Biomedical Engineering Reference
In-Depth Information
SHG microscopy depend largely on the precision of the experimental measurement. As described in
Section 1.3.3, additional
z
-polarized field contributions can be as much as ~25% of the
X
and
Y
polar-
ized contributions when using high NA oil- or water-immersion objectives, but drop off quickly as the
NA decreases.
Although the influence on polarization is often minimal, the Guoy phase shift does significantly
impact the scaling of the SHG intensity with the sample volume. For thin samples much smaller than
the focal volume, the SHG intensity scales with the square of the number density. However, the detected
intensity departs significantly from this quadratic scaling as the thickness increases due to the collective
coherent interferences from dispersion, birefringence, and the Guoy phase shift. The length scale over
which this asymptotic approach arises is dictated in the transmitted direction by the degree of focusing
through the competition between changes in
z
0
and
l
c
G
/2
versus those arising through dispersion from
l
c
f
.
1.5 Summary
The primary objective of this chapter is to provide an initial conceptual and mathematical framework
for interpreting image contrast in SHG microscopy measurements, focusing on simplified methods
valid in key limiting conditions. A matrix-based approach was presented for recasting the tensor math-
ematics into a more intuitive form and providing expandability to systematically include increasing lev-
els of complexity in both the sample and the analysis. Limits of thin and thick samples were considered,
along with effects in the limits of gentle and tight focusing. A key emphasis was centered on treating
polarization-dependent measurements in SHG microscopy. This introductory chapter was designed to
serve as a general starting point before advancing to some of the specific applications described in sub-
sequent chapters.
Acknowledgments
This work was supported as part of the Center for Direct Catalytic Conversion of Biomass to Biofuels,
an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic
Energy Sciences under Award # DE-SC0000997. GJS also acknowledges support from NIH R01.
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