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Spectral Contrast Algorithm: The Math Behind Peak Purity Calculations - Tip252

Article number: 222977

OBJECTIVE or GOAL

In this article we discuss the Spectral Contrast algorithm, the math behind Peak Purity calculations when using the ACQUITY™ PDA Detector. 

The Spectral Contrast algorithm measures the shape difference between spectra as per the following steps:
•    Spectra are baseline corrected by subtracting interpolated baseline spectra between peak baseline liftoff and baseline touchdown
•    Spectra are converted into vectors in n-dimensional space
•    Vector lengths are normalized
•    The vectors are moved into a two-dimensional plane and the angle between them is measured
•    An angle of 0 degrees means the spectral shape is identical and an angle of 90 degrees indicates no spectral overlap
 

ENVIRONMENT

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PROCEDURE

 

Spectral Contrast Angle
The shapes of Spectrum A and Spectrum B are represented by vectors.  is the Spectral Contrast Angle which is the difference between spectral shapes (figure 1).


Figure_1.png

EXAMPLE 1
In the first example, we have two very different compounds resulting in a Spectral Contrast Angle of 53 (figure 2).


Figure_2.png


EXAMPLE 2
In the second example, we have two compounds which are structurally related resulting in a Spectral Contrast Angle of 10 (figure 3).
Figure_3.png


EXAMPLE 3
In the third example, we have two compounds which are very similar and only differ by a CH2 resulting in a Spectral Contrast Angle of 0.5 (figure 4).
Figure_4.png


Threshold Angle
Small but significant differences between spectra can result from factors other than absorbance properties. Multiple spectra of the same compound may exhibit slight differences because of:


•    Detector Noise – statistical and thermal variations add electronic noise to the absorbance measurement, which is magnified when viewing spectra for the same compound at different concentrations (figure 5). 
Figure_5.png
This results in fluctuations in the baseline and is called baseline noise. The magnitude of this noise can be predicted by selecting a Noise Interval in the Processing Method. 

•    Photometric Error – at absorbance greater than 1AU, a combination of effects can produce slight variations in Beer’s Law. While this has a negligible effect on quantitation, it can be a significant source of spectral inhomogeneity (figure 6).
Figure_6.png


•    Variations in Solvent Composition – changes in solvent pH or composition during gradient chromatography can affect the shape of a spectrum (figure 7).
Figure_7.png

•    High Sample Concentration

The Threshold Angle is the largest Spectral Contrast Angle between spectra due to nonideal phenomena (figure 8). 
Figure_8.png


Comparing the Spectral Contrast Angle to the Threshold Angle helps to determine whether the shape difference between spectra is significant. In general, a Spectral Contrast Angle less than its Threshold Angle indicates that the shape differences are due to nonideal phenomena and that no evidence exists for significant differences between the spectra. A Spectral Contrast Angle greater than its Threshold Angle indicates that the shape differences are due to significant differences between the spectra.
 

 

ADDITIONAL INFORMATION

Final Note: This can be done with either the Pro or QuickStart interface.

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