Biomedical Engineering Reference
In-Depth Information
have cross sections between 4 and 60 GM [66]. As comparison we can con-
sider NADH that at its excitation maximum, 700 nm, shows a cross section
of 0.02 GM [61]. Quantum dots can show cross sections up to 2,000 GM.
4.5 Two-Photon Optical Sectioning
In the following we will describe how two-photon (or multi-photon) excitation
allows to spatially control excitation along the optical axis, limiting the ex-
citation volume to a sub-femtoliter volume, thus allowing optical sectioning.
We discussed above that the fluorescence signal emitted under two-photon
excitation will depend on the second power of the excitation intensity. We can
therefore consider that the intensity delivered point by point on the sample,
I
ex
, is proportional to the lens PSF, which in the paraxial approximation is
described by (4.4). Therefore, we can expect that the fluorescent signal emit-
ted by the sample
I
em
(
x, y, z
) will be proportional to
I
ex
and for the axial and
radial components of
I
em
- introducing the dimensionless variables
u, v
-we
get [67]
2
J
1
(
v
)
v
4
sin(
u/
4)
u/
4
4
I
em
(0
,v
)=
h
(0
,v
)
2
I
em
(
u,
0) =
h
(
u,
0)
2
∝
∝
.
(4.17)
These expressions are identical to the axial and radial parts of the total
PSF of a confocal system (ref. (4.6)). However, it must be noted that while
confocal microscopy achieves this result at the detection side, by means of the
pinhole, in two-photon excitation the dependence of the fluorescence intensity
on the inverse of the 4th power of the axial coordinate is achieved directly
in the excitation step. This means that while in confocal microscopy a thick
volume of the sample is excited and the selection of the in-focus contribution is
obtained through the pinhole at the detection level, in two-photon excitation,
only the molecules in a small volume (order of the femtoliter) around the focal
point are properly excited and emit fluorescence [68,69]. This fact also implies
that the contributes far-off the focal plane (depending on the NA of the lens)
will not be affected by photobleaching [70,71] or phototoxicity [72-74] and do
not contribute to the signal detected if a TPE architecture is used. In this
way we have no need for a pinhole as all the fluorescent emission is supposed
to be originated at the focal plane.
This means that TPE is intrinsically three-dimensional as it allows for
optical sectioning by collecting images of the sample plane-by-plane and then
reconstructing the three-dimensional map of the emitted fluorescence (ref.
Fig. 4.5). It must be underlined that since all the fluorescence collected is nec-
essarily originated at the focal point, the e
ciency of the collection of the
signal is much higher than in the confocal case. In TPE, in fact, over 80% of
the signal arise from a 700-1,000 nm (depending on the NA of the objective)
thick region around the focal plane [54, 75]. This results in a reduction in
