Biomedical Engineering Reference
In-Depth Information
parameter. If we make the approximation that it varies in a linear manner between
z
= −
b
and
z
= +
b
, we
have an accumulated phase shift across the focus of
π
4
(3.15)
k
G
≈
b
and the coherence length can now be approximated as
≈
4
3
b
(3.16)
l
FTHG
,
c eff
If we use the geometrical relation between the NA and the waist at the focus, we have
1
(3.17)
b
∝
NA
2
so finally
1
l
FTHG
,
∝
(3.18)
c eff
NA
2
This result is consistent with the coherence lengths calculated in Figure 3.4: for example, the ratio
between the size of the structures that yield a maximum signal for the NAs of 0.8 and 1.2 is equal to
≈ 2/0.9 ≈ 2.2, while the ratio between the squared NAs is equal to 2.25.
Figure 3.4 also illustrates the difference in the images obtained with two different excitation NAs in a
zebrafish embryo. In this particular example, it is quite visible that, although higher NA imaging reveals
smaller details, it results in decreased contrast of the large structures. In the lower resolution image, the
cell contours are more clearly revealed than the smaller intracellular organelles, which make possible
the algorithmic detection of cell shapes, as illustrated in Section 3.2.13.
3.2.7 influence of Dispersion
To discuss the influence of the linear dispersion, we consider the slightly different geometry of a slab
perpendicular to the
z
-axis. Figure 3.5 illustrates the influence of linear dispersion on the THG signal
n
ω
-
n
3
ω
1.0
(a)
(b)
-0.03
0
+0.03
χ
(3)
= 1
χ
(3)
= 0
0.5
THG
0.0
0
1
2
3
4
5
6
d
Slab width
d
(µm)
FIgurE 3.5
Influence of dispersion on the THG signal from a slab. (a) Geometry considered. (b) F-THG signal as
a function of slab width in the case of negative, null, and positive dispersion. Conditions:
n
3ω
= 1.5, 1.47 <
n
ω
< 1.53,
NA
= 1.2, λ = 1.2 μm.
