Fast algorithms for the analysis of single and double exponential decay curves with a background term. Application to time‐resolved imaging microscopy

Computer programs have been developed to determine decay time constants from a temporal sequence of digitized images with decaying intensities characterized by either single or double exponentials plus a constant background term. The very fast algorithms are evaluated at every pixel position. A non-iterative Prony-like method provides high quality initial estimates that are used for the subsequent non-linear least-squares procedure in which the normal equations are solved directly. Error analysis routines enable a pixel-by-pixel estimation of the quality of the experimental data. The stand-alone programs were fully integrated into a commercial image-processing environment (SCIL-Image) for a convenient and optimal display of the decay analysis. The features of the programs are illustrated by the analysis of simulated image data. With current workstations, the fitting routines (including reading of data, initial estimate and error analysis) require 0.13 ms/pixel using the single exponential algorithm applied to 50 time points, and 1.37 ms/pixel for 100 time points and the double exponential algorithm. The programs are of general applicability and have been used to analyse data from time-resolved fluorescence, phosphorescence, and photobleaching-based microscopy. Two examples of the latter case are shown, illustrating the utility of the programs for the quantitative evaluation of spatially resolved fluorescence resonance energy transfer (FRET) and for generating contrast by allocating specific cellular structures to particular decay components in a fluorescence image.