Ultrasonic inspection is the primary method of Non-Destructive Evaluation (NDE) for the detection of planar flaws in engineering components. In recent years phased array technology has been adopted for use in NDE following success in related fields, such as medical and sonar applications. Phased array technology provides increased flexibility relative to single element monolithic transducers and the development of controlling hardware with large numbers of parallel channels has allowed the use of large phased arrays able to focus at long range, and offer increased performance. Full Matrix Capture (FMC) is a method of recording data using a phased array transducer that allows image reconstruction to be performed for any inspection technique than could be deployed using delay laws applied to the transmit voltage pulses applied to the array and receiving amplifiers. FMC technology provides a step change in inspection flexibility, and also provides the opportunity to take advantage of imaging techniques that are not practical to implement using phased arrays in the conventional way. However, existing inspection calibration procedures defined in standards do not allow these benefits to be fully realised. This thesis reports the development of a calibration framework designed for FMC based inspection for both rigid and conformable wedge mounted arrays. A large part of this work has been the development of acceptance limits on transducer performance variations. The developments of these limits have required a significant amount of modelling work, often using a Monte Carlo approach. To accommodate this, modelling tools have been developed to investigate the effect of array element directivity, sensitivity, and relative phase on system performance. For conformable phased arrays the effect of surface profile measurement accuracies has also been assessed. The developed calibration framework includes the tools necessary to monitor transducer performance throughout an inspection, with minimum impact on inspection duration. A means of calibrating imaging tools against known reflectors, in accordance with established industrial practice, has also been produced.