Circular fringe projection technique for out-of-plane deformation measurements

Fringe projection is,a widely used technique for measurement of out-of-plane deformation of diffusely reflecting objects. Among the various fringe patterns employed for projection, usage of linear fringes is most common. However, the phase function of linear fringes has 2 pi periodicity, thereby leading to ambiguity in determining whole-field out-of-plane deformation of dynamic objects. This paper presents a new method of measurement of whole-field out-of-plane deformation of targets by projecting a circular fringe pattern. New technique of fringe analysis is introduced to estimate the underlying phase distribution of the fringe pattern from a single image. In this technique, the fringe pattern is coordinate transformed into polar coordinates, and then Fourier fringe analysis technique is employed to obtain its phase. Subsequent to unwrapping, the phase map is re-transformed to Cartesian coordinates. The phase map obtained after coordinate transformation is converted to out-of-plane deformation map using camera calibration parameters. Simulations are carried out to establish the analysis method. Experimental validation is performed with the development of circular grating based fringe projection system.