Computer Simulation of Four-Step Phase-Shifting Digital Holography

Digital holography is a technique for obtaining three-dimensional object topography by recording and reconstructing light wavefront information. The four-step phase-shifting method is a commonly used phase retrieval technique in digital holography, which introduces reference light with known phase shifts to interfere with object light, records multiple interference patterns, and ultimately calculates the wrapped phase.

In computer simulation, the first step involves constructing a virtual object light field, which can be a simple 2D image or 3D structure. The simulation then models the interference process between reference light and object light, where the reference light must incorporate four different phase shifts: 0, π/2, π, and 3π/2. From the intensity distributions of the four interference patterns, the wrapped phase can be calculated using the four-step phase-shifting algorithm. Code implementation typically involves creating phase-shifted reference waves using complex exponential functions and calculating phase values through arctangent operations on intensity ratios.

Phase unwrapping is a crucial subsequent processing step because the phase obtained from the four-step phase-shifting method is wrapped modulo 2π. Phase unwrapping algorithms are required to recover the continuous absolute phase distribution. Through computer simulation, we can validate algorithm effectiveness and optimize parameter settings, thereby providing theoretical support for practical experiments. Common unwrapping algorithms include quality-guided path following and least-squares methods, which can be implemented using spatial derivative calculations and iterative solvers.