Abstract

Mie theory is used to investigate the degree to which a response from an optical particle counter (OPC) can be made monotonic when sizing particles of a given refractive index. This investigation is restricted to OPC designs that use monochromatic illumination and have coaxial light-collection optics. By systematically exploring the angular limits of the collection optics, it is found that, for certain limits, a very nearly monotonic response can be achieved for a nonresonant cavity OPC for a range of refractive indices. In contrast, for a resonant cavity instrument, this investigation did not reveal any angular limits where the response is close to being monotonic, unless the refractive index of the particles being sized has a large imaginary component.

© 1988 Optical Society of America

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References

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  1. R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).
    [CrossRef]
  2. R. G. Pinnick, D. M. Garvey, L. D. Duncan, “Calibration of Knollenberg FSSP Light-Scattering Counters for Measurement of Cloud Droplets,” J. Appl. Meteorol. 20, 1049 (1981).
    [CrossRef]
  3. D. M. Garvey, R. G. Pinnick, “Response Characteristics of the Particle Measuring Systems Active Scattering Aerosol Spectrometer Probe (ASASP-X),” Aerosol Sci. Technol. 2, 477 (1983).
    [CrossRef]
  4. B. Y. H. Liu, W. W. Syzmanski, K. Ahn, “On Aerosol Size Distribution Measurement by Laser and White Light Optical Particle Counters,” J. Environ. Sci. page 19 (May/June1985).
  5. D. D. Cooke, M. Kerker, “Response Calculations for Light-Scattering Aerosol Particle Counters,” Appl. Opt. 14, 734 (1975).
    [CrossRef] [PubMed]
  6. R. G. Knollenberg, Particle Measuring Systems, Inc.; private communication (1986).
  7. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  8. R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Baton Rouge, 1987).
  9. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).
  10. E. D. Hirleman, “Laser Based Single Particle Counters for in situ Particle Diagnostics,” Opt. Engl. 19, 854 (1980).

1985 (1)

B. Y. H. Liu, W. W. Syzmanski, K. Ahn, “On Aerosol Size Distribution Measurement by Laser and White Light Optical Particle Counters,” J. Environ. Sci. page 19 (May/June1985).

1983 (1)

D. M. Garvey, R. G. Pinnick, “Response Characteristics of the Particle Measuring Systems Active Scattering Aerosol Spectrometer Probe (ASASP-X),” Aerosol Sci. Technol. 2, 477 (1983).
[CrossRef]

1981 (1)

R. G. Pinnick, D. M. Garvey, L. D. Duncan, “Calibration of Knollenberg FSSP Light-Scattering Counters for Measurement of Cloud Droplets,” J. Appl. Meteorol. 20, 1049 (1981).
[CrossRef]

1980 (1)

E. D. Hirleman, “Laser Based Single Particle Counters for in situ Particle Diagnostics,” Opt. Engl. 19, 854 (1980).

1979 (1)

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).
[CrossRef]

1975 (1)

Ahn, K.

B. Y. H. Liu, W. W. Syzmanski, K. Ahn, “On Aerosol Size Distribution Measurement by Laser and White Light Optical Particle Counters,” J. Environ. Sci. page 19 (May/June1985).

Auvermann, H. J.

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).
[CrossRef]

Bohren, C. F.

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

Cooke, D. D.

Duncan, L. D.

R. G. Pinnick, D. M. Garvey, L. D. Duncan, “Calibration of Knollenberg FSSP Light-Scattering Counters for Measurement of Cloud Droplets,” J. Appl. Meteorol. 20, 1049 (1981).
[CrossRef]

Garvey, D. M.

D. M. Garvey, R. G. Pinnick, “Response Characteristics of the Particle Measuring Systems Active Scattering Aerosol Spectrometer Probe (ASASP-X),” Aerosol Sci. Technol. 2, 477 (1983).
[CrossRef]

R. G. Pinnick, D. M. Garvey, L. D. Duncan, “Calibration of Knollenberg FSSP Light-Scattering Counters for Measurement of Cloud Droplets,” J. Appl. Meteorol. 20, 1049 (1981).
[CrossRef]

Hirleman, E. D.

E. D. Hirleman, “Laser Based Single Particle Counters for in situ Particle Diagnostics,” Opt. Engl. 19, 854 (1980).

Huffman, D. R.

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

Kerker, M.

Knollenberg, R. G.

R. G. Knollenberg, Particle Measuring Systems, Inc.; private communication (1986).

Liu, B. Y. H.

B. Y. H. Liu, W. W. Syzmanski, K. Ahn, “On Aerosol Size Distribution Measurement by Laser and White Light Optical Particle Counters,” J. Environ. Sci. page 19 (May/June1985).

Pinnick, R. G.

D. M. Garvey, R. G. Pinnick, “Response Characteristics of the Particle Measuring Systems Active Scattering Aerosol Spectrometer Probe (ASASP-X),” Aerosol Sci. Technol. 2, 477 (1983).
[CrossRef]

R. G. Pinnick, D. M. Garvey, L. D. Duncan, “Calibration of Knollenberg FSSP Light-Scattering Counters for Measurement of Cloud Droplets,” J. Appl. Meteorol. 20, 1049 (1981).
[CrossRef]

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).
[CrossRef]

Syzmanski, W. W.

B. Y. H. Liu, W. W. Syzmanski, K. Ahn, “On Aerosol Size Distribution Measurement by Laser and White Light Optical Particle Counters,” J. Environ. Sci. page 19 (May/June1985).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Aerosol Sci. Technol. (1)

D. M. Garvey, R. G. Pinnick, “Response Characteristics of the Particle Measuring Systems Active Scattering Aerosol Spectrometer Probe (ASASP-X),” Aerosol Sci. Technol. 2, 477 (1983).
[CrossRef]

Appl. Opt. (1)

J. Aerosol Sci. (1)

R. G. Pinnick, H. J. Auvermann, “Response Characteristics of Knollenberg Light-Scattering Aerosol Counters,” J. Aerosol Sci. 10, 55 (1979).
[CrossRef]

J. Appl. Meteorol. (1)

R. G. Pinnick, D. M. Garvey, L. D. Duncan, “Calibration of Knollenberg FSSP Light-Scattering Counters for Measurement of Cloud Droplets,” J. Appl. Meteorol. 20, 1049 (1981).
[CrossRef]

J. Environ. Sci. (1)

B. Y. H. Liu, W. W. Syzmanski, K. Ahn, “On Aerosol Size Distribution Measurement by Laser and White Light Optical Particle Counters,” J. Environ. Sci. page 19 (May/June1985).

Opt. Engl. (1)

E. D. Hirleman, “Laser Based Single Particle Counters for in situ Particle Diagnostics,” Opt. Engl. 19, 854 (1980).

Other (4)

R. G. Knollenberg, Particle Measuring Systems, Inc.; private communication (1986).

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

R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Baton Rouge, 1987).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

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Figures (7)

Fig. 1
Fig. 1

Simplified diagram of an OPC showing the truncation angles θf and θr. These define a solid angle that has axial symmetry about the laser beam. Light scattered within this solid angle is sensed by the photodetector of the OPC.

Fig. 2
Fig. 2

Black dots indicate the response values between the size parameter limits of ~4 and 100, calculated for the size parameters of Table I. These response values were calculated for truncation angles of θf = 45°, θr = 135°, and a refractive index of 1.33. The curve is a spline fit to the individual response values.

Fig. 3
Fig. 3

Nonresonant cavity instrument contour plots of the monotonicity parameter s for the four refractive indices. The black dots mark the location of the largest s value that defines the improved truncation angles. (For m = 1.95–0.66i, and m = 1.50–1.0i, the improved truncation angles were arbitrarily specified to be θf = 20°, θr = 100°, because θf = 5°, θr = 175°, as indicated in this figure, are impractical limits for OPC construction.)

Fig. 4
Fig. 4

Nonresonant cavity OPC responses for (1) the compromise truncation angles (θf = 18°, θr = 99°), (2) a forward-scattering instrument (θf = 4°, θr = 22°), and (3) a wide-angle instrument (θf = 45°, θr = 135°). These responses, shown for the four refractive indices, have been computed using a very fine step size between adjacent size parameters.

Fig. 5
Fig. 5

Resonant cavity instrument contour plots of the monotonicity parameter s for the four refractive indices. The black dots mark the location of the largest s value that defines the improved truncation angles.

Fig. 6
Fig. 6

Resonant cavity OPC responses for the compromise truncation angles (θf = 7°, θr = 71°). Also shown are the responses for a wide-angle OPC with θf = 35°, θr = 120°. These responses, shown for the four refractive indices, have been computed using a very fine step size between adjacent size parameters.

Fig. 7
Fig. 7

Average relative error Er(•) and the maximum relative error Em(□) plotted vs monotonicity parameter s. The dashed line is a line of regression fit to Em vs s; the solid line is a line of regression fit to Er vs s.

Tables (5)

Tables Icon

Table I The 100 Size Parameters for Which Responses are Calculated

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Table II Nonresonant Cavity Instrument: Improved Truncation Angles

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Table III Nonresonant Cavity Instrument: Compromise Truncation Angles

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Table IV Resonant Cavity Instrument: Improved Truncation Angles

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Table V Resonant Cavity Instrument: Compromise Truncation Angles

Equations (6)

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R = λ 2 2 π θ f θ r 1 2 [ | S 1 ( x , m , θ ) | 2 + | S 2 ( x , m , θ ) | 2 ] sin θ d θ ,
R = λ 2 2 π θ f θ r 1 2 [ | S 1 ( x , m , θ ) + S 1 ( x , m , π θ ) | 2 + | S 2 ( x , m , θ ) + S 2 ( x , m , π θ ) | 2 ] sin θ d θ
R ( θ f , θ r , x j , m ) = σ ( θ r , x j , m ) σ ( θ f , x j , m ) .
t ( θ f , θ r , x i ) = log 10 [ R ( θ f , θ r , x , m ) ] log 10 ( x ) | x i ,
s ( θ f , θ r ) = minimum [ t ( θ f , θ r , x i ) ] , i = 1 , 99 .
E r ( θ f , θ r , m ) = 1 150 Δ x ( θ f , θ r , x , m ) x d x / 1 150 d x ,

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