A review and tutorial discussion of noise and signal-to-noise ratios in analytical spectrometry—III. Multiplicative noises

Abstract

In this review, signal-to-noise ratios are discussed in a tutorial fashion for the case of multiplicative noise. Multiplicative noise is introduced simultaneously with the analyte signal and is therefore much more difficult to reduce than additive noise. The sources of noise, the mathematical representation of noise, and the major types of noises in emission and luminescence spectrometry are discussed. If the limiting source of noise is multiplicative white noise, the signal-to-noise ratio for optimal sampling time τs increases as the square root of the response or integration time of the readout and is independent of the rate at which sample and reference are measured. The variation of multiplicative flicker noise with variation in sampling time, τs, time interval between sample and reference measurements, T, and response (τr) or integration (τi) time is discussed in some detail. The optimal system for the case of multiplicative noise is a dual channel approach in which the sample and reference are measured simultaneously and a ratio of signals is taken. Although the best reference in most cases of interest to analytical chemists is a calibration standard, it is often impossible to measure a sample and a calibration standard simultaneously and so an internal standard, a detector monitoring the source intensity, etc., may be useful.