Calibration of a free-form mirror for optical 3D measurements using a generalized camera model

A new methodology is presented which enables the use of optical free-forms instead of classical beamers for fringe projection based optical 3D surface measurements. Although optical free-forms allow the generation of approximately sinusoidal fringes for phase shifting profilometry, they cannot produce Gray code like pattern for robust phase unwrapping. The principal idea of this work is the consideration of the fringe producing free-form mirror as an optical component of the sensor system which should be used for 3D point calculation. In order to do so, a description of the spatial distribution of the considered rays will be realized. This corresponds to a calibration of the free-form. The approach of a generalized model is used for the calibration instead of selecting a certain camera model as the telecentric or the pinhole model. This generalized camera model will be described in this work.