Fringe projection profilometry without explicit projector calibration

Metric three-dimensional reconstruction by fringe projection profilometry requires calibrating the employed camera and projector. However, the calibration process is more difficult for projectors than for cameras. This work presents a reconstruction method where the projector parameters are not required explicitly. For this, we assume the projector follows the pinhole model and single-axis fringe projection is employed. The theoretical principles are explained, and the proposed method is validated experimentally by a metric three-dimensional reconstruction. The results provide a theoretical framework for further generalization, including implicit camera calibration and lens distortion, while keeping the metric reconstruction capability.