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BSA Flow Software Installation and User's Guide - CSI

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For reflection (Equation 7-16)<br />

The formulas expressing the geometrical factor for detector i are given<br />

below for reflection <strong>and</strong> (first order) refraction.<br />

⎧ ϑ<br />

ϑ<br />

ϑ<br />

ϑ ⎫<br />

βi = ⋅ 2⎨<br />

1 − cos ⋅ cosϕ<br />

i ⋅ cosψ<br />

i + sin ⋅ sinψ<br />

i − 1 − cos ⋅ cosϕ<br />

i ⋅ cosψ<br />

i − sin ⋅ sinψ<br />

i ⎬<br />

⎩ 2<br />

2<br />

2<br />

2 ⎭<br />

For first order refraction (Equation 7-17)<br />

The refractive index of the particle, n 2 , does not appear in this expression.<br />

In practice this means that in situations where the exact value of the<br />

refractive index is not known, reflection may be a useful scattering mode.<br />

β<br />

⎡ 2<br />

2<br />

2 1 + n − ⋅ ⋅ − + − ⋅ ⋅<br />

⎢⎣<br />

rel 2 nrel<br />

fi<br />

1 nrel<br />

2 nrel<br />

i = + i−<br />

where:<br />

n<br />

rel<br />

For second order refraction<br />

Figure 7-20: The definition of three different light scattering modes for water<br />

droplets in air.<br />

n2<br />

=<br />

n<br />

1<br />

n 2 = particle refractive index<br />

ϑ<br />

ϑ<br />

f i±<br />

= 1+ cos ⋅ cosϕ<br />

⋅ cosψ<br />

i ± sin ⋅sinψ<br />

i<br />

2<br />

2<br />

β i cannot be given as a closed form solution, but must be solved for<br />

numerically by an iterative process.<br />

<strong>BSA</strong> <strong>Flow</strong> <strong>Software</strong>:Reference guide 7-25<br />

f<br />

⎤<br />

⎥⎦

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