. However, existing AWI techniques relying on stepwise and model-free stochastic optimizations have resulted in inefficient tests. To address these issues, deterministic adaptive wavefront interferometry (DAWI) is firstly introduced in this paper based on backpropagation (BP), which employs a loss function to simultaneously reconstruct and sparsify initial incomplete interferometric fringes until they are nulled. Each iteration of BP requires two phase shifts. Through simulations, we have verified that freeform wavefront error with a peak-to-valley (PV) of up to 168 lambda can be fully compensated in tens of iterations using a 1024 x 1024 pixel area of a liquid-crystal spatial light modulator. In experiments, we accomplished a null test of a freeform surface with 80% missing interference fringes in 39 iterations, resulting in a surface profile error PV of 66.22 lambda and measurement error better than lambda/4. The DAWI has at least 20 times fewer iterations in fringe reconstruction than the 3 -step AWI methods, and nearly an order of magnitude fewer iterations in the whole process, paving the way for significantly enhanced efficiency, generality and precision in freeform surface adaptive interferometry.