Raman Images. Jeremy M. Shaver 1, Eunah Lee 2, Andrew Whitley 2, R. Scott Koch. 1. Eigenvector Research, Inc. 2. HORIBA Jobin Yvon, Inc.

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5 years ago
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1 Analyzing and Visualizing Large Raman Images Jeremy M. Shaver 1, Eunah Lee 2, Andrew Whitley 2, R. Scott Koch 1 1. Eigenvector Research, Inc. 2. HORIBA Jobin Yvon, Inc.

2 What is a Large Image? Gone from hundreds of spectra to tens of thousands of spectra complicated DOE or time series = 5 spectra 256 pixels x 256 pixels = spectra x 5 "slabs" (depth profile) = 3.2 million spectra!

3 5 samples (height ht =.2 inches = ½ cm) x 5 slabs = 3.2 million samples (131 inches = 19 feet = 1 story building = 33 meters) x256 = samples (26.2 inches = 66.5 cm)

4 Factor Based Image Analysis Techniques Principal Component Analysis (PCA) Provides good concise summary of correlated samples and variables Multivariate Curve Resolution (MCR) Provides physically significant significant representation of underlying spectra and where they show up Partial Least Squares (PLS) Provides "targeted" analysis of concentrations or spectral patterns

PCA On Entire Image Raman Shift (cm 1 ) Raman Shift (cm 1 ) P ixels in the image (sam mples) P ixels in the image (sam mples) If model contains 1 principal components

5 PCA On Entire Image Raman Shift (cm 1 ) Raman Shift (cm 1 ) P ixels in the image (sam mples) P ixels in the image (sam mples) If model contains 1 principal components (k=1) scores = 1 columns loadings = 1 rows X = GB Scores & Loadings = 6 MB >65, samples for 256 x 256 image (or 4 x 4 x 41 image) >1, variables at.3 cm 1 resolution

6 Principal Component Analysis on Images (the math, graphically speaking) variables (size = n) Step 1. calculate one of these two matrices s (size = m) sample n by n matrix m by m matrix ( m 2 elements) m >65, samples for 256 x 256 image (or 4 x 4 x 41 image) n >1, variables at.3 cm 1 resolution (or when combined with another spectroscopy!!)

7 Avoiding Memory Problems Do X T X"peacemeal" (segments e of spectra) may still not have enough memory for X T X must read file a second time to get scores! Spatial or Spectral compression Wavelets, binning (co adding, averaging, etc) Must choose filter carefully to avoid artifacts PCA results must be converted back to original variables/pixels throughfilter Sequential PCA With Model Updating Read file ONCE, get (close to true) scores and loadings

8 Sequential PCA with Updating Step 1: Segmenting the data X X

9 Sequential PCA with Updating Step 2: Analysis of first block λ 1 = eigenvalues (magnitude of factors) Directly related to how much of these spectral patterns we saw in X 1

10 Sequential PCA with Updating Step 3: Analysis of subsequent blocks

11 Sequential PCA with Updating Step 3: Analysis of subsequent blocks P x is an approximation of the loadings calculated if X was analyzed as a whole!

12 Sequential PCA with Updating Step 4: Correction of Scores Use Rotation matrices (R 1 and R 2 ) to rotate T 1, T 2, T 3 into T x (approximation of scores for X)

13 How Close an Approximation? 2 (or 3) Influences Sufficient Factors if the eentire eimage can be accurately modeled with k factors, then any subregion will require no more than k factors (in practice, use 2k factors) Correlated Noise Noise captured in each factor will vary. Low S/N ratio factors are more approximate. Sizeof the sub regions For low S/N factors, larger sub regions will improve the approximation.

14 Polystyrene Beads 51 x 51 x 51 spatial p dimension 124 spectral points (15 18 cm 1) Raman Shift (cm-1) 14 First Principal Component Loading 152 Raman Shift frequencies (variables) 16 18

15 Full vs. Sequential PCA on Reduced dspectral Range 1 6 le) ues (log scal Eigenval significant components green = full PCA blue = sequential PCA Basically identical for Principal Component Number

16 Loadings for Full and Sequential PCA PC 1 green = full llpca blue = sequential PCA R 2 = PC 2 R 2 = PC 3 R 2 = Raman Shift (cm-1)

17 Score Images for Sequential PCA (Unfolded 3D Images) R 2 = R 2 = R 2 = NoVisualDifferences (onlyshowing sequential here)

18 Difference between "True" Scores and Sequential Scores 1 5 PC Sample PC 2 x Sample 1 PC 3 x Sample PC 4 x Sample x 1 4

19 Sequential PCA on Full Spectrum significant components Eigenva alues (log scale e) x 51 x 51 pixels = spectra 124 Raman Shift frequencies (variables) Sequential PCA ONLY Principal Component Number

20 Loadings on PCs 1 and 2.25 Loadings on PC 1 Loadings on PC 2 Loadings on PC 1, Loading gs on PC Raman Shift (cm-1)

21 Scores on PC 1 5 Slice at z = x Image of PC y

22 Scores on PC 2 More Raman Less Baseline Slice at z = x Image of PC y

23 Scores on PC 2 Less Raman More Baseline Slice at z = x Image of PC y

24 MCR or PLS without X? MCR from PCA? PCA: X = TP T MCR: X = CS T = TRP T (where R is a rotation matrix and T and P capture sufficient variance) PLS from PCA? PCA: X = TP T perform PLS on T or P (again assuming T and P capture sufficient variance)

The latest trend of hybrid instrumentation

The latest trend of hybrid instrumentation Multivariate Data Processing of Spectral Images: The Ugly, the Bad, and the True The results of various multivariate data-processing methods of Raman maps recorded with a dispersive Raman microscope are