Flexible geometrical calibration for fringe-reflection 3D measurement

System geometrical calibration is a challenging task in fringe-reflection 3D measurement because the fringe displayed on the LCD screen does not lie within the camera's field of view. Commonly, a flat mirror with markers can accomplish system geometrical calibration. However, the position of the markers must be precisely located by photogrammetry in advance. In this Letter, we introduce a calibration method by use of a markerless flat mirror. Experiments in phase measuring deflectometry demonstrate that the proposed method is simple and flexible.