研究目的
To analyze the relation between the surface shape and measurement error when simpli?cation/assumption is used in phase measuring de?ectometry (PMD), and to develop a ray tracing simulation model for studying the measurement accuracy and scope of gradient models in PMD.
研究成果
The ray tracing simulation model effectively analyzes measurement errors in PMD due to surface shape simplifications. Experimental results confirm that increasing height or gradient exponentially aggravates errors. For the specific setup, a ratio of screen-reference plane distance to height STD greater than 200 ensures gradient errors below 0.5%. This approach can be extended to other analytical models in PMD.
研究不足
The analytical gradient model assumes small height and slope variations, leading to errors for non-quasi-plane surfaces. The simulation and experiments are specific to the setup used; results may vary with different system geometries. The method requires accurate calibration of system parameters.
1：Experimental Design and Method Selection:
A ray tracing simulation model was developed using Matlab to simulate the PMD system, including a LCD screen, CCD camera, and test surface. The model was used to analyze the influence of surface height and gradient on measurement accuracy by comparing simulated and true gradients.
2：Sample Selection and Data Sources:
The test surfaces included a plane mirror moved with a displacement stage to vary height, a plane mirror rotated with a rotation stage to vary gradient, and three types of mirrors (plane mirror, 20,000 mm radius sphere mirror, 5000 mm radius sphere mirror).
3：List of Experimental Equipment and Materials:
LCD screen (1366 × 768 pixels), CCD camera (Manta G-125B/C, 1200 × 1600 pixels), 50 mm focal length lens, displacement stage (minimum scale 0.02 mm), rotation stage, and various mirrors.
4：02 mm), rotation stage, and various mirrors.
Experimental Procedures and Operational Workflow:
4. Experimental Procedures and Operational Workflow: For height variation, the plane mirror was moved using the displacement stage, and phase distributions were recorded and analyzed. For gradient variation, the mirror was rotated, and phase distributions were extracted. The gradient was calculated using Eq. (1), and errors were computed by comparison with true values. Simulations were conducted by changing surface shape in the model and tracing phases.
5：Data Analysis Methods:
Gradient errors were calculated as the difference between measured and true gradients. Simulation results were compared with experimental data to validate the model. Statistical measures like standard deviation (STD) were used.
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