Experimental solid mechanics relies heavily on surface displacement and deformation gradient measurements. Digital image/ speckle correlation (DISC) uses digital image processing to resolve displacement and deformation gradient fields. The practical implementation of DISC involves important challenges such as computation complexity and the discrepancy of the sensitivities and accuracies claimed in previous studies. We develop an iterative, spatial-gradient based algorithm, which uses only first-order spatial derivatives of the images before and after deformation. Simulated images are then used to verify this algorithm, as well as to study the impact of speckle size on the accuracy. Based on these simulations, the sensitivity of DISC to displacement and deformation gradient, as well as an optimal speckle size for optimal accuracy, is recommended. The algorithm is then calibrated using rigid body translation and rotation, and an application of DISC to thermomechanical diagnostics of electronic packaging is also presented.