Chapter 3 – Making Light Work in Biology  79

The maximum switching frequency for an AOTF (i.e., to switch between an “off” state in

which the incident light is not deviated, and an “on” state in which it is deviated) is several

tens of MHz; thus, an AOTF can select different colors dynamically, more than four orders

of magnitude faster than the sampling time of a typical fluorescence imaging experiment,

though the principal issues with an AOTF is a drop in output power of >30% in passing

through the device and the often prohibitive cost of the device.

3.5.2  FLUORESCENCE EMISSION

The difference in wavelength between absorbed and emitted light is called the Stokes shift. The

full spectral emission profile of a particular fluorophore, φEM(λ), is the relation between the

intensity of fluorescence emission as a function of emission wavelength normalized such that

the integrated area under the curve is 1. Similarly the spectral excitation profile of a particular

fluorophore, φEX(λ), represents the variation of excitation absorption as a function of incident

wavelength, which looks similar to a mirror image of the φEM(λ) profile offset by the Stokes shift.

A typical fluorescence microscope will utilize the Stokes shift by using a specially coated

filter called a dichroic mirror, usually positioned near the back aperture of the objective lens

in a filter set consisting of a dichroic mirror, an emission filter, and, if appropriate, an excita­

tion filter (Figure 3.3b). The dichroic mirror reflects incident excitation light but transmits

higher wavelength light, such as that from fluorescence emissions from the sample. All

samples also generate elastically scattered light, whose wavelength is identical to the incident

light. The largest source of elastic back scatter is usually from the interface between the glass

coverslip/​slide on which the sample is positioned and the water-​based solution of the tissue

often resulting in up to ~4% of the incident excitation light being scattered back from this

interface. Typical fluorescent samples have a ratio of emitted fluorescence intensity to total

back scattered excitation light of 10⁻⁴ to 10⁻⁶. Therefore, the dichroic mirror ideally transmits

less than a millionth of the incident wavelength light.

Most modern dichroic mirrors operate as interference filters by using multiple etalon

layers of thin films of dielectric or metal of different refractive indices to generate spectral

selectivity in reflectance and transmission. A single etalon consists of a thin, optically trans­

parent, refractive medium, whose thickness w is less than the wavelength of light, which

therefore results in interference between the transmitted and reflected beams from each

optical surface (a Fabry–​Pérot interferometer operates using similar principles). With refer­

ence to Figure 3.3c, the phase difference Δφ between a pair of successive transmitted beams is

(3.23)

∆ϕ

π

θ

λ

= ^{4 nwcos}

where

λ is the free-​space wavelength

n is the refractive index of the etalon material

The finesse coefficient F is often used to characterize the spectral selectivity of an etalon,

defined as

(3.24)

F

R

R

=

−

(

)

4

1

2

where R is the reflectance, which is also given by 1 –​ T where T is the transmittance, assuming

no absorption losses. By rearrangement

(3.25)

T

F

=

+

(

)

1

1

2

2

sin

/

∆ϕ