Three-Step, Four-Step, and Five-Step Phase-Shifting Methods with Corresponding Phase Unwrapping Techniques

Phase-shifting method is a widely used technique in optical interferometry that calculates phase distribution by acquiring multiple phase-shifted interferograms. Among these, three-step, four-step, and five-step algorithms are common phase-shifting methods, each with distinct characteristics suitable for different measurement scenarios.

Three-Step Phase-Shifting Method The three-step method is the simplest phase-shifting algorithm requiring only three interferograms, typically with a phase step of 120° (2π/3). Phase information is extracted through intensity calculations from three images. Implementation typically involves solving trigonometric equations using arctangent functions. The main advantage is fast computation speed, but due to limited data points, it has weaker noise resistance and is susceptible to environmental disturbances. Code implementation often uses matrix operations to calculate phase maps from intensity values.

Four-Step Phase-Shifting Method The four-step method employs four interferograms with typical phase steps of 90° (π/2). Compared to the three-step method, it demonstrates better noise resistance and effectively reduces errors caused by non-uniform background illumination. Algorithm implementation typically involves a more robust phase calculation formula that cancels out common-mode noise. However, requiring more data acquisition results in relatively slower measurement speed. The code structure often includes additional calibration steps for intensity normalization.

Five-Step Phase-Shifting Method The five-step method further improves phase measurement accuracy by calculating phase from five interferograms, generally with 72° (2π/5) steps. With increased data points, it exhibits stronger noise suppression capabilities, making it suitable for high-precision measurement applications. Implementation typically uses advanced least-squares fitting algorithms to extract phase information. The trade-off is increased computational complexity, requiring optimized code for real-time processing.

Phase Unwrapping Phase unwrapping is a crucial post-processing step in phase-shifting methods that removes 2π phase jumps to recover continuous phase information. Common unwrapping algorithms include path-following methods, least-squares approaches, and Fourier-transform based techniques. Path-following methods work well in low-noise environments by tracking phase continuity paths, while least-squares methods demonstrate better robustness in noisy conditions by minimizing global phase discrepancies. Code implementation often involves quality-guided unwrapping or branch-cut algorithms for complex phase fields.

Applications and Optimization Phase-shifting methods and phase unwrapping are widely applied in optical 3D profilometry, interferometric imaging, and vibration analysis. In practical implementations, appropriate phase-shift steps should be selected based on measurement requirements, and noise suppression algorithms should be integrated during the unwrapping stage to enhance measurement accuracy. Code optimization techniques include parallel processing for large datasets and GPU acceleration for real-time applications.