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Calibration of optical particle counters: Comparison between theoretically and experimentally derived results
J. Aerosol Sci., Vol. 21, Suppl. Printed in Great Britain.
i, pp. S521-S524,
1990.
Calibration of Optical Particle Counters: Comparison M w ~
0021-8502/90 $3.00 + 0.00 Pergamon Press plc
theoretically and experimentally derived
results B. Sachweh 1, H. Umhauer 2 and H. B/Rtner 1
Lehrstuhl fiirMechanische Verfahrenstechnik und Str6mungsmechanik, UniversitRt Kaiserslautern Postfach 3049, D-6750 Kalserslautern Institut ftirMechanische Verfahrenstechnik und Mechanik, Universit~t Karlsruhe Richard-Willstatter-AUee, D-7500 Karlsruhe
Introduction Optical Particle Counters (OPCs) with an optically defined measuring volume are suited for the measurement of particle size and concentration, i f the particle motion or dispersion is not to be influenced. True in situ measurements are practicable without sampling and the associated problems. Examples of application are given in agglomerates with low adherence, liquid particles with high vapour pressure and toxic materials or carrier fluid. The measurement information utilized by the OPC is the scattering of light by a single particle, which is illuminated in a small detection area. A correlation between light scattering intensity and the particle size has to be determined. This calibration is usually performed by experiments. The practical use of the OPC can be improved, if the calibration curves for different materials are theoretically defined. A solution of Maxwell's equation for light scattered by a spherical particle is given by Mie [I] for illumination in a plane wave front. The calibration curves are numerically predictable by that theory, if the refractive index of the material and the optical data of the OPC are well known. Instrument design
photo-multiplier
\1/ mlL,/~ ~
S ----~ ~
~
Analogue signal detector aoerture II
lens II
Digital s'gna et,aluatio~t
oDe,lure I
~s
Illuminating sylte~ (OpUCOl o~is I)
Fig. 1: Instrument design The measurement instrument consists of 3 fundamental components: A detector head for primary registration of measurement information, a power supply for the lamp, the photomultiplier and the signal amplifier and an analogue resp. digital signal evaluation. White light is projected into a flow tube containing the test aerosol. Light scattered at an average angle of 90" is detected by a photomultiplier. Photons impinging upon the cathode generate an electron current, which is successively amplified. The rate of amplification is adjustable by the accelerating voltage, restricted by the signal to noise ratio of output pulses generated. A preamplifier integrated into the detector head yields an output voltage ranging from 0 to 10 Volts. This output signal chracterizes the light scattering intensity and is to be correlated to the particle size. Two calibration methods are presently practicable: The measurement oF different monodisperse aerosols (Latex,...) or the aerodynamic calibration [2], using the well known separating characteristic of a small labor~tory separator to obtain a characteristic size o-f a polydisperse aerosol. The latter is the only method for materials resulting from industrial processes. $521
$522
B. S A C H W E H
eta!.
Optical fundamentals If particles are illuminated in a plane, monochromatic wave field, scattering of light is detectable as a sum of refraction, diffraction and retlection of an incident light beam. The Mie calculation results in the Mie intensity, which depends on the solid angle ~, the angle of polarization ~o, the particle diameter x, the wave length A and the complex refractive index m(A). The intensity of light scattered at an angle 0 in a distance r from the particle is defined by
I(~,0,r) =
I0 (i1(~'0)+i2(~'0)) 2 k2 r2 '
(1)
if unpolarized light is used. To take into account the geometry of the illuminating and collecting lens a weighting function F(0,~) [3] has to be integrated into calculation. This function depends on the scattering angle 0 and the angle 4,, which characterizes the inclination of an illuminating ray to the optical axis of the detector system. The influence on the light scattering intensity is negligible, if particles smaller than 4/~m are investigated. The deviation form experimental data increases for greater particles. For description of the wave length dependence of the optical components the emissivity of the light source E(A) and the sensitivity of the photomultiplier tube L(A) has to be considered. The intensity of light scattered at angles from 01 to 02 in a wavelength-spectrum from AI to A2 is given by:
= fff
F(0,4 ) de d0dA
(2)
The numerical calculation of calibration curves is performed by two steps on an IBM-AT compatible Personal-Computer: Stev 1: Calculation of the Mie scattering functions for a size parameter range from c~m l.n to ~ m ~ at a constant
A0:
wavelength
2 Io A o
I(a'01""02'~1'"~2) --'--~8 - - ~
ff
F(0,~)(il(c~,t~ ) + i2(a,0)) d 0 d ~
(3)
The distance r from the detection area is set to 1, because the influence of this parameter on the light scattering intensity can be included into the transfer parameter K, defined by Eq. (6), if the results are plotted into a logarithmic diagram.
Stev 2: Determination of scattering intensity for incident white light with regard to the spectral functions and the geometry of optical components: A2 I(x) = f ~ I(a) E(A) L(A ) dA; (4) The calibration curve at a particle diameter x is derived from the result of step 1 by calculation of the size parameter a for an instantaneous wave length A =
7( X
A
=
~'X 0
(s)
A0
The limits of main calculation parameters for the OPC investigated are given below in Table 1 including the integration step width. sensitivity range: aperture of lenses: size parameter:
290 - 700 nm 12 ° 0.9 - 79
(step: 1 nm) (step: 0.5 ° ) (step: 0.1)
Table h Calculation parameter range Matching of the theoretically derived results (dimensionless light intensity) to the photomultiplier output voltage is required. The transfer parameter K can be obtained-by comparison of the pulse height U for an arbitrary material at a representative particle diameter x with the light scattering intensity calculated: K = U(x). = const. I (~) K has to be constant for all material fulfilling the physical conditions of Mie calculation.
(6)
Calibration of optical particle counters
$523
Results of inte~omparison between experimemtal and numerical data The Optical Particle Counter investigated (HC15, Polytec GmbH, Waldbronn) uses a peak value detektor for signal evaluation. The pulses resulting from the photomultiplier tube are not filtered for noise reduction. 8.00
-
4.00 -
/
1.00 o
>
./
0.60 -
I E
|
0.20
•
0.08 0.04
J"
/
o
o
/_
/
/
Y
/
/
/
/
•
moosurom4ml d ~ Q ~O"Calcul~k~
I
0.01 / 0.2
I
0.6 1.0 particle size [ ~ m ]
I
4.0
8.0
Fig. 2: Calibration curve for latex particles of an OPC-HC15 using peak value detection T h e experimental calibration was carried out with monodisperse latex aerosols (refractive index m=1.60). In the complete size range no sufficient correlation between calculation and measurement can be achieved. The distortion of the experimental calibration data results from the peak height analyzing of the photomultiplier signals. The stochastic component of the pulses leads to an amplitude fluctuation, which depends on the pulse height resp. the particle size. For small particles this effect increases, so that an overrating in relation to greater particles is unavoidable, i f the pulse height is taken for signal characterization.
8.00. 4.00-
1.00-
/a
0.60Q
'-
0.20-
"
0.08
@
0.04
0.01- / 0.2
f
/
/
/
j
/ M1e--calcul~lon
/ I
D exp. data: wotw
I 0.6
1.0
4.0
".-
I 8.0
particle size [ p m ]
Fig. 3: Calibration for latex and water of an OPC-HC15 using a mean value signal evaluation A good correlation for latex particles is obtained by using the mean value of the signal spectrum for intercomparison. Problems occur, if the signal flanks are taken into calculation, because of a size dependent lowering of the mean value. To realize this extensive evaluation technique special software algorithms were developed at our institute. A special hardware design enables the analosue to digital converting of the ulses and the fur signal processing. good agreement between numerically and experimentally derived results becomes obvious in the investigated particle size range (0.4 - 7.0/an). The transfer parameter K also gives good correlation in the
$524
B. S A C H W E H et al.
calculation of the calibration curve for water droplets. The experimental data were achieved by the aerodynamic calibration method using a small laboratory cyclone for droplet separation. An alternative measurement instrument was developed by Umhauer [4] and consists of the same fundamental components like the OPC - HC15. The following features characterize this instrument: -
two measurement volumes for correction of the counting error resulting from particles situated at the boundary of the detection volume. improved signal evaluation by using analogue filter techniques 8.00. 4.00-
/
o >
/
/
1.00"
r Lm
/
I
/
0.60-
JE 0
.c
0.20-
D a.
0.08 -.
-//
/
2/
/
/
0.04 -.,
/ • exp. dote Lo~o:< M~e - caicuiatlon
I
0.01
0.2
0.6
1.0 particle
4.0
I 8.0
size [~m]
Fig. 4: Calibration curve of an OPC - A70 for latex particles The signal filtering decreases the influence of overrating by the peak value detection, because of the smoothing effect on the signal amplitude. But it is not possible to get the good correlation of the mean value detection. Summary The quality of the correlation between numerically and theoretically derived results for calibration of OPCs strongly depends on the signal evaluation method. There exists an influence of the spectral functions of the optical components, which has to be included into calculation. The weighting function for the geometry of optical arrangement is negligible for particles smaller than 4/an. Only one transfer parameter enables the correct numerical calibration for different materials. For calibration of unknown aerosols only a small number of experimental data points has to be measured and a wide range of sizes can numerically be determined. Symbols (not defined) il,t(a,t~) Io k
M/e-intensity in (1) and perpendicular (2) to the plane of polarization intensity of incident radiation wave n u m b e r size parameter
References [1] Mie,G.: Beitriige zur Optik triiber Medien, Ann. Physik 25 (1908), p. 377 - 445 [2] Sachweh,B.,Bfittner H,: Measuring Droplet Sizes with an Optical Particle Counter: Aerodynamic Calibration and Extension of the Measuring Range to Smaller Sizes, J. Aerosol Sci. 19(1988) 7, p. g 5 3 - 956 [3] Hodkinson, J.R., Greenfield, J.R.: Response Calculations for Light - Scattering Aerosol Counters and Photometers,Applied Optics 4 (1965) 11, p. 1463 - 1474 [4] Umhaner, H.: Par tikelgr613en-Z~hlanalyse durch Streulichtmessung Meflvolumenabgrenzung, J. Aerosol Sci 14 (1983) 3. p. 344 - 348
bei
rein
optischer
i, pp. S521-S524,
1990.
Calibration of Optical Particle Counters: Comparison M w ~
0021-8502/90 $3.00 + 0.00 Pergamon Press plc
theoretically and experimentally derived
results B. Sachweh 1, H. Umhauer 2 and H. B/Rtner 1
Lehrstuhl fiirMechanische Verfahrenstechnik und Str6mungsmechanik, UniversitRt Kaiserslautern Postfach 3049, D-6750 Kalserslautern Institut ftirMechanische Verfahrenstechnik und Mechanik, Universit~t Karlsruhe Richard-Willstatter-AUee, D-7500 Karlsruhe
Introduction Optical Particle Counters (OPCs) with an optically defined measuring volume are suited for the measurement of particle size and concentration, i f the particle motion or dispersion is not to be influenced. True in situ measurements are practicable without sampling and the associated problems. Examples of application are given in agglomerates with low adherence, liquid particles with high vapour pressure and toxic materials or carrier fluid. The measurement information utilized by the OPC is the scattering of light by a single particle, which is illuminated in a small detection area. A correlation between light scattering intensity and the particle size has to be determined. This calibration is usually performed by experiments. The practical use of the OPC can be improved, if the calibration curves for different materials are theoretically defined. A solution of Maxwell's equation for light scattered by a spherical particle is given by Mie [I] for illumination in a plane wave front. The calibration curves are numerically predictable by that theory, if the refractive index of the material and the optical data of the OPC are well known. Instrument design
photo-multiplier
\1/ mlL,/~ ~
S ----~ ~
~
Analogue signal detector aoerture II
lens II
Digital s'gna et,aluatio~t
oDe,lure I
~s
Illuminating sylte~ (OpUCOl o~is I)
Fig. 1: Instrument design The measurement instrument consists of 3 fundamental components: A detector head for primary registration of measurement information, a power supply for the lamp, the photomultiplier and the signal amplifier and an analogue resp. digital signal evaluation. White light is projected into a flow tube containing the test aerosol. Light scattered at an average angle of 90" is detected by a photomultiplier. Photons impinging upon the cathode generate an electron current, which is successively amplified. The rate of amplification is adjustable by the accelerating voltage, restricted by the signal to noise ratio of output pulses generated. A preamplifier integrated into the detector head yields an output voltage ranging from 0 to 10 Volts. This output signal chracterizes the light scattering intensity and is to be correlated to the particle size. Two calibration methods are presently practicable: The measurement oF different monodisperse aerosols (Latex,...) or the aerodynamic calibration [2], using the well known separating characteristic of a small labor~tory separator to obtain a characteristic size o-f a polydisperse aerosol. The latter is the only method for materials resulting from industrial processes. $521
$522
B. S A C H W E H
eta!.
Optical fundamentals If particles are illuminated in a plane, monochromatic wave field, scattering of light is detectable as a sum of refraction, diffraction and retlection of an incident light beam. The Mie calculation results in the Mie intensity, which depends on the solid angle ~, the angle of polarization ~o, the particle diameter x, the wave length A and the complex refractive index m(A). The intensity of light scattered at an angle 0 in a distance r from the particle is defined by
I(~,0,r) =
I0 (i1(~'0)+i2(~'0)) 2 k2 r2 '
(1)
if unpolarized light is used. To take into account the geometry of the illuminating and collecting lens a weighting function F(0,~) [3] has to be integrated into calculation. This function depends on the scattering angle 0 and the angle 4,, which characterizes the inclination of an illuminating ray to the optical axis of the detector system. The influence on the light scattering intensity is negligible, if particles smaller than 4/~m are investigated. The deviation form experimental data increases for greater particles. For description of the wave length dependence of the optical components the emissivity of the light source E(A) and the sensitivity of the photomultiplier tube L(A) has to be considered. The intensity of light scattered at angles from 01 to 02 in a wavelength-spectrum from AI to A2 is given by:
= fff
F(0,4 ) de d0dA
(2)
The numerical calculation of calibration curves is performed by two steps on an IBM-AT compatible Personal-Computer: Stev 1: Calculation of the Mie scattering functions for a size parameter range from c~m l.n to ~ m ~ at a constant
A0:
wavelength
2 Io A o
I(a'01""02'~1'"~2) --'--~8 - - ~
ff
F(0,~)(il(c~,t~ ) + i2(a,0)) d 0 d ~
(3)
The distance r from the detection area is set to 1, because the influence of this parameter on the light scattering intensity can be included into the transfer parameter K, defined by Eq. (6), if the results are plotted into a logarithmic diagram.
Stev 2: Determination of scattering intensity for incident white light with regard to the spectral functions and the geometry of optical components: A2 I(x) = f ~ I(a) E(A) L(A ) dA; (4) The calibration curve at a particle diameter x is derived from the result of step 1 by calculation of the size parameter a for an instantaneous wave length A =
7( X
A
=
~'X 0
(s)
A0
The limits of main calculation parameters for the OPC investigated are given below in Table 1 including the integration step width. sensitivity range: aperture of lenses: size parameter:
290 - 700 nm 12 ° 0.9 - 79
(step: 1 nm) (step: 0.5 ° ) (step: 0.1)
Table h Calculation parameter range Matching of the theoretically derived results (dimensionless light intensity) to the photomultiplier output voltage is required. The transfer parameter K can be obtained-by comparison of the pulse height U for an arbitrary material at a representative particle diameter x with the light scattering intensity calculated: K = U(x). = const. I (~) K has to be constant for all material fulfilling the physical conditions of Mie calculation.
(6)
Calibration of optical particle counters
$523
Results of inte~omparison between experimemtal and numerical data The Optical Particle Counter investigated (HC15, Polytec GmbH, Waldbronn) uses a peak value detektor for signal evaluation. The pulses resulting from the photomultiplier tube are not filtered for noise reduction. 8.00
-
4.00 -
/
1.00 o
>
./
0.60 -
I E
|
0.20
•
0.08 0.04
J"
/
o
o
/_
/
/
Y
/
/
/
/
•
moosurom4ml d ~ Q ~O"Calcul~k~
I
0.01 / 0.2
I
0.6 1.0 particle size [ ~ m ]
I
4.0
8.0
Fig. 2: Calibration curve for latex particles of an OPC-HC15 using peak value detection T h e experimental calibration was carried out with monodisperse latex aerosols (refractive index m=1.60). In the complete size range no sufficient correlation between calculation and measurement can be achieved. The distortion of the experimental calibration data results from the peak height analyzing of the photomultiplier signals. The stochastic component of the pulses leads to an amplitude fluctuation, which depends on the pulse height resp. the particle size. For small particles this effect increases, so that an overrating in relation to greater particles is unavoidable, i f the pulse height is taken for signal characterization.
8.00. 4.00-
1.00-
/a
0.60Q
'-
0.20-
"
0.08
@
0.04
0.01- / 0.2
f
/
/
/
j
/ M1e--calcul~lon
/ I
D exp. data: wotw
I 0.6
1.0
4.0
".-
I 8.0
particle size [ p m ]
Fig. 3: Calibration for latex and water of an OPC-HC15 using a mean value signal evaluation A good correlation for latex particles is obtained by using the mean value of the signal spectrum for intercomparison. Problems occur, if the signal flanks are taken into calculation, because of a size dependent lowering of the mean value. To realize this extensive evaluation technique special software algorithms were developed at our institute. A special hardware design enables the analosue to digital converting of the ulses and the fur signal processing. good agreement between numerically and experimentally derived results becomes obvious in the investigated particle size range (0.4 - 7.0/an). The transfer parameter K also gives good correlation in the
$524
B. S A C H W E H et al.
calculation of the calibration curve for water droplets. The experimental data were achieved by the aerodynamic calibration method using a small laboratory cyclone for droplet separation. An alternative measurement instrument was developed by Umhauer [4] and consists of the same fundamental components like the OPC - HC15. The following features characterize this instrument: -
two measurement volumes for correction of the counting error resulting from particles situated at the boundary of the detection volume. improved signal evaluation by using analogue filter techniques 8.00. 4.00-
/
o >
/
/
1.00"
r Lm
/
I
/
0.60-
JE 0
.c
0.20-
D a.
0.08 -.
-//
/
2/
/
/
0.04 -.,
/ • exp. dote Lo~o:< M~e - caicuiatlon
I
0.01
0.2
0.6
1.0 particle
4.0
I 8.0
size [~m]
Fig. 4: Calibration curve of an OPC - A70 for latex particles The signal filtering decreases the influence of overrating by the peak value detection, because of the smoothing effect on the signal amplitude. But it is not possible to get the good correlation of the mean value detection. Summary The quality of the correlation between numerically and theoretically derived results for calibration of OPCs strongly depends on the signal evaluation method. There exists an influence of the spectral functions of the optical components, which has to be included into calculation. The weighting function for the geometry of optical arrangement is negligible for particles smaller than 4/an. Only one transfer parameter enables the correct numerical calibration for different materials. For calibration of unknown aerosols only a small number of experimental data points has to be measured and a wide range of sizes can numerically be determined. Symbols (not defined) il,t(a,t~) Io k
M/e-intensity in (1) and perpendicular (2) to the plane of polarization intensity of incident radiation wave n u m b e r size parameter
References [1] Mie,G.: Beitriige zur Optik triiber Medien, Ann. Physik 25 (1908), p. 377 - 445 [2] Sachweh,B.,Bfittner H,: Measuring Droplet Sizes with an Optical Particle Counter: Aerodynamic Calibration and Extension of the Measuring Range to Smaller Sizes, J. Aerosol Sci. 19(1988) 7, p. g 5 3 - 956 [3] Hodkinson, J.R., Greenfield, J.R.: Response Calculations for Light - Scattering Aerosol Counters and Photometers,Applied Optics 4 (1965) 11, p. 1463 - 1474 [4] Umhaner, H.: Par tikelgr613en-Z~hlanalyse durch Streulichtmessung Meflvolumenabgrenzung, J. Aerosol Sci 14 (1983) 3. p. 344 - 348
bei
rein
optischer