Waters 996, Operator'S Manual

Page: 57 / 76

Spectral Contrast Angles 57
5
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 2-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, then 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 degrees to 90 degrees. A Spectral Contrast
angle near 0 degrees indicates little shape difference between the compared spectra.
Matching a spectrum to itself produces a Spectral Contrast angle of exactly 0 degrees.
The maximum Spectral Contrast angle, 90 degrees, 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 (62.3°).