Three-Frequency Four-Step Phase-Shifting Method

Core Principles and Implementation of the Three-Frequency Four-Step Phase-Shifting Method

In structured light 3D measurement, phase-shifting methods are widely adopted due to their high precision and noise resistance. The three-frequency four-step approach effectively resolves phase ambiguity in traditional single-frequency methods through multi-frequency combinations and phase unwrapping strategies.

Key Steps Analysis

Multi-Frequency Grating Projection The system projects cosine gratings with low, medium, and high frequencies (e.g., frequencies 1, 4, 16) sequentially. Each frequency requires four phase shifts (0°, 90°, 180°, 270°), totaling 12 images. Frequency differences establish a coarse-to-fine hierarchical phase measurement framework.

Wrapped Phase Calculation For each frequency's four phase-shifted images, wrapped phase is computed using arctangent functions. High-frequency phases provide rich details but suffer from ambiguity, while low-frequency phases offer broader unambiguous ranges with reduced resolution, creating complementary advantages.

Phase Unwrapping and Fusion Phase unwrapping progresses from lowest to highest frequency: - Low-frequency phase serves as global unambiguous reference - Medium-frequency phase unwraps using low-frequency results - High-frequency phase inherits unwrapped medium-frequency results Final fusion yields absolute phase where high-frequency determines precision and low-frequency ensures robustness.

3D Coordinate Transformation Combining camera-projector calibration parameters, absolute phase maps to 3D coordinates on object surfaces to complete reconstruction.

Technical Advantages Strong noise immunity: Multi-frequency cross-validation suppresses ambient light interference High dynamic range: Low frequencies handle large height variations; high frequencies capture fine details Real-time optimization: 4-step method reduces projection volume by 20% compared to traditional 5-step approaches

Application Extensions This method suits measurements of reflective surfaces and complex topological objects, excelling in industrial inspection and cultural heritage digitization. Future enhancements may integrate Gray code for improved phase boundary accuracy.