Astigmatism-Based Displacement Sensing for Curved Optical Surfaces

Accurate surface profile measurement is a critical step in the fabrication of high-quality optical surfaces. In this article, a metrology system is developed to measure curved optical surfaces in a noncontact manner utilizing an astigmatism-based optical probe. The probe is first built by introducing astigmatism into traditional confocal setups, where the information of surface displacement and slope is encoded into spot images. A multilayer neural network (MNN) is then employed to fit the dependence of image features on surface parameters. With the gradients provided by the neural network, surface parameters can be retrieved from spot images in the measurement using the gradient-based Levenberg–Marquardt algorithm. The surface profile is finally reconstructed by scanning the probe over the optical surface. Experimental measurements demonstrate that the rms measurement error is less than
$0.12 ~\mu \text{m}$
for 0° slope and
$0.43 ~\mu \text{m}$
for 10° slope. As the system does not need customized optical components and high-precision rotary stages, it provides a low-cost but powerful tool to measure optical surface profiles with slopes less than 10°, which is expected to be widely applied in optical fabrication.