Digital holography is an emerging field of new paradigm in general
imaging applications. We present a review of a subset of the research
and development activities in digital holography, with emphasis on
microscopy techniques and applications. First, the basic results from
the general theory of holography, based on the scalar diffraction
theory, are summarized, and a general description of the digital
holographic microscopy process is given, including quantitative phase
microscopy. Several numerical diffraction methods are described and
compared, and a number of representative configurations used in digital
holography are described, including off-axis Fresnel, Fourier, image
plane, in-line, Gabor, and phase-shifting digital holographies. Then we
survey numerical techniques that give rise to unique capabilities of
digital holography, including suppression of dc and twin image terms,
pixel resolution control, optical phase unwrapping, aberration
compensation, and others. A survey is also given of representative
application areas, including biomedical microscopy, particle field
holography, micrometrology, and holographic tomography, as well as some
of the special techniques, such as holography of total internal
reflection, optical scanning holography, digital interference
holography, and heterodyne holography. The review is intended for
students and new researchers interested in developing new techniques and
exploring new applications of digital holography.