Getting rid of Rayleigh

Åsmund Rinnan

IntroductionFluorescence

Lightsource

Sample

Detector

Excitessample

Emittedfrom sample

IntroductionFluorescence

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

=

A

B

C

IntroductionPARAFAC & Fluorescence

IntroductionPARAFAC & Fluorescence

Catechol

Hydroquinone

Introduction”Faking” fluorescence

IntroductionLight scatter

IntroductionLight scatter – The trouble maker

Excita

tion

Emission

2n

d o

rder

Rayle

igh

1st

ord

er

Rayle

igh

Ram

an

IntroductionLight scatter

IntroductionBi-linearity

IntroductionWhy is this a problem?

X

X

ExampleFluorescence & PARAFAC

Getting rid of Rayleigh

•Subtraction of standard

•Cut off and insert missing/ zeros

•Weights•Modeling of Rayleigh

Subtracting a standard

Missing values

Missingvalues

Zeros

Signal/ Data area

Thygesen, Rinnan, Barsberg & Møller

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

WOW!

None Weighted

Non-Negativity Zeros

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

Weighting - MILES

Emission loadings Excitation loadings

Band of missing values

Using a band of missing valuesHard weights

Emission loadings Excitation loadings

Using a band of missing valuesMILES weights

Emission loadings Excitation loadings

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!

Modeling Rayleigh

• A Gauss-Lorentz curve fitting method

Modeling Rayleigh

Rinnan, Booksh & Bro

Modeling Rayleigh

With constraints even better

Emission loadings Excitation loadings

Rinnan, Booksh & Bro

• Thanks to: Rasmus Bro, Karl Booksh, Lisbeth G Thygesen, Søren Barsberg, Jens K S Møller and Charlotte Andersen

• Thank you for your attention