LAUSR

The phase measuring deflectometry (PMD) has been widely applied to measure specular objects. However, the placement of the calibration mirror is still challenging: excessively large or small angles may cause the calibration algorithm to fail or render the optimization matrix that is rank deficient. To address this issue, we implemented the three-mirror method, which is a maker-free calibration method that is widely applied in the PMD field, and improve it from two aspects. First, the original three-mirror method is limited by the number of mirror poses. The proposed “Group-optimal” method enumerates all possible combinations by grouping them in triplets of mirror poses, and then, the solutions for each triplet will be filtered with a threshold and will be regarded as initial values to converge the algorithm. This process allows the algorithm to calibrate the system using data from more poses. Second, the algorithm could automatically generate the next optimal pose and guide the users in positioning the mirror’s pose, ensuring that the optimization matrix is full rank, i.e., the solution is not ambiguity. Experiments have proved the validity: The red peak and valley (PV) value of the measured plane mirror was reduced originally from the 221.80 to 74.05 nm, and the root-mean-square (rms) value was decreased from 66.56 to 19.82 nm. The PV value of the measured spherical mirror was reduced originally from 256.31 to 127.49 nm, and the rms value was decreased from 87.22 to 45.87 nm. Compared with other calibration methods, this method does not require a marker or customized calibration mirror and achieves the same level of accuracy, which is providing a more flexible, economical, and efficient approach for a PMD system in large-scale industry applications.