44 Spectral Contrast Theory
5
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 technique forms a vector for each spectrum
in an n-dimensional space. The two spectral vectors are compared mathematically to
compute the angle between the two vectors.
Just as in 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.
5.3 Spectral Contrast Angles
Spectra that have the same shape have vectors that point in the same direction. Spectra that
have different 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 is 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 near 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 Spectral Contrast angle and spectral shape
differences, consider the pairs of spectra shown in Figure 5-3, Figure 5-4, and Figure 5-5.
Spectra with Different Shapes
In Figure 5-3, the absorbance spectra of two compounds, A and B, are distinctly different,
and therefore, have a large Spectral Contrast angle.
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