A study on carrier phase distortion in phase measuring deflectometry with non-telecentric imaging

Abstract

In phase measuring deflectometry (PMD), the fringe pattern deformed according to slope deviation of a specular surface is digitized employing a phase-shift technique. Without height-angle ambiguity, carrier-removal process is adopted to evaluate the variation of surface slope from phase distribution when a quasi-plane is measured. However, the difficulty lies in the fact that the nonlinearity is generally contained in the carrier frequency due to the restrictions of system geometries. This paper investigates nonlinear carrier components introduced by the generalized imaging process in PMD. Furthermore, the analytical expression of carrier components in PMD is presented for the first time. The presented analytical form of carrier components can be extended to analyze and describe various effects of system parameters on carrier distortion. Assuming a pinhole perspective model, carrier phase distribution of arbitrary geometric arrangement is modeled as a function of spatial variables by exploring ray tracing method. As shown by simulation and experimental results, the carrier distortion is greatly affected by non-telecentric camera operation. Experimental results on the basis of reference subtraction technique further demonstrate that restrictions on reflection system geometry can be eliminated when the carrier phase is removed elaborately.