December 5, 2017, 715004753 Rev. B
Page 62
5.2
Representing spectra as vectors
The spectral contrast algorithm uses vectors to quantify differences in the shapes of spectra,
converting baseline-corrected spectra to vectors and then comparing the vectors. Spectral vectors
have two properties:
•
Length – Proportional to analyte concentration.
•
Direction – Determined by the relative absorbance of the analyte at all wavelengths (its
absorbance spectrum). Direction is independent of concentration for peaks that are less
than 1.0 absorbance units (AU) across the collected wavelength range.
Vector direction contributes to the identification of a compound, because the direction is a function
of the absorbance compound’s spectrum. The ability of spectral vectors to differentiate
compounds depends on the resolution of spectral features. As both wavelength range and spectral
resolution increase, the precision of a spectral vector for the resultant spectrum increases. A
detector-derived vector can include absorbances in the range of 190 to 800 nm. To enhance
spectral sensitivity, set the bench resolution to 1.2 nm.
Tip:
Do not include wavelengths where there is no analyte absorbance.
5.2.1
Vectors derived from two wavelengths
The spectral contrast algorithm uses vectors to characterize spectra. To understand the vector
principle, consider the figure below, which contains two vectors based on the spectra depicted in
the previous figure.
Figure 5–2:
Plotting vectors for two spectra
In this figure, the axes reflect the absorbance units of the two wavelengths used to calculate the
absorbance ratio of the previous figure. The head of the vector for Compound A lies at the
intersection of the absorbance values (for 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 (
), 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 63
).
TP02836
0
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
AU at 245 nm
AU a
t 257 nm
Compound B
Compound A
Summary of Contents for 2998
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