Accurate phase–height mapping algorithm for PMP

Abstract

In phase measurement profilometry (PMP), the projector can be regarded as another camera according to the reversibility of the light path principle. The relationship of projecting spatial points to image plane of camera and projector is studied, and the phase–height mapping equation without projector distortion is obtained. The equation is then expanded to a polynomial for the convenience of calibration. Furthermore, the relation between the distortion value and the phase is investigated. Finally the phase–height mapping algorithm considering projector distortion and its polynomial expression are acquired. The accuracy of approximation is studied and compared with another two existing algorithms by computer simulation. It is revealed that the absolute error of the new algorithm expressed with quartic polynomial reaches 5.380× 10−3 mm and its standard deviation reaches 3.354× 10−4 mm under general lens distortion. The accuracy of the new algorithm is the highest among the three algorithms. In experiment, the standard deviation of the measurement reaches 0.04 mm even though the result is affected by measurement error.