Abstract

We present a miniaturized particle sensor collecting scattered light in two solid angle intervals by Fresnel ring lenses. The particle size is determined from the ratio of both scattering amplitudes (intensity ratio) in addition to a linear diversity combining technique, generating a 3D particle size matrix that reduces the ambiguity by the index of refraction on the particle size identification. A signal-to-noise ratio of 30.3 was achieved for 147 nm sized polystyrene latex particles. Measurements of polydisperse particle size distribution show good agreement with the results by a scanning mobility particle sizer.

© 2014 Optical Society of America

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References

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  1. D. Black, M. McQuay, and M. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Progr. Energy Combust. Sci. 22, 267–306 (1996).
    [CrossRef]
  2. L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
    [CrossRef]
  3. J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
    [CrossRef]
  4. A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
    [CrossRef]
  5. H. A. Beck, R. Niessner, and C. Haisch, “Development and characterization of a mobile photoacoustic sensor for on-line soot emission monitoring in diesel exhaust gas,” Anal. Bioanal. Chem. 375, 1136–1143 (2003).
    [CrossRef]
  6. C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
    [CrossRef]
  7. R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).
  8. R. Harrison and J. Yin, “Particulate matter in the atmosphere: which particle properties are important for its effects on health?” Sci. Total Environ. 249, 85–101 (2000).
    [CrossRef]
  9. K. Tsutsui, K. Koya, and T. Kato, “An investigation of continuous-angle laser light scattering,” Rev. Sci. Instrum. 69, 3482–3786 (1998).
    [CrossRef]
  10. D. G. Brennan, “Linear diversity combining techniques,” Proc. IEEE 91, 331–356 (2003).
    [CrossRef]
  11. F. Zhao, Z. Gong, H. Hu, M. Tanaka, and T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
    [CrossRef]
  12. V. V. Berdnik and V. A. Loiko, “Retrieval of size and refractive index of spherical particles by multiangle light scattering: neural network method application,” Appl. Opt. 48, 6178–6187 (2009).
    [CrossRef]
  13. M. Kocifaj and M. Držík, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol Sci. 28, 797–804 (1997).
    [CrossRef]
  14. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

2011 (1)

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

2009 (2)

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

V. V. Berdnik and V. A. Loiko, “Retrieval of size and refractive index of spherical particles by multiangle light scattering: neural network method application,” Appl. Opt. 48, 6178–6187 (2009).
[CrossRef]

2005 (1)

C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
[CrossRef]

2003 (2)

H. A. Beck, R. Niessner, and C. Haisch, “Development and characterization of a mobile photoacoustic sensor for on-line soot emission monitoring in diesel exhaust gas,” Anal. Bioanal. Chem. 375, 1136–1143 (2003).
[CrossRef]

D. G. Brennan, “Linear diversity combining techniques,” Proc. IEEE 91, 331–356 (2003).
[CrossRef]

2002 (1)

A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
[CrossRef]

2000 (2)

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

R. Harrison and J. Yin, “Particulate matter in the atmosphere: which particle properties are important for its effects on health?” Sci. Total Environ. 249, 85–101 (2000).
[CrossRef]

1998 (1)

K. Tsutsui, K. Koya, and T. Kato, “An investigation of continuous-angle laser light scattering,” Rev. Sci. Instrum. 69, 3482–3786 (1998).
[CrossRef]

1997 (2)

M. Kocifaj and M. Držík, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol Sci. 28, 797–804 (1997).
[CrossRef]

F. Zhao, Z. Gong, H. Hu, M. Tanaka, and T. Hayasaka, “Simultaneous determination of the aerosol complex index of refraction and size distribution from scattering measurements of polarized light,” Appl. Opt. 36, 7992–8001 (1997).
[CrossRef]

1996 (1)

D. Black, M. McQuay, and M. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Progr. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Ahlquist, N. C.

A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
[CrossRef]

Beck, H. A.

H. A. Beck, R. Niessner, and C. Haisch, “Development and characterization of a mobile photoacoustic sensor for on-line soot emission monitoring in diesel exhaust gas,” Anal. Bioanal. Chem. 375, 1136–1143 (2003).
[CrossRef]

Berdnik, V. V.

Black, D.

D. Black, M. McQuay, and M. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Progr. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Bonin, M.

D. Black, M. McQuay, and M. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Progr. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Brennan, D. G.

D. G. Brennan, “Linear diversity combining techniques,” Proc. IEEE 91, 331–356 (2003).
[CrossRef]

Brook, J.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Burnett, R.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Cakmak, S.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Chen, D.-R.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Clarke, A. D.

A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
[CrossRef]

Dann, T.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Delocla, C.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Držík, M.

M. Kocifaj and M. Držík, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol Sci. 28, 797–804 (1997).
[CrossRef]

Goldberg, M.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Gong, Z.

Haisch, C.

H. A. Beck, R. Niessner, and C. Haisch, “Development and characterization of a mobile photoacoustic sensor for on-line soot emission monitoring in diesel exhaust gas,” Anal. Bioanal. Chem. 375, 1136–1143 (2003).
[CrossRef]

Harrison, R.

R. Harrison and J. Yin, “Particulate matter in the atmosphere: which particle properties are important for its effects on health?” Sci. Total Environ. 249, 85–101 (2000).
[CrossRef]

Hayasaka, T.

He, L.

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Howell, S.

A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
[CrossRef]

Hu, H.

Huang, H.

C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
[CrossRef]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Kato, T.

K. Tsutsui, K. Koya, and T. Kato, “An investigation of continuous-angle laser light scattering,” Rev. Sci. Instrum. 69, 3482–3786 (1998).
[CrossRef]

Kim, W.

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

Kocifaj, M.

M. Kocifaj and M. Držík, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol Sci. 28, 797–804 (1997).
[CrossRef]

Koya, K.

K. Tsutsui, K. Koya, and T. Kato, “An investigation of continuous-angle laser light scattering,” Rev. Sci. Instrum. 69, 3482–3786 (1998).
[CrossRef]

Krewski, D.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Li, L.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Liang, C.

C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
[CrossRef]

Loiko, V. A.

McQuay, M.

D. Black, M. McQuay, and M. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Progr. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Moore, K.

A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
[CrossRef]

Niessner, R.

H. A. Beck, R. Niessner, and C. Haisch, “Development and characterization of a mobile photoacoustic sensor for on-line soot emission monitoring in diesel exhaust gas,” Anal. Bioanal. Chem. 375, 1136–1143 (2003).
[CrossRef]

Ozdemir, S. K.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Özdemir, S. K.

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

Philips, O.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Ren, B.

C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
[CrossRef]

Tanaka, M.

Tsutsui, K.

K. Tsutsui, K. Koya, and T. Kato, “An investigation of continuous-angle laser light scattering,” Rev. Sci. Instrum. 69, 3482–3786 (1998).
[CrossRef]

Vincent, R.

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

Xiao, Y.-F.

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Yang, L.

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Yin, J.

R. Harrison and J. Yin, “Particulate matter in the atmosphere: which particle properties are important for its effects on health?” Sci. Total Environ. 249, 85–101 (2000).
[CrossRef]

Zhao, F.

Zhao, Y.

C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
[CrossRef]

Zhu, J.

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Anal. Bioanal. Chem. (1)

H. A. Beck, R. Niessner, and C. Haisch, “Development and characterization of a mobile photoacoustic sensor for on-line soot emission monitoring in diesel exhaust gas,” Anal. Bioanal. Chem. 375, 1136–1143 (2003).
[CrossRef]

Appl. Opt. (2)

Inhalation Toxicol. (1)

R. Burnett, J. Brook, T. Dann, C. Delocla, O. Philips, S. Cakmak, R. Vincent, M. Goldberg, and D. Krewski, “Association between particulate- and gas-phase components of urban air pollution and daily mortality in eight Canadian cities,” Inhalation Toxicol. 12, 15–39 (2000).

J. Aerosol Sci. (1)

M. Kocifaj and M. Držík, “Retrieving the size distribution of microparticles by scanning the diffraction halo with a mobile ring-gap detector,” J. Aerosol Sci. 28, 797–804 (1997).
[CrossRef]

J. Atmos. Ocean. Technol. (1)

A. D. Clarke, N. C. Ahlquist, S. Howell, and K. Moore, “A miniature optical particle counter for in situ aircraft aerosol research,” J. Atmos. Ocean. Technol. 19, 1557–1566 (2002).
[CrossRef]

Nat. Nanotechnol. (1)

L. He, S. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[CrossRef]

Nat. Photonics (1)

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2009).
[CrossRef]

Proc. IEEE (1)

D. G. Brennan, “Linear diversity combining techniques,” Proc. IEEE 91, 331–356 (2003).
[CrossRef]

Proc. SPIE (1)

C. Liang, H. Huang, B. Ren, and Y. Zhao, “A miniaturized laser-diode-based optical sensor for laser particle counter,” Proc. SPIE 5634, 375–380 (2005).
[CrossRef]

Progr. Energy Combust. Sci. (1)

D. Black, M. McQuay, and M. Bonin, “Laser-based techniques for particle-size measurement: a review of sizing methods and their industrial applications,” Progr. Energy Combust. Sci. 22, 267–306 (1996).
[CrossRef]

Rev. Sci. Instrum. (1)

K. Tsutsui, K. Koya, and T. Kato, “An investigation of continuous-angle laser light scattering,” Rev. Sci. Instrum. 69, 3482–3786 (1998).
[CrossRef]

Sci. Total Environ. (1)

R. Harrison and J. Yin, “Particulate matter in the atmosphere: which particle properties are important for its effects on health?” Sci. Total Environ. 249, 85–101 (2000).
[CrossRef]

Other (1)

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

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Figures (16)

Fig. 1.
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 3.2/7.1/9.5mm. The first Fresnel lens fully covered the available space at the lens mount.

Fig. 2.
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.

Fig. 3.
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 r1 and the scattering position. Hence, the effective detector area and the scattering angles depend on the scattering position (see Figs. 4 and 5).

Fig. 4.
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.

Fig. 5.
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 ±1mm around the laser beam waist (12.5/10.5mm), 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.

Fig. 6.
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.

Fig. 7.
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.

Fig. 8.
Fig. 8.

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

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).

Fig. 10.
Fig. 10.

Scheme of the measurement setup. The particles are generated out of a liquid suspension (ultra pure H2O) by dry N2, 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 80kS/s.

Fig. 11.
Fig. 11.

A minimum of three sampling points are needed for processing; hence the minimum TOF is 37 μs at 80kS/s or 10 μs at 333kS/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 9μm at the laser beam waist, for which a minimum sampling rate of 333kS/s and a flow rate of <0.3l/min are needed, 55 μm (minimum at 0.3l/min flow rate and 80kS/s) and 90 μm (minimum at 0.5l/min flow rate and 80kS/s). Hence, the minimum detectable H2O particle/droplet size varies accordingly between about 90 nm (333kS/s sampling, 0.3l/min flow rate) and about 200 nm (80kS/s sampling, 0.5l/min flow rate) for a minimum SNR=2 and LDC noise of 1.4 mVrms.

Fig. 12.
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 (500/700/1000/1600nm) were used where the actual diameters of PSL and silica particles differed.

Fig. 13.
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%.

Fig. 14.
Fig. 14.

Minimal detectable concentration of PSL particles at 33 mW output power and 0.5l/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.

Fig. 15.
Fig. 15.

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

Fig. 16.
Fig. 16.

Comparison of the measurement results of DEHS particles. As described in Section 2.A, only scattering amplitudes with at least 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.

Equations (9)

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Idet=PdetAdet=NS(dp,λ,θ,n)r2Ilas,
Adet,eff=(tan2βtan2α)·o2π,
i=f2·dl1l2f1f2oof1dl1l2f2f1oof1,
y=V·a=ioa.
1/f=1/o+1/i,
θ=arctan(1o(rldl1l2(rlk1+dl1l2k))),
Ilas=2Plasπw02(w(z)w0)2exp(2r2w(z)2),
U(t)=1σ2πexp(t22σ2),
U(t)dt=U^2πσ·erf(Δt2σ),

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