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 (C) 2011 John Wiley & Sons, Ltd.