Mitigating dead‐time effects during multivariate analysis of ToF‐SIMS spectral images

ToF‐SIMS spectra are formed by bombarding a surface with a pulse of primary ions and detecting the resultant ionized surface species using a time‐of‐flight mass spectrometer. Typically, the detector is a time‐to‐digital converter. Once an ion is detected using such detectors, the detector becomes insensitive to the arrival of additional ions for a period termed as the (detector) dead‐time. Under commonly used ToF‐SIMS data acquisition conditions, the time interval over which ions arising from a single chemical species reach the detector is on the order of the detector dead‐time. Thus, only the first ion reaching the detector at any given mass is counted. The event registered by the data acquisition system, then, is the arrival of one or more ions at the detector. This behavior causes ToF‐SIMS data to violate, in the general case, the assumption of linear additivity that underlies many multivariate statistical analysis techniques. In this article, we show that high‐mass‐resolution ToF‐SIMS spectral‐image data follow a generalized linear model, and we propose a data transformation and scaling procedure that enables such data sets to be successfully analyzed using standard methods of multivariate image analysis. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparison of a new dead‐time correction method and conventional models for SIMS analysis

Recently, secondary ion mass spectrometry (SIMS) has been used in the analysis of not only impurities but also matrix elements, thus requiring a wide dynamic range for SIMS analysis. However, SIMS detectors, which are mostly used in pulse counting systems, have difficulties with detector saturation. In this paper, we investigate whether a dead‐time model that was developed for X‐ray measurement is applicable for SIMS analysis. We then compare a new correction method with conventional correction methods for detector saturation in SIMS analysis. We report that the new method can better correct the intensity in regions of higher intensity than that achieved by conventional methods. Copyright © 2012 John Wiley & Sons, Ltd.     

High‐resolution peak analysis in TOF SIMS data

High mass resolution time‐of‐flight secondary ion mass spectrometry (TOF SIMS) can provide a wealth of chemical information about a sample, but the analysis of such data is complicated by detector dead‐time effects that lead to systematic shifts in peak shapes, positions, and intensities. We introduce a new maximum‐likelihood analysis that incorporates the detector behavior in the likelihood function, such that a parametric spectrum model can be fit directly to as‐measured data. In numerical testing, this approach is shown to be the most precise and lowest‐bias option when compared with both weighted and unweighted least‐squares fitting of data corrected for dead‐time effects. Unweighted least‐squares analysis is the next best, while weighted least‐squares suffers from significant bias when the number of pulses used is small. We also provide best‐case estimates of the achievable precision in fitting TOF SIMS peak positions and intensities and investigate the biases introduced by ignoring background intensity and by fitting to just the intense part of a peak. We apply the maximum‐likelihood method to fit two experimental data sets: a positive‐ion spectrum from a multilayer MoS₂ sample and a positive‐ion spectrum from a TiZrNi bulk metallic glass sample. The precision of extracted isotope masses and relative abundances obtained is close to the best‐case predictions from the numerical simulations despite the use of inexact peak shape functions and other approximations. Implications for instrument calibration, incorporation of prior information about the sample, and extension of this approach to the analysis of imaging data are also discussed.     

Multivariate statistical analysis of non‐mass‐selected ToF‐SIMS data

Cluster LMIGs are now regarded as the standard primary ion guns on time‐of‐flight secondary ion mass spectrometers (ToF‐SIMS). The ToF‐SIMS analyst typically selects a bombarding species (cluster size and charge) to be used for material analysis. Using standard data collection protocols where the analyst uses only a single primary bombarding species, only a fraction of the ion‐beam current generated by the LMIG is used. In this work, we demonstrate for the first time that it is possible to perform ToF‐SIMS analysis when all of the primary ion intensity (clusters) are used; we refer to this new data analysis mode as non‐mass‐selected (NMS) analysis. Since each of the bombarding species has a different mass‐to‐charge ratio, they strike the sample at different times, and as a result, each of the bombarding species generates a spectrum. The resulting NMS ToF‐SIMS spectrum contains contributions from each of the bombarding species that are shifted in time. NMS spectra are incredibly complicated and would be difficult, if not impossible, to analyze using univariate methodology. We will demonstrate that automated multivariate statistical analysis (MVSA) tools are capable of rapidly converting the complicated NMS data sets into a handful of chemical components (represented by both spectra and images) that are easier to interpret since each component spectrum represents a unique and simpler chemistry. Copyright © 2008 John Wiley & Sons, Ltd.     

Simple statistically based alternatives to MAF for ToF‐SIMS spectral image analysis

The maximum autocorrelation factors technique (MAF) is becoming increasingly popular for the multivariate analysis of spectral images acquired with time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) instruments. In this article, we review the conditions under which the underlying chemical information can be separated from the large‐scale, non‐uniform noise characteristic of ToF‐SIMS data. Central to this pursuit is the ability to assess the covariance structure of the noise. Given a set of replicate images, the noise covariance matrix can be estimated in a straightforward way using standard statistical tools. Acquiring replicate images, however, is not always possible, and MAF solves a subtly different problem, namely, how to approximate the noise covariance matrix from a single image when replicates are not available. This distinction is important; the MAF approximation is not an unbiased statistical estimate of the noise covariance matrix, and it differs in a highly significant way from a true estimate for ToF‐SIMS data. Here, we draw attention to the fact that replicate measurements are made during the normal course of acquiring a ToF‐SIMS spectral image, rendering the MAF procedure unnecessary. Furthermore, in the common case that detector dead‐time effects permit no more than one ion of any specific species to be detected on a single primary ion shot, the noise covariance matrix can be estimated in a particularly simple way, which will be reported. Copyright © 2011 John Wiley & Sons, Ltd.     

Multivariate analysis of ToF‐SIMS data using mass segmented peak lists

Time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) provides detailed molecular insight into the surface chemistry of a diverse range of material types. Extracting useful and specific information from the mass spectra and reducing the dimensionality of very large datasets are a challenge that has not been fully resolved. Multivariate analysis has been widely deployed to assist in the interpretation of ToF‐SIMS data. Principal component analysis is a popular approach that requires the generation of peak lists for every spectrum. Peak list sizes and the resulting data matrices are growing, complicating manual peak selection and analysis. Here we report the generation of very large ToF‐SIMS peak lists using up‐binning, the mass segmentation of spectral data in the range 0 to 300 m/z in 0.01 m/z intervals. Time‐of‐flight secondary ion mass spectrometry data acquired from a set of 4 standard polymers (polyethylene terephthalate, polytetrafluoroethylene, poly(methyl methacrylate), and low‐density polyethylene) are used to demonstrate the efficacy of this approach. The polymer types are discriminated to a moderate extent by principal component analysis but are easily skewed with saturated species or contaminants present in ToF‐SIMS data. Artificial neural networks, in the form of self‐organising maps, are introduced and provide a non‐linear approach to classifying data and focussing on similarities between samples. The classification outcome achieved is excellent for different polymer types and for spectra from a single polymer type generated by using different primary ions. This method offers great promise for the investigation of more complex systems including polymer classes and blends and mixtures of biological materials.     

Final report on VAMAS round‐robin study to evaluate a correction method for saturation effects in DSIMS

A Versailles Project on Advanced Materials and Standards round robin test (RRT) has been conducted to evaluate the linearity of the instrumental intensity scale and correction method using an approximation intermediate extended dead time model with parameters derived from two different isotope depth profiles. Nine organizations in five countries participated. An arsenic‐implanted silicon wafer and a film of BN diffused into a Si wafer were supplied by the National Institute of Advanced Industrial Science and Technology along with instructions for the RRT. The instruments used to analyze ¹⁰³(AsSi)^? and ¹⁰⁵(AsSi)^? from arsenic‐implanted samples were five quadrupole‐type SIMS and four magnetic‐sector type SIMS. The instruments used to analyze ¹⁰B⁺ and ¹¹B⁺ from the BN‐diffused samples were three quadrupole‐type SIMS, four magnetic‐sector type SIMS, and one time‐of‐flight type SIMS. We validated the usefulness of the approximation intermediate extended dead time model to correct saturated intensities for all SIMS in this RRT. The optimum extension parameter ρ tends to be affected by the ratio of the maximum reliable intensity to the maximum intensity in raw profiles. From the ratio, ρ may be predicted when the intensity reaches full saturation. On the other hand, ρ is also affected by lateral non‐uniformity of intensity. In practice, because the maximum intensity does not reach full saturation and the intensity is not laterally uniform, ρ is likely to be smaller than its predicted value. Copyright © 2015 John Wiley & Sons, Ltd.     

Hidden information in principal component analysis of ToF‐SIMS data: On the use of correlation loadings for the identification of significant signals and structure elucidation

In this paper, an improved approach to interpret results of principal component analysis (PCA) of time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) spectra is presented. Signals are typically observed in different intensity ranges in a single ToF‐SIMS spectrum due to different sensitivity factors and surface concentrations. This can complicate the PCA interpretation, because loadings are reported to be strongly affected by these intensity changes. In contrast, it is shown here that correlation loadings are unaffected by these differences. In particular, correlation loadings were successfully used to identify signals with relatively low intensity but high significance. These signals may be overlooked when only loadings are used. This is particularly true in failure analysis, where ToF‐SIMS is used to screen for initially unknown signals that may be relevant for the characteristics/failure of a product. As a model study, the concept was applied to investigate ageing of Li‐ion batteries by ToF‐SIMS. In this data set, the significance of impurities that affect the quality of Li‐ion batteries was identified only by correlation loadings, whereas the loadings were found to overestimate the influence of other matrix signals. In addition, correlation loadings aid in the chemical identification and helped to successfully assign unknown peaks.     

The statistics of ToF‐SIMS data revisited and introduction of the empirical Poisson correction

Generation of time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) data involves two overarching processes: secondary ion production and secondary ion detection. The interpretation of ToF‐SIMS data is facilitated if the intensities of the as‐measured mass spectra are proportional to the abundances of the species under investigation. While secondary ion yield is normally taken to be a linear process, ion detection is not owing to detector dead‐time effects. Consequently, methods have been devised that attempt to linearize, or correct, data that are affected by the dead time. In this article, we review the statistics of ToF‐SIMS data generation and confirm a report in the literature that abundance estimates from so‐called Poisson corrections are biased. We show that these corrections are only unbiased asymptotically and that a rigorous probabilistic analysis can quantitatively account for the observed bias. Two sources of bias are identified, one having a statistical basis and one due to the form of the correction equation at high ion detection rates. Based on insights gained from this analysis, we propose a new correction equation, the empirical Poisson correction, which largely eliminates the statistical bias. The performance of the proposed correction is illustrated by reanalyzing 14 experimentally measured datasets that suffer from varying levels of dead‐time effects. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantification and methodology issues in multivariate analysis of ToF‐SIMS data for mixed organic systems

Multivariate methods, such as principal component analysis (PCA) and multivariate curve resolution (MCR), are often employed to aid the analysis of large complex data sets such as time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) images. There is, however, much confusion over the most appropriate choice of method for any given application and the effects of data preprocessing, which is exacerbated by the confusing terminologies and the use of jargon in this field. In the present study, a simple model system consisting of a ToF‐SIMS image of an immiscible polymer blend is used to evaluate PCA and MCR in the accurate identification, localisation and quantification of the phase‐separated polymer domains, using four data preprocessing methods (no scaling, normalisation, variance scaling and Poisson scaling). This highlights significant issues and challenges in the quantitative multivariate analysis of mixed organic systems, including the discrimination of chemically significant features from experimental noise, the resolution of weak chemical contributions and potential bias introduced by data preprocessing. Multivariate analysis using Poisson scaling, identified as the most suitable data preprocessing method for both PCA and MCR, demonstrates a marked improvement upon traditional (manual) analysis and provides valuable additional information that is difficult to detect using traditional analysis. Using these results, we present recommendations for the optimum use of multivariate analysis by analysts and provide guidance on selecting the most appropriate methods. Confusing terminology is also clarified. © Crown copyright 2008. Reproduced with the permission of Her Majesty's Stationery Office. Published by John Wiley & Sons, Ltd.     

Determination of rank by median absolute deviation (DRMAD): a simple method for determining the number of principal factors responsible for a data matrix

Median absolute deviation (MAD) is a well‐established statistical method for determining outliers. This simple statistic can be used to determine the number of principal factors responsible for a data matrix by direct application to the residual standard deviation (RSD) obtained from principal component analysis (PCA). Unlike many other popular methods the proposed method, called determination of rank by MAD (DRMAD), does not involve the use of pseudo degrees of freedom, pseudo F‐tests, extensive calibration tables, time‐consuming iterations, nor empirical procedures. The method does not require strict adherence to normal distributions of experimental uncertainties. The computations are direct, simple to use and extremely fast, ideally suitable for online data processing. The results obtained using various sets of chemical data previously reported in the chemical literature agree with the early work. Limitations of the method, determined from model data, are discussed. An algorithm, written in MATLAB format, is presented in the Appendix. Copyright © 2008 John Wiley & Sons, Ltd.     

ToF‐SIMS for the characterization of hyperbranched aliphatic polyesters: probing their molecular weight on surfaces based on principal component analysis (PCA)

A series of 2,2‐bis(hydroxymethyl)propionic acid (Bis‐MPA) hyperbranched aliphatic polyesters with different molecular weights (generations) is analysed for the first time by time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS). The main negative and positive low‐mass fragments are identified in the fingerprint part of the spectra (m/z < 400) and are principally assigned to fragmentation of the Bis‐MPA repeating units. In addition, it is shown that the fragmentation pattern is highly affected by the functional end‐groups. This is illustrated for a phthalic acid end‐capped hyperbranched polymer and for an acetonide‐terminated dendrimer analog. Also, typical fragments assigned to the ethoxylated pentaerythritol core molecule are detected. These ions show decreasing intensities with increasing molecular weight. This intensity dependency on the generation is used to calibrate the molecular weight of hyperbranched polyesters on the surface. To obtain quantitative information, a principal component analysis (PCA) multivariate statistical method is applied to the ToF‐SIMS data. The influence of different normalization procedures prior to PCA calculation is tested, e.g. normalization to the total intensity, to the intensities of ions assigned to the Bis‐MPA repeating unit or to intensities of fragments due to the core molecule. It is shown that only one principal component (PC1) is needed to describe most of the variance between the samples. In addition, PC1 takes into account the generation effect. However, different relationships between the PC1 scores and the hyperbranched mass average molecular weights are observed depending on the normalization procedure used. Normalization of data set ion intensities by ion intensities from the core molecule allows linearization of the SIMS intensities versus the molecular weight and allows the hyperbranched polymers to be discriminated up to the highest generations. In addition, PCA applied to ToF‐SIMS data provides an extended interpretation of the spectra leading to further identification of the correlated mass peaks, such as those of the Bis‐MPA repeating unit (terminal, dendritic and linear) and those of the core molecule. Finally, the work presented demonstrates the extreme potential of the static ToF‐SIMS and PCA techniques in the analysis of dendritic molecules on solid surfaces. Copyright © 2003 John Wiley & Sons, Ltd.     

Efficient encoding and rapid decoding for interactive visualization of large three‐dimensional hyperspectral chemical images

Interactive visualization of data from a new generation of chemical imaging systems requires coding that is efficient and accessible. New technologies for secondary ion mass spectrometry (SIMS) generate large three‐dimensional, hyperspectral datasets with high spatial and spectral resolution. Interactive visualization is important for chemical analysis, but the raw dataset size exceeds the memory capacities of typical current computer systems and is a significant obstacle. This paper reports the development of a lossless coding method that is memory efficient, enabling large SIMS datasets to be held in fast memory, and supports quick access for interactive visualization. The approach provides pixel indexing, as required for chemical imaging applications, and is based on the statistical characteristics of the data. The method uses differential time‐of‐flight to effect mass‐spectral run‐length‐encoding and uses a scheme for variable‐length, byte‐unit representations for both mass‐spectral time‐of‐flight and intensity values. Experiments demonstrate high compression rates and fast access. Copyright © 2009 John Wiley & Sons, Ltd.     

Extraction of hidden information of ToF‐SIMS data using different multivariate analyses

Time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) is a powerful tool for determining surface information of complex systems such as polymers and biological materials. However, the interpretation of ToF‐SIMS raw data is often difficult. Multivariate analysis has become effective methods for the interpretation of ToF‐SIMS data. Some of multivariate analysis methods such as principal component analysis and multivariate curve resolution are useful for simplifying ToF‐SIMS data consisting of many components to that explained by a smaller number of components. In this study, the ToF‐SIMS data of four layers of three polymers was analyzed using these analysis methods. The information acquired by using each method was compared in terms of the spatial distribution of the polymers and identification. Moreover, in order to investigate the influence of surface contamination, the ToF‐SIMS data before and after Ar cluster ion beam sputtering was compared. As a result, materials in the sample of multiple components, including unknown contaminants, were distinguished. Copyright © 2014 John Wiley & Sons, Ltd.     

Detecting changes in arabidopsis cell wall composition using time‐of‐flight secondary ion mass spectrometry

Time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) was previously used to characterize lignocellulosic materials, including woody biomass. ToF‐SIMS can acquire both rapid spectral and spatial information about a sample's surface composition. In the present study, ToF‐SIMS was used to characterize the cell walls of stem tissue from the plant model organism, Arabidopsis thaliana. Using principal component analyses, ToF‐SIMS spectra from A. thaliana wild‐type (Col‐0), cellulose mutant (irx3), and lignin mutant (fah1) stem tissues were distinguished using ToF‐SIMS peaks annotated for wood‐derived lignocellulose, where spectra from the irx3 and fah1 were characterized by comparatively low polysaccharide and syringyl lignin content, respectively. Spatial analyses using ToF‐SIMS imaging furthermore differentiated interfascicular fiber and xylem vessels based on differences in the lignin content of corresponding cell walls. These new data support the applicability of ToF‐SIMS peak annotations based on woody biomass for herbaceous plants, including model plant systems like arabidopsis. Copyright © 2015 John Wiley & Sons, Ltd.     

A novel multi‐mode data processing method and its application in industrial process monitoring

Multi‐mode process monitoring is a key issue often raised in industrial process control. Most multivariate statistical process monitoring strategies, such as principal component analysis (PCA) and partial least squares, make an essential assumption that the collected data follow a unimodal or Gaussian distribution. However, owing to the complexity and the multi‐mode feature of industrial processes, the collected data usually follow different distributions. This paper proposes a novel multi‐mode data processing method called weighted k neighbourhood standardisation (WKNS) to address the multi‐mode data problem. This method can transform multi‐mode data into an approximately unimodal or Gaussian distribution. The results of theoretical analysis and discussion suggest that the WKNS strategy is more suitable for multi‐mode data normalisation than the z‐score method is. Furthermore, a new fault detection approach called WKNS‐PCA is developed and applied to detect process outliers. This method does not require process knowledge and multi‐mode modelling; only a single model is required for multi‐mode process monitoring. The proposed method is tested on a numerical example and the Tennessee Eastman process. Finally, the results demonstrate that the proposed data preprocessing and process monitoring methods are particularly suitable and effective in multi‐mode data normalisation and industrial process fault detection. Copyright © 2014 John Wiley & Sons, Ltd.     

A new approach to express ToF SIMS depth profiling

We propose a new approach to express SIMS depth profiling on a TOF.SIMS‐5 time‐of‐flight mass spectrometer. The approach is based on the instrument capability to independently perform raster scans of sputter and probe ion beams. The probed area can be much smaller than the diameter of a sputter ion beam, like in the AES depth profiling method. This circumstance alleviates limitations on the sputter beam–raster size relation, which are critical in other types of SIMS, and enables analysis on a curved‐bottomed sputter crater. By considerably reducing the raster size, it is possible to increase the depth profiling speed by an order of magnitude without radically degrading the depth resolution. A technique is proposed for successive improvement of depth resolution through profile recovery with account for the developing curvature of the sputtered crater bottom in the probed area. Experimental study of the crater bottom form resulted in implementing a method to include contribution of the instrumental artifacts in a nonstationary depth resolution function within the Hofmann's mixing–roughness–information depth model. The real‐structure experiment has shown that the analysis technique combining reduction of a raster size with a successive nonstationary recovery ensures high speed of profiling at ~100 µm/h while maintaining the depth resolution of about 30 nm at a 5 µm depth. Copyright © 2015 John Wiley & Sons, Ltd.     

On the use of the observation‐wise k‐fold operation in PCA cross‐validation

Cross‐validation (CV) is a common approach for determining the optimal number of components in a principal component analysis model. To guarantee the independence between model testing and calibration, the observation‐wise k‐fold operation is commonly implemented in each cross‐validation step. This operation renders the CV algorithm computationally intensive, and it is the main limitation to apply CV on very large data sets. In this paper, we carry out an empirical and theoretical investigation of the use of this operation in the element‐wise k‐fold (ekf) algorithm, the state‐of‐the‐art CV algorithm. We show that when very large data sets need to be cross‐validated and the computational time is a matter of concern, the observation‐wise k‐fold operation can be skipped. The theoretical properties of the resulting modified algorithm, referred to as column‐wise k‐fold (ckf) algorithm, are derived. Also, its performance is evaluated with several artificial and real data sets. We suggest the ckf algorithm to be a valid alternative to the standard ekf to reduce the computational time needed to cross‐validate a data set. Copyright © 2015 John Wiley & Sons, Ltd.     

Adsorption of genetically engineered proteins studied by time‐of‐flight secondary ion mass spectrometry (TOF‐SIMS). Part B: hierarchical cluster analysis (HCA)

In Part A, we adopted principal component analysis (PCA) for the analysis of TOF‐SIMS data to assess the binding specificity of GBP‐1 to metallic Au, Ag and Pd. Within a given set of data, PCA aids in the interpretation of the TOF‐SIMS spectra by capitalizing on the differences from one spectrum to another. In Part B, we introduce another multivariate statistical method called ‘hierarchical cluster analysis (HCA)’, where visualization of the similarity and difference in data is readily observed, from which a variety of adsorption conditions of GBP‐1 were characterized. Copyright © 2007 John Wiley & Sons, Ltd.     

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

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. © 2015 The Authors. Surface and Interface Analysis published by John Wiley & Sons Ltd.