Chapter 3 – Making Light Work in Biology  63

proportional to the incident intensity and the slice’s width. It is empirically obeyed up to high

scatterer concentrations beyond which electrostatic interactions between scatterers become

significant. Here, σ is the mean absorption cross-​sectional area of the tissue, which depends

on the wavelength λ, and C is the concentration of the absorbing molecules. The absorbance

A is often a useful quantity, defined as

(3.4)

A

I

I

= −



^



^

log

0

For a real tissue over a wide range of z, there may be heterogeneity in terms of the types

of molecules, their absorption cross-​sectional areas, and their concentrations. The Beer–​

Lambert law can be utilized to measure the concentration of a population of cells. This is

often cited as the optical density (OD) measurement, such that

(3.5)

OD

A

L

=

where L is the total path length over which the absorbance measurement was made.

Many basic spectrophotometers contain a cuvette, which is standardized at L =​ 1 cm,

and so it is normal to standardize OD measurements on the assumption of a 1 cm path

length.

Note that the absorbance measured from a spectrophotometer is not exclusively due to

photon absorption processes as such, though photon absorption events may contribute to

the reduction in transmitted light intensity, but rather scattering. In simple terms, general

light scattering involves an incident photon inducing an oscillating dipole in the electron

molecular orbital cloud, which then reradiates isotropically. The measured reduction in

light intensity in passing through a biological sample in a standard VIS light spectropho­

tometer is primarily due to elastic scattering of the incident light. For scattering particles,

the size of single cells is at least an order of magnitude greater than the wavelength of the

incident light; this phenomenon is due primarily to Mie scattering. More specifically, this

is often referred to as “Tyndall scattering”: Mie scattering in a colloidal environment in

which the scattering particles may not necessarily be spherical objects. A good example is

the rod-​shaped bacteria cells. Differences in scatterer shape results in apparent differences

in OD; therefore, caution needs to be applied in ensuring that like is compared to like in

terms of scatterer shape when comparing OD measurements, and if not, then a shape

correction factor should be applied. Note that some absorbance spectrometers are capable

of correcting for scattering effects.

These absorbance measurements are particularly useful for estimating the density of

growing microbial cultures, for example, with many bacteria an OD unit of 1.0 taken at a

conventional wavelength of 600 nm corresponds to ~10⁸ cells mL⁻¹, equivalent to a typical

cloudy looking culture when grown to “saturation.” Spectrophotometry can be extended into

colorimetry in which an indicator dye is present in the sample, which changes color upon

binding of a given chemical. This can then be used to report whether a given chemical reac­

tion has occurred or not, and so monitoring the color change with time will indicate details

of the kinetics of that chemical reaction.

3.2.2  FLUORIMETRY

A modified spectrophotometer called a fluorimeter (or fluorometer) can excite a sample

with incident light over a narrow band of wavelengths and capture fluorescence emissions.

For bulk ensemble average in vitro fluorimetry investigations, several independent physical

parameters are often consolidated for simplicity into just a few parameters to characterize the

sample. For example, the absorption cross-​section for a fluorescent sample is related to its