80

3.5  Fluorescence Microscopy: The Basics

A maximum T of 1 occurs when the OPL difference between successive transmitted beams,

2nw cos θ, is an integer number of wavelengths; similarly the maximum R occurs when the

OPL equals half integer multiples of wavelength. The peaks in T are separated by a width Δλ

known as the free spectral range. Using Equations 3.23 through 3.25, Δλ is approximated as

(3.26)

∆λ

λ

θ

≈

peak

nl

2

2

cos

where λpeak is the wavelength of the central T peak. The sharpness of each peak in T is

measured by the full width at half maximum, δλ, which can be approximated as

(3.27)

δλ

λ

π

≈

peak

w F

2

Typical dichroic mirrors may have three or four different thin film layers that are generated

by either evaporation or sputtering methods in a vacuum (see Chapter 7) and are optimized

to work at θ =​ 45°, the usual orientation in a fluorescence microscope.

The transmission function of a typical VIS light dichroic mirror, TD(λ) is thus typically

<10⁻⁶ for λ < (λcut-​off − Δλcut-​off/​2) and more likely 0.90–​0.99 for λ > (λcut-​off +​ Δλcut-​off/​2), up until

using the VIS light maximum wavelength of ~750 nm, where λcut-​off is the characteristic cutoff

wavelength between lower wavelength high attenuation and higher wavelength high trans­

mission, which is usually optimized against the emission spectra of a particular fluorescent

dye in question. The value Δλcut-​off is a measurement of the sharpness of this transition in

going from very high to very low attenuation of the light, typically ~10 nm.

In practice, an additional fluorescence emission filter is applied to transmitted light, band­

pass filters such that their transmission function TEM(λ) is <10⁻⁸ for λ < (λmidpoint –​ Δλmidpoint/​2)

and for λ > (λmidpoint +​ Δλmidpoint/​2) and for λ between these boundaries is more likely 0.90–​0.99,

where λmidpoint is the midpoint wavelength of the band-​pass window and Δλmidpoint is the band­

width of the window, ~10–​50 nm depending on the fluorophore and imaging application

(Figure 3.3d).

The fluorescence quantum yield (Φ) gives a measure of the efficiency of the fluorescence

process as the ratio of emitted photons to photons absorbed, given by

(3.28)

Φ

Φ

=

=

∑

k

k

s

i

n

i

i

1

where

ks is the spontaneous rate of radiative emission

Φi and ki are the individual efficiencies and rates, respectively, for the various

decay processes of the excited state (internal conversion, intersystem crossing,

phosphorescence)

The fluorescence emission intensity IEM from a given fluorophore emitting isotropic­

ally (i.e., with equal probability in all directions), which is detected by a camera, can be

calculated as

(3.29)

I

I

T

T

T

E

EM

abs

D

EM

OTHER

camera

λ

π

λ φ λ

λ

λ

λ

λ

( ) =



^



^

( )

( )

( )

( )

Ω

Φ

4

( )

( )

where

Iabs is the total absorbed light power integrated over all wavelengths

Ω is the collection angle for photons of the objective lens