Unified approach for rough phase measurement without phase unwrapping by changing the sensitivity factor

Abstract

Phase evaluation is extraordinarily important in optical, acoustic and radar techniques where coherent signals are employed as information carriers. In most of the cases, phase information are obtained from an inverse trigonometric function and wrapped into −π to π. A phase unwrapping process is thus required to obtain the final unwrapped phase which represents the ultimate physical quantity to be measured. One-dimensional phase unwrapping is easily achieved by adding or subtracting an integer multiple of 2π to the wrapped phase to establish a smooth phase map. Two-dimensional phase unwrapping, however, is quite troublesome and an elegant unwrapping routing should be chosen in most of the cases to deal with phase residues caused by noise and other error sources. It would be valuable if two-dimensional phase unwrapping can be avoided and the physical quantity obtained directly. In the past, researchers have proposed other methods such as the multiple wavelengths approach which incorporates information from multiple wavelengths to eliminate the need for phase unwrapping. In this study, we extend the multiple wavelengths approach by varying the sensitivity factor, which is more convenient and cost-effective, to achieve the aim of requiring no phase unwrapping. Furthermore, an elegant phase derivative approach is used to solve the phase ambiguity problem in the multiple wavelengths method. Both simulation results and real experiment data of shadow moiré and shearography demonstrate the usefulness of this method, especially for discontinuous surface profile measurements such as steps. Advantages and disadvantages for the proposed method are also discussed in this paper.