Synthetic Aperture Lensless Digital Holographic Microscopy (SALDHM) for Superresolved Biological Imaging - Biomedical Optical Phase Microscopy and Nanoscopy - page 168

The holographic principle proposed by Gabor was immediately applied to the visible range
by Rogers [4] . However, its applicability was limited due to the low coherence of the
available light sources in the visible spectrum yielding holograms with a low quality
interference contrast. It was with the invention of the laser [5] when Leith and Upatnieks
alleviated some of the drawbacks provided by the Gabor's concept and extended the
applicability of holography. Leith and Upatnieks [6 8] abandoned the in-line configuration

proposed by Gabor and externally reinserted the reference beam at the recording plane in an
angle (off-axis geometry). The off-axis holographic method resolved the twin image
problem since in this configuration the actual and twin conjugate images were separated in
space after the reconstruction. At the same years, Denisyuk [9,10] proposed reflection
holography where signal and reference waves strike the photographic plate from opposite
sides, which also suppressed the conjugate image. Also in 1965, Stroke [11] reported on a
new way to record a different type of hologram named lensless Fourier transform (FT)
hologram. Here, the reference beam diverges from the same plane where the object is
placed, and the reconstruction requires a focusing lens or a mirror system to provide the
Fourier transformation of the recorded hologram. Finally, Gabor and Goss [12] reported on
an interference microscope in which the reference beam is externally inserted in on-axis
geometry and two quadrature phase-shifted interferograms are recorded in a single
photographic plate. This was the first evidence of phase-shifting holography.

From its first evidence [13] till now [14] , electronic image recording devices (typically a
Charge-Coupled Device (CCD) or a Complementary Metal Oxide Semiconductor (CMOS)
camera) have replaced holographic recording media, resulting in a new technology named
digital holography (DH). DH avoids chemical processing and other time-consuming
procedures ascribed to classical holography, and enables numerous capabilities from the
numerical post-processing of the recorded hologram carried out digitally. Just as an
example, DH has mirrored classical holographic approaches such as the Gabor's approach
[15,16] , implementations based on the Leith and Upatnieks' setups [17,18] , as well as
Fourier holographic architectures [19,20] , and phase-shifting algorithms [21,22] . However,
although most of the remarkable properties of DH were previously known [23] , their
practical implementations have been restricted because of the strong requirements for the
computer's capabilities concerning digital image acquisition and processing.

One of the remarkable applications of DH is provided in the field of digital in-line
holographic microscopy (DIHM) [15,16,24] . In DIHM, an electronic device records the
in-line hologram incoming from the superposition of a reference beam (the portion of
the propagating spherical wave that travels without being diffracted by the sample) and an
imaging beam (the portion of the propagating wave which is diffracted by the sample).
By “in-line” we mean that both reference and imaging beams are generated along the same
propagation direction and travel together along almost the same optical path. In other
words, DIHM supposes a practical implementation of the Gabor's concept in the visible