Particle optical diameter was calculated from the intensity of the scattering signal following the relationship provided by the manufacturer and described by Algorithm 1 in Appendix . Essentially, the optical diameter is assumed to be proportional to the overall intensity of scattering signal by summing the detection over all angles for each particle measured. The fluorescence spectrum from each particle was corrected before the analysis following the manufacturers guidelines using Algorithm 2 in Appendix .

The manufacturer does not provide a standardised method to determine particle size. We applied two methods to determine particle diameter. The first method is based on the two holographic images taken of each particle. The average area of the particle is calculated from the two images by counting all pixels that make up the particle. Then, assuming that the particles are spherical, the diameter is computed and converted from pixels to micrometres using the resolution of the holographic images (0.6 µm/pixel). This method is applicable only for particles with diameter of 10 µm and larger; smaller particles cannot be measured with this method because of limitations in the reconstruction software used at the time. For small particles, a second method, using the forward-scattering signal from the trigger laser, is applied. This is done in three steps: the part of the raw signal up to a value of 800 is kept, and then a high-pass filter is applied to remove the base of the signal. A cut-off at a value of 7880 is used, which is roughly equivalent to the median of the first part of the signal for 1 µm particles. Thereafter, the integral of the remaining signal is computed, and the equation d=aIb using the median of the scattered light integral (I) for each particle diameter (d) is fitted, where a=1630, and b=0.61 (with a and b having been determined empirically from the presented data).

The counting efficiency, EDUT, is calculated as ∑iEi,DUT/N, with Ei,DUT=Ci,DUT/Ci,ref, where Ci,DUT and Ci,ref are the number concentrations measured by the DUT and the reference optical particle counter, respectively, and N being the total number of measurements (typically 25). Because of the higher flow rates and therefore higher particle counts registered by the DUT compared to the reference counter, the statistical uncertainties in CDUT are expected to be small (<10 %). It must be noted, however, that bioaerosol monitors can also suffer from large systematic errors, for instance, due to uncertainties in the aerosol flow rate, coincidence losses, impaction losses in the sampling system, misalignment of the laser beam, and size-dependent particle losses in the concentrator. These systematic errors are in practice much larger than the statistical uncertainty in CDUT or the uncertainty in Cref (6 %–7 %).

For small particles, the counting efficiency of the WIBS-NEO increases with particle diameter from 54 % for 0.5 µm to a maximum of 90 % for particles with 0.9 µm diameter (Table ). This is in line with the results of , who found counting efficiencies of 50 % and 100 % for particles 489 and 690 nm in diameter, respectively. Beyond the peak at 0.9 µm, the counting efficiency tends to drop with increasing particle diameters (61 %–83 % at 2 µm and 57 % for 5 µm particles; Table ). The WIBS-NEO appears to reach an upper detection limit for particles larger than 10 µm, detecting just 4 % of the particles with a diameter of 10 µm compared to the reference counter. This observed drop in the detection rate for bigger particles is somewhat surprising since the WIBS-NEO is expected to be able to detect particles up to 30 µm. Although the exact reasons for this behaviour are unclear, it cannot be ruled out that the specific WIBS-NEO used in our study required a technical service by the manufacturer.

The Rapid-E shows a maximum counting efficiency of 58 % for the 10 µm PSL, while at 5 µm diameter 42 % of the particles are detected. The lower detection limit was found to be around 2 µm, where only 1 % to 4 % of the particles are detected. At 1 µm diameter, almost no PSLs are detected by the Rapid-E (Table ).

The Poleno does not detect particles with 0.5 µm diameter and appears to have its lower detection limit at approximately 1 µm, where the counting efficiency is 3.81 (Table ). This increased counting efficiency is potentially because the trigger laser was set too sensitively, resulting in noise being counted as particles during the 1 µm measurement sequence. At 2 µm the Poleno performs well, with a counting efficiency ranging from 82 %–98 %. However an effect of the concentrator on the measurements for particles at 2 µm diameter cannot be ruled out. Note that the counting efficiency of the Poleno strongly depends on the performance of the virtual impactor, also at small particle sizes. Small shifts in the cut-off curve of the impactor can have a large effect on the counting efficiency, for example, at 2 µm. For larger particles, the concentration measured by the Poleno is strongly enhanced due to the concentrator unit. It is expected that the plateau values of the concentrator's enrichment curve are quite robust and could be used to correct concentration values with reasonably small uncertainty. However, the plateau efficiency could not be determined with the tested PSL diameters. For particles with 5 µm diameter a concentration factor of 7.85 and for the particles with 10 µm diameter a factor of 123.79 was observed, which is still far below the theoretical maximal enhancement factor of 1000. This indicates that both tested diameters (5 and 10 µm) are on the lower end of the cut-off curve (Fig. b). It is therefore not recommended to use the values in Table  to correct the concentration of the Poleno measurements within this size range.

A counting efficiency that is too low or high does not mean that a particular device is unable to provide valuable measurements in practice. If the counting efficiency is well known and stable, a scaling curve over the relevant size range can be determined for each instrument. To evaluate whether measurements are indeed scalable, we compute the root mean square error deviation (RMSD) between the scaled reference and DUT counts. The RMSD is a combination of the uncertainties from the reference and DUT measurements as well as from other potential uncertainties related to the experimental set-up. Since we cannot precisely assign the error to each of the potential sources we assume that the DUT is the only source of error, and thus we can interpret the RMSD as an upper bound of the error for each instrument. The lower the RMSD the better the measurements are suited for scaling without significantly increasing the uncertainty. The RMSDs for the different measurement sequences with all particle diameters are given in Table .

Out of the three devices tested, the WIBS-NEO is the only one able to perform robust measurements for particles with diameters from 0.5 to 2 µm (RMSD between 10 % and 14 %). For particles with larger diameters, the RMSD increases to 25 % for the 5 and 10 µm PSL (Fig. ). The Rapid-E shows an RMSD of 25 %–29 % for particles with diameters between 2 and 10 µm. For the 1 µm particles the RMSD of 89 % indicates that the measurements are noisy and thus below the detection limit of the device. The Poleno shows relatively high RMSD values of 30 %–39 % for the 2 µm particles but a lower RMSD of 12 % for the 5 µm particles. At 10 µm, the RMSD is slightly higher, at 20 %.

Note that all values are based on relatively small statistical samples (≤30 measurement points). It also has to be mentioned that the scaling factor can be very sensitive to particle size. In such a case, the capability of determining the particle size becomes an important uncertainty factor when scaling the concentrations.

The WIBS-NEO has well-distinguished peaks at 0.9, 1, 5, and 10 µm (Fig. b and d) and thus appears to provide precise sizing for each particle within this size range. Deviations in (geometric) mean optical diameter measured for a certain PSL sample from nominal geometric diameter are small and within uncertainty in optical sizing methods. The measurement at 0.5 µm shown in Fig. a may be truncated at the small size end due to the lower size detection limit of the WIBS (see also counting efficiency results in Sect. ). Interestingly, the different types of PSL particles tested appear to impact the measurements to a certain extent. In particular, for the 2 µm particles, the red PSLs show a peak at 3.3 µm, while the plum purple and blue PSL peaks are closer to the actual particle optical diameters of 2.3 and 2.2 µm, respectively (Fig. c). The variation in measured (geometric) mean diameters for the three different PSL samples with nominal geometric diameters between 2.0 and 2.1 µm is considerably greater than the expected optical sizing precision. In particular the red PSLs appear at around 1.6 times the nominal size. This suggests a larger scattering cross-section of the red PSLs compared to the blue and plume purple PSLs at the wavelength of the sizing laser (635 nm).

The Rapid-E was unable to detect 1 µm particles and does not show a distinct peak for any of the 2 µm PSLs either. For these particles the size distribution curve shows no clean peak (Fig. a), indicating that the detection limit is likely above 2 µm for this device. The peak for the 5 µm particles is well defined and therefore indicates that the Rapid-E is able to accurately detect particles in this size. For the size distribution of the 10 µm diameter particles, a first narrow peak just below 5 µm and a second broader peak at 10 µm with a large tail towards smaller diameters can be observed in Fig. b. The large tail towards lower sizes could be an indication of a misalignment of the laser. The discontinuity of the size distributions at 5 µm in Fig. b is a direct consequence of using an intensity-to-particle relationship with a discontinuous first derivative (Fig. , Algorithm 1 in Appendix ). This suggests potential for improving the sizing method for particles with diameters smaller than 10 µm, but this was not within the scope of this study.

The Swisens Poleno is unable to detect 0.5 µm diameter particles. For the 1 µm diameter PSL particles, the size distribution shows a well-defined peak at 1.05 µm (Fig. a), indicating that the device is able to distinguish particles in this size range well. At 2 µm diameter (Fig. b), the size distributions show well-defined peaks for the red, plum-purple, and blue particles, with slight differences in positioning around 2 µm. The 5 µm size distributions show a well-defined peak, although the size is slightly overestimated (Fig. c). The 10 µm particle size distribution also shows a well-defined peak, but again the size is overestimated at about 10.7 µm. The shoulder of the 5 and 10 µm size distributions at smaller particle sizes may indicate the need to realign the laser and particle beams and/or the detection optics. When comparing the two methods of particle size estimation used for the Poleno device (see Sect. ), the method based on the holographic images results in a very clean and sharp peak compared to the trigger signal method (Fig. d). This suggests that the image-based method should be used for the Poleno device for large particles.

The Rapid-E's fluorescence spectra correspond relatively well with those from the reference data (Fig. ). For the plum purple PSL particles (λ=425 nm) both the reference and Rapid-E exhibit a broad peak in the range λ=400–450 nm, with the Rapid-E slightly shifted towards longer wavelengths. For the blue PSL particles (λ=447 nm) the opposite is true, with the Rapid-E signal slightly shifted towards shorter wavelengths and with a significant tail in this direction. The red PSL particles (λ=579 nm) show a less defined peak in the expected range (around 580 nm), but there is a strong signal from 400–450 nm, where no peak is seen in the reference data.

Table  shows the percentage of particles measured by the Rapid-E with peak fluorescence emission at the correct wavelength. Despite the spectra not showing peaks at the expected wavelengths, a notable number of measured particles show maximum fluorescence at these wavelengths.

The reference data, when averaged for the different Poleno windows, are very similar for all excitation wavelengths once the first- and second-order elastic scattering peaks have been removed (Fig. ). Overall, the Poleno compares well with the reference data for the three different PSLs tested. The limited spectral resolution of the device does not allow the same level of comparison as the Rapid-E; however, the available measurement points are all close to the reference data. Note that the values for the 335–380 nm detection window are discarded as a result of the first-order elastic scattering, so no points are shown for this wavelength range.