3.1.1 Determination of efficiencies for optical particle detection and particle mass measurements

Knowing the particle beam properties at the PDUs, the ablation spot, and the vaporizer is essential for interpreting and evaluating measured data. For proper detection of the sampled particles, a sufficient overlap of the particle beam with the laser beams and the vaporizer is required. The optical particle detection efficiency of the PDUs was determined by comparison of count rates of the individual detection units (PDU1 and PDU2) with those of either a condensation particle counter (CPC) or an optical particle counter (OPC) as the reference device (see Sect. S3 in the Supplement). In this way, the particle numbers or, indirectly, the mass concentrations measured by the ERICA-AMS can be associated with the number concentration of the sample airflow. The measured polystyrene latex (PSL) particle sizes and the respective measurement setups are shown in Sect. S3 in the Supplement.

To determine the size-dependent and ADL-position-dependent optical detection efficiency DE_PDU at the detection units with PSL particles (see Table S5 in the Supplement), the ADL was tilted in steps and DE_PDU was measured at different ADL positions x_pos while the position of the detection laser was kept constant. Hereafter, this procedure is referred to as the “ADL position scan”. This approach, which is similar to the method reported by, e.g., Marsden et al. (2016) and Clemen et al. (2020), is described by Molleker et al. (2020). DE_PDU was determined for each lens position x_pos according to Eq. (1).

Here, ${\stackrel{\mathrm{‾}}{\mathrm{cts}}}_{\mathrm{Det}}$ is the averaged value of the number of particles per second counted by each PDU over 30 s, Φ_ERICA is the volume flow into the ERICA, and ${\stackrel{\mathrm{‾}}{c}}_{\mathrm{ref}}$ is the value of the number of particles per volume unit averaged over 30 s at the reference device. A typical result of an ADL position scan for PSL particles at PDU1 and PDU2 is shown in the Supplement (Sect. S5.4, Fig. S13). The curve fit to the ADL position scan can be described as a convolution integral of a rectangular top-hat function of the effective detection laser width 2r_eff,L, since the scattered light is only detected above a certain intensity threshold, and a 2-D Gaussian distribution function representing the particle beam cross section. The effective laser beam radius r_eff,L is the laser beam radius wherein a particle is registered. The convolution is described by Eq. (2) according to Molleker et al. (2020):

The variable σ is a measure for the particle beam width, i.e., the particle beam radius, and x₀ corresponds to the value of x_pos at the peak value. This x₀ value is also called the modal value of the ADL position scan. The parameter A_scan is a scaling parameter of the peak value of the ADL position scan and accounts for losses, e.g., ADL transmission efficiency values smaller than unity. Equation (2) is used as a curve-fit function for determining the values of the parameters r_eff,L, x₀, σ, and A_scan. A plateau, such as the one shown in Fig. S13a in the Supplement, indicates a narrow particle beam with respect to the effective laser width for the respective measurement.

For the measurements of particles with sizes from 218 to 834 nm, it was assumed that the particle losses between PDU1 and PDU2 are negligible. Therefore, the curve fitting for both detection units was performed simultaneously for each particle size with both data sets (PDU1 and PDU2) by a comprehensive analysis, which allows us to combine two data sets into one single common curve-fitting procedure. In the following, this procedure is referred to as “combined curve fitting”. During this combined curve-fitting procedure, the variable A_scan was linked for both PDUs by determining one A_scan value for PDU1 and PDU2 simultaneously. Thus, only one value for A_scan per measured particle size was obtained.

For the evaluation of the measurement with PSL particles of 108 nm in size, a different approach was chosen because losses between PDU1 and PDU2 seemed reasonable due to the particle beam divergence (Huffman et al., 2005). Therefore, the evaluation was carried out without the combined curve-fitting procedure and, thus, individually for the measurements at PDU1 and PDU2. Due to the mathematical relation between the variables r_eff,L and A_scan during the curve fitting, it was not possible to determine both variables at the same time. Therefore, r_eff,L was calculated separately and kept constant during the curve fitting. Considering the size dependence of the scattered light intensity based on Mie scattering, $r_{\mathrm{eff},\mathrm{L},\mathrm{108}\mathrm{nm}}$ was estimated for the measurement with PSL particles of a size of 108 nm, adopting suitable software routines following Bohren and Huffman (1998). The value of $r_{\mathrm{eff},\mathrm{L},\mathrm{218}\mathrm{nm}}$, determined for the measurements of particles with sizes of 218 nm, was used as base for the estimation. The result of the calculations showed that a particle of 108 nm scatters the same amount of light as a particle of 218 nm, when it is closer to the focus by a factor of 0.955. Thus, $r_{\mathrm{eff},\mathrm{L},\mathrm{108}\mathrm{nm}}=\mathrm{0.955}\cdot r_{\mathrm{eff},\mathrm{L},\mathrm{218}\mathrm{nm}}$ was used as a curve-fit constant for the evaluation of the measurement with PSL particles of 108 nm (see Sect. S5.1.1 in the Supplement). Since this calculation is based on a Gaussian laser beam profile, it can only be seen as an approximation and especially since the outer parts of the laser beam might deviate from a Gaussian profile due to diffraction and reflection in the laser beam setup.

In addition to the particle detection efficiency for PSL particles, the optical particle detection efficiencies of particle counting at both PDUs were determined according to Eq. (1) for ammonium nitrate (AN) particles between 91 and 814 nm in size (see Sect. S3 in the Supplement). Besides the singly charged, the doubly charged particles have to be considered when using a differential mobility analyzer (DMA) for size selection out of a polydisperse aerosol. For this, a newly developed, iterative method was adopted and is described in detail in Sect. S5.2 in the Supplement. Briefly, the curve-fit function of Eq. (2) was extended by a second term for the doubly charged particles and two weighing factors to account for the fractions of the particle charges (see Eq. S15 in the Supplement). As for the measurements with PSL particles, the parameters r_eff,L, σ, x₀, and A_scan could be determined by a combined curve-fitting procedure (for exceptions see Sect. S5.2 in the Supplement).

Simultaneously to the measurements with AN particles at the detection units PDU1 and PDU2 of the ERICA-LAMS, the mean mass concentration of AN was measured with the ERICA-AMS, similarly to the approach described in Liu et al. (2007). The efficiency with which particle mass concentrations were measured with the ERICA-AMS was determined. While this quantity is equivalent to the “collection efficiency” (CE; e.g., Canagaratna et al., 2007; Matthew et al., 2008; Drewnick et al., 2015) in AMS measurements, we define it as “particle mass detection efficiency” for consistency with the ERICA-LAMS discussion. As a reference, we used the CPC to obtain the mean particle number concentration and calculated the input mass concentration. The curve-fitting evaluation method applied afterwards also accounts for the doubly charged particle fraction and is described in detail in Sect. S5.2 in the Supplement. By the curve-fitting procedure, the parameters r_eff,V (effective vaporizer radius), σ, x₀, and A_scan could be determined (see Sect. S5.2 in the Supplement for definitions and exceptions). All these parameters, r_eff,L, r_eff,V, σ, x₀, and A_scan, are essential for adjustment procedures of the instrument and to interpret the obtained laboratory and field mass spectra. Furthermore, the determined parameters are used in Sect. 3.1.2 to characterize the particle beam and in Sect. 3.2.2 and 3.3.2 to determine the optical particle detection efficiency and the particle mass detection efficiency, respectively.

Overall, the parameters serve as a means for the evaluation of the performance of the instrument.

3.1.2 Particle beam properties

The parameters r_eff,L, r_eff,V, σ, x₀, and A_scan were determined by the curve-fitting functions (Eqs. 2 and S15 and S17 in the Supplement) and are thus in the dimension relative to the ADL position x_pos as read out on the micrometer adjustment screw (see Sect. S1.3 in the Supplement). Below, the parameters were rescaled, using the intercept theorem, to the dimension of the particle beam at the specific position (PDU1, PDU2, ablation spot, and ERICA-AMS vaporizer).

Figure 3The particle beam diameter w_part ($\mathrm{1}/\sqrt{e}$ diameter) as a function of particle size d_va for PSL (squares) and AN (circles) particles measured at the detection units PDU1 (red, left ordinate) and PDU2 (blue, left ordinate) and for AN particles measured at the ERICA-AMS vaporizer (right ordinate, black). The reference values for number concentrations were obtained from the experimental setup with either the CPC or the OPC (Setup B or Setup C, respectively; see Fig. S8 in the Supplement). The AN particle beam diameter at the ablation spot (brown triangles, left ordinate) and the ERICA-AMS vaporizer (green triangles, right ordinate) were calculated by extrapolation of the measurement at PDU2. The uncertainty in PSL particle size is given by NIST certificates and converted to d_va. The uncertainty in AN particle size d_va is estimated to be 3 % (Hings, 2006). These uncertainties for PSL and AN particle sizes are the same for Figs. 3 to 7 and 12. The uncertainties in the particle beam diameters result from the curve fittings (1 standard deviation).

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The curve fittings yield the standard deviation σ, which is proportional to the particle beam $\frac{\mathrm{1}}{\sqrt{e}}$ radius at each detector (PDU or vaporizer). The particle beam diameter w_part is defined as 2σ, i.e., the $\frac{\mathrm{1}}{\sqrt{e}}$ diameter of the Gaussian distribution function. In Fig. 3, w_part is displayed as a function of the particle size d_va at various locations within the instrument. The particle beam diameter w_part is approximately 0.1 mm at PDU1 and 0.2 mm at PDU2 for particle sizes above 400 nm. For PSL particles of 108 nm in size, the w_part values are 5 times (7 times) wider at PDU1 (PDU2). The measurements with the OPC for larger diameters indicate a trend for w_part from 0.10 to 0.18 mm. For AN particles of 335 nm in size, a minimum of w_part was found, as the corresponding values for w_part at PDU1 and PDU2 are 0.04 and 0.03 mm, respectively. At the vaporizer, the largest value for w_part of 2.2 mm was measured for AN particles of 91 nm in size, which is narrower than the width of the vaporizers' physical cross-sectional diameter of 3.8 mm. Thus, by adjusting the ADL properly, all investigated AN particles larger than 91 nm can be collected by the vaporizer. The overall curve shapes at each PDU depict a “V”, where the smaller and the larger particles show a larger w_part than particles of 335 nm in size. Smaller particles can be deflected by collisions with residual gas molecules, and larger particles are over-focused by the ADL due to their inertia (Zhang et al., 2002; Peck et al., 2016). Considering the geometry of the instrument, w_part at the ablation spot and at the ERICA-AMS vaporizer can also be extrapolated from the respective w_part for AN at PDU2. The longer travel distance for the particles and the particle beam divergence (Huffman et al., 2005) result in a 3.3-fold-broader w_part for AN particles at the vaporizer than at PDU2. The calculation yields a maximum w_part of 0.48 mm at the ablation spot, a value which is approximately 2 times the ablation laser beam diameter w_0,dia (see overlap parameter determination below in this section), and w_part of 1.07 mm at the vaporizer (both for AN particles of 548 nm in size).

In the following, the overlap of the particle beam with the detection laser focus is discussed. Considering an optical laser beam diameter w_0,dia of 60 µm of the PDUs (see Sect. 3.2.1), the particle beam diameter w_part is wider by a factor of 2 to 3 (PSL, d_va > 400 nm). However, the laser intensity of a Gaussian beam provides intensities larger than zero also for radial distances above w₀ and the scattered light might be sufficient for particles to be detected. The maximum distance from the laser axis where particles can be detected is represented by the parameter r_eff,L and not w₀. Figure 4 shows the effective laser beam radii r_eff,L and r_eff,V as a function of the particle size d_va. Overall, for PSL particles, r_eff,L is between 0.1 and 0.4 mm. The shape of the curve of the effective laser beam radius depends on the response function of the scattered light intensity as a function of size, where an increase to larger sizes is expected. For the measurements with PSL particles of 108 nm and AN particles of 91 and 138 nm in size, this is inevitable since the values of r_eff are calculated based on the Mie scattering according to a rough estimation (see Sect. S5.1 in the Supplement). For larger particles or the measurements with the OPC as the reference device, an increase in r_eff,L with particle size would be expected. Due to the fact that the OPC measurements were performed with various PMT threshold values (see Sect. S3 in the Supplement), r_eff,L appears lower than the CPC reference measurements, and thus, r_eff,L for particle sizes above 834 nm is underestimated in Fig. 4. The AN measurement results do not agree with the results of the measurements with PSL particles, possibly due to a different refractive index of AN as compared to that of PSL. The vaporizer width determined by the ADL position scans, i.e., r_eff,V, agrees with the vaporizer's physical dimension of a 1.9 mm radius.

Figure 4The effective detection laser radius r_eff,L as a function of particle size d_va determined for PDU1 (red, left ordinate) and PDU2 (blue, left ordinate) with PSL (squares) and AN (circles) particles and the effective vaporizer radius r_eff,V as a function of particle size d_va for the ERICA-AMS vaporizer (right ordinate, black) determined with AN particles. CPC and OPC measurements are as for Fig. 3. The physical vaporizer radius is marked by a dashed gray line. The uncertainties in the effective radii result from the curve fittings (1 standard deviation). The uncertainty in r_eff,L for the PSL measurement with particle size of 108 nm was estimated to be 0.002 mm (PDU1) and 0.004 mm (PDU2), and the uncertainties in r_eff,L for the AN measurements with particle sizes of 138 and 91 nm are conservatively estimated to be 0.009 mm at PDU1 and 0.014 mm at PDU2. These values are the approximated maximum uncertainties in r_eff,L in the considered size range of 213 to 814 nm at PDU1 and PDU2. For the measurement with AN particles of 91 nm in diameter, the uncertainty in r_eff,V was estimated to be 0.08 mm.

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Figure 5The overlap parameters S_detect,L, S_detect,V, and S_ablation as a function of particle size d_va for PSL (squares) and AN (circles) particles. S_detect,L was determined for PSL and AN particles at PDU1 (red) and PDU2 (blue). S_detect,V was determined for AN particles at the ERICA-AMS vaporizer (black). S_ablation was calculated for AN particles at the laser ablation spot (brown). CPC and OPC measurements are as for Fig. 3. The horizontal dashed gray line illustrates where the ratio equals 1. The uncertainties in S_detect,L, S_detect,V, and S_ablation result from the curve-fitting values (1 standard deviation).

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To determine the overlap of the particle beam with the detection laser beam, the particle beam diameter w_part is compared to the effective laser diameter $d_{\mathrm{eff},\mathrm{L}}=\mathrm{2}{r}_{\mathrm{eff},\mathrm{L}}$. Therefore, the overlap parameter $S_{\mathrm{detect},\mathrm{L}}=w_{\mathrm{part}}/d_{\mathrm{eff},\mathrm{L}}$ was calculated for different particle sizes at the PDUs as the maximum possible overlap of w_part and d_eff,L for each measurement at lens position x_pos=x₀. The parameter $S_{\mathrm{detect},\mathrm{V}}=w_{\mathrm{part}}/d_{\mathrm{eff},\mathrm{V}}$ (with $d_{\mathrm{eff},\mathrm{V}}=\mathrm{2}{r}_{\mathrm{eff},\mathrm{V}}$) expresses the overlap of the particle beam with the effective vaporizer width. Both are shown in Fig. 5. The horizontal gray line marks an overlap parameter of 1. All investigated particle sizes below that line are detected sufficiently well within 1σ of the particle beam width. That is the case, within their uncertainties, for all measurements except for PSL particles of 108 nm in size. The reason for this is a large w_part for the smallest particles resulting from a large particle divergence caused by the small particle inertia for this size (Zhang et al., 2002). The values of S_detect,L of the measurements with the OPC are overestimated, since the resulting values of r_eff,L are underestimated due to the varying threshold during the measurements (see Sect. S3 in the Supplement). However, the values are below a ratio of 1. It has to be remarked that a value above 1 does not indicate impossible particle detection by the PDUs but just a reduced detection efficiency. As shown in Sect. S4 in the Supplement, the PDUs can detect particles in a size range between 80 and 5145 nm, although not with such efficiency as in the size range between ∼ 180 and 3170 nm (see Sect. 3.2.2).

An overlap parameter S_ablation can also be determined for the overlap of the particle beam and the ablation laser spot by dividing the particle beam diameter w_part, exemplarily for AN particles, at the ablation laser spot (see brown curve in Fig. 3) by the determined optical laser beam waist w_0,dia of 250 µm ($S_{\mathrm{ablation}}=w_{\mathrm{part}}{w}_{\mathrm{0},\mathrm{dia}}$). The determination of the parameter w_0,dia is shown in Sect. 3.2.1. In Fig. 5, S_ablation is plotted versus the particle size d_va. The calculated fraction of the illuminated area of the UV ablation laser spot is between 0.23 (at d_va=335 nm) and 1.91 (at d_va=548 nm). Although the particle beam is larger than the ablation laser beam waist diameter for most particle sizes, it is possible to ablate particles and measure them with the mass spectrometer. This indicates again that w_0,dia is not the most meaningful measure for the overlap. It also leads to the conclusion that particles can experience largely different laser intensities depending on the position of the particle within the ablation laser beam. At least, S_ablation smaller than 1 indicates that 1σ of the particle beam is within the w_0,dia of the ablation laser spot.

All the data shown for the parameters S_detect,L, S_detect,V, and S_ablation are the maximum possible values of the respective particle sizes obtained when performing the ADL adjustment separately for each particle size.

3.2.1 Detection and ablation laser beam widths

For characterization of the laser beams of the PDUs and the ablation laser, a razor blade was moved stepwise perpendicularly into the respective laser beam (with steps of 0.01 mm). These characterization experiments were performed in a separate measurement setup. The remaining energy was measured using a bolometer (high-sensitivity thermal sensor model 3A, Ophir Optronics Solutions Ltd.) in the case of the diode lasers and by an energy meter (model EnergyMax™-USB, J-25MB-LE, Coherent, Inc., USA) for the pulsed UV ablation laser. The results of the measurements are provided in Sect. S2 in the Supplement.

To measure the beam waist radius w₀ of the detection laser in two dimensions (x and y), the razor blade was positioned directly at the focal point. Curve fits of the Gaussian error function (Eq. 3) were applied to all data sets, with P₀ for the power offset of the fitted curve, P_max the maximum power, pos₀ the central position of the Gaussian distribution, pos the horizontal position of the blade (i.e., the independent variable), and w₀ the beam $\mathrm{1}/e^{\mathrm{2}}$ radius of the Gaussian intensity profile (Skinner and Whitcher, 1972; Araújo et al., 2009).

It was found that the laser spot has an oval cross-sectional shape with the dimensions of w₀ = (30.3 ± 1.2) µm and w₀ = (20.0 ± 0.9) µm (measurement in the x and y directions, respectively). Thus, the $\mathrm{1}/e^{\mathrm{2}}$ diameter ($w_{\mathrm{0},\mathrm{dia}}=\mathrm{2}{w}_{\mathrm{0}}$) can be determined for the x direction as w_0,dia = (60.6 ± 2.4) µm and for the y direction as w_0,dia = (40.0 ± 1.8) µm. The average irradiance over the beam cross section ($\mathrm{1}/e^{\mathrm{2}}$ of intensity) of the laser can be estimated as 2.1 × 10³ W cm⁻². Since the detection units are identical in construction, this measurement represents both detection units.

The procedure of the characterization of the ablation laser beam is similar to the one adopted for the detection lasers. Here, however, a cross-sectional scan is performed at eight different positions along the laser beam's optical axis. To evaluate the whole beam waist, the $\mathrm{1}/e^{\mathrm{2}}$ radii w were plotted versus the position of the razor blade from the lens z_pos. To determine the focal length z₀, the Rayleigh range z_R, and the beam waist radius w₀ at the axial position z_pos, the curve fit of the Gaussian near-field equation (Eq. 4; Siegman, 1986) was applied:

From exposures on photosensitive paper, the laser beam profile appeared radially symmetrical, and this measurement was performed only in one orientation. The curve fitting results in a Rayleigh range z_R of 7.5 mm, a focal length z₀ of 76.4 mm, and a beam waist radius w₀ of 125 µm. Thus, the beam waist diameter w_0,dia is approximately 250 µm, resulting in an average irradiance over the beam cross section ($\mathrm{1}/e^{\mathrm{2}}$ of intensity) of the laser of 1.36 × 10⁹ W cm⁻². It has to be mentioned that particles can encounter very different laser irradiance depending on their trajectory through the Gaussian profile since the detection and the ablation laser beam waists are much larger than the diameters of the sampled particles (Marsden et al., 2018). The ablation laser beam waist radius and energy density are sufficient for particle ablation, and the measured values are comparable to those of other single-particle mass spectrometers, like the ALABAMA (Köllner, 2019) and A-ATOFMS (Su et al., 2004).

3.2.2 Optical particle detection efficiency

We determined the optical detection efficiencies for PSL and AN particles at PDU1 and PDU2 for two cases: the largest possible, i.e., the maximum, detection efficiency DE_max and the detection efficiency for the set ADL position (x_pos = 10.55 mm) during the deployment in Kathmandu, Nepal (KTM), DE_KTM. Both DE_max and DE_KTM combine the optical detection efficiency measurements with PSL and AN particles described in Sect. 3.1.1. Section S5.6 in the Supplement provides a listing of all relevant equations.

The parameter DE_max was determined for each measurement. For this, the determined set of parameters (r_eff,L, σ, x₀, and A_scan) of each curve fitting, was re-inserted into the respective Eq. (2) or Eq. (S15). For the maximum possible detection efficiency DE_max, the variable x_pos equals the modal value of the ADL position scan x₀, thereby compensating for the size-dependent particle beam shift (see Sect. S5.7 in the Supplement). To obtain the DE_max values in practice, the ADL has to be readjusted for each particle size.

Figure 6Maximum detection efficiency DE_max as a function of particle size d_va for PSL (squares) and AN (circles) particles measured at PDU1 (red) and PDU2 (blue). CPC and OPC measurements are as for Fig. 3. The estimated d₅₀ (50 % of the maximum) values of the optical detection are marked by vertical dashed gray lines. The uncertainties in DE_max reflect the conservatively estimated value of 10 %.

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Figure 6 presents the largest possible, i.e., the maximum, detection efficiency DE_max at ADL position x₀ as a function of the particle size d_va. The values of DE_max for PSL particles with particle sizes larger than 200 nm is above 0.60, reaching the value of 1 for particle sizes of 834 nm at PDU1. The parameter d₅₀ is typically used to characterize the detection limits of single-particle counting devices. The parameter d₅₀ is defined as 50 % of the maximum DE_max value. Here, the low d₅₀ value of the optical particle detection is between the particle sizes 108 and 218 nm. The upper d₅₀ value lies slightly above a particle size of 3150 nm. Interpolations or extrapolations for the measurements with PSL particles are used to estimate the d₅₀ values. We found 180 nm as the lower and 3170 nm as the upper d₅₀ value. At PDU2, the DE_max is lower, which can be explained by the broader particle beam at PDU2 compared to PDU1. The curve progression of the particle measurements up to particle sizes of 1000 nm follows the expected response function of the light scattering, especially the decreasing DE_max at small particle sizes. The decreasing DE_max values for large particles and be explained by the reduced transmission of the ADL due to particles losses by inertial impaction.

Figure 7Detection efficiency DE_KTM as a function of particle size d_va experimentally determined for PSL (squares, panel a) and AN (circles, panel b) particles measured at the detection units PDU1 (red) and PDU2 (blue) for the ADL setting during field deployment in Kathmandu, Nepal. The estimated d₅₀ values (PDU1) are marked by vertical red lines. The uncertainties in DE_KTM reflect the conservatively estimated value of 10 %.

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Due to the size-dependent particle beam shift, and thus the DE_max for various particle sizes is found at various lens settings, a compromise for all particle sizes has to be found to adjust the ADL. To choose the optimum ADL position, AN particles with various sizes were measured with the ERICA-AMS at different ADL positions. The position that yields the highest mass concentration signal as compromise for all sizes is defined as the best ADL position. We found x_pos = 10.55 mm as the optimum ADL position, which was subsequently applied during the field deployment in Kathmandu, Nepal (KTM). Figure 7 shows the optical detection efficiency during field deployment in KTM DE_KTM as a function of the particle size d_va at this specific ADL position. The calculations of the parameter DE_KTM are based on Eqs. (2) or (S15) and are shown in Sect. S5.6 in the Supplement. Here, besides x_pos = 10.55 mm, all other parameter values of the singly charged fraction were adopted from the curve-fitting results of the individual measurements. In Fig. 7a, the detection efficiency DE_KTM of PSL particles is plotted as a function of the particle size d_va. The graph shows an increase with particle size up to a maximum for DE_KTM of 0.74 for a particle size of 410 nm. By interpolation, the lower d₅₀ value at PDU1 is 190 nm and the upper d₅₀ value is 745 nm. Due to the relatively low maximum DE_KTM value for PSL measurements at PDU2 (0.53) compared to PDU1, the d₅₀ values found at PDU2 (160 and 750 nm) are misleading. In Fig. 7b it can be seen that d₅₀ exhibits a pronounced difference for particles with optical properties other than PSL such as AN. Except for the measurement with particle sizes of 213 nm at PDU1, all AN particle measurements (Fig. 7b) result in a DE_KTM larger than 0.40 and reach their maximum here for particle sizes of 335 nm (PDU2) and 548 nm (PDU1), both having values around 0.86. Here, solely d₅₀ can be determined for the measurement with AN particles at PDU1 to 270 nm.

The measurements demonstrated in this section have shown that detection efficiency varies with particle size and type. The efficiency of the optical detection strongly depends on the adjustment of the instrument as well as the optical and the aerodynamic properties of the particle.

3.2.3 Hit rate

Another relevant parameter to describe the performance of a single-particle laser ablation mass spectrometer is the hit rate HR. The definition of HR (see Eq. 5), also called ablation efficiency, is the number of acquired spectra N_spectra, i.e., particles successfully ionized by the ablation laser and recorded by the oscilloscope, divided by the number of laser shots N_shots, i.e., attempts to ablate particles (Su et al., 2004):

This definition is largely independent from ambient particle number concentration and the idle time of the laser but rather reflects the adjustment of the instrument. For each particle for which a laser shot is triggered, the aerodynamic particle size is determined by the TC. With the ERICA-LAMS, HR values of up to 1 (not shown) could be achieved in the laboratory for PSL particles of a certain size after optimizing the PMT thresholds and the pulse generator multiplier (see Sect. 2.3) value for the corresponding particle size. To assess on the smallest detectable particle size, the detection units PDU1 and PDU2 were optimized for the following experiment for PSL particles of 218 nm size.

Figure 8The hit rate HR (black, left ordinate); the number of spectra N_spectra (blue, right ordinate, log scale); and the number of detected particles, i.e., ablation laser shots N_shots (red, right ordinate, log scale), as a function of particle size d_va (logarithmic bin size) for ambient urban aerosol. Only the spectra with size information within the calibrated size range were processed (see Sect. S4 in the Supplement). Uncertainties in HR, N_shots, and N_spectra are based on counting statistics.

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To determine the hit rate for ambient aerosol, ambient air from outside the laboratory was sampled. Only spectra of particles with diameters in the range of calibration (see Sect. S4 in the Supplement) were considered. The ablation laser was adjusted to the maximum HR for ambient aerosol, by varying the pulse generator multiplier and adjusting DM1 (Fig. 2). The average ablation laser pulse energy was 3.2 mJ. Figure 8 shows the HR of the described experiment as a function of the particle size d_va. Furthermore, N_spectra and N_shots are plotted as a function of particle size. In the size range from 100 to 1000 nm, HR values of more than 10 % are achieved. At the particle sizes between 200 and 300 nm, at approximately 230 nm, a maximum of 0.52 was found. The reason for the maximum at this particular particle size might be the selected optimization in the adjustment of the detection and ablation units. Particles are detected by the PDU as soon as their scattered light is sufficiently intense. This might be earlier for larger particles due to the higher r_eff,L, and thus the timing might not be optimal for all particle sizes. In addition, a large particle beam divergence (see Sect. S5.7 in the Supplement) can lead to a low HR for small particles (d_va < 200 nm) as well as for large ones (d_va > 400 nm). This curve progression reflects the experimentally determined particle beam width w_part and the overlap parameter S_ablation (see Fig. 5 in Sect. 3.1.2). Furthermore, the HR is less than unity over all sizes, which may be due to the ionization efficiency of particle components in the LDI process. Besides the particle size, HR also depends on the particle shape and the chemical composition of the particle (Su et al., 2004) as well as on the laser intensity of the ablation laser (Brands et al., 2011).

3.2.4 Single-particle mass spectra

Single-particle mass spectra from laboratory tests

To study mass spectra of different chemical compounds, solutions of sodium chloride (NaCl), ammonium nitrate (AN; NH₄NO₃), benz[a]anthracene (BaA; C₁₈H₁₂), and a gold-sphere suspension were nebulized. Details on the experimental setup, as well as on the properties of the studied particles, are provided in Sect. S3 in the Supplement. If not mentioned separately, all mass spectra were processed by the evaluation software CRISP (Klimach, 2012). During this processing, the mass-to-charge ratio ($m/z)$ of all spectra is calibrated and each peak area is integrated over 25 signal acquisition samples before and after the determined $m/z$ peak center. In the resulting so-called stick spectra, a stick reflects the ion peak area in units of millivolts of sample of the specific $m/z$. To determine the ion peak area threshold of the ERICA-LAMS, i.e., minimum peak that can be detected, the data set of the first field campaign (see Sect. 4) was used. The ion peak area threshold is defined as the ion peak area at $m/z$ on which during ambient measurements typically no signals occur ($m/z$ 2 to $m/z$ 6 for cations, $m/z$ 2 to $m/z$ 11 for anions). To determine the ion peak area threshold, the normalized cumulative signal intensity distributions for each usually unoccupied $m/z$ were made and the overall 99 % threshold was determined (Köllner et al., 2017). Below this ion peak area threshold, 99 % of the baseline noise is present (Köllner et al., 2017). The result for cations and anions is an ion peak area threshold value of 7 mV sample.

Figure 9Exemplary stick mass spectra ($m/z$) of four laboratory-generated single particles as measured by the ERICA-LAMS. Left: cations; right: anions. (a) NaCl particle; (b) AN particle; (c) benz[a]anthracene (BaA) particle; (d) gold particle (note the abscissa for panel d is up to $m/z$ 400; the anion shows no peak above the ion peak area threshold of 7 mV sample).

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As an example, Fig. 9a presents a bipolar ion mass spectrum of a single sodium chloride particle as detected by the ERICA-LAMS during laboratory measurements. Other pure substance spectra are shown in Fig. 9b for a single AN particle. The spectral patterns detected by the ERICA-LAMS are comparable and in good agreement with results produced by other established single-particle mass spectrometers, e.g., the ALABAMA (Brands et al., 2011; Köllner et al., 2017), ATOFMS (Gard et al., 1997; Gross et al., 2000; Liu et al., 2000), and a modified LAAPTOF (Ramisetty et al., 2018). Also for ambient stratospheric particles, Schneider et al. (2021) have shown that spectra from the ERICA-LAMS and ALABAMA are comparable.

We further investigated BaA particles, as BaA has been identified as a component of soot (Lima et al., 2005). A characteristic example of their mass spectra is shown in Fig. 9c. Therein, the C_n and the C_nH_m pattern is clearly visible in both the cation and the anion spectra, being indicative of polycyclic aromatic hydrocarbons (PAHs; e.g., Hinz et al., 1999). Also, the molecular peak at $m/z$ 228 appears in the spectrum (C₁₈H${}_{\mathrm{12}}^{+}$). This observation is consistent with the typical performance of mass spectrometers employing lasers with a wavelength of 266 nm, which results in less fragmentation as compared to those with a wavelength of 193 nm (Thomson et al., 1997). The four examples shown here demonstrate that the ERICA-LAMS provides valid single-particle mass spectra that are comparable to those of other instruments in the literature.

It is noteworthy that an important prerequisite for the later application of the ERICA during airborne measurements was the capability to detect the presence of gold particles in the sampled aerosols. Gold can be used as a marker for self-contamination. By plating the sampling inlet with gold, it can safely be assumed that if gold-containing particles are found, this indicates that they have removed material from the inlet (Dragoneas et al., 2022). To test the instrument's capability of measuring gold particles, dispersions of gold spheres (d_va = 3860 nm) were used. A typical bipolar spectrum is displayed in Fig. 9d. In addition to the signal on $m/z$ 197 from the Au⁺ cation, the peak of the Au${}_{\mathrm{2}}^{+}$ cation on $m/z$ 394 was consistently present, providing a good indication that actual gold particles were detected, even in the absence of an isotopic pattern or specific anion signal. The Na⁺, K⁺, and Ca⁺ signals in the spectra can be attributed to the residual buffer solution of the gold-particle dispersion. The identification of particle types for which the evidence is based on hardly ionizable substances, such as gold, is only possible if the content of well-ionizable substances is moderate (Reilly et al., 2000), since otherwise no Au signal might be obtained.

Mass spectral resolution

The mass spectral resolution R_MS is a measure for the mass separation performance of the mass spectrometer and is defined as $R_{\mathrm{MS}}=\mathrm{\Delta }\frac{M}{M}$. The parameter ΔM is defined as the full width at half maximum of M, i.e., the $m/z$ value. Thus, a higher value of R_MS indicates a better separation of the $m/z$ peaks in the mass spectra. Appropriate separation is particularly necessary for the identification of neighboring nominal masses like $m/z$ 39 and $m/z$ 40 (for K⁺ and Ca⁺) as well as for signals caused by isotopes, e.g., elements such as tin and lead. In Fig. 10, details of two different raw cation spectra from two ambient aerosol particles are presented. Here, the output voltage signal of the digitizer is displayed as a function of the digitizer sample number (1.6 ns per sample). The particles of the presented spectra were recorded during the StratoClim campaign (July and August 2017) at ground level at the airport of Kathmandu, Nepal. The signal intensities correspond to the isotopic abundance of tin (Fig. 10a) and lead (Fig. 10b). The occurrence of both species can be expected in a polluted environment as in Kathmandu, Nepal. Out of these mass spectra, R_MS of the ERICA-LAMS can be estimated to be 200 for cations at $m/z$ 120 (Fig. 10a) and 700 at $m/z$ 200 (Fig. 10b). For anion spectra we found an R_MS of about 600 at both $m/z$ 100 and $m/z$ 200. The R_MS values of other single-particle mass spectrometers are comparable to the ones presented here. Brands (2009) states for the ALABAMA a resolution of 200 for cations of $m/z$ 108 and of 600 for anions of $m/z$ 120. The resolution of the A-ATOFMS (at $m/z$ 100) is 500 for cations and 800 for anions (Pratt et al., 2009). Without any specific $m/z$ value, Gemayel et al. (2016) state for the LAAPTOF an R_MS of above 600 for both polarities.

Figure 10Details of cation raw spectra (voltage output versus ion flight time in the B-ToF-MS) of two ambient single particles at the airport of Kathmandu, Nepal. (a) Tin isotopic pattern (d_va = 277 nm). (b) Lead isotopic pattern (d_va = 311 nm).

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3.3.1 Mass spectral resolution and data preparation

The ERICA-AMS mainly adopts elements of the commercial AMS from Aerodyne (see Sect. 2.1). The observed mass resolution of 800 at $m/z$ 200 during ambient aerosol sampling (see Sect. S6 in the Supplement) is comparable with that of commercial C-ToF-MS instruments (Drewnick et al., 2005). The conversion of the ion flight time to an $m/z$ is done using predefined calibration peaks. We use the peaks for CH⁺, O${}_{\mathrm{2}}^{+}$, SO${}_{\mathrm{2}}^{+}$,¹⁸²W⁺, ¹⁸⁴W⁺, and ¹⁸⁶W⁺, species for which the exact $m/z$ ratio is known and which occur in every spectrum due to their existence in the vacuum background or outgassing of the heated tungsten filament. The wide range of covered $m/z$ values allows us to fit a relation of the three-parameter time of flight to $m/z$, which is then valid for the whole spectrum. The common Ar⁺ peak is not used because in measurements shortly after evacuating the chamber, the residual organic peak at the same nominal mass of $m/z$ 40 can disturb the determination of the peak center. The software integrates the signal at each particular $m/z$ ratio to generate a stick spectrum. The signal occurring between the $m/z$ peaks is used to estimate a baseline, which is subtracted during this integration. Stick spectra are generated for measurements with open and closed shutters to subtract the instrument background signal from the aerosol measurement signal in order to obtain the aerosol contribution only. The difference between the total and the background signal results in the aerosol signal. The open–closed cycle is set to 10 s (see Sect. 2.4). A so-called “fragmentation table” is used to attribute the individual $m/z$ peaks to certain species (air, organics, nitrate, sulfate, ammonium, and chloride; Allan et al., 2004). The fragmentation table can be manually adapted to compensate for instrument-specific deviations. Along with the particles, a small fraction of the gaseous components are measured, which still exhibit the most dominant peaks at $m/z$ 28 (N₂), $m/z$ 30 (O₂), and $m/z$ 40 (Ar) in the mass spectrum (see Fig. 11). A more detailed description of the evaluation procedure can be found in, e.g., Allan et al. (2004) and Fröhlich et al. (2013).

Figure 11Example of an ambient aerosol average spectrum collected during the field campaign in Kathmandu, Nepal (averaged over the entire campaign period). Cumulative species (air, organics, nitrate, sulfate, ammonium, and chloride) colored according to their fraction in the applied fragmentation table.

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3.3.2 Particle mass detection efficiency

Similarly to the determination of the optical detection efficiencies for PSL and AN particles at PDU1 and PDU2 (see Sect. 3.2.2), the particle mass detection efficiency for AN particles was determined at the ERICA-AMS vaporizer for two cases: DE_max and DE_KTM. Like with the optical detection efficiency, DE_max and DE_KTM combine the particle mass detection efficiency measurements with AN particles described in Sect. 3.1.1 (see also Sect. S5.6 in the Supplement).

The parameter DE_max was determined for each measurement at the ERICA-AMS vaporizer by re-inserting the determined set of parameters (r_eff,V, σ, x₀, and A_scan) of each curve fitting in Eq. (S17).

Figure 12Maximum detection efficiency DE_max (non-filled markers) and the detection efficiency DE_KTM (filled markers; ADL setting during field deployment in Kathmandu, Nepal) as a function of particle size d_va experimentally determined for AN particles measured at the ERICA-AMS vaporizer. The d₅₀ values of the AMS measurement lie outside the applied particle range. The uncertainties in DE_max and DE_KTM reflect the conservatively estimated value of 10 %.

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Figure 12 presents the maximum possible particle mass detection efficiency DE_max at ADL position x₀ as a function of the particle size d_va. The DE_max values found for the measurements at the ERICA-AMS vaporizer are not comparable in absolute terms with the DE_max values found for the AN measurements at PDU1 and PDU2 (Fig. 7) since the measurements at the position of the ERICA-AMS vaporizer are analogous to an ionization efficiency (IE) calibration measurement (see Sect. 3.3.3). During this IE calibration, among other losses, the transmission losses in the ADL are compensated for. However, this measurement on the ERICA-AMS vaporizer demonstrates that the decreasing DE_max values for smaller sizes at the PDUs are caused not by losses in the ADL but by the inability to detect small particles by adopted optical means. No d₅₀ value could be determined for the measurements on the vaporizer. Even though the data point at 91 nm indicates a lower d₅₀ cutoff, we assume that the particle size range in which the ERICA-AMS can measure is between ∼ 120 and 3500 nm, as specified by Xu et al. (2017) for the ADL type used here.

Figure 12 also shows the particle mass detection efficiency during field deployment in KTM DE_KTM as a function of the particle size d_va at the ADL position x_pos = 10.55 mm. The calculations of the parameter DE_KTM are based on Eq. (S17) and are shown in Sect. S5.6 in the Supplement. For the measurements at the vaporizer, no d₅₀ values can be determined because the results are above 50 % of their maximum DE_KTM values over the entire size range. The DE_KTM at the vaporizer is 1 due to the normalization by the IE calibration, as explained above (see also Sect. 3.3.3).

Overall, the AMS part shows a fairly stable efficiency around 1 for the examined size range after calibration with AN particles of 483 nm in size. This is highly desirable to ensure the quantitative measurement of the AMS.

3.3.3 Ionization efficiency

By means of a calibration with a test aerosol of AN, the IE can be determined and the peak areas obtained from integration can be converted into a quantitative measure of the aerosol mass concentration of the atmosphere. In order to determine the IE of the ERICA-AMS, in a first step the average signal of a single ion must be measured. This is done by considering single mass spectrum extractions. The assumption is that a rarely occupied $m/z$ signal has a very low probability of experiencing the arrival of two ions in the same extraction. The peak area of these $m/z$ signals, averaged over multiple events where the signal is above the noise threshold, then represents the average single-ion signal (SIS). The SIS is given in units of millivolt nanoseconds (mV ns) and depends on multiple factors, mostly the type and condition of the MCP detector, the applied high voltages and the resulting field strengths, the temperature, and the gain of the signal amplifier. After voltage adjustment of the MCP a SIS of around 0.8 mV ns was obtained.

The IE is determined with AN particles applying Setup B as described in Sect. S3 in the Supplement (Fig. S8). The so-created monodisperse aerosol is sampled by the instrument as well as by a CPC for reference. This mass-based approach is similar to the one described in Drewnick et al. (2005) and considers the transmission efficiency through the ADL and the possible losses due to particle beam divergence. As a reference zero, a measurement through a filter is performed. The IE calibration factor in Tofware is then adjusted so that the nitrate signal equals the nitrate mass load determined by the CPC. To calculate the mass load from the CPC data, several corrections have to be applied. For instance, doubly charged particles of a larger size are also transmitted through the DMA due to the same electrical mobility, which will also contribute to the mass load. To reduce this effect, we choose a rather large particle size of 483 nm for the calibrations so that the corresponding larger-sized particles of 814 nm are not generated by the nebulizer in a high quantity. By measuring the concentration of singly charged 814 nm particles and calculating the charge ratio generated by the neutralizer according to Tigges et al. (2015), we correct for the effect of doubly charged 814 nm particles (see Sect. S5.3 in the Supplement). In addition the Jayne shape factor has to be applied (Jayne et al., 2000). The IE is usually given for nitrate and is strongly dependent on the flux of electrons for ionization. The ERICA achieves an IE of 2000 ions pg⁻¹, or 2.05 × 10⁻⁷ ions per molecule. This is lower than reported for the Aerodyne AMS (Canagaratna et al., 2007), partly due to operation at a lower filament emission current of 1.6 mA. Other test aerosol species can be used to determine a species-dependent relative ionization efficiency (RIE). The RIE of ammonium ${\mathrm{RIE}}_{{\mathrm{NH}}_{\mathrm{4}}}$ and the RIE for sulfate ${\mathrm{RIE}}_{{\mathrm{SO}}_{\mathrm{4}}}$ were determined by independent measurements of AN particles and ammonium sulfate particles according to Canagaratna et al. (2007). An averaged ${\mathrm{RIE}}_{{\mathrm{NH}}_{\mathrm{4}}}$ of 4.4 and ${\mathrm{RIE}}_{{\mathrm{SO}}_{\mathrm{4}}}$ of 0.97 were calculated. The default RIE values of the organic compounds (RIE_org=1.4) and for chloride (RIE_Chl=1.3) and for nitrate (${\mathrm{RIE}}_{{\mathrm{NO}}_{\mathrm{3}}}=\mathrm{1.1}$) were adopted from Canagaratna et al. (2007).

With the IE and RIE values, the ion count signal can be converted into an aerosol mass. Together with the known flow into the instrument (Φ_ERICA = 1.48 cm³ s⁻¹), the mass concentration of the particulate matter is calculated (Canagaratna et al., 2007). Due to the installed constant pressure inlet (Molleker et al., 2020), which keeps the pressure in the ADL constant, the volumetric flow into the instrument increases with decreasing ambient pressure. With the assumption of a stable instrument temperature, this leads to a constant mass flow or normal flow (NTP, 20 ^∘C and 1013 hPa). Thus, the dimension of the measurement result is mass per normal volume.

3.3.4 Detection limits

Several methods can be used to determine the detection limit (DL) for the species measured by an AMS as described by Drewnick et al. (2009). One approach is the calculation based on the ion-counting statistics during a measurement with the shutter closed (closed signal), denoted as DL_stat. The most common approach is a measurement of the signal noise during a measurement of filtered air, denoted as DL_filter. Especially during in-flight measurements, this filter-based method cannot be representative of the whole flight due to changing vacuum, temperature, and instrument background conditions. Thus, for field measurements a detection limit DL_spline was calculated from the closed signal after applying a spline-based detrending method comparable to Schulz et al. (2018) and Reitz (2011). In each case the DL is defined as 3 times the standard deviation of the respective signal. The detection limits of all species are given in Table 1 for each method. The statistical approach as well as the filter-based method is based on a long-term filter measurement in the lab, while DL_spline was determined from the measurements during the StratoClim 2017 campaign. The differences are reasonable because DL_stat does not consider interferences with other species, especially water and air, whereas DL_spline was measured under different conditions regarding pumping time and consequently instrument background. The detection limits are slightly higher than reported for other airborne instruments (e.g., Schulz et al., 2018) due to not only a different time basis but also a rather strong air beam signal in our instrument (see Sect. 3.3.5).

Table 1Detection limits of the species measured by the ERICA-AMS determined with several methods. DL_stat and DL_filter measured under lab conditions. DL_spline measured during the StratoClim field campaign. The limits are given for one measurement cycle (10 s) and are expected to reduce with longer averaging times t proportionally to $\mathrm{1}/\sqrt{t}$.

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3.3.5 Air beam and water signal

The ADL is supposed to focus particles into a narrow beam into the vacuum chamber while the air molecules are strongly diverging after the end of the lens. However, some of the air is also propagating towards the ion source and generates ions at $m/z$ ratios of 14 (N⁺), 16 (O⁺), 28 (N${}_{\mathrm{2}}^{+}$), 32 (O${}_{\mathrm{2}}^{+}$), 40 (Ar⁺), and 44 (CO${}_{\mathrm{2}}^{+}$) as well as the corresponding isotopes. This signal, the so-called “air beam” signal, can on one hand be used for diagnostic purposes but on the other hand introduces uncertainties into measuring particle signals at the corresponding $m/z$. An air beam signal as small as possible is thus desirable, e.g., to reduce the detection limit of aerosol species. In the ERICA-AMS, we experienced a rather strong air beam signal of around 2.9 × 10⁶ ions s⁻¹ (see Fig. 11). This is larger than reported by Canagaratna et al. (2007) (1.5× 10⁶ to 2.5 × 10⁶ ions s⁻¹), with a 5-fold higher IE value at the same time. We found out that the reason lies in the assembly of the ERICA. Since the front part of the instrument was optimized for laser ablation mass spectrometry, a rather large conical skimmer with an inner diameter of 1.9 mm was built in after the ADL for the separation of air and particles. While this causes no problem for the laser ablation part, it leads to a substantial transfer of air molecules towards the following stages of the vacuum chamber. For improvement, a newly designed skimmer with an opening of 1 mm and a channel of 21.5 mm length was implemented in order to reduce the air beam signal by a factor of 6.7, resulting in 4.4 × 10⁵ ions s⁻¹. Since this skimmer was implemented in 2019, earlier campaigns, like StratoClim 2017, were conducted with the large air beam signal. Additionally, interferences of particle signals with the signal of residual water influence the detection limit of ammonium. Here, the background water vapor in the vacuum plays a role. We experience an intense water signal of 2.5 × 10⁶ up to 1 × 10⁷ ions s⁻¹ depending on instrument temperature and pumping time. This water signal occurs independently of the shutter position and thus does not directly relate to the air beam streaming into the instrument but to the background vacuum conditions.