Intrinsic feature revelation of phase-to-height mapping in phase measuring profilometry

In traditional phase measuring profilometry (PMP) setup, the connecting line between the exit pupil center of projector and entrance pupil center of CCD camera must parallel to the reference plane and the optical axes of projector and CCD camera must intersect at the same point on the reference plane. At this condition, the coefficients of phase-to-height mapping are constants because they are proved to be only dependent on the structural parameters. But lots of experimental results show that some of coefficients are not constants. Further analyzing this phenomenon, it is found that the above two restricted conditions can hardly to be guaranteed due to the invisible of the exit pupil, the entrance pupil and the optical axes. The more popular situation is that the above connecting line may not parallel to the reference plane and the above optical axes do not intersect on the reference plane. So a new universal mapping algorithm is derived at this situation. It reveals some of coefficients of the mapping really remain constants which are dependent on only the structural parameters, while some of coefficients are really not constants which are dependent on not only the structural parameters but also the phase distribution of the reference plane. It also reveals that the traditional mapping algorithm is just a special case of the derived mapping algorithm. Furthermore, it reveals that the accuracy of PMP can be improved distinctly by calibrating the phase of the reference plane. Experimental results have shown the feasibility and validity of the derived phase-to-height mapping algorithm.