Ptychography aims to completely revolutionise imaging in visible light, X-rays and Electron wavelengths by providing a robust platform for sub-Nyquist high-resolution real-time imaging. This thesis explores the framework of the very promising implementation of ptychography called the Ptychographic Iterative Engine (PIE). The PIE algorithm provides an elegant solution to the phase problem that facilitates recovery of complex representations of both the illuminating wave and the object of interest. The aim of this thesis is to present work done on the study of the machinery behind the PIE algorithm. This thesis formulates the solution provided by the PIE algorithm in reciprocal space; this shows the exact minimisation routine implemented by the PIE update function and provides a unified framework for quantifying the performance of the PIE algorithm. This work is timely because it highlights aspects of the PIE algorithm that permits practical implementation of bandwidth extrapolation of a specimen from a small detector and demonstrates the uniqueness of the corresponding solution provided by the PIE algorithm. This thesis also presents a viable scheme that utilises the redundancy of the ptychographic dataset to greatly reduce the sampling requirement on the detector; thus optimising the dataset size employed in real-time high-resolution reconstruction of the specimen over a wide field of view.