Non-destructive testing (NDT) is the process of non-invasive material examination. Within this field, ultrasonic inspection is one method of examination used to detect flaws in structural and functional industrial components, to assess their structural integrity and fitness for service. Conventional NDT ultrasonic array techniques transmit on multiple elements in parallel, according to a focal law, which facilitates beam steering, focussing and scanning within the test component. Received signals are then 'stacked' to generate images of the test component. With the advent of affordable high speed computing, novel data acquisition techniques based on sequential transmission are now able to be developed, which allow images to be generated using advanced signal processing and image reconstruction algorithms. One such data acquisition technique known as Full Matrix Capture (FMC), has received considerable research attention in recent years, largely because it allows fully focused images of test components to be generated. This project provides an improved understanding of the FMC technique and associated signal processing algorithms. It achieves this through the development of novel inspection techniques and signal processing algorithms. Collectively algorithms developed within this work were termed Sequential Phased Array (SPA). Initially comparisons were made between conventional ultrasonic techniques and the SPA algorithms in terms of image quality and speed of inspection. A novel approach was then suggested to facilitate inspection through dual-layered media, separated by a refractive interface using the SPA algorithms. The use of sparse arrays to enhance the speed of inspection using the SPA algorithms was also investigated, and the trade-off between speed of inspection against image degradation was addressed. Finally a novel approach to calibration of a FMC based system was developed, in order to provide uniform image sensitivity during inspection.