Biomedical Engineering Reference
In-Depth Information
9.3.2.8 in-Focus configuration
In this configuration, the sensor is placed in the image plane of an optical imaging system. It records the
hologram of the in-focus object wave interfering with the reference wave. Processing of the hologram,
for example, by off-axis filtering in the Fourier domain or by phase-shifting holography, directly leads to
retrieval of the in-focus object wavefront. Again, no numerical field propagation is required.
9.3.2.9 Fresnel configuration
In this configuration, the sensor is located at some position between an image plane and a Fourier plane,
along the optical axis. It records the hologram of the out-of-focus object wave, often called a Fresnel
zone plate, interfering with the reference wave. One characteristic of this configuration is that hologram
processing retrieves the out-of-focus object wavefront as it was in the recording plane. Numerical field
propagation is therefore essential to end up with an in-focus image, and, as we will see, offers some
interesting advantages.
9.4 Reconstruction of Digital SHG Holograms
In this section, we address the numerical reconstruction process of digital holograms in general and,
more particularly, of holograms recorded from second-harmonic signals.
9.4.1 numerical Field Propagation
In Goodman's experiment of 1967, the optical setup was in a Fourier transform configuration, mean-
ing that the digital sensor recorded the intensity of the Fourier transform of the image subject. In this
simple case, the image reconstruction consists of a numerical Fourier transform of the recorded frame.
A very important progress in digital holography is the report of numerical field propagation by
Kronrod et al
.
(1972). In their experiment, a photographic plate located some finite distance away from
an image plane was successively exposed, developed, optically magnified and, finally, digitized by
means of a input−output device. But because they were working in a Fresnel configuration, their image
reconstruction algorithm had to cope with numerical field propagation to produce an in-focus image.
Numerical field propagation is based on diffraction algorithms should be seen as the numerical coun-
terparts of physical light propagation.
9.4.1.1 numerical Focusing and extended Depth of Field
The ability to numerically simulate light propagation has had a huge impact in digital holography and
really contributed to its development. For one, it removed all constraints for keeping the specimen and
the digital sensor exactly in conjugate planes. Numerical focusing made holographists completely forget
about small focus errors. In a Fresnel configuration, the hologram never records the in-focus object
wave, but thanks to numerical field propagation always returns the in-focus image. Focusing problems
are quite common in high-magnification microscopy. Numerical focusing is thus very useful in this
field, especially for very long-term experiments, for example, lasting several hours, where the focus
may change due to mechanical relaxation. It is also very promising for microscopic investigation of
specimens in very rough environment, for example, a moving vehicle, satellite, or a random positioning
machine (Pache et al
.
, 2010).
Numerical field propagation does not only serve to compensate focus errors, but it is also a way
to achieve an extended depth of field for the complex field retrieved from a single hologram can be
reconstructed at different distances to bring in focus different sections of a specimen which height
exceeds the depth of field of a given imaging system (Ferraro et al
.
, 2005; Colomb et al
.
, 2010). Forty
times increases in depth of field have been reported by numerical field propagation in digital holog-
raphy (Colomb et al
.
, 2010).
