Modeling single molecule detection probabilities in microdroplets. Final report Page: 2 of 4
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Modeling Fluorescence Collection from Single Molecules in Liquid Microspheres
Steven C. Hill
Army Research Laboratory White Sands Missile Range, NM 88002-5501
Optimization of molecular detection efficiencies is of cen-
tral importance in analytical applications involving single
molecule detection . In addition to limitations imposed
on the fraction of molecules which can be detected by the
average signal-to-noise ratio, experimental factors such as
excitation inhomogeneity and molecular diffusion conspire
to further limit "molecular detectability." Recent single
molecule detection experiments in microdroplets suggest
that such experimental limtations can be significantly re-
duced  primarily because the molecule cannot diffuse
away from the excitation volume. However, unlike fluores-
cence detection from bulk streams where the fluorescence
intensity is isotropic in space, the large refractive index
change at the surface of microdroplets implies that the flu-
orescence intensity collected by a lens will be strongly de-
pendent on the position of the molecule within the droplet.
In addition, the same refractive index discontinuity at the
droplet surface produces a complicated excitation inten-
sity distribution within the droplet. Thus, issues such
as whether molecules near the surface of the sphere can
"hide" from the detector as a result of total internal re-
flection of emission near the droplet surface, or poor ex-
citation efficiency due to the molecule being located in a
"shadow" region of the droplet will have a potential effect
on molecular detection efficiencies. Here we discuss nu-
merical tools for modeling the fluorescence collected from
a single molecule within a microsphere as a function of its
position and orientation, the size of the droplet, the numer-
ical aperture of the collection lens, the detection geometry,
the type of illumination (planewave or counterpropagating
plane wave), and the linewidth of the emitting molecule.
To model the fluorescence from single molecules
(point sources) within microspheres we use a semiclassi-
cal formalism , in which the molecule is modeled as a
dipole emitting at a single frequency. The fields radiated
by the dipole are expressed in spherical coordinates. The
additional fields induced inside and outside the sphere are
determined by matching the boundary conditions.
Figure 1 illustrates the fluorescence collected from
various points inside a 8 pm diameter droplet. The lens is
positioned along the z axis and has a numerical aperture of
0.5. The dipole is assumed to rotate rapidly relative to the
fluorescence lifetime, and so dipole orientation effects are
averaged, and the results are independent of the azimuthal
angle. Enhancement or inhibition of rates (predicted at a
single frequency) has not been observed when the droplet is
large enough that the fluorescent bandwidth extends over
Figure 1: Fluorescence collected from randomly oriented
dipoles. The emission is integrated over frequency when
the linewidth is 100 cm-1, and the center frequency of the
transition is 16666.7 cm-1. The diameter of the droplet
is 8 tm, and the refractive index is 1.34. The NA of the
collection lens is 0.5. The results are shown as a function
of the normalized positions inside the sphere, x/a and z/a,
where a is the radius of the sphere.
several morphology-dependent resonances (MDRs) of the
droplet. To approximate the actual situation, we assume
a Lorentzian lineshape function for the emission from the
molecule, and integrate over the emission wavelengths. Be-
cause the MDRs of the droplet can have large effects even
though their linewidths may be narrow, we approximate
the fluorescence collected as a non-resonant background
and a number of Lorentzian functions. The integration
over the products of the Lorentzians is then done analyti-
Figure 2 shows the internal intensity of a sphere (8
pm diameter, with a refractive index of 1.34) illuminated
with a plane wave. Figure 3 shows the internal intensity
of the same sphere illuminated with counterpropagating
Figure 4 illustrates the fluorescence collected from one
cross-section of a sphere illuminated with a plane wave.
The fluorescence collected is the product of the internal
intensity generated with a plane wave, and the normal-
ized fluorescence collected from a randomly oriented di-
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Hill, S.C. Modeling single molecule detection probabilities in microdroplets. Final report, report, March 1, 1996; United States. (digital.library.unt.edu/ark:/67531/metadc673063/m1/2/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.