Improving Quantitative EDS Chemical Analysis of Alloy Nanoparticles by PCA Denoising: Part I, Reducing Reconstruction Bias

Scanning transmission electron microscopy is a crucial tool for nanoscience, achieving sub-nanometric spatial resolution in both image and spectroscopic studies. This generates large datasets that cannot be analyzed without computational assistance. The so-called machine learning procedures can exploit redundancies and find hidden correlations. Principal component analysis (PCA) is the most popular approach to denoise data by reducing data dimensionality and extracting meaningful information; however, there are many open questions on the accuracy of reconstructions. We have used experiments and simulations to analyze the effect of PCA on quantitative chemical analysis of binary alloy (AuAg) nanoparticles using energy-dispersive X-ray spectroscopy. Our results demonstrate that it is possible to obtain very good fidelity of chemical composition distribution when the signal-to-noise ratio exceeds a certain minimal level. Accurate denoising derives from a complex interplay between redundancy (data matrix size), counting noise, and noiseless data intensity variance (associated with sample chemical composition dispersion). We have suggested several quantitative bias estimators and noise evaluation procedures to help in the analysis and design of experiments. This work demonstrates the high potential of PCA denoising, but it also highlights the limitations and pitfalls that need to be avoided to minimize artifacts and perform reliable quantification.

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Principal component transforms of triaxial recordings by singular value decomposition

Geophysics ◽

10.1190/1.1443068 ◽

1991 ◽

Vol 56 (4) ◽

pp. 528-533 ◽

Cited By ~ 43

Author(s):

G. M. Jackson ◽

I. M. Mason ◽

S. A. Greenhalgh

Keyword(s):

Singular Value Decomposition ◽

Time Window ◽

Signal To Noise Ratio ◽

Random Noise ◽

Principal Component ◽

Singular Value ◽

Data Matrix ◽

Single Station ◽

Window Selection ◽

Value Decomposition

Polarization analysis can be achieved efficiently by treating a time window of a single‐station triaxial recording as a matrix and doing a singular value decomposition (SVD) of this seismic data matrix. SVD of the triaxial data matrix produces an eigenanalysis of the data covariance (cross‐energy) matrix and a rotation of the data onto the directions given by the eigenanalysis (Karhunen‐Loève transform), all in one step. SVD provides a complete principal components analysis of the data in the analysis time window. Selection of this time window is crucial to the success of the analysis and is governed by three considerations: the window should contain only one arrival; the window should be such that the signal‐to‐noise ratio is maximized; and the window should be long enough to be able to discriminate random noise from signal. The SVD analysis provides estimates of signal, signal polarization directions, and noise. An F‐test is proposed which gives the confidence level for the hypothesis of rectilinear polarization. This paper illustrates the analysis and interpretation of synthetic rectilinearly and elliptically polarized arrivals at a single triaxial station by SVD.

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Quantitative Chemical Analysis of Sub-Micron Phase Segregation In Polyurethane Polymers by Soft X-Ray Spectromicroscopy

Microscopy and Microanalysis ◽

10.1017/s1431927600011430 ◽

1997 ◽

Vol 3 (S2) ◽

pp. 909-910

Author(s):

A.P. Hitchcock ◽

S.G. Urquhart ◽

E.G. Rightor ◽

W. Lidy ◽

H. Ade ◽

...

Keyword(s):

Chemical Analysis ◽

Spatial Resolution ◽

Chemical Properties ◽

Phase Segregation ◽

Quantitative Chemical Analysis ◽

X Ray ◽

Scanning Transmission ◽

Complex Polymers ◽

Physical And Chemical ◽

Quantitative Chemical

Phase segregation is important in determining the physical and chemical properties of many complex polymers, including polyurethanes. Achieving a better understanding of the connections between formulation chemistry, the chemical nature of segregated phases, and the physical properties of the resulting polymer, has the potential to greatly advance the development of improved polyurethane materials. However, the sub-micron size of segregated features precludes their chemical analysis by most existing methods. Near edge X-ray absorption spectroscopy carried out with sub micron spatial resolution provides one of the few suitable means for quantitative chemical analysis (speciation) of individual segregated phases. We have used the NSLS and ALS scanning transmission x-ray microscopes (STXM) to record images and spectra of both model and real polyurethane polymers. Relative to energy loss spectroscopy in a transmission electron microscope, STXM has remarkable advantages with regard to a much lower radiation damage rates and much higher spectral resolution (∼0.1 eV at the C ls edge), with a spatial resolution (∼0.1 μm) adequate for many real world problems in polymer analysis.

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Quantitative Chemical Speciation of Multi-Phase Polymers Using Zone Plate x-ray Microscopy

Microscopy and Microanalysis ◽

10.1017/s1431927600024168 ◽

1998 ◽

Vol 4 (S2) ◽

pp. 808-809

Author(s):

A.P. Hitchcock ◽

S.G. Urquhart ◽

H. Ade ◽

E.G. Rightor ◽

W. Lidy

Keyword(s):

Chemical Analysis ◽

Spatial Resolution ◽

Phase Segregation ◽

Zone Plate ◽

Quantitative Chemical Analysis ◽

X Ray ◽

Scanning Transmission ◽

Complex Polymers ◽

Multi Phase ◽

Quantitative Chemical

Phase segregation is important in determining the properties of many complex polymers, including polyurethanes. Achieving a better understanding of the links between formulation, chemical nature of segregated phases, and physical properties, has the potential to aid development of improved polymers. However, the sub-micron size of segregated features precludes detailed chemical analysis by most existing methods. Zone-plate based, scanning transmission X-ray microscopes (STXM) at NSLS and ALS provide quantitative chemical analysis (speciation) of segregated polymer phases at ∼50 nm spatial resolution. Image sequences acquire much more data with less radiation damage, than spot spectra. After alignment, they provide high quality near edge spectra, and thus quantitative analysis, at full spatial resolution.Fig. 1 shows an image and spectra acquired with the NSLS STXM of a macro-phase segregated TDI polyurethane. Spectral decomposition using model polymer spectra is used to measure the local urea, urethane and polyether content.

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Resolution in the Scanning Transmission Electron Microscope

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100095522 ◽

1972 ◽

Vol 30 ◽

pp. 454-455

Author(s):

M. G. R. Thomson

Keyword(s):

Electron Microscope ◽

Transmission Electron Microscope ◽

Spherical Aberration ◽

Signal To Noise Ratio ◽

Scanning Transmission Electron Microscope ◽

Dark Field ◽

Objective Lens ◽

Scanning Transmission Electron ◽

Transmission Electron ◽

Scanning Transmission

The variation of contrast and signal to noise ratio with change in detector solid angle in the high resolution scanning transmission electron microscope was discussed in an earlier paper. In that paper the conclusions were that the most favourable conditions for the imaging of isolated single heavy atoms were, using the notation in figure 1, either bright field phase contrast with β0⋍0.5 α0, or dark field with an annular detector subtending an angle between ao and effectively π/2.The microscope is represented simply by the model illustrated in figure 1, and the objective lens is characterised by its coefficient of spherical aberration Cs. All the results for the Scanning Transmission Electron Microscope (STEM) may with care be applied to the Conventional Electron Microscope (CEM). The object atom is represented as detailed in reference 2, except that ϕ(θ) is taken to be the constant ϕ(0) to simplify the integration. This is reasonable for θ ≤ 0.1 θ0, where 60 is the screening angle.

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Background subtraction in STEM energy-loss mapping

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100112774 ◽

1984 ◽

Vol 42 ◽

pp. 568-569

Author(s):

R.D. Leapman ◽

K.E. Gorlen ◽

C.R. Swyt

Keyword(s):

Energy Loss ◽

Signal To Noise Ratio ◽

Statistical Error ◽

Scanning Transmission Electron Microscope ◽

Reference Image ◽

Inverse Power Law ◽

Transmission Electron ◽

Least Squares Fit ◽

Scanning Transmission ◽

Single Number

The determination of elemental distributions by electron energy loss spectroscopy necessitates removal of the non-characteristic spectral background from a core-edge at each point in the image. In the scanning transmission electron microscope this is made possible by computer controlled data acquisition. Data may be processed by fitting the pre-edge counts, at two or more channels, to an inverse power law, AE-r, where A and r are parameters and E is energy loss. Processing may be performed in real-time so a single number is saved at each pixel. Detailed analysis, shows that the largest contribution to noise comes from statistical error in the least squares fit to the background. If the background shape remains constant over the entire image, the signal-to-noise ratio can be improved by fitting only one parameter. Such an assumption is generally implicit in subtraction of the “reference image” in energy selected micrographs recorded in the CTEM with a Castaing-Henry spectrometer.

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Some Quantification Problems in Parallel EELS Images

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100133771 ◽

1990 ◽

Vol 48 (2) ◽

pp. 36-37

Author(s):

G. Botton ◽

G. L’Espérance ◽

M.D. Ball ◽

C.E. Gallerneault

Keyword(s):

Electron Microscope ◽

Imaging System ◽

Signal To Noise Ratio ◽

Scanning Transmission Electron Microscope ◽

Acquisition Time ◽

Thickness Variation ◽

Transmission Electron ◽

Distribution Of Elements ◽

Scanning Transmission ◽

Present Distribution

The recently developed parallel electron energy loss spectrometers (PEELS) have led to a significant reduction in spectrum acquisition time making EELS more useful in many applications in material science. Dwell times as short as 50 msec per spectrum with a PEELS coupled to a scanning transmission electron microscope (STEM), can make quantitative EEL images accessible. These images would present distribution of elements with the high spatial resolution inherent to EELS. The aim of this paper is to briefly investigate the effect of acquisition time per pixel on the signal to noise ratio (SNR), the effect of thickness variation and crystallography and finally the energy stability of spectra when acquired in the scanning mode during long periods of time.The configuration of the imaging system is the following: a Gatan PEELS is coupled to a CM30 (TEM/STEM) electron microscope, the control of the spectrometer and microscope is performed through a LINK AN10-85S MCA which is interfaced to a IBM RT 125 (running under AIX) via a DR11W line.

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