Precision VLBI astrometry: Instrumentation, algorithms and pulsar parallax determination

(Abridged) This thesis describes the development of DiFX, the first general-purpose software correlator for radio interferometry, and its use with the Australian Long Baseline Array (LBA) to complete the largest VLBI pulsar astrometry program undertaken to date in the Southern Hemisphere. This two year astrometry program has resulted in the measurement of seven new pulsar parallaxes, more than trebling the number of measured VLBI pulsar parallaxes in the Southern Hemisphere. The measurements included a determination of the distance and transverse velocity of PSR J0437-4715 with better than 1% accuracy, enabling improved tests of General Relativity, and the first significant measurement of parallax for the famous double pulsar system PSR J0737-3039A/B, which will allow tests of General Relativity in this system to proceed to the 0.01% level. The DiFX software correlator developed to enable this science has been extensively tested and is now an integral part of the upgraded LBA Major National Research Facility; furthermore, it has been selected to facilitate a substantial sensitivity upgrade for the US Very Long Baseline Array.