Introduction

This paper is intended to answer some of the questions that frequently arise during the selection and use of Optical Particle Counters (OPCs):

1. What is particle counting efficiency and why should it be 50% at the most sensitive sizing threshold?
2. What is the meaning of OPC resolution and why is it important?
3. How will counting efficiency affect data for actual particle distributions in cleanrooms as compared to data from monosized calibration particles?

Most optical particle counters currently offered use some type of light source to illuminate a sample volume, an optical system to collect the particle-caused light pulse, a means of converting the collected light into an electrical signal, and electronics to determine particle size from the pulse produced. While the specific design varies considerably between manufacturers and between instruments of differing sensitivity and flowrate, the fundamental principles of operation of optical particle counters are quite similar across the industry.

Particle Counting Efficiency

Particle counting efficiency is an expression of the probability that a particle counter will sense and thus count a particle passing through the sample volume. This probability is a function of size up to a certain critical size above which all particles are normally sensed and counted. Figure 1 (download pdf file for all figures) displays three plots of counting efficiency versus particle size. Curve A (the vertical line) shows a counting efficiency curve for a hypothetical OPC with "perfect" sizing resolution, curve B shows the curve for a real-world OPC with "good" resolution, and curve C shows the curve for an OPC with "poor" resolution (Note 1). Note that while the signal produced by the particles is distributed symmetrically about the nominal most sensitive threshold, the exponential relationship between particle size and signal returned causes the counting efficiency curve to be asymmetrical. The discussion of 50% counting efficiency is deferred until after the section on Sensor Resolution because it relies on an understanding of particle counter resolution.

Particle Sensor Resolution

A particle counter's "resolution" is its ability to resolve small differences in particle size. A number of factors combine to cause the resolution of an OPC to be other than perfect. These include the uniformity of illumination of the sampling volume, the quality of the optical system, the quality of the electronics in the Pulse Height Analyzer, and noise due to photon statistics (Note 2).

If it were possible to introduce particles all exactly the same size to a real-world particle counter, the factors above would cause the reported distribution to be the familiar "bell curve" (normal or Gaussian) shape. Figure 2 displays the reported distributions which would result from introducing a group of particles all exactly the same size to OPCs with "perfect", "good" and "poor" resolution.

Note that with perfect resolution, the particle counter would always put each of the particles in the same size class regardless of the width of the size class.

FIGURE 2 (Download this paper for all tables and figures) (293.0 KB)

The resolution described up to this point could be called "fundamental" resolution because it is the best resolution of which the instrument is capable.

Note that the minimum possible width of the OPC size classes or "channels" tends to be determined by the fundamental resolution. Thus a particle counter with "good" resolution can have more size classes across the range of the instrument than a particle counter with "poor" resolution.

The term "instrument resolution" relates to the number of particle size classes selected by the manufacturer to span the size range of the instrument. The minimum possible width of the size classes is limited by the fundamental resolution. The instrument resolution selected for Particle Measuring Systems' particle counters is much more coarse than the fundamental resolution. This is done to simplify use of the instrument and because these instruments are used in applications where high instrument resolution is not required.

Particle Measuring Systems also manufactures a number of Optical Particle Spectrometers with the instrument resolution selected to be near the fundamental resolution. The Laser Aerosol Spectrometer, LAS-X II, has 100 size classes over the range from 0.09 microns to 7.5 microns. The High Sensitivity Laser Aerosol Spectrometer, HSLAS, has 100 size channels over the range from 0.06 microns to 1.0 micron. This spectrometer has 8 size channels coincident with the range of particle sizes spanned in Curve B of Figure 1 ("good" resolution OPC) from 0% to 100% counting efficiency!

Optical Particle Spectrometers are used by Particle Measuring Systems to calibrate the "in-house standard" particle counters that are used to check calibration on production OPCs. Commercially available "monosized" standard particles are used with the OPCs and display a narrow distribution from all not being exactly the same size. The distribution reported by the particle counter is the combination of the distribution contributed by the OPC's resolution (or lack thereof) and the distribution contributed by the standard particles used to calibrate or check resolution. Thus the effect of imperfect resolution is to broaden the reported distribution.

Sensor resolution may be quantified by introducing a sample of standard particles to the OPC. If the variance of the standard particles distribution is VarStd, the variance of the distribution reported by the OPC is VarRpt, and the mean diameter is D, then:

% resolution = (100/D)SQRT(VarRpt - VarStd)

While "% resolution" is a term used in some specifications, you may be more familiar with the synonymous terms "Coefficient of Variation" and "Relative Standard Deviation".

A useful indication of particle counter resolution may be provided by specifying the point where counting efficiency reaches 100%. Since the stated sensitivity defines the particle size at 50% counting efficiency, with the size corresponding to 100% counting efficiency, one can calculate the approximate resolution. For example, Particle Measuring Systems specifies the 100% counting efficiency size at 0.14 microns for both the LASAIR® II - 110 particle counter and MLPC-101-HP particle counter with a sensitivities of 0.1 micron. This corresponds to a resolution of about 10% (Note 3). The particle size corresponding to 0% and 100% counting efficiency is annotated on curves A, B, and C of Figure 1.

There are two factors that affect the apparent sensitivity and resolution of an OPC, but are beyond the control of the designer. The light scattered from a particle follows Mie theory and is a function of the ratio of the refractive index of the particle to the refractive index of the transport media and the size and shape of the particle. Most particle counter are calibrated using polystyrene latex spheres in a transport media of air or water, although some are calibrated in oil. A real-world distribution of particle refractive indices will produce an apparent degradation of resolution, while a change in the refractive index of the transport media will produce an apparent change in sensitivity. Although special calibrations are available for certain combinations of particle and media refractive indices, it is generally considered to be impractical to calibrate each OPC for a specific combination.

50% Particle Counting Efficiency

Having established that real-world particle counters do not have perfect resolution, it may be instructive to examine counting efficiency curve B in Figure 1 from a different perspective. Since the curve is not vertical, it is necessary to specify the point on the curve that corresponds to the nominal sensitivity. The point selected by Particle Measuring Systems and most other manufacturers is the 50% level of counting efficiency.

Before discussing the reasoning underlying the decision to set the most sensitive threshold at the 50% level of counting efficiency, it is important to understand what is referred to as "half count" calibration. Selection of the mean size of a narrow distribution of standard particles at or very near a sizing threshold is a standard procedure in the industry because it facilitates calibration of the particle counter. If a sizing threshold is positioned at the mean size, and the calibration sample is otherwise free of background counts, the counts will be split evenly between the adjacent size classes sharing the threshold as a common boundary. This procedure is referred to as "half count" calibration. A relatively small shift in the sizing threshold under test produces an easily detectable difference in the counts in those adjacent size classes.

Selection of the 50% level of counting efficiency, to specify the most sensitive threshold of a particle counter, produces sizing results at that threshold consistent with the results obtained at the other thresholds. Figure 3 illustrates this by showing a tri-modal distribution of standard particles, with the size corresponding to each mode equal to a particle counter particle sizing threshold. Note that at each of the three thresholds shown, 50% of the standard particles fall below the threshold and 50% fall above. At all thresholds above the most sensitive threshold, 100% of the particles should be sensed and counted, with half of each calibration population falling below its respective threshold and half falling above. The only difference at the most sensitive threshold is that the 50% that fall below are not counted (Note 4).

FIGURE 3 (Download this paper for all tables and figures) (293.0 KB)

Selection of the 50% level of counting minimizes dependence on sensor resolution when selecting the most sensitive threshold. With the use of the 50% level of counting efficiency, variations in resolution result in a different displacement from the nominal threshold for the 0% and 100% counting efficiency points, but do not result in moving the nominal threshold (Figure 1). At any selection other than 50% counting efficiency, a change in resolution results in a change in the nominal threshold. For instance, if the 100% level of counting efficiency were selected, the nominal most sensitive threshold would only be valid for the particle counter on which the selection was made. Differences in optical and electronic components and design differences would result in movement of the actual most sensitive threshold because of a change in resolution. The same logic would apply to any other threshold setting where one is using a half count determination of that threshold.

In addition, selection of the size corresponding to 50% counting efficiency in a particle counter is essential for meaningful comparison of OPC data with higher resolution instruments such as the LAS-X II or the HSLAS II. As you can see from curve B of Figure 1, an OPC with "good" resolution, which counts 100% at 0.14 microns, would count about 95% at 0.12, about 50% at 0.10, etc. The range from 0.10 to 0.14 microns, corresponding to the size difference between 50% and 100% counting efficiency for the "good" resolution particle counter, equates to a sizing error spanning four HSLAS size classes! Thus, the selection of a particle counter's most sensitive threshold at other than 50% counting efficiency will result in significant counting errors relative to data collected by high resolution instruments.

Actual Particle Distributions

Since the discussion up to this point has focused on sampling monosized standard particles, it is reasonable to discuss the effects of counting efficiency on data collected from actual distributions. Most actual distributions are much broader than the distributions of the "monosized" particles, and much broader than the particle size range spanned from 0% to 100% counting efficiency for the particle counters in Figure 1. Since this is the case, the slope of the distribution becomes important in predicting the effect of the counting efficiency of a particle counter on the reported distribution.

In Figure 1 (Download this paper for all tables and figures) (293.0 KB) the particle size range for each OPC corresponding to the most sensitive threshold is illustrated by the shaded area to the left and right of that threshold. Moving from right to left across that range, the particle concentration in many environments increases at a much faster rate than the particle counter counting efficiency decreases. This causes all particle counters with imperfect resolution to tend to overcount in distributions where the concentration increases rapidly with decreasing particle size. Because the "poor" resolution OPC counts a larger fraction of the smaller particles in the relatively higher concentration area than does the "good" resolution particle counter, the "poor" resolution particle counter overcounts at a significantly higher rate. To calculate the expected total difference in counts between the two particle counters, it would be necessary to integrate the product of the concentration and the counting efficiency across the size range from 0% to 100% counting efficiency for both particle counters.

To compensate for the effects of imperfect resolution, final calibration of the particle counters manufactured by Particle Measuring Systemsis done with reference to a "standard" particle counter while both instruments are sampling diluted ambient air.

Summary

When selecting the most sensitive threshold of a particle counter it is important to select the size at which the counting efficiency is 50%. This selection produces results consistent at each threshold and with data from higher resolution instruments. Perhaps most important, when monosized particles are introduced to a particle counter, selection of the mean pulse amplitude to define the threshold setting for the mean size of those particles allows exact definition of that relationship for all OPCs. This is true no matter what the sensor resolution might be and no matter what the relative standard deviation might be for the particles.

(Download this paper with all tables and figures) (293.0 KB)

NOTES

Note 1

Percent resolutions selected to illustrate "good" and "poor" are 10% and 25% respectively.

Note 2

A low signal to noise ratio (S/N) can also produce an apparent degradation of the resolution by allowing artifacts (noise pulses) to be counted as particles. For purposes of this discussion, we will assume that the S/N ratio is adequate to allow us to ignore this factor.

Note 3

Response curves in Figure 1 and the distributions in Figure 2 reflect the effect of resolution of the OPC only (not the resolution of the standard particles). Thus, the variance of the standard particles in the expression for % resolution may be set to 0. The term SQRT (VarRpt - VarStd) may then be reduced to SQRT(VarRpt). This is the standard deviation of the distribution, which would be produced by the OPC if it sampled a group of particles all exactly the same size. This standard deviation may be inferred from the point at which the collection efficiency reaches about 100% in Figure 1. Since 99.994% of the area under a normal distribution is encompassed by a displacement of four standard deviations to either side of the mean, we can state with reasonable accuracy that a displacement of 0.04 microns from a mean size of 0.1 microns is approximately equal to four standard deviations to the right of the mean. Thus:

% resolution = (100/0.1)(0.04/4) = 10%

Note 4

Actually, as discussed in the section on Sensor Resolution, the number is exactly 50% only for the hypothetical OPC with "perfect" resolution.

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Updated 10/97