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Spectral contrast theory 57
Vectors derived from multiple wavelengths
When absorbance ratios are limited to two wavelengths, the chance that two
different spectra share the same absorbance ratio is greater than if
comparison is made using absorbance ratios at many wavelengths. Therefore,
the spectral contrast algorithm uses absorbances from multiple wavelengths
to form a vector in an n -dimensional vector space, where n is the number of
wavelengths from the spectrum.
To compare two spectra, the spectral contrast algorithm forms a vector for
each spectrum in an n -dimensional space. The two spectral vectors are
compared mathematically to compute the spectral contrast angle.
As with the two-wavelength comparison, a spectral contrast angle of zero in
n -dimensional space means that all ratios of absorbances at corresponding
wavelengths match. Conversely, if any comparison of ratios does not match,
the corresponding vectors point in different directions.
Spectral contrast angles
Spectra of identical shape have vectors that point in the same direction.
Spectra of varying shapes have vectors that point in different directions. The
angle between the two vectors of any two spectra, the spectral contrast angle,
quantifies the magnitude of the shape difference between the spectra. The
spectral contrast angle expresses the difference in direction between the
spectral vectors of two spectra.
A spectral contrast angle can vary from 0° to 90°. A spectral contrast angle
approaching 0° indicates little shape difference between the compared spectra.
Matching a spectrum to itself produces a spectral contrast angle of exactly 0°.
The maximum spectral contrast angle, 90°, indicates that the two spectra do
not overlap at any wavelength.
To illustrate the relationship between the spectral contrast angle and spectral
shape differences, consider the pairs of spectra shown in the next three
figures.
Spectra with different shapes
In the following figure, the absorbance spectra of two compounds, A and B, are
distinctly different. They therefore produce a large spectral contrast angle
(62.3°).