Fast combined-frequency phase extraction for phase shifting profilometry.

Area of Science:

• Optical Metrology
• 3D Measurement Techniques
• Image Processing

Background:

• Phase shifting profilometry (PSP) systems suffer from nonlinearities causing fringe harmonics and inaccurate phase maps.
• High-order fringe harmonics are a significant source of error in PSP measurements.
• Accurate phase extraction is crucial for reliable 3D surface reconstruction.

Purpose of the Study:

• To develop an efficient and accurate method for phase extraction in PSP systems.
• To address the challenge of fringe harmonic distortions in captured images.
• To improve the performance of PSP by reducing phase errors.

Main Methods:

• Formulated phase extraction as a maximum likelihood estimation (MLE) problem, incorporating different frequency images and a high-order fringe harmonic model.
• Proposed a combined-frequency phase extraction (CFPE) solution utilizing a latent phase map.
• Employed the expectation-maximization (EM) framework for efficient optimization.

Main Results:

• The CFPE method achieved high-order accuracy while reducing execution time to approximately 5% of a high-order baseline method.
• Demonstrated significant performance improvements in both efficiency and accuracy on synthetic and practical measurement data.
• Validated the effectiveness of modeling high-order fringe harmonics for error reduction.

Conclusions:

• The proposed CFPE method offers a substantial advancement in PSP for accurate and efficient 3D measurements.
• CFPE effectively mitigates phase errors caused by fringe harmonics, leading to improved measurement reliability.
• The detailed implementation and experimental setup are provided to facilitate further research in optical metrology.