Due to the ‘invisible’ property of the specular surface, it is difficult for the stitching deflectometry to identify the overlapping area. Previously, markers were used on the unit under test with a roughly known shape to find the overlapping area. We propose a marker-free stitching deflectometry that utilizes the stereo-iterative algorithm to calculate the sub-aperture point cloud without height-slope ambiguity, and the overlapping area is identified with the point cloud datum. The measured area is significantly enlarged. The simulation and experiments are conducted to verify the proposal and evaluate the accuracy. We test a high-quality flat with 190mm diameter, the measurement error is below 100nm RMS with comparison to the interferometer.

As a highly accurate metrology, phase measuring deflectometry (PMD) can be used for in-situ surface shape measurement. However, due to the reflection off the back surface, PMD cannot measure both the front and back surfaces of the transparent planar element simultaneously. Therefore, this paper proposes a method for measuring the front and back surfaces of the transparent planar element. The phase distribution corresponding to the front and back surfaces can be firstly acquired by multi-frequency fringe deflectometry. Then, the front and back surface shapes can be obtained by inverse ray-tracing and nonlinear optimization. Numerical simulation and experiment verify the proposed method. The surface shape of window glass with a thickness of 10 mm is measured in the experiment. The surface shape error is around 50 nm in the root mean square with a diameter of 51 mm.

A camera calibration method for phase measuring deflectometry (PMD) based on the entrance pupil center (EPC) of the camera lens is proposed. In our method, the position of the entrance pupil of the camera lens is first measured; next the absolute coordinates of the EPC are calibrated by using a reference flat and an external stop that is mounted in front of the camera lens; then the EPC as the camera coordinates is used for PMD. The feasibility of the proposed method is verified by simulation. The surface shapes of a planar optical element and a planar window glass are separately measured in our experiments, and a subwavelength accuracy level is achieved. Meanwhile, the effects of the camera lens with different aperture settings on captured images are investigated (including exposure time, image contrast, and measurement accuracy). The experimental results show that the exposure time required declines with the decrease in the f-number, and the measurement accuracy is higher than others when the f-numbers are changed from f/5.6 to f/11.

No abstract

Phase measuring deflectometry (PMD) is a competitive method for specular surface measurement that offers the advantages of a high dynamic range, non-contact process, and full field measurement; furthermore, it can also achieve high accuracy. Camera calibration is a crucial step for PMD. As a result, a method based on the calibration of the entrance pupil center is introduced in this paper. Then, our proposed approach is compared with the most popular photogrammetric method based on Zhang’s technique (PM) and Huang’s modal phase measuring deflectometry (MPMD). The calibration procedures of these three methods are described, and the measurement errors introduced by the perturbations of degrees of freedom in the PMD system are analyzed using a ray tracing technique. In the experiment, a planar window glass and an optical planar element are separately measured, and the measurement results of the use of the three methods are compared. The experimental results for the optical planar element (removing the first 6 terms of the Zernike polynomial) show that our method’s measurement accuracy reached 13.71 nm RMS and 80.50 nm PV, which is comparable to accuracy values for the interferometer.