A new model for measuring object shape using non-collimated fringe-pattern projections

Successful measurement of object shape using projected fringe patterns depends on various factors, most importantly in the final stage of relating the measured unwrapped phase distribution to the object height. Although various phase- to- height models exist in the literature, the different approaches employ numerous assumptions and simplifications which could render the derived model inaccurate or very sensitive to parameter variations. In this paper, the phase- to- height model presented by Rajoub et al ( 2005 J. Opt. A: Pure Appl. Opt. 7 368 - 75) will be extended to work with systems using non- collimated projections of fringe patterns. The true ( or physical) spatial phase distribution existing over the object's surface as a result of the projected fringe pattern is first calculated using projector- to- object ray tracing. The camera image of the object's shape is then obtained through image mapping transformations assigning the pixels with intensities that correspond to the previously calculated 3D spatial phase. This mapping combined with the previously calculated spatial phase provides us with the expression that relates the phase as seen by the camera to the object's height. Unlike existing approaches, the proposed approach is universal in the sense that it is not restricted to certain optical arrangements and does not rely on oversimplified geometries. Therefore, it will be very useful in helping us understand the various effects of system parameters on the measurement outcome.