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Getting rid of Rayleigh
Åsmund Rinnan
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IntroductionFluorescence
Lightsource
Sample
Detector
Excitessample
Emittedfrom sample
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IntroductionFluorescence
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IntroductionPARAFAC
ijk
F
fkfjfifijk ecbax
1
X is the EEMa are the scoresb are the emissionspectrac are the excitationspectraE is the residuals
Can be seen as an expansion of PCA from two-way data to multi-way data
ij
F
fjfifij eptx
1
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=
A
B
C
IntroductionPARAFAC & Fluorescence
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IntroductionPARAFAC & Fluorescence
Catechol
Hydroquinone
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Introduction”Faking” fluorescence
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IntroductionLight scatter
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IntroductionLight scatter – The trouble maker
Excita
tion
Emission
2n
d o
rder
Rayle
igh
1st
ord
er
Rayle
igh
Ram
an
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IntroductionLight scatter
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IntroductionBi-linearity
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IntroductionWhy is this a problem?
X
X
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ExampleFluorescence & PARAFAC
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Getting rid of Rayleigh
•Subtraction of standard
•Cut off and insert missing/ zeros
•Weights•Modeling of Rayleigh
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Subtracting a standard
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Missing values
Missingvalues
Zeros
Signal/ Data area
Thygesen, Rinnan, Barsberg & Møller
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Example
• 18 wood samples• 4 different levels of p-benzoquinone adsorbed in
the fiber cell walls• 30 emission wavelengths x 35 excitation
wavelengths
Thygesen, Rinnan, Barsberg & Møller
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WOW!
None Weighted
Non-Negativity Zeros
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So, now Rayleigh is finished, right?
• The data presented so far is a bit simple Sugar data
Excitation
Emission 1st o
rder
Ray
leig
h
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Weighting - MILES
Emission loadings Excitation loadings
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Band of missing values
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Using a band of missing valuesHard weights
Emission loadings Excitation loadings
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Using a band of missing valuesMILES weights
Emission loadings Excitation loadings
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Another method?Why, why, why?
• The Rayleigh scatter width has to be estimated quite accurately
• The band width of missing data should also be correct
• What about an automatic method of removing the Rayleigh scatter, that was not so prone to the estimation of the width of the Rayleigh scatter?
• Modeling the Rayleigh is the answer!
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Modeling Rayleigh
• A Gauss-Lorentz curve fitting method
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Modeling Rayleigh
Rinnan, Booksh & Bro
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Modeling Rayleigh
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With constraints even better
Emission loadings Excitation loadings
Rinnan, Booksh & Bro
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• Thanks to: Rasmus Bro, Karl Booksh, Lisbeth G Thygesen, Søren Barsberg, Jens K S Møller and Charlotte Andersen
• Thank you for your attention
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