Three-Step Phase Shift Method for Structured Light 3D Reconstruction

The Structured Light Three-Step Phase Shift Method, also known as Structured Light Triangulation, is a fundamental technique in 3D scanning for reconstructing object shapes and surface topography. This approach operates on triangulation principles, where a predefined light pattern is projected onto the target object, and 3D geometry is calculated by analyzing distortions in the reflected pattern. Implementation typically involves projecting three phase-shifted sinusoidal patterns with phase offsets of 0, 2π/3, and 4π/3 radians. The core algorithm calculates phase values using the formula: φ = arctan(√3*(I₁ - I₃) / (2I₂ - I₁ - I₃)), where I₁, I₂, I₃ represent intensity values from the three patterns. This phase information is then unwrapped and converted to 3D coordinates through triangulation calculations involving camera and projector parameters. Key functions in implementation include: - Pattern generation: Creating phase-shifted sinusoidal patterns using grating equations - Phase demodulation: Extracting phase information from captured images - Phase unwrapping: Resolving 2π ambiguities in phase maps - Coordinate transformation: Converting phase values to 3D points using calibration matrices This method finds extensive applications in industrial design, reverse engineering, and medical imaging due to its high accuracy and robustness against surface variations. The technique's efficiency makes it suitable for real-time 3D reconstruction systems when optimized with GPU acceleration.