Jeremy M. Shaver

Maximum entropy method for frequency domain fluorescence lifetime analysis. 1. Effects of frequency range and random noise

The maximum entropy method (MEM) provides a self-modeling fit to data in which minimization of the χ(2) goodness-of-fit parameter is coupled with maximization of a statistical entropy function. We have found that MEM provides an excellent visual description of the uncertainties, errors, and limitations associated with the distributions which it recovers. To more accurately interpret fluorescence lifetime distributions recovered by the MEM from frequency domain lifetime data, a detailed examination of the effects of frequency range, noise, data set size, and sample heterogeneity was carried out for both simulated and real data. Results clearly demonstrate that the frequency range in which data are collected can affect the number and nature of the fluorescence lifetime components that are recovered by MEM, and the quality of the data at the frequencies that are optimal for a given lifetime is also crucial. Expansion of sufficient data sets to include more frequencies, or more replicates at the same frequencies, provides little improvement over the original data set when the lifetimes are well-windowed by the frequency range. Synergism among multiple components in a sample can affect the recovered distribution, by shifting and splitting poorly windowed components and broadening the recovered peaks for all components. These effects are related to the number of components for which evidence must be found.

Total Lifetime Distribution Analysis for Fluorescence Fingerprinting and Characterization

A new technique, total lifetime distribution analysis (TLDA), is described for rapid, sensitive, and accurate lifetime characterization of complex samples. Multiharmonic Fourier transform technology in a commercial, frequency-domain fluorescence lifetime instrument allows rapid acquisition of TLDA data. High sensitivity derives from the use of the entire fluorescence emission from the sample in the lifetime measurement. The maximum entropy method (MEM) provides a consistent basis for modeling of the lifetime data for accurate recovery of the total lifetime distribution of the sample. Because MEM is self-modeling, it is not subject to the same sources of bias that influence nonlinear least-squares fits of lifetime data to a priori models. These features make TLDA an effective tool for sample characterization and fingerprinting that is based on the responsiveness of fluorescence lifetime to the chemical composition and dynamic processes that contribute to the uniqueness of the sample. TLDA results are presented for coal liquids and a humic substance. The effect of signal intensity on lifetime recovery is investigated, and comparison is made between MEM and conventional nonlinear least-squares for data analysis.

Fluorescence Studies of Complex Coal Liquid Samples Using the Lifetime Synchronous Spectrum (LiSS)

An analysis of coal liquids is demonstrated in the first application of the lifetime synchronous spectrum (LiSS) to the characterization of complex samples. The measurement of wavelength-resolved fluorescence lifetimes in the LiSS is shown to enhance the fingerprinting of coal liquids relative to conventional synchronous luminescence spectroscopy. The concentration independence of fluorescence lifetimes of individual compounds provides unique information about the composition of the coal liquids and the sources of their spectral features, indicating similarities among different samples and leading to the identification of regions in the synchronous spectra that are best for discriminating among the samples. The LiSSes also provided information about the nature of the processes responsible for spectral red shifts that occurred with increasing concentration of coal liquid.

Loopy MSC : A Simple Way to Improve Multiplicative Scatter Correction

Multiplicative scatter correction (MSC) is a widely used normalization technique. It aims to correct spectra in such a way that they are as close as possible to a reference spectrum, generally the mean of the data set, by changing the scale and the offset of the spectra. When there are other differences in the spectra than just a scale and an offset, the mean spectrum changes after MSC. As a result, another MSC, with the new mean spectrum as the reference, will result in an additional correction. This paper studies the effect of multiple applications of MSC.

Multivariate Curve Resolution Applied to Infrared Reflection Measurements of Soil Contaminated with an Organophosphorus Analyte

Multivariate curve resolution (MCR) is a powerful technique for extracting chemical information from measured spectra of complex mixtures. A modified MCR technique that utilized both measured and second-derivative spectra to account for observed sample-to-sample variability attributable to changes in soil reflectivity was used to estimate the spectrum of dibutyl phosphate (DBP) adsorbed on two different soil types. This algorithm was applied directly to measurements of reflection spectra of soils coated with analyte without resorting to soil preparations such as grinding or dilution in potassium bromide. The results provided interpretable spectra that can be used to guide strategies for detection and classification of organic analytes adsorbed on soil. Comparisons to the neat DBP liquid spectrum showed that the recovered analyte spectra from both soils showed spectral features from methyl, methylene, hydroxyl, and P=O functional groups, but most conspicuous was the absence of the strong PO–(CH2)3CH3 stretch absorption at 1033 cm−1. These results are consistent with those obtained previously using extended multiplicative scatter correction.

Estimation of trace vapor concentration pathlength in plumes for remote sensing applications from hyperspectral images

Hyperspectral images in the long wave-infrared can be used for quantification of analytes in stack plumes. One approach uses eigenvectors of the off-plume covariance to develop models of the background that are employed in quantification. In this paper, it is shown that end members can be used in a similar way with the added advantage that the end members provide a simple approach to employ non-negativity constraints. A novel approach to end member extraction is used to extract from 14 to 53 factors from synthetic hyperspectral images. It is shown that the eigenvector and end member methods yield similar quantification performance and, as was seen previously, quantification error depends on net analyte signal. Mismatch between the temperature of the spectra used in the estimator and the actual plume temperature was also studied. A simple model used spectra from three different temperatures to interpolate to an “observed” spectrum at the plume temperature. Using synthetic images, it is shown that temperature mismatch generally results in increases in quantification error. However, in some cases it caused an off-set of the model bias that resulted in apparent decreases in quantification error.

Decompositions using maximum signal factors

Maximum autocorrelation factors (MAF) and whitened principal components analysis are gaining popularity as tools for exploratory analysis of hyperspectral images. This paper shows that the two approaches are mathematically identical when signal and noise (clutter) are defined similarly. It also shows that the MAF metaphor can be generalized to encompass a wide variety of signal processing objectives referred to generically as maximum signal factors while retaining the interpretability of principal components analysis. A subspace projection approximation of the data prior to decomposition is also introduced, which reduces computational memory requirements. For the hyperspectral images studied, it was demonstrated to bring more signal of interest into the first factor as compared with the approach that did not use the subspace approximation. Also, it is expected to significantly reduce the number of scores images needed to be inspected during exploratory analysis. Copyright

GENERATION OF A NEW SPECTRAL FORMAT, THE LIFETIME SYNCHRONOUS SPECTRUM (LISS), USING PHASE-RESOLVED FLUORESCENCE SPECTROSCOPY

A new fluorescence spectral format is introduced in which fluorescence lifetime is shown as a function of synchronously scanned wavelength to generate a Lifetime Synchronous Spectrum (LiSS). Lifetimes are determined in the frequency domain with the use of Phase-Resolved Fluorescence Spectroscopy (PRFS) to obtain the phase of the fluorescence signal. Theory and construction of the LiSS are presented and experimental results are shown for solutions of single components and simple binary and ternary mixtures. These results show how the lifetime information in the LiSS augments the steady-state intensity information of a standard synchronous spectrum, providing unique information for identification of components and resolution of overlapping spectral peaks. The LiSS technique takes advantage of noise reduction inherent in the extraction of lifetime from PRFS in addition to standard spectral smoothing techniques. The precision of phase determination through PRFS is found to be comparable to that of direct phase measurements at normal fluorescence intensities and superior for low-intensity signals.