Processing of Four-Step Phase-Shifting Interferograms

The processing of four-step phase-shifting interferograms is a crucial technique in optical measurement and phase analysis, primarily used for high-precision wavefront reconstruction. The core workflow involves interferogram acquisition, phase extraction, and phase unwrapping steps, typically implemented through numerical algorithms in environments like MATLAB or Python.

Phase Extraction Method The four-step phase-shifting method captures four interferograms with phase differences of π/2 between consecutive frames, then calculates the wrapped phase using an arctangent function. In code implementation, this involves pixel-wise operations: I1, I2, I3, I4 represent the intensity values of four interferograms, where phase φ = atan2(I4 - I2, I1 - I3). This algorithm effectively eliminates background intensity and modulation amplitude interference, yielding high-precision phase distribution through vectorized array computations.

Unwrapping Algorithm Since extracted phase values are wrapped within the [-π, π] interval, unwrapping algorithms are required to remove discontinuities and restore true phase. Common methods include path-dependent algorithms (e.g., Goldstein branch-cut method) and least-squares approaches. Path-dependent methods use quality maps to guide unwrapping paths, while least-squares methods solve Poisson's equation via discrete cosine transforms (DCT). Code implementation often involves handling phase gradients and residue detection, with noise-robust variants employing weighting functions for different noise conditions.

Application Scenarios This technology is widely applied in optical component inspection, holographic imaging, and micro-nano structure measurement, providing reliable basis for high-precision surface analysis. For beginners, understanding interferogram generation mechanisms (simulated via Zernike polynomials or experimental setups) and selecting appropriate unwrapping algorithms based on noise characteristics are key to mastering this technique. Practical implementation typically requires image preprocessing (filtering, normalization) and validation through synthetic data with known phase profiles.