Comparison of linear and non-linear calibration methods for phase-shifting surface-geometry measurement

Abstract

In fringe-projection surface-geometry measurement, phase unwrapping techniques produce a continuous phase distribution that contains the height information of the 3-D object surface. To convert the phase distribution to the height of the 3-D object surface, a phase-height conversion algorithm is needed, essentially determined in the system calibration which depends on the system geometry. Both linear and non-linear approaches have been used to determine the mapping relationship between the phase distribution and the height of the object; however, often the latter has involved complex derivations. In this paper, the mapping relationship between the phase and the height of the object surface is formulated using linear mapping, and using non-linear equations developed through simplified geometrical derivation. A comparison is made between the two approaches. For both methods the system calibration is carried out using a least-squares approach and the accuracy of the calibration is determined both by simulation and experiment. The accuracy of measurement using linear calibration data was generally higher than using non-linear calibration data in most of the range of measurement depth.