# Absolute distance contouring and a phase unwrapping algorithm for phase maps with discontinuities.

Xie, X (1997) Absolute distance contouring and a phase unwrapping algorithm for phase maps with discontinuities. Doctoral thesis, Liverpool John Moores University.

## Abstract

This thesis describes a new technique, absolute distance contouring, and a phase unwrapping algorithm for phase maps with discontinuities.
Absolute distance contouring, which is based on the shadow moire method, using the rotation of a grating, is a technique which can be used for the measurement of absolute distance from the grating to the object and the determination of an object's height. By the selection of suitable rotation angles, images are captured at different positions of the grating to obtain the required data. The technique is divided into three different methods, according to the number of images required for each measurement and the rotation angles. These are known as: the absolute distance contouring method, the four-image method, and the three-image method.
Using these methods, the three-dimensional shape of the object can be obtained directly and it is not necessary to determine the absolute moire fringe order nor to judge the hills and valleys of the object's surface. Some of the problems of the previous shadow moire methods can be solved and some inconvenience can be overcome by the proposed methods. The techniques have been verified by experimental work which was carried out on a specially designed system. The results show that the methods are fast and the accuracy is better than 10μm. The maximum measurable range is related to the geometry of the optical system and the rotation angles.
The phase unwrapping algorithm is a technique to obtain the correct phase distribution for a phase map with discontinuities. A crossed grating, which has two sets of lines in two different directions, is projected onto the surface to be measured. The modulated grating image, which is equal to the superposition of two separate modulated images, is captured and Fourier transformed. The two images are separated in the Fourier domain. After filtering and frequency shifting, they are inverse transformed to obtain two phase maps with different precisions. Phase unwrapping at each pixel is carried out independently and the correct phase values can be obtained in the presence of discontinuities caused by a surface with steps or noise. This fast algorithm has been verified experimentally by measuring the shapes of objects with height steps, and it only requires a single image for each measurement.
The methods of absolute distance contouring and the new phase unwrapping algorithm are new techniques for the measurement of three-dimensional object profile, which will find application in many areas.

Item Type: Thesis (Doctoral) T Technology > TJ Mechanical engineering and machinery General Engineering Research Institute 23 Feb 2017 10:31 24 May 2018 10:25 10.24377/LJMU.t.00005572 http://researchonline.ljmu.ac.uk/id/eprint/5572