Optimizing Sensitivity: True Counts Versus Background Counts for Low Concentration Measurements

Optical particle counters usually offer the option to measure smaller particles at the cost of increased background (electronic noise) counts. This can be done by adjusting the threshold d* of the counter, or a set of thresholds, or the sensitivity. We explore the trade-off between more true counts, T(d*), at a lower particle size threshold vs. more false counts, F(d*), at the lower threshold. Amplification or thresholds may be adjusted or, more simply, some channels of a multichannel instrument used while others are ignored. If no correction for mean false count rate is to be made and if the false count increases monotonically as the threshold decreases (dF/dd* < 0) and increases more rapidly than the true count (dF/dd* < dT/dd* < 0) and if we wish to limit F to a fraction of T, F ≤ kT, then measurement of lower T concentrations, in the size range near the threshold, requires raising, not lowering, the threshold. Data on false counts (measuring clean air) from an optical particle counter are presented and compared with counts expected from a power-law particle size distribution assumed for cleanroom aerosols in U.S. Federal Standard 209D (U.S. GSA, 1988). The results indicated the cumulative false count was approximately proportional to the inverse of the cube of the threshold diameter. This is a stronger dependence on threshold size than is the Federal Standard 209 particle size distribution, a plausible T(d*). It was decided to raise the threshold of the optical particle counter's smallest sizing channel, which did improve the ratio of signal to noise. If a correction for the mean false count rate, E(F), is to be subtracted from the total count, C, data to get a corrected count, C* = C - E(F), and if the criterion for selecting the optimal threshold is to minimize standard deviation of C* divided by the mean of C*, it is shown that where C and T are Poisson variables, often a good approximation, the optimal d* is where dln(C*)/dd* = 2d ln(T)/dd*.