Waters 2998, Руководство оператора

Страница: 76 / 122

5-4 Spectral Contrast Theory
Compound A), at the two wavelengths represented by each axis. The
remaining vector is similarly derived from the spectrum of Compound B.
Compound B’s vector points in a direction different from Compound A’s.
Expressed by the spectral contrast angle (
θ
), this difference reflects the
difference between the two compounds’ absorbance ratios at wavelengths
245 nm and 257 nm. A spectral contrast angle greater than zero indicates a
shape difference between spectra (see “Spectral contrast angles” on page 5-4 ).
Finally, note that the length of the vectors is proportional to concentration.
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,
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.