1. Introduction

Laser-based detection of particles in air has made significant progress since its first commercial applications decades ago [1]. In recent years, new sensor techniques have been developed, e.g., whispering gallery mode resonators and ring resonators, pushing the detection limit to particles with sizes below 10 nm [2,3]. To monitor the particle concentration in everyday environments more efficiently, miniaturization and mobility of the sensors are obligatory. Complex setups are less suitable for this application, whereas most available systems are capable of delivering particle size sensitivity only above 0.25 μm, e.g., the Particle Measuring Systems Handilaz and the Grimm EDM 107, or are quite complex, e.g., photoacoustic sensor systems [4–6].

Particles with diameters below 2.5 μm (PM2.5) or even below 0.1 μm are the most interesting, as smaller particles are expected to exhibit a higher health risk [7,8].

In this paper we describe an optical particle sensor (OPS) that uses laser light scattering and whose structural parts are completely composed of plastics. It has high accuracy and sensitivity down to particles with diameters of 147 nm and an expected particle size limit near 90 nm. The measurement technique is based on an intensity ratio approach, which allows continuous operation of the system without repeated calibration. To further enhance the reliability, linear diversity combining (LDC) is applied, which uses the mean-free sum of both scattering signals analog to the intensity ratio approach. This combined detection scheme additionally allows a further reduction of the well-known uncertainty of the particle size identification by the index of refraction.

Section 2 explains this approach and the setup in more detail before Section 3 shows the results of measurements.

2. Approach

A. Optical Setup: Fresnel Ring Lenses and Laser Beam Shaping

The light scattering intensity ratio is a well-established technique to reliably sense particles when crossing a laser beam and determine its particle size [1]. In most applications, single detectors or detector arrays are used to collect the scattered light at two separate solid angle sections. The particle size can then be derived from the ratio of both amplitudes using either calibration results or scattering theory, e.g., Mie or Rayleigh theory.

The intensity of the collected scattered light $I_{\det }$ can in general be described by

To increase the sensitivity, one can collect a higher amount of scattered light using mirrors or lenses [9]. As spherical mirrors show the problem of image distortion, and elliptical mirrors only allow collection of scattered light from a small spatial fraction of the laser beam without image distortion, we use Fresnel lenses. In comparison to aspherical glass lenses, this kind of lens has the great advantage of low $f$-numbers and can thus be positioned close to the source of the light scattering while collecting a major fraction of the scattered light.

In our setup we place the Fresnel lenses in the forward scattering direction ($\text{scattering angles}<45°$) as larger particles scatter the major fraction of light at low angles.

We use three Fresnel lenses on a single lens mount to collect two solid angle intervals: the first is positioned toward the laser beam source and spans around the laser beam trap, collecting and collimating the scattered light (see Figs. 1 and 2). Behind this lens, two Fresnel ring lenses are combined. The smaller ring spans around the back part of the laser beam light trap, and the second ring spans around the smaller ring as its inner diameter equals the outer diameter of the smaller ring lens. Transparent adhesive is used to fix the position of the lenses and seal the lenses and the lens mount gas-tight. To support two separate angle intervals, the collected and collimated scattered light needs to be imaged onto two separate avalanche photodiodes (APDs). For this purpose, the Fresnel ring lenses are cut eccentrically, which means an off-center cut (see Fig. 1). The effective detector area of the Fresnel lenses covering a solid angle interval $[\alpha ‥\beta ]$ can be described in general by

 

Fig. 1. Fresnel lenses were used to collect and image the scattered light by particles crossing a laser beam. At front, toward the laser beam, there is one single Fresnel lens collecting and collimating the scattered light. On the back of the lens mount, two separate, eccentrically cut Fresnel ring lenses image the collimated light onto two APDs. The distance of the off-center cut to the original center a determines the lateral imaging (see Fig. 2). Hence, two separate solid angle intervals are measured. The larger Fresnel ring lens spans around the smaller Fresnel ring lens, which spans around the laser beam trap like the single lens at front. Transparent adhesive is used to create a gas-tight seal and to fix the lens positions. $a$ was chosen as 3.3 mm; the radii of the ring lenses were $3.2/7.1/9.5\mathrm{mm}$. The first Fresnel lens fully covered the available space at the lens mount.

Download Full Size | PDF

 

Fig. 2. Top: Scheme of the sensor setup in cross section showing the three main mounting parts: the cover (including the inlet nozzle), the lens mount (see Fig. 1), and the main chamber. Particles enter the measurement chamber through the inlet nozzle from top; the scattered light is collected and collimated by a first single Fresnel lens and then imaged onto two APDs by two separate Fresnel ring lenses (see Fig. 3). The distance between the laser beam waist and the first Fresnel lens is 11.5 mm. Bottom: photo of the system.

Download Full Size | PDF

Figure 2 shows a scheme of the sensor setup. The sensor system comprises three mounts, manufactured using rapid prototyping: the cover including the inlet nozzle, the measurement chamber with a mount for the laser optics and the APDs, and the mount for the Fresnel lenses. The laser optics consists of two aspherical lenses forming a well-defined laser beam for particle scattering with a small beam waist. The inlet nozzle directs the aerosol stream through the laser beam, and the position of the laser beam waist is aligned with the center of the aerosol stream.

The imaging of the scattered light onto the APDs can be described using geometrical optics. The image distance $i$ is given by

Hence, the position and size of the resulting image on the detectors directly relate to the position of the particle in the laser beam. If the eccentrical cut $a$ is large, $y$ is large too, resulting in a high imaging angle, which can possibly result in a partial blocking of the scattered light by the light trap. Therefore, $a$ should be as small as possible. Ideally, it is only limited by the minimum distance of the detectors. In conflict, the imaging distance $i$ should be as low as possible to achieve a low magnification of the image to minimize the photodetector area necessary to collect the full image. The detector noise increases with increasing photodetector area, thus reducing the achievable minimum signal-to-noise ratio (SNR).

The inner and outer diameters of the Fresnel ring lenses are constant, thus leading to certain scattering angle intervals collected by both Fresnel ring lenses. As the scattering position varies, the collected scattering angles vary as well (see Figs. 3 and 4). As a result, the detector areas vary as well [see Eq. (2) and Fig. 5]. Therefore, the scattering amplitudes can vary for the same particle sizes, depending on the scattering position. Ideally, the effective detection areas should be constant. Comparing the ratios of the actual detection areas at $\pm 1\mathrm{mm}$ around the laser beam waist ($12.5/10.5\mathrm{mm}$), the ratios of the according detection areas differ by about 4%, inducing an equal error on the uniqueness of the measurement results. To limit these errors, the spatially accepted range around the laser beam waist should be as small as possible. Considering Eq. (3) and the relation

 

Fig. 3. Beam of the scattered light after Fresnel lens 1 can be divergent (solid line) or convergent (dashed line) depending on the position of the particles in the laser beam in correlation with the focal length of the first Fresnel lens. The collected scattering angles are defined by the constant Fresnel ring lens radii $r_1$ and the scattering position. Hence, the effective detector area and the scattering angles depend on the scattering position (see Figs. 4 and 5).

Download Full Size | PDF

 

Fig. 4. Inner and outer diameters of the Fresnel lenses are fixed, leading to a certain collected scattering angle interval for the smaller ring lens [a‥b] and an interval [b‥c] for the larger ring lens. However, the effective scattering angles vary, depending on the scattering position (see Fig. 3). This leads to a variation of the scattering behavior for the same particle size, depending on the scattering position. To limit this error, the spatially accepted range around the laser beam waist should be as small as possible.

Download Full Size | PDF

 

Fig. 5. Calculation of the ratio of the effective detection areas, depending on the scattering position (distance to the first Fresnel lens). Ideally, the effective detection areas should be constant for both solid angle intervals. However, the amount of collected light depends on the scattering position (see Fig. 3). For example, comparing the ratios of the effective detection areas at $\pm 1\mathrm{mm}$ around the laser beam waist ($12.5/10.5\mathrm{mm}$), the ratios differ by about 4%, inducing an equal error on the uniqueness of the measurement result. Hence, the spatially accepted range around the laser beam waist should be as small as possible.

Download Full Size | PDF

As a result of using Fresnel ring lenses, the radial distance $r$ in Eq. (1) depends on the cosine of the scattering angle.

The laser beam is highly focused to maximize the amplitudes of the scattered light. Its beam intensity reduces with increasing distance to the laser beam waist as illustrated in Fig. 6, leading to a variation of the amplitudes of the scattered light depending on the scattering position. This dependency can be compensated by identifying the scattering position and correcting the amplitudes accordingly. This is carried out by determining the length of the scattering signals, termed time of flight (TOF) from here onwards. The diameter of the Gaussian laser beam is defined at the lateral position where the signal has dropped to $1/{\mathrm{e}}^2$, hence 13.5% of the amplitude. The intensity of a radial laser beam profile is generally given by

 

Fig. 6. Laser beam intensity decreases laterally as the laser beam diameter increases, hence leading to scattering amplitudes depending on the scattering position. As the TOF of the particle through the laser beam is characteristic to the laser beam diameter, this effect can be minimized using a calibration measurement.

Download Full Size | PDF

The TOF is derived from the integral of the scattering signal. Integrating and solving Eq. (7) for a certain spatial trajectory in $z$ leads to

However, multiple scattering positions can lead to the same TOFs although the laser beam intensity is different (see Fig. 7). This would ultimately lead to a wrong correction of the scattering amplitudes by the method described above. To identify the scattering position uniquely, the lateral parts of the laser beam were blocked by a slit-shaped aperture at the laser optics between the first and second lenses. Thus only the center part of the laser beam is left (see Fig. 7 top). This technique, however, leads to an interference pattern of the laser beam intensity (Fresnel diffraction) instead of a clear top-hat profile. In far-field measurements of the laser beam profile using a WinCamD-UCD15 we found a variation of the average peak intensity of about $\pm 20\%$. In the transverse direction, the laser beam still shows a Gaussian-like profile (see Fig. 7 bottom).

 

Fig. 7. Top, scheme: ideally, particles cross the laser beam around its beam waist (position 1). When particles cross the laser beam away from the beam waist in the $z$ direction, e.g., at position 2a, they can lead to scattering signals with a TOF that equals the TOF at the laser beam waist. Hence, the scattering position cannot be distinguished and the scattering amplitudes cannot be corrected (see Fig. 6). When a particle crosses the laser beam at position 2b, the errors as described in Figs. 4 and 5 may be too large, as well as the resulting image exceeding the APD area. To limit these errors, two measures are taken: using a slit-shaped aperture blocking the lateral part of the laser beam (solid line) and limiting the accepted TOF in the processing (red lateral line). Bottom, optical far-field measurements: using a slit-shaped aperture, the resulting laser beam profile does not equal an ideal top-hat profile, but shows a fluctuation (A-A) that reduces the TOF reliability. On the other axis, it still shows a Gaussian-like shape from which the TOF is determined.

Download Full Size | PDF

Depending on the scattering position, the image can exceed the photodetector area. Hence, the spatial range of acceptance needs to be limited by accepting only an according TOF interval. On the other hand, it is very useful to accept a large spatial range to increase the speed of the acquisition of a particle size distribution. In total, if the particle concentration is high or the measurement time only plays a minor role, a smaller interval should be chosen.

The position of the laser beam waist needs to match with the center of the radial-symmetric aerosol stream. Figure 8 shows a simulation of the velocity field using Comsol Multiphysics. From the center to a lateral position of $\pm 1\mathrm{mm}$ from the laser beam waist, the velocity reduces to half of its peak value ($2.4\mathrm{m}/\mathrm{s}$ peak at a flow rate of $0.5\mathrm{l}/\min$). Thus the TOFs increase proportionally with increasing distance to the laser beam waist. Therefore, the correction of the scattering amplitudes has to be derived from calibration measurements with a monodisperse particle size.

 

Fig. 8. Comsol Multiphysics simulation (3D, cross section) of the velocity field of the aerosol stream exiting the inlet nozzle with $0.5\mathrm{l}/\min$ inlet flow: from center (laser beam waist) to lateral distances the velocity reduces significantly. At the center, the velocity equals about $2.4\mathrm{m}/\mathrm{s}$. Hence, the TOF increases to lateral positions.

Download Full Size | PDF

B. Signal Processing: Intensity Ratio and Linear Diversity Combining

Besides the well-known intensity ratio technique, we use a LDC technique, which is known from wireless communication to offer the maximal SNR for multiple signal channels [10]. In our sensor system, a LDC equals the mean-free sum of the scattering signals of both angle intervals and delivers a maximal SNR. The average white Gaussian noise (AWGN) of the scattering signals increases by ${\sigma }^2={\sigma }_1^2+{\sigma }_2^2$, whereas the LDC signal equals the sum of the SNR of both APDs.

The identification of the scattering amplitudes and TOFs uses four steps. First, the cross covariance of both scattering signals is generated and only signals with amplitudes exceeding $\mathrm{SNR}=2$ are accepted for further processing.

In a second step, the LDC signal is analyzed for symmetric Gaussian scattering events and the corresponding amplitudes and TOFs are determined. Only highly symmetric scattering events are accepted. This reduces the problem of coincident particles as these would likely lead to nonsymmetric scattering events. There are two exceptions, however: when coincident particles cross the laser beam at the very same time, and if a large and a small particle cross coincidently, where the scattering signal by the large particle dominates and the small particle only leads to a small fluctuation of the total scattering signal.

In a third step, the scattering amplitude of each event is determined in both scattering signals. To increase the SNR, the noise on the signals is reduced by a Savitzky–Golay polynomial filter of order 2 and a window length of 7, when the number of data points of an event exceeding $\mathrm{SNR}=1$ is larger than the filter window length.

In a fourth step, the optimal scattering amplitudes of both angle intervals and the amplitude ratios are determined. The accuracy of the evaluated amplitudes directly relates to its SNR, and the LDC amplitude equals the sum of both amplitudes. Therefore, the difference between the LDC amplitude (maximal SNR) and the amplitude with the higher SNR of both scattering angles equals the remaining amplitude. Using this approach, it is possible to detect scattering amplitudes with $\mathrm{SNR}<2$ on one solid angle interval, which would normally not be accepted.

Then, the particle size is identified using a 3D matrix.

C. Particle Size Identification: 3D Matrix

Multiple particle sizes and indices of refraction can lead to the same scattering amplitudes. This ambiguity is a major problem of the intensity ratio approach. In the past, it was treated, e.g., by using an additional laser wavelength, polarization, or additional scattering information [11–13].

In a more straightforward approach to support a unique particle size identification, we include the LDC amplitude as another axis besides the amplitude ratio. This leads to a 3D matrix with the particle size on the $z$ axis. The 3D matrix is simulated using Mie theory and the BHmie algorithm [14], supporting an arbitrary number of indices of refraction and particle sizes. For example, when measurements take place in a well-confined environment where only one certain particle type is present, the simulation is carried out for that single index of refraction. Otherwise, multiple indices of refraction and other intervals of particle sizes can be considered, depending on the purpose of the measurement and the environment. Then, for a measured pair of amplitude ratio and LDC amplitude, the next neighbor in the 3D matrix is chosen as the particle size (see Fig. 9).

 

Fig. 9. Particles with different sizes and indices of refraction can generally lead to the same scattering signal ratio. Therefore, to support a unique particle size identification, we include the mean-free sum of both scattering signals (LDC, linear diversity combining) as another axis, thus leading to a 3D matrix with the particle size on the $z$ axis. Here, an excerpt of a simulation using Mie theory assuming five different indices of refraction between 1.3 (water) and 1.7, including all particle sizes in 75…2500 nm (98 steps), is shown as it is used in the measurements. For a measured pair of signal ratios and LDC amplitude (solid lines), the next neighbor is chosen as the particle size (dashed circle).

Download Full Size | PDF

Figure 9 shows an excerpt of a simulated matrix assuming five equally distant indices of refraction from 1.3 (water) to 1.7 and 98 equally distant particle sizes in the interval of 75…2500 nm. The matrix uses the LDC amplitudes as the $x$ axis, the amplitude ratio as the $y$ axis, and the corresponding particle diameters as the $z$ axis.

There is one flaw, however. Multiple combinations of particle size and index of refraction can lead to the same LDC amplitudes and amplitude ratio in the simulation. Then, two (or more) different particle sizes can have the same LDC amplitude/amplitude ratio combination in the matrix. It is not possible to determine which particle size is correct. In this case, the average of the multiple particle sizes is taken as the result.

There are three matrix positions in the above-mentioned matrix where multiple (two) particle sizes were found as possible solutions each. These particle sizes differ by $<20\%$. Hence, the total error induced on the particle size determination remains small.

Variations of the laser beam output power, the detector sensitivities, and pollution of the Fresnel lenses directly influence the scattering amplitudes. This problem can be reduced by exploiting the signal offset generated by the background light. The variations can then be compensated according to changes of the signal offset.

The reliability of the matrix method strongly depends on the certainty of the LDC amplitudes. As the laser beam profile shows a significant variation and a steady slope at its edges (see Fig. 7 top), an error remains. As the amplitude ratio is not affected by this variation and is therefore more reliable, it should be weighed significantly stronger when determining a particle size. We found a weighing factor of 4 to be optimal.

3. Measurements

A scheme of the measurement setup is shown in Fig. 10. The particles were generated from a liquid suspension (ultra pure ${\mathrm{H}}_2\mathrm{O}$) by dry ${\mathrm{N}}_2$ and the aerosol stream dried by a diffusion dryer before entering the SMPS+C reference measurement system (Grimm 5.403) and the OPS. The system uses a laser diode emitting at 450 nm with 33 mW output power (Osram 450B), APDs of Hamamatsu (S8664–20K), a transimpedance amplifier with ${10}^5\mathrm{V}/\mathrm{A}$ by Femto (DHPCA-100), an analog–digital converter (ADC) with 16 bit resolution in $\pm 10\mathrm{V}$ and $80\mathrm{kS}/\mathrm{s}$ (ADwin-light-16), and aspherical Fresnel lenses. The laser beam with a divergence half angle of 8° generated a laser beam waist of $\sim 3\mathrm{\mu m}$ (calculated). It was shaped by a slit-shaped aperture with 0.3 mm slit width. A flow rate of $0.55\mathrm{l}/\min$ was used for measurements, and only TOFs with $37\mathrm{\mu s}<\mathrm{\Delta }t<200\mathrm{\mu s}$ were accepted. 37 μs was chosen to guarantee at least three sampling points. Comsol simulations showed a velocity of $\sim 2.4/1.2\mathrm{m}/\mathrm{s}$ (center/lateral); hence the spatial range of acceptance was about $\pm 0.85\mathrm{mm}$ around the laser beam waist where the laser beam diameter varied between $\sim 90$ and $\sim 240\mathrm{\mu m}$. An optical loss of 20% was assumed in the simulations considering the Fresnel lenses, which have an opaqueness of 92%. The distance between the laser beam waist and the first Fresnel lens was 11.5 mm, leading to average scattering angle intervals of about 29.5‥37.0° and 15.6‥29.4°, and effective detector areas of 95 and $68{\mathrm{mm}}^2$ after a partial blockage by the lens mount.

 

Fig. 10. Scheme of the measurement setup. The particles are generated out of a liquid suspension (ultra pure ${\mathrm{H}}_2\mathrm{O}$) by dry ${\mathrm{N}}_2$, and the aerosol stream dried by a diffusion dryer before entering the SMPS+C reference measurement system and the OPS, which uses a laser diode with 450 nm wavelength and 33 mW output power. The sampling rate for both scattering signals was $80\mathrm{kS}/\mathrm{s}$.

Download Full Size | PDF

Figure 11 shows simulated LDC amplitudes for ${\mathrm{H}}_2\mathrm{O}$ particles with an index of refraction of 1.3 using multiple particle sizes and laser beam diameters. A minimum of three sampling points are needed for processing; hence the minimum TOF is 37 μs at $80\mathrm{kS}/\mathrm{s}$ or 10 μs at $333\mathrm{kS}/\mathrm{s}$, respectively, which equal certain minimal measurable laser beam diameters, depending on the aerosol velocity. The smallest particle can be detected at the laser beam waist (highest laser beam intensity), for which a minimum sampling rate of $333\mathrm{kS}/\mathrm{s}$ and a flow rate $<0.3\mathrm{l}/\min$ is needed, 55 μm laser beam diameter equals the minimum at $0.3\mathrm{l}/\min$ flow rate and $80\mathrm{kS}/\mathrm{s}$, and 90 μm equals the minimum at $0.5\mathrm{l}/\min$ flow rate and $80\mathrm{kS}/\mathrm{s}$. Hence, the minimum detectable polystyrene latex (PSL) particle size varies accordingly between near 90 nm ($333\mathrm{kS}/\mathrm{s}$ sampling, $0.3\mathrm{l}/\min$ flow rate) and about 200 nm ($80\mathrm{kS}/\mathrm{s}$ sampling, $0.5\mathrm{l}/\min$ flow rate) for a minimum $\mathrm{SNR}=2$ and LDC noise of 1.4 mVrms. However, this is spatially limited, hence providing only a very small efficiency for small particle sizes. Larger particles or particles with higher indices of refraction scatter high amounts of light distant to the beam waist as well and are thus more efficiently detected. Figure 12 shows the measured SNR of PSL and silica particles. In measurements with PSL particles with 147 nm diameter and a flow rate of $0.3\mathrm{l}/\min$ we found a SNR of 30.3.

 

Fig. 11. A minimum of three sampling points are needed for processing; hence the minimum TOF is 37 μs at $80\mathrm{kS}/\mathrm{s}$ or 10 μs at $333\mathrm{kS}/\mathrm{s}$, respectively. These equal certain minimum laser beam diameters, depending on the aerosol velocity. The maximal (uncorrected) LDC amplitude depends on the minimal acceptable laser beam diameter, which is $\sim 9\mathrm{\mu m}$ at the laser beam waist, for which a minimum sampling rate of $333\mathrm{kS}/\mathrm{s}$ and a flow rate of $<0.3\mathrm{l}/\min$ are needed, 55 μm (minimum at $0.3\mathrm{l}/\min$ flow rate and $80\mathrm{kS}/\mathrm{s}$) and 90 μm (minimum at $0.5\mathrm{l}/\min$ flow rate and $80\mathrm{kS}/\mathrm{s}$). Hence, the minimum detectable ${\mathrm{H}}_2\mathrm{O}$ particle/droplet size varies accordingly between about 90 nm ($333\mathrm{kS}/\mathrm{s}$ sampling, $0.3\mathrm{l}/\min$ flow rate) and about 200 nm ($80\mathrm{kS}/\mathrm{s}$ sampling, $0.5\mathrm{l}/\min$ flow rate) for a minimum $\mathrm{SNR}=2$ and LDC noise of 1.4 mVrms.

Download Full Size | PDF

 

Fig. 12. Measurement results of the SNR of PSL ($n=1.61$) and silica ($n=1.47$) particles with multiple sizes at 33 mW output power of the laser beam. A SNR of 30.3 was achieved for PSL particles 147 nm in diameter. Even particle diameters ($500/700/1000/1600\mathrm{nm}$) were used where the actual diameters of PSL and silica particles differed.

Download Full Size | PDF

The amplitude ratios using Mie theory are shown in Fig. 13 for PSL particles and compared with measurement results using monodisperse particle suspensions with a flow rate of $0.3\mathrm{l}/\min$. There is a high agreement between simulation and measurement results with an average relative deviation of 8%.

 

Fig. 13. Comparison of the scattering amplitude ratio (angle intervals 29.5‥37.0° and 15.6‥29.4°) between simulation and measurement results using PSL particles. The average deviation equals 8%.

Download Full Size | PDF

Ahead of operation, the particle size dependent detection efficiency of the sensor system was calibrated using the SMPS reference system and PSL particles. The result can be seen in Fig. 14. The minimal detectable particle concentration decreases with increasing particle size. For example, the minimal particle concentration for 600 nm sized particles needs to be at least $100/{\mathrm{cm}}^3$, whereas particles with 1800 nm in diameter only require a concentration of about $10/{\mathrm{cm}}^3$.

 

Fig. 14. Minimal detectable concentration of PSL particles at 33 mW output power and $0.5\mathrm{l}/\min$ flow rate, derived from measurements. It strongly depends on the particle size and needs to be considered to determine the actual particle concentration, e.g., as in the measurement shown in Fig. 15.

Download Full Size | PDF

The correction factors for the scattering amplitudes using the TOFs were determined from measurements using monodisperse PSL with 296 nm. We found an accuracy of the particle size determination of 10%–20%.

The performance of the sensor system including the LDC and matrix method at $0.5\mathrm{l}/\min$ flow rate was compared with SMPS measurements using a polydisperse solution containing PSL ($n=1.610$) with sizes of 147, 296, 496, 707, and 903 nm and silica ($n=1.466$) with sizes 490, 730, and 990 nm (see Fig. 15). About 10,000 scattering events were detected on average per minute, and only scattering amplitudes with $\mathrm{SNR}\ge 10$ were accepted for evaluation. In total, the results of the OPS and the SMPS are in good agreement and the size accuracy of the OPS shows to be $\pm 10\%–20\%$, depending on the particle size. Concentration drops, e.g., at 400 nm, were not as well resolved as by the SMPS system and show room for improvement. Particles with diameters of $\sim 700$ and $\sim 900\mathrm{nm}$ show the largest deviation, which can be addressed to the deviation between the realistic and the assumed indices of refraction.

 

Fig. 15. Comparison of the measurement results of the OPS using the 3D matrix technique (see Fig. 9) and $0.5\mathrm{l}/\min$ flow rate, and the SMPS reference system, using PSL and silica particles. The SMPS can detect particles with sizes up to $\sim 1100\mathrm{nm}$. There is good agreement between both results. The deviation can be addressed to the variation of the laser beam profile (see Fig. 7).

Download Full Size | PDF

The result of measurements using DEHS particles (Di-2-Ethylhexyl-Sebacat, $n=1.46$) are shown in Fig. 16. The results also agree well with the SMPS reference measurement. However, a concentration drop can be observed in the OPS result at very small particle sizes. This can be addressed to the required minimum SNR of 10 in the processing, as described in Section 2.A.

 

Fig. 16. Comparison of the measurement results of DEHS particles. As described in Section 2.A, only scattering amplitudes with at least $\mathrm{SNR}=10$ were accepted, hence leading to a drop of the final particle concentration at the minimal detectable particle sizes (red circle). The results are in good agreement.

Download Full Size | PDF

4. Conclusion and Outlook

We present a miniaturized sensor system with an enhanced intensity ratio approach using a LDC technique. The sensor system is capable of detecting particles with sizes of at least 147 nm with a SNR of 30.3. It offers a reduced dependence on the index of refraction for the correct particle size identification using a 3D matrix method. To magnify the sensitivity, we use Fresnel ring lenses to increase the effective detection area. As the structural components consist of plastic material, it seems feasible to produce the basic system using injection molding, thus minimizing the costs of the system. To further improve the performance of the present proof-of-concept OPS, an ADC with a higher sampling rate is highly beneficial, allowing a more precise identification of the TOFs and improved signal filtering, thus offering a lower particle size detection limit.

If the size of the sensor system is not as important as for this work, additional methods can be used to minimize the interference effects on the laser beam intensity by the laser beam aperture, e.g., using an inverse Gaussian filter.