Noise reduction in X-ray photoelectron spectromicroscopy by a singular value decomposition sorting procedure

Walton, John; Fairley, Neal

doi:10.1016/j.elspec.2005.02.003

Cited by 65 publications

(53 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, using Eqns (1) and (2), B 0 = 4083 eV 2 and A H p = 8.841 eV 2 were obtained respectively from the reference Ag sample. In the same way B 1 and A p were obtained for each pixel for a given sample.…”

Section: Analysis Results and Discussionmentioning

confidence: 99%

“…Recently, images of film thickness, after noise reduction by principal component analysis (PCA), were obtained [2] using ratios of peak area to background signal [3] for each pixel and by ARXPS imaging. [4] A method for quantitative XPS which, by analysis of the peak shape, automatically accounts for the effect of variation in atomic concentration with depth was developed by Tougaard [1,5 -7] and Tougaard and Hansen.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nondestructive quantitative XPS imaging of depth distribution of atoms on the nanoscale

Hajati

Coultas

Blomfield

et al. 2008

Surface & Interface Analysis

View full text Add to dashboard Cite

show abstract

Section: Analysis Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nondestructive quantitative XPS imaging of depth distribution of atoms on the nanoscale

Hajati

Coultas

Blomfield

et al. 2008

Surface & Interface Analysis

View full text Add to dashboard Cite

show abstract

“…independent) components. [12,13] Until now, these methods have been difficult to apply to very large datasets such as spectra associated with two-dimensional (2D) images or threedimensional (3D) depth-profiles because the size of the dataset is too large to hold in the memory of commonly available personal computers (PCs). In recent work, [14] we applied the new 'random vectors' (RVs) method of SVD proposed by Halko [15] and co-authors to time-of-flight (ToF)-SIMS images for the first time.…”

Section: Introductionmentioning

confidence: 99%

Rapid multivariate analysis of 3D ToF‐SIMS data: graphical processor units (GPUs) and low‐discrepancy subsampling for large‐scale principal component analysis

Cumpson

Fletcher

Sano

et al. 2016

Surface & Interface Analysis

View full text Add to dashboard Cite

Principal component analysis (PCA) and other multivariate analysis methods have been used increasingly to analyse and understand depth-profiles in XPS, AES and SIMS. For large images or three-dimensional (3D) imaging depth-profiles, PCA has been difficult to apply until now simply because of the size of the matrices of data involved. In a recent paper, we described two algorithms, random vector 1 (RV1) and random vector 2 (RV2), that improve the speed of PCA and allow datasets of unlimited size, respectively. In this paper, we now apply the RV2 algorithm to perform PCA on full 3D time-of-flight SIMS data for the first time without subsampling. The dataset we process in this way is a 128 × 128 pixel depth-profile of 120 layers, each voxel having a 70 439 value mass spectrum associated with it. This forms over a terabyte of data when uncompressed and took 27 h to process using the RV2 algorithm using a conventional windows desktop personal computer (PC). While full PCA (e.g. using RV2) is to be preferred for final reports or publications, a much more rapid method is needed during analysis sessions to inform decisions on the next analytical step. We have therefore implemented the RV1 algorithm on a PC having a graphical processor unit (GPU) card containing 2880 individual processor cores. This increases the speed of calculation by a factor of around 4.1 compared with what is possible using a fast commercially available desktop PC having central processing units alone, and full PCA is performed in less than 7 s. The size of the dataset that can be processed in this way is limited by the size of the memory on the GPU card. This is typically sufficient for two-dimensional images but not 3D depth-profiles without sampling. We have therefore examined efficient sampling schemes that allow a good approximate solution to the PCA problem for large 3D datasets. We find that low-discrepancy series such as Sobol series sampling gives more rapid convergence than random sampling, and we recommend such methods for routine use. Using the GPU and low-discrepancy series together, we anticipate that any time-of-flight SIMS dataset, of whatever size, can be efficiently and accurately processed into PCA components in a maximum of around 10 s using a commercial PC with a widely available GPU card, although the longer RV2 approach is still to be preferred for the presentation of final results, such as in published papers.

show abstract

“…independent) components. [14,15] Consider the simple case of an image containing just four pixels, as shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Multivariate analysis of extremely large ToFSIMS imaging datasets by a rapid PCA method

Cumpson

Sano

Fletcher

et al. 2015

Surf. Interface Anal.

View full text Add to dashboard Cite

Principal component analysis (PCA) and other multivariate analysis methods have been used increasingly to analyse and understand depth profiles in X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES) and secondary ion mass spectrometry (SIMS). These methods have proved equally useful in fundamental studies as in applied work where speed of interpretation is very valuable. Until now these methods have been difficult to apply to very large datasets such as spectra associated with 2D images or 3D depth-profiles. Existing algorithms for computing PCA matrices have been either too slow or demanded more memory than is available on desktop PCs. This often forces analysts to 'bin' spectra on much more coarse a grid than they would like, perhaps even to unity mass bins even though much higher resolution is available, or select only part of an image for PCA analysis, even though PCA of the full data would be preferred.We apply the new 'random vectors' method of singular value decomposition proposed by Halko and co-authors to time-of-flight (ToF)SIMS data for the first time. This increases the speed of calculation by a factor of several hundred, making PCA of these datasets practical on desktop PCs for the first time. For large images or 3D depth profiles we have implemented a version of this algorithm which minimises memory needs, so that even datasets too large to store in memory can be processed into PCA results on an ordinary PC with a few gigabytes of memory in a few hours. We present results from ToFSIMS imaging of a citrate crystal and a basalt rock sample, the largest of which is 134GB in file size corresponding to 67 111 mass values at each of 512 × 512 pixels. This was processed into 100 PCA components in six hours on a conventional Windows desktop PC.

show abstract

Noise reduction in X-ray photoelectron spectromicroscopy by a singular value decomposition sorting procedure

Cited by 65 publications

References 21 publications

Nondestructive quantitative XPS imaging of depth distribution of atoms on the nanoscale

Nondestructive quantitative XPS imaging of depth distribution of atoms on the nanoscale

Rapid multivariate analysis of 3D ToF‐SIMS data: graphical processor units (GPUs) and low‐discrepancy subsampling for large‐scale principal component analysis

Multivariate analysis of extremely large ToFSIMS imaging datasets by a rapid PCA method

Contact Info

Product

Resources

About