Quantitative modeling of camera noise propagation in binocular fringe projection profilometry

While binocular fringe projection profilometry (BFPP) affords high-precision three-dimensional metrology, its ultimate precision remains intrinsically bounded by stochastic image intensity noise. The paper proposes a comprehensive uncertainty quantification framework that rigorously traces noise propagation from raw image acquisition through phase demodulation to spatial coordinate reconstruction in binocular fringe projection architectures. The theoretical formulation unifies an affine camera noise model, multi-frame phase-shifting algorithms, and geometric covariance propagation analysis into a cohesive analytical pipeline. Experimental verification utilizing a calibrated dual-camera system on precision spherical artifacts validates the predictive capability for smooth spherical geometries: phase deviation predictions achieve relative errors below 5% (mean: 4.17%), while three-dimensional reconstruction coordinate repeatability is constrained to sub-0.01 mm levels. Generalization to complex geometries involving sharp edges, concave features, or spatially varying reflectivity requires additional experimental validation. Notably, over 90% of reconstructed surface points attain relative errors below 5%, constituting a precision enhancement exceeding 400% (factor of ∼4.76×) relative to conventional homoscedastic noise models. These results establish a rigorous theoretical basis for the uncertainty-aware optimization of binocular structured light systems.