Spectral Imaging: Methods, Design, and Applications - Biomedical Optical Imaging Technologies: Design and Applications - page 151

information in a bright-field measurement is the absorption as calculated from
the transmission data.
The absorption spectrum of a dye molecule depends on the concentration of
the molecules c, the light path length in the sample l , and on the extinction
coefficient "./ that describes the probability of one molecule to absorb light quanta
at wavelength . The absorption can be found by using the Beer-Lambert law:

I./ D I 0 ./ 10 "./cl : (4.17)

I./ is the measured transmission spectrum through the sample while I 0 ./
is the spectrum of the light source as measured with the same conditions with-
out the sample. These spectra would be defined here in dimensions of flux
(photons/cm 2 /s/wavelength, Œcm 2 s 1 nm 1 .
An index j is used to distinguish different absorbing molecules, " j ./ and the
dimensionless term at the exponent of Eq. 4.17 is defined as

Absorbance D "./ c l: (4.18)

The absorbance is linear with the number of molecules along the optical path in
the sample. For the physical units, we use the extinction coefficient in molar density
ŒM 1 cm 1 and the molecules concentration c in mol/l [ 63 ] (M, the molar, has units
of mol/l).
An absorbance of 0.3, 1, and 2 relates to absorption values of 50, 90, and
99%, corresponding to transmission of 50, 10, and 1%. It can be measured over
at least four orders of magnitude, but with imaging equipment, it is reduced
due to higher noise levels. When the sample contains few absorbing stains, the
transmission spectrum has a complex structure [ 64 ] and the absorbance is equal

to A./ D P i " i ./ c i l i , which is similar to the case of fluorescence and it can
be calculated from the measured transmission, A./ D log .I./=I 0 .//.The
division operation may insert noise wherever the background spectrum is very low,
and in order to prevent it, the “tails” of the spectra where the intensity is weak
are seldom excluded from the calculation. If the absorption spectra of the different
stains are measured separately, it is possible to calculate the concentration of each
stain in the image.
A few studies have indicated the applicability of spectral imaging for multiple-
color bright-field applications such as histological sections [ 65 ], tissue sections and
cervical smears [ 66 ].

4.5.3.4 Principle Components Analysis (PCA)

The spectral analysis methods described above require reference input by the user
and belong to a family of algorithms called supervised classification methods.
There are also algorithms called non-supervised classification methods that do not
require reference spectra as an input. In these methods, the algorithm determines