Improving the signal-to-noise ratio of Faraday cup aerosol electrometer based aerosol instrument calibrations

ABSTRACT

This study introduces a new bipolar measurement routine for particle number concentration calibrations. In the new routine, singly-charged particles of opposite polarities are measured sequentially with a Faraday cup aerosol electrometer (FCAE). We compared the bipolar routine to the traditional FCAE routine, where particle signal and electrometer offset are measured in turns, by calibrating a single CPC on a wide particle number concentration range (from 1000 to 77,000 cm⁻³) with both routines. By increasing the signal-to-noise ratio, the bipolar routine decreases the type A uncertainty of the calibration especially at low particle concentrations. In practice, the new routine enables shortening the measurement times by 80% at the lowest particle concentrations which, in practice, corresponds to hours.

Copyright © 2016 American Association for Aerosol Research

EDITOR:

• Peter H. McMurry

1. Introduction

On a global scale, ambient particulate matter annually causes millions of deaths (Lim et al. 2012). At the moment, air quality monitoring relies on particle mass concentration measurements next to surveillance of the concentrations of gaseous species (e.g., NO_x, CO₂, O₃). However, while ultrafine aerosol particles (D_p < 100 nm) contribute negligibly to particle mass concentration (Kittelson 1998), at the same time they cause numerous severe health problems (Pope et al. 1995; Ibald-Mulli et al. 2004; Pöschl 2005). Other metrics, such as Particle Number (PN) and surface area concentrations are measured aside the particle mass, for instance, in order to evaluate the health effects of aerosols.

Particle number concentration is also important in many industrial applications, such as in clean room facilities (ISO 14644–12) and in the vehicle particulate matter (PM) emission control (European Commission 2008). Both in ambient air quality monitoring and in vehicle PM emission measurements, PN is measured using Condensation Particle Counters (CPCs, e.g., Agarwal and Sem 1980). In the latter application, the CPCs are subject to annual calibrations where the detection efficiency of the CPC is determined (Giechaskiel et al. 2009).

Liu and Pui (1974) introduced a method to primary number concentration calibrations by using an aerosol electrometer (AE) as a number concentration reference and a differential mobility analyzer (DMA; Knutson and Whitby 1975) as a source of monomobile particles (i.e., particles of the same electrical mobility). Even today, this technique is the most commonly applied calibration method in the submicrometer particle size range, and it is applied for calibration purposes by several metrology institutes (Högström et al. 2014). In terms of number concentration, this calibration method is usually limited to concentrations larger than 1000 particles/cm³ which corresponds to ∼2.7 fA electric current at 1 L/min AE inlet flow rate. On one hand, this is due to the uncertainty of the AE calibration factor and, on the other hand, due to prolonged measurement times, required for eliminating the effect of random electrical noise and fluctuations in the input number concentration.

In a traditional measurement routine, successive measurements of zero and nonzero calibration concentration are repeated several times (Högström et al. 2011; Sakurai and Ehara 2011). With this routine, the data averaging time required for the elimination of random noise of the AE and the fluctuations of the applied particle generator can be several hours. Recent developments in the measurement techniques of small electric currents will in the near future enable decreasing the type B uncertainty of the electric current measurement by orders of magnitude (Drung et al. 2015). Applying these high-accuracy instruments in AE measurements would lower the type B (i.e., instrument-origin) uncertainty, thus increasing the impact of the type A uncertainty which is estimated by statistical methods.

In this study, we introduce a bipolar measurement routine for the aerosol instrument calibrations, applicable to the plateau region. This routine is a common practice, for example, in electrometer calibrations but has not been applied in aerosol measurements. The new routine is described and tested experimentally, and the results are compared with the results obtained using the traditional measurement routine. Although the routine could be tested computationally, an experimental approach was preferred to find out the practical effect in aerosol instrument calibrations.

2. FCAE-based measurement procedures and related uncertainties

The electric current measured by an electrometer is a sum of two components, namely, the signal induced by some outer source (charged particles in aerosol measurements) and the offset signal (I₀) induced, among others, by disturbances in the electrometer itself (Keithley Instruments 2004). Typically, the offset of an electrometer is a nonzero value between ±5 fA (Jarret and Owen 2013). The offset is sensitive to measurement conditions (e.g., temperature, humidity) and might drift if the conditions are unstable. The offset signal level affects all measured signals. Figure 1 illustrates how a shift in the offset level correspondingly transfers into the output signals I_p and I_n. The subscripts p and n, respectively, refer to positive and negative polarities. Although the change in the offset level alters the absolute signals (AS), the difference between any two signals (DS) stays the same if particle concentration remains stable.

Figure 1. An illustration of the electrometer signal measurement. A shift in the offset signal (I₀) changes the particle signal (subscript p for positive and n for negative polarity) also, but the difference between any two signals remains unchanged.

2.1. Unipolar measurement routine

In FCAE-based measurements, the offset and the particle signal are traditionally measured sequentially. In this article, this is called the unipolar measurement routine. Experimental data of a parallel FCAE and CPC measurement conducted with the unipolar routine is shown in Figures 2a and b, respectively. In one measurement cycle, the offset is recorded for 1 min before and after the particle signal which is also measured for 1 min. The mean value of each 1-min measurement is calculated by averaging the last 30 s, as indicated by arrows. Each measurement cycle, i, yields one corrected current value, ΔI_i, which in the unipolar routine is determined with Equation (1[1] )

Figure 2. FCAE current and CPC concentration in the unipolar (a and b) and bipolar (c and d) measurement cycle extracted from actual measurement data. Subscripts p and n represent electric signals induced by particles with positive and negative charge, respectively.

[1] where the subscript n refers to particle signal measurement conducted with charged particles and subscript 0 to offset measurement. The FCAE concentration of a cycle is derived according to Equation (2[2] ) [2] where Q is the volumetric flow rate (cm³/s) through the Faraday cup (FCUP), n the number of charges per particle, e elementary charge, γ calibration factor of the electrometer and η_FCUP the detection efficiency of the FCUP.

In addition to monitoring the offset level, the routine enables checking the CPC zero reading (i.e., whether the CPC count drops to zero when particle-free gas is measured). However, if the zero reading is in order, the offset measurement gives no extra information of the CPC performance, thus consuming valuable measurement time.

2.2. Bipolar measurement routine

Here we introduce a bipolar measurement routine where singly-charged particles of opposite polarity and equal concentration are measured in turns. To apply the technique in aerosol instrument calibrations, the magnitude of the absolute signals (i.e., the PN concentration) should remain constant regardless of the polarity of the particle charge. Thus, the difference between the two signals is double compared to the unipolar routine leading to increased signal-to-noise ratio (S/N ratio).

Subplots c and d in Figure 2 show, respectively, the FCAE current and the corresponding CPC concentration in a measurement cycle conducted with the bipolar routine. Now, the particle concentration is nearly continuously measured—the concentration shortly drops only as the particle polarity is switched. The corrected current of a cycle in the bipolar routine is determined with Equation (3[3] ) [3] where the mean value of two negative particle signals, i.e., one before (I_n,i) and one after (I_n,i+1) positive particle signal measurement, is subtracted from the current induced by the positively charged particles (I_p,i). This ensures that the possible changes in the offset level are taken into account in the same time interval as in the unipolar routine. The difference between negative and positive particle signals must be divided by the factor of two in order to determine the FCAE concentration without doubling the number of particles.

Since three consecutive particle signal measurements (I_n,i, I_p,i, I_n,i+1) are used to determine the corrected current of a measurement cycle, the corresponding CPC concentration is also determined by using three consecutive concentration mean values according to Equation (4[4] ) [4]

Although the concentration of the CPC could be determined in a simpler way, the presented equation is preferred in order to determine the concentration of the CPC and the FCAE in a similar way (compare Equations (3[3] ) and (4[4] )).

2.3. Type A uncertainty of a corrected current value in a single measurement cycle

The standard uncertainty of a single corrected current value obtained from one measurement cycle can be estimated with Equation (5[5] ) (JCGM 2008) [5] where x_i are variables from which the corrected current is determined from (x_i = I_n,i, I_0,i, I_0,i+1 for unipolar case and x_i = I_n,i, I_n,i+1, I_p,i for bipolar case) and u(x_i) the standard uncertainty of the component x_i. Thus, the standard uncertainty of a single corrected current value in the unipolar routine is [6] and in the bipolar routine [7]

If the standard uncertainties of each current component are, for simplicity, assumed to be the same (i.e., u(I_n,i) = u(I_0,i) = u(I_p,i) etc.), comparing the standard uncertainties of the cycles obtained with the two routines shows that the bipolar measurement routine can, in theory, decrease the standard uncertainty of a corrected current value by a factor of two compared to the unipolar routine. [8]

In addition to theoretical calculations, we applied the presented uncertainty analysis to experimental data where each measurement comprised of 15 repeated measurement cycles. The standard uncertainty of each particle/offset measurement was calculated from the experimental standard deviation of the current values from which the mean values are calculated. The standard uncertainty and relative standard uncertainty (u(ΔI_i) /ΔI_i) of each cycle was determined individually. The mean values for three concentration levels in the unipolar and bipolar case are shown in Table 1. All results are given as standard uncertainties (coverage factor k = 1). The results indicate that the bipolar measurement routine does, in practice, decrease the relative uncertainty of a single measurement cycle approximately by a factor of two as proposed by the approximation in Equation (8[8] ).

Table 1. Comparison between the standard uncertainties and relative standard uncertainties (k = 1) of single measurement cycles obtained by unipolar and bipolar measurement routines. The presented values are mean values of the results calculated for 15 measurement cycles.

	CFCAE (cm^−3)	u(ΔI) (fA)	u(ΔI)/ΔI (%)
Unipolar	950	0.0738	3.0
Bipolar		0.0418	1.17
Unipolar	18,800	0.1366	0.27
Bipolar		0.0842	0.16
Unipolar	76,900	0.2288	0.11
Bipolar		0.1370	0.067

3. Experimental

The detection efficiency values and associated uncertainty values of a single CPC were determined for six PN concentrations ranging from 1000 to 77 000 cm⁻³ with both unipolar and bipolar measurement routines. The measurements were conducted with the setup presented in Figure 3. The aerosol was generated with the Single Charge Aerosol Reference (SCAR) where singly-charged particles are selected from a primary nanoaerosol (GMD∼12 nm) with a DMA (Model 3085, TSI Inc., Shoreview, MN, USA) and then grown to a desired size range (here 170 nm) by condensational growth. A detailed description of the operation of the SCAR may be found in Yli-Ojanperä et al. (2010). The aerosol flow was divided to the FCAE, the CPC under calibration (A20, Airmodus) and an SMPS (DMA 3071A + CPC 3775, TSI Inc.). The number size distribution of the aerosol was measured with the SMPS before each calibration point to ensure the size distribution of the aerosol remained unchanged.

Figure 3. Measurement setup.

In order to generate particles of both polarities, the unipolar DC power supply normally connected to the DMA of the SCAR was replaced with a bipolar DC power supply (FuG Elektronik GmbH). Thus, switching the polarity of the DMA from negative to positive enabled changing the polarity of the generated particles in seconds. In the CPC calibration the objective is to determine the detection efficiency of the CPC at constant concentration levels. Since the charging probability of a bipolar charger depends on the polarity, equal concentrations of both particle polarities were generated by selecting slightly different primary particle sizes for opposite particle polarities. Once the concentration for negatively charged particles was known, the SCAR DMA voltage for positively charged particles was adjusted in order to generate the same output concentration as for the negatively charged particles. The CPC under calibration was used to monitor the concentrations. The primary particles were grown in the same conditions to about 170 nm, resulting to practically identical size distributions (see online supplementary information [SI], Figure S1).

With both routines, the measurements comprised of 15 repeated measurement cycles. For each cycle, the detection efficiency of the CPC was determined as the ratio between the CPC and FCAE concentrations. The type A uncertainty was determined from the experimental standard deviation of the detection efficiency values whereas the type B uncertainty was estimated based on instrument specifications, calibration data and earlier studies (Högström et al. 2011). It should be noted that the type B uncertainty depends on the electrometer calibration factor which is here assumed to be the same for both routines. A detailed description of the data and uncertainty analysis is given in the SI.

4. Results and discussion

Figure 4 shows the type A uncertainty of the CPC detection efficiency as a function of measurement cycles at three measured concentrations (950 cm⁻³, 18,800 cm⁻³ and 76,900 cm⁻³). The results obtained by the unipolar measurement routine are plotted with grey symbols and the results obtained by the bipolar routine are plotted with black symbols. The horizontal lines present the type B uncertainty levels. The numerical values of the type B, type A and overall expanded uncertainties of the CPC detection efficiency for all measured concentrations after the 31-min long measurement are shown in Table 2.

Figure 4. Type A uncertainty (coverage factor k = 2) of the CPC detection efficiency with respect to the number of measurement cycles.

Table 2. Type B (k = 1), type A (k = 1) and overall expanded uncertainties (k = 2) of the CPC detection efficiency, determined by both uni- and bipolar measurement routines (measurement time 31 min, i.e., 15 measurement cycles).

		Type A uncertainty (k = 1)		Overall uncertainty (k = 2)
CFCAE (cm^−3)	Type B uncertainty (k = 1)	Unipolar	Bipolar	Unipolar	Bipolar
950	2.33E-04	4.80E-02	2.14E-02	1.01E-01	5.25E-02
2,300	1.24E-04	3.46E-02	1.21E-02	7.28E-02	3.28E-02
5,500	5.89E-05	8.60E-03	6.49E-03	2.30E-02	2.01E-02
18,800	2.43E-05	4.42E-03	2.57E-03	1.32E-02	1.11E-02
49,800	2.41E-05	1.52E-03	1.34E-03	1.03E-02	1.02E-02
76,900	2.41E-05	1.42E-03	1.06E-03	1.02E-02	1.00E-02

The type A uncertainty decreases with increasing concentration due to increasing S/N-ratio in the FCAE measurement. The type B uncertainty is constant with time but depends on the level of the measured electric current and, therefore, also decreases with increasing concentration. The bipolar measurement routine yields a lower type A uncertainty than the unipolar routine at every concentration level. The greatest impact can be seen at low particle concentrations where the S/N-ratio is small. For example, at the lowest measured concentration level, the type A uncertainty is two times bigger in the unipolar routine than in the bipolar routine. By comparing the type A and type B uncertainties, it can be seen that at low concentrations (below 10,000 cm⁻³) the type A uncertainty is the dominating uncertainty component. For instance, the type A uncertainty of the lowest concentration does not reach the type B uncertainty level in Figure 4. At higher concentrations, on the contrary, the type A uncertainty quickly goes below the type B uncertainty with the bipolar measurement routine. Thus, the type B uncertainty is the dominating uncertainty component at high particle concentrations.

The measurement times required for the type A uncertainty to reach the type B uncertainty level are compared in Figure 5 between the two measurement routines. For those concentrations where the type A uncertainty did not reach the type B uncertainty level during the measurement, the measurement times were calculated computationally by increasing the amount of measurement cycles while the standard deviation of the detection efficiency was assumed to be the same as in the 31-min measurement. In Figure 5, the sudden step in the measurement time at low concentration with unipolar routine appears for two reasons. Firstly, the measurement time does not depend linearly on particle concentration. This can also be seen in Figure 4 where at low particle concentrations the type A uncertainty stays above the type B uncertainty whereas at high concentration, regardless of the measurement routine, the type B uncertainty level is quickly reached. Secondly, the type B uncertainty decreases stepwise with increasing concentration (see Table 2).

The bipolar measurement routine requires a significantly shorter measurement time than the unipolar routine at low concentration levels—at the best case, the measurement time shortens by hours. In conclusion, the bipolar measurement routine is clearly superior to the unipolar routine at low particle concentration in the plateau region. However, it should be noted that if a size-dependent region, such as the lower detection limit of a CPC, were calibrated, it is not possible to accurately determine both concentration and particle size with the bipolar routine at low particle sizes (∼10 nm). In this case, the unipolar routine would be applied in the measurement.

5. Summary

A new FCAE-based measurement routine was introduced and experimentally tested. In the new routine, singly-charged particles of opposite polarity and equal concentration are measured sequentially whereas traditional FCAE-based measurements are conducted by measuring particle signal and electrometer offset in turns. The bipolar measurement routine has several advantages compared to the unipolar routine. Firstly, it enables measuring particle concentration nearly continuously which enables shortening the measurement time of the calibration. According to our results, the measurement times may be cut down by hours at the lowest particle concentration levels by applying the bipolar routine. Secondly, the bipolar routine increases the S/N ratio of the FCAE measurement, thus decreasing the type A uncertainty of the measurement. Since the measurement techniques of low currents are improving, the type B uncertainty can be expected to decrease significantly in the near future. In this case, lowering the type A uncertainty becomes more and more relevant also at high particle concentrations. From low to moderate particle concentration levels, where the type A uncertainty is the dominating uncertainty component, the bipolar measurement routine already enables decreasing the overall uncertainty which, in the end, increases the accuracy of the CPC calibration.

Funding

This work was financially supported by the Graduate School of Tampere University of Technology. The Finnish Foundation for Technology Promotion (Tekniikan edistämissäätiö) is also acknowledged for financial support.

Notes

¹ The type B uncertainty depends on the electrometer calibration coefficient that is determined only to certain electric currents. Therefore, the type B uncertainty decreases stepwise with increasing concentration. It should also be noted that the decrease is nonlinear.

² Although the overall uncertainty decreases even after the type A uncertainty reaches the type B uncertainty level, the point where the two uncertainty components are equal was chosen, for convenience, to represent the optimal duration of the measurement.

Figure 5. Required measurement time for the type A uncertainty to reach the type B uncertainty level as a function of particle number concentration. Note that the type B uncertainty decreases stepwise with increasing concentration.