Digital holography has received recent attention for many imaging and sensing applications, including imaging through turbulent and turbid media, adaptive optics, three-dimensional projective display technology and optical tweezing. It holds several advantages over conventional imaging and wavefront sensing, chief among these being significantly fewer and simpler optical components and the retrieval of complex field. A significant obstacle for digital holography in real-time applications, such as wavefront sensing for high-energy laser systems and high-speed imaging for target tracking, is the fact that digital holography is computationally intensive; it requires iterative virtual wavefront propagation and hill-climbing algorithms to optimize sharpness criteria. This research demonstrates real-time methods for digital holography based on approaches for optimal and adaptive identification, prediction, and control of optical wavefronts. The methods presented integrate minimum-variance wavefront prediction into dynamic digital holography schemes to accelerate the wavefront correction and image sharpening algorithms. Further gains in computational efficiency are demonstrated in this work with a variant of localized sharpening in conjunction with predictive dynamic digital holography for real-time applications. This "subspace correction" method optimizes sharpness of local regions in a detector plane by parallel independent wavefront correction on reduced-dimension subspaces of the complex field in a spectral plane
