Biomedical Engineering Reference
In-Depth Information
the process, three photons with frequency ω are destroyed and a photon with frequency 3ω is cre-
ated. We find that the incident photon energy 3
h
ω is equal to the generated photon energy
h
(3ω). As
with the process of SHG, there is only virtual-level transition involved in the process of THG. No
energy is deposited in the interacted material since the energy-conservation rule is fulfilled in the
up-conversion process.
Unlike SHG, which only occurs in noncentrosymmetric materials, THG is principally allowed
in all materials, since the third-order susceptibility χ
(3)
is nonvanishing regardless of the symme-
try of materials. It is supposed that THG can be induced because the phase-matching condition
(Δ
k
= 3
k
ω
−
k
3ω
= 0) is satisfied. However, owing to the Gouy phase shift under strong focusing con-
ditions, positive phase mismatching is needed to compensate the phase shift for efficient generation
of the THG radiation, while THG is found to vanish in isotropic materials with a negative phase
mismatch (normal dispersion), that is, Δ
k
= 3
k
ω
−
k
3ω
≤ 0. The Gouy phase shift, also called a phase
anomaly, is a well-known particularity of a focused light beam, in which the phase of the light beam
shifts by a half-cycle when propagating through the focal center, and an effective dilation of light
wavelength near the focal center is produced (Born and Wolf, 1999). Based on the coherent nature
of THG, the phase anomaly can lead to destructive interference between the THG radiation induced
before and after the focus center and cause the vanishing of the THG. Therefore, an efficient THG
can only be produced at interfaces, where constructive interference possibly occurs due to changes of
dispersion or to the nonlinear susceptibility of materials. Since a negative phase mismatch is common
for most of the natural materials, including bio-tissues, THG is rarely observed in an isotropic bulk
tissue. Based on the interface-sensitive nature of THG, THG microscopy is useful for imaging trans-
parent objects that are difficult to be observed with a conventional microscope. Additionally, more
and more important endogenous THG contrasts are being discovered in bio-tissues. THG micros-
copy is progressively emerging as a useful tool for morphological investigation, molecular imaging,
and diagnosis in biology and medicine.
14.2.2 3D Spatial Resolution
In SHG microscopy, image formation can be considered as a convolution result of the excitation point
spread function (PSF) and the features of the specimens. Since the SHG intensity has a quadratic depen-
dence on the excitation light intensity, as mentioned above, the excitation of SHG is restricted to just
near the focal spot and the size of the effective PSF can be reduced by a factor of 2 (Squier and Müller,
2001). The lateral resolution can be given by
1
2
0.51
λ
0.36
λ
,
r
=
⋅
≈
(14.8)
NA
NA
and the axial resolution can be given by
1
2
n
NA
λ
0.7
n
NA
λ
.
d
z
=
⋅
≈
(14.9)
2
2
In contrast to the confocal pinhole in a confocal microscope, the restriction of SHG excitation can
be considered to be a virtual pinhole, by which not only can the out-of-focus information be elimi-
nated to increase the spatial resolution, but also the out-of-focus excitation can be avoided to reduce the
photodamage.
Image formation in THG microscopy can be considered in a similar way to that of SHG microscopy.
Since the THG intensity has a cubic dependence on the excitation light intensity (Squier and Muller
2001), the excitation is restricted to a narrower region near the focal spot than with SHG. The size of the
