Decomposition of the Resonant Mie Scattering Efficiency Database

The Mie scattering efficiency database can be reorganised into a matrix (a block of numbers) in which each row is an individual Q curve. This matrix hereafter is denoted as Q, where the bold font indicates a matrix according to standard linear algebra notation. If our raw spectrum to be corrected comprises 2000 absorbance values, then the 1000 Q curve matrix will have 1000 rows and 2000 columns (a 1000x2000 matrix). 

Using principal component analysis (PCA) this Q matrix can be summarised as a small number (such as 10) of principal components (PCs). The Q matrix can be decomposed into a scores matrix, T, and a loadings matrix, P, and the 

These loading vectors can be incorporated into an EMSC model to give  

To calculate the corrected spectrum, 13 parameters need to be estimated, 2 for the constant and sloping baselines, 1 for the multiplicative factor and 10 for the loadings which describe the scattering curve. These parameters are estimated using a least squares fitting algorithm as before. 

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