This thesis concerns the application of Quantitative Digital Image Pro­cessing to some problems in the domain of Optical Engineering. The applications addressed are those of automatic two dimensional phase unwrapping and the analysis of images from high speed particle image displacement velocimetry. The first application involves subdivision of the two dimensional image of a wrapped phase map into small two dimensional areas or tiles, which are unwrapped individually, in order that discontinuities may be localised to small areas. In this case the discontinuities have a contained effect on the unwrapped phase solution. The concept of minimum spanning trees, from Graph Theory, is employed to minimise the effect of such local discontinuities by computation of an un­wrapping path which avoids areas likely to be discontinuous in a probabilistic manner. This approach is implemented over two hierarchical levels, the first level identifying pixel level discontinuities such as spike noise, the second ad­dressing larger scale discontinuities which may not be detected by pixel level comparisons, but which can be detected by comparison of the local solutions of image areas larger than the pixel. The second application is in the area of Particle Image Displacement Velocimetry (PIDV). A digital processing method is developed for high speed PIDV. In high speed PIDV the seeding is sparsely distributed. This method attempts to pair individual particle images, rather than statistically average the positions of a large number of particle images as is the case with other analysis methods. The digital processing method is suitable for use with Video PIDV whose feasibility has recently been demonstrated.