Biomedical Engineering Reference
In-Depth Information
have enough time to relax back to the ground state as this is a prerequi-
site for the absorption of another pair of photons. If not, saturation effects
arise, leading to a worsening of the axial and radial resolution of the sys-
tem [59]. The application of (4.16) allows to choose for proper optical and
laser parameters that maximize excitation out of the saturation regime. In
particular, the typical values for the ultra-fast lasers used in two-photon mi-
croscopy have
τ
p
=80
100 MHz. The last considerations
must be given about the two-photon cross section
δ
2
. Because of the fact that
the quantum-mechanical selection rules for two-photon excitation differ from
their one-photon counterpart, it is not easy to extend the data for conven-
tional absorption to the non-linear case even if a simple “rule of thumb” can be
considered. In fact, in general we can expect to have a two-photon excitation
peak at a wavelength that is the double of the one-photon excitation maxi-
mum. However, the knowledge of the global trend of two-photon cross-section
for a particular molecule requires the direct measurement. Figure 4.4 shows
the TPE cross section for some of the most common fluorescent molecules.
Because of the wide nature of the excitation spectra it can be noted that
one single wavelength can be used for the simultaneous excitation of multiple
dyes [60, 61]. It has been showed that endogenous fluorescent molecules like
flavoproteins, NAD(P)H and tryptophane exhibit TPE fluorescence [61, 62]
and also the fluorescent proteins like GFP (green fluorescent protein) are
capable of undergoing TPE [63-65]. The two-photon cross-sections are gen-
erally expressed in GM (Goppert-Mayer, 1 GM = 10
−
58
m
4
s). GFP variants
−
150 fs and
f
p
=80
−
10
3
Rhodamine B
10
2
Bodipy FI
10
Bis-MSB
Coumarin
Dil
10
0
Dansyl
Fluorencein
DAPI
10
−
1
Lucifer Yellow
10
−
2
Pyrene
Cascade Blue
10
−
3
600
700
900
Wavelength (nm)
800
1000
1100
TI: Sapphire
SHG of Cr: YAG
SHG of Cr: Forsterite
Cr: LiSGAF
Cr: LiSAF
Nd: YLF or Nd:glass
Fig. 4.4.
Exemplary two-photon cross-sections for some typical fluorophores for
biological imaging. The bars represent typical emissions of commonly used laser
sources for TPE
