Biomedical Engineering Reference
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Up to this point, holography was essentially considered an imaging technique, enabling the
possibility of lensless imaging or the capability of focusing images recorded out of focus
through the recovery of the full wave front. The digital treatment, contrary to the classical
approach, considers the wave front as a combination of amplitude and phase, which led to
the development of quantitative phase imaging through holography [98] .
5.2.3 Digital Holography Methods
The two main approaches to recovering the object wave are namely temporal decoding, i.e.,
phase shifting, and spatial decoding, i.e., off-axis methods.
Phase shifting reconstruction methods are based on the combination of several frames, and
enable the suppression of the zero order and the twin image through temporal sampling
[99,100] . The most well-known phase-shifting algorithm, proposed by Yamaguchi and
Zhang [95] as previously mentioned, is based on the recording of four frames separated by
a phase shift of a quarter of a wavelength. Various combinations of frames derived from
interferometry have been considered [96,99] and many different waves have been
developed to produce the phase shift including high-precision piezo-electric transducers
which move a mirror in the reference wave or acousto-optics modulators which use the
light frequency shift, etc.
One of the main issues in the phase shifting method is the requirement of several frames for
reconstruction in interferometric set-ups, which are commonly very sensitive to vibrations,
so that it could be difficult to ensure stable phase shifts and an invariant sample state during
acquisition. In addition, the requirements on the accuracy of the phase shifts are rather high
with regard to displacements in the order of magnitude of hundreds of nanometers,
implying the use of high-precision transducers. Consequently, several attempts were made
to either reduce the required number of frames for reconstruction, which led to two-frame
reconstruction [101,102] or to enable the recoding of the various phase shift frames
simultaneously, by employing, for example, multiplexing methods [103] . On the other hand,
more refined algorithms were developed in order to loosen the accuracy requirements of
phase shift methods [104
106] .
The second main approach to recovering the object wave is based on off-axis configuration,
so that the different diffraction terms encoded in the hologram (zero-order wave, real
image, and virtual image, cf. Figure 5.1 ) are propagating in different directions, enabling
their separation for reconstruction. This configuration was the one employed for the first
demonstration of a fully numerical recording and reconstruction holography [93,94] .
In practice, reconstruction methods based on off-axis configuration usually rely on Fourier
methods to filter one of the diffraction terms. This concept was first proposed by Takeda
et al. [107] in the context of interferometric topography. The method was later extended for
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