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.