Shape measurements using temporal phase unwrapping

Abstract: This licentiate thesis is devoted to shape measurements using two different optical methods. The first one is a classical triangulation method, which uses projected fringes. The second one is a new interferometric method, which uses wavelength scanning. Both are whole field measuring methods. The main goal of the project has been to analyse the performance of an analysis scheme for absolute shape measurements called temporal phase unwrapping. This method permits the user to determine the absolute distance from the detector (usually a CCD-detector) to the object. A generalised version of the temporal phase unwrapping scheme is called reduced temporal phase unwrapping. The scheme uses an arbitrary number of fringe maps with varied fringe pitch, to calculate phase (shape). A thorough investigation is made of the performance of this algorithm. A single channel and a multi channel approach is considered. Expressions are found that relates the physical quantities to phase errors. In these simulations the single channel approach was found to be the most robust one. Expressions that relate the measurement accuracy and the unwrapping reliability, respectively, to the reduction of the fringe sequence were also found. As expected the measurement accuracy is not affected by a shorter fringe sequence while a significant reduction in the unwrapping reliability is found, as compared to the complete negative exponential sequence. The strength of reduced temporal phase unwrapping is demonstrated experimentally, in a projected fringe three-channel system. Instead of letting each channel carry phase-stepped images each channel can carry images with a change in fringe pitch. This significantly reduces noise, but at least three images needs to be acquired. It is also shown that the temporal phase unwrapping analysis scheme can be used to evaluate experimental data from wavelength scanning interferometry. Two unwrapping strategies are considered: fitting to a reversed exponential sequence and complex Fourier-transform ranging. The achievable accuracy for both methods ultimately depend on the tuning width, the speckle correlation, and random noise in the optical setup.