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.