Biomedical Engineering Reference
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the objective. For a reflected-light microscope, the objective will serve to carry the excitation beam to
the specimen, while, for a transmitted-light microscope, it will collect the fundamental laser illumi-
nation along with the second-harmonic signal. It is therefore essential that the objective is capable of
withstanding high power without damaging.
Another important criterion in the selection of a microscope objective is its transmission efficiency. If
the objective serves to deliver the ultrafast laser pulses to the specimen, one must also make sure that the
objective has a good transmittance at the fundamental wavelength. Also, while the transmittance of all
microscope objectives is very good in the visible spectrum, it abruptly drops, for some models and manu-
facturers, close to or below 400 nm. Of course, this is only relevant for fundamental laser wavelengths in the
red, near-infrared spectrum that generate second harmonic in the extreme blue or near-UV wavelengths.
For example, a Leica Hi-Plan 63×, 0.75 NA objective was used in Shaffer et al . (2010b), while a Zeiss
Epiplan 50×, 0.5 NA objective was used in Masihzadeh et al . (2010).
9.3.2.4 SHG Reference crystal
A very important aspect of holographic SHG imaging is the generation of the second-harmonic refer-
ence wave. It is one thing to generate second harmonic in the specimen, but one must also produce
a clean reference wave at the same frequency for holograms to be possibly recorded. This is typically
achieved by inserting a frequency doubler crystal in the reference arm.
Most of the time, frequency doubling is made in a beta-barium borate (BBO) crystal (Pu et al . , 2008;
Shaffer et al . , 2009), but use of potassium dihydrogen phosphate (KDP) crystals has also been reported
(Masihzadeh et al . , 2010). Such crystals generally support phase matching of type I , in which two photons
having an ordinary polarization with respect to the crystal combine to form one SHG photon having
an extraordinary polarization. In opposition, type II phase matching requires the two initial photons to
have a perpendicular polarization. Actually, there now exist many solutions for generation of the second-
harmonic reference wave and it is most likely that many more will become available in the future.
9.3.2.5 optical Delay Lines
The ultrafast lasers used for holographic SHG imaging generally have very short temporal coherence
length. For interference to occur, the optical paths of the object and the reference arms must be precisely
matched to this coherence length value. As an indicator, a 250 fs pulse has a coherence length close to
75 μm. Therefore, precise adjustable optical delay lines are necessary to match the optical paths.
A very simple implementation of such delay lines can be realized with a mirror pair on a translation
stage, as in Pu et al . (2008) and Masihzadeh et al . (2010) and illustrated in Figure 9.3.
9.3.2.6 optical configurations for Recording of Digital Holograms
There exist many optical configurations for hologram recording, and almost every one has its own
related recipe for hologram reconstruction. In fact, there might be as many configurations as there are
holographists and slight variations on a common theme are frequent. Here, we distinguish between
three different configurations for hologram recording, classified by the reconstruction process required
to reconstruct an in-focus image from the hologram. We briefly describe their main differences, but go
no further. See Kreis (2005) for more details.
9.3.2.7 Fourier configuration
In this configuration, the sensor records a hologram of the optical Fourier transform of the object. This
can be achieved either by placing the digital sensor in the Fourier plane of an imaging lens, or by placing
it very far from the object, in a lensless configuration. In the Fourier configuration, the hologram recon-
struction process is rather simple and only consists of a Fourier transform of the hologram to retrieve
the in-focus object wavefront. No numerical field propagation is required.
The most famous example of such implementation is the lensless Fourier configuration used by
Goodman and Lawrence (1967).
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