Error Analysis of Simple Algorithms for Determining Fluorescence Lifetimes in Ultradilute Dye Solutions

Abstract

We have evaluated the use of two simple algorithms for determining the decay parameters describing a single exponential process for dyes with nanosecond and subnanosecond fluorescence lifetimes in the limit of low concentrations and high backgrounds from scattered photons generated by the solvent using experimental and Monte Carlo simulation results. These algorithms, the maximum likelihood estimator (MLE) and the rapid lifetime determination (RLD), are computationally easy to perform, allowing the evaluation of large amounts of data quickly and efficiently. The MLE and RLD methods were used to calculate the fluorescence lifetimes of three near-IR dyes with lifetimes spanning the range of 0.57 ns to 1.12 ns. For low-concentration conditions and high background-to-fluorescence ratios, the MLE method resulted in larger errors when compared to RLD, although both methods yielded comparable standard deviations. However, when the interval over which the lifetime was calculated within the decay profile was shifted to latter times in order to reduce the amount of scattered photons included in the calculation, significant improvements in the accuracy were observed with the use of MLE. Shifting the start channel of the calculation to latter time channels within the decay profile did not affect the lifetime with the use of RLD. Inclusion of large amounts of scattering photons was found to bias the calculated lifetime to lower values, reducing the accuracy of the determination. The relative standard deviations for MLE and RLD were found to be approximately 2–3% at a background-to-fluorescence ratio of 0.5. The absolute relative error in the methods at the 0.50 background-to-fluorescence ratio ranged from 14 to 27% for MLE and 8 to 18% for the RLD method when the calculation was initiated at t = 0. This error was found to decrease to < 1% with the use of MLE when the calculation was initiated at t ≈ 100 ps.