Temporal phase unwrapping: development and application of real-time systems for surface profile and surface displacement measurement

Industrial adoption of whole-field optical metrology has been hindered by the interpretation of the resulting wrapped phase data using traditional spatial unwrapping algorithms. These algorithms typically require long computation times and are often unable to provide unique solutions. An alternative approach described by Huntley and Saldnert simplifies the data analysis by using a time-series of wrapped phase maps to unwrap the data temporally, and has the advantage that errors due to noise and specimen boundaries do not propagate spatially. However, viability of the algorithm is restricted by the need to store and subsequently analyse very large datasets. This thesis describes the development and application of an instrument that implements the temporal phase unwrapping algorithm (TPUA) in real-time to overcome these problems and allows whole-field optical techniques to become more intuitive by enabling quasi-live results to be displayed. Tradeoffs across the multiple domains of algorithm, hardware and software are discussed, including decomposition of the algorithm onto particular architectures and implementation using a commercial pipeline image processing system. In the first application, the surface profile of discontinuous objects is measured using a Digital Mirror Device spatial light modulator (SLM) to project an optimised sequence of sinusoidal white light fringes onto the object surface at 60 frames s-'. Less than 0.5 s is required to measure and display approximately 250,000 co-ordinates with a precision of better than one part in 5,000 of the field of view. Issues affecting the performance of white light projected fringe profilometers implemented using SLMs are investigated. Defocusing of the projector is shown to be a critical limiting factor, with a precision of better than one part in 20,000 of the field of view being achieved when optimised. A speckle interferometer is used in the second application to measure object displacement. Quasi-live unwrapped speckle interferograms are displayed at 15 frames s-' using either a piezoelectric transducer-mounted prism or a Pockels cell as the phase-stepping device. The reference speckle interferogram is automatically updated at regular intervals allowing arbitrarily large deformations to be measured. The signal-to-noise ratio of the calculated displacement fields can be improved by performing real-time temporal least-squares fitting.