The estimation of phase errors in synthetic aperture imagery is important for high quality images. Many methods of autofocus, or the estimation of phase errors from the measured data, are developed using certain assumptions about the imaged scene. This thesis develops improved methods of phase estimation which make full use of the information in the recorded signal. This results in both a more accurate estimate of the image phase error and improved imagery compared to using standard techniques. The standard phase estimation kernel used in echo-correlation techniques is shear-average. This technique averages the phase-difference between each ping over all range-bins, weighted by the signal strength. It is shown in this thesis that this is not the optimal method of weighting each phase estimate. In images where the signal to clutter ratio (SCR) is not proportional to the signal amplitude, shear-average does not meet the predicted error bound. This condition may be met by many image types, including those with shadows, distributed targets and varying surface structure. By measuring the average coherence between echos at each range-bin, it is possible to accurately estimate the variance of each phase estimate, and weight accordingly. A weighted phase-difference estimation (WPDE) using this coherence weighting meets the performance bound for all images tested. Thus an improved performance over shear-average is shown for many image types. The WPDE phase estimation method can be used within the framework of many echo-correlation techniques, such as phase-gradient autofocus (PGA), phase curvature estimation, redundant phase-centre or displaced phase-centre algorithms. In addition, a direct centre-shifting method is developed which reduces bias compared to the centre-shifting method used in PGA. For stripmap images, a weighted phase curvature estimator shows better performance than amplitude weighted shear-average for images with high SCR. A different method of phase estimation, known as sharpness maximisation, perturbs an estimate of the phase error to maximise the sharpness of the reconstructed image. Several improvements are made to the technique of sharpness maximisation. These include the reduction of over-sharpening using regularisation and an improvement in accuracy of the phase estimate using range-weighting based on the coherence measure. A cascaded parametric optimisation method is developed which converges significantly faster than standard optimisation methods for stripmap images. A number of novel insights into the method of sharpness maximisation are presented. A derivation of the phase that gives maximum intensity squared sharpness is extended from a noncoherent imaging system to a coherent spotlight system. A bound on the performance of sharpness-maximisation is presented. A method is developed which allows the direct calculation of the result of a sharpness maximisation for a single ping of a spotlight synthetic aperture image. The phase correction that maximises sharpness can be directly calculated from the signal in a manner similar to a high-order echo-correlation. This calculation can be made for all pings in a recursive manner. No optimisation is required, resulting in a significantly faster phase estimation. The techniques of sharpness maximisation and echo-correlation can be shown to be closely related. This is confirmed by direct comparisons of the results. However, the classical intensity-squared sharpness measure gives poorer results than WPDE and different sharpness measures tested for a distributed target. The standard methods of shear average and maximisation of the intensity-squared sharpness measure, both perform well below the theoretical performance bound. Two of the techniques developed, WPDE and direct entropy minimisation perform at the bound, showing improved performance over standard techniques. The contributions of this thesis add considerably to the body of knowledge on the technique of sharpness maximisation. This allows an improvement in the accuracy of some phase estimation methods, as well as an increase in the understanding of how these techniques work on coherent imagery in general.