A new phase-to-height mapping algorithm with loose constraints based on phase measuring profilometry is proposed to improve the measurement accuracy of PMP and relax the constraints of its system. The algorithm requires neither the linking line between the optic centers of the projection system and the imaging system to be parallel to the reference plane

nor the projecting optic axis and the imaging optic axis to be on the same plane. Just by making sure that the imaging optic axis is vertical to the reference plane can the phase-to-height mapping be successfully realized. The mathematic model of the algorithm was deduced in detail

and it was found that the phase-to-height mapping was not only related to the structure parameters of the 3D measurement system but also to the phase distribution of reference plane. In actual measurement

it is difficult to guarantee that the linking line between the optical centers of the projection system and the imaging system is parallel to the reference plane

but the new phase-to-height mapping algorithm avoids this challenge

thus providing a true reflection of the actual measurement system. It also makes the experimental system easier to build. Experimental results show that the mean absolute errors and the root mean square errors of the proposed method were no more than 0.031mm and 0.040 mm

respectively. The algorithm could relax the constraints when building the measurement system and make the beam path easier to realize. The effectiveness of the proposed algorithm was verified by the experiment

indicating that the proposed algorithm is superior to the traditional algorithm in terms of accuracy and repeatability.