Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols

Guocai Shu; Tryfon T. Charalampopoulos

doi:10.1364/AO.39.006713

Applied Optics
Vol. 39,
Issue 36,
pp. 6713-6724
(2000)
•https://doi.org/10.1364/AO.39.006713

Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols

Guocai Shu and Tryfon T. Charalampopoulos

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Guocai Shu and Tryfon T. Charalampopoulos, "Unified inversion scheme that uses light scattering for morphological parameters and optical properties of aggregated aerosols," Appl. Opt. 39, 6713-6724 (2000)

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Abstract

A robust scheme for characterizing chainlike aggregated aerosols by use of nonintrusive light-scattering measurements is presented. This scheme entails the selection of suitable scattering quantities and their optimal measurement angles; the development of an inversion algorithm to yield the complex refractive index of agglomerates m = n + ik, the primary particle diameter d _p, the number of primary particles per agglomerate N _p, the number density of agglomerates n _A, and the volume fraction of agglomerates f _v; and evaluation of the uncertainties of the inferred parameters that correspond to measuring uncertainties. The data-inversion algorithm is based on the exact formulation of light scattering for agglomerates that consist of primary particles in the Rayleigh limit and therefore has solid theoretical foundations. In addition, this approach yields all the desired parameters of the aggregated aerosols by using in situ light-scattering measurements with a minimum of possible uncertainties. Furthermore, the methodology developed here can be extended to aerosols with other types of morphology and optical property.

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Set Number	Pairing Set	Minimum Inversion Uncertainty (%) of
Set Number	Pairing Set	n	k	x	N _p
1	R _vv(15°), R _hv(130°), K _vve(165°), R _hh(80°)	1.9	5.0	3.7	5.1
2	R _vv(15°), R _hv(15°), K _hhe(75°), R _hh(85°)	2.3	4.2	3.2	4.8
3	R _vv(15°), R _hv(15°), K _hve(65°), R _hh(80°)	1.8	5.4	4.7	5.0

x	N _p	Optimum Angles				Uncertainty (%) of
x	N _p	R _vv	R _hv	K _vve	R _hh	n	k	x	N _p
m = 1.7 + i 0.7
0.15	10	15	165	15	80	7.8	11.1	8.7	8.1
0.2	10	15	165	15	80	5.8	8.3	5.9	4.8
0.3	10	15	130	165	80	1.9	5.0	3.7	5.1
0.3	5	15	165	50	80	6.5	11.0	7.5	7.5
0.3	15	15	90	90	80	1.9	4.8	3.7	6.6
0.3	20	15	110	100	70	2.2	5.9	3.9	8.1
m = 1.6 + i 0.6
0.15	10	15	165	15	80	6.7	11.7	8.1	7.9
0.2	10	15	165	15	80	5.0	8.7	5.5	5.0
0.3	10	15	140	165	80	1.8	5.2	3.6	5.2
0.3	5	15	165	25	85	6.2	11.2	7.4	6.9
0.3	15	15	165	85	80	1.8	5.0	3.7	6.5
0.3	20	15	105	100	75	1.6	5.6	3.5	9.3

Example of Data Inversion	Case 1	Case 2
Simulated experimental data (assuming 5% error in measurement)	R _vv(15°) = 3.4 ± 0.2	R _vv(15°) = 4.2 ± 0.2
	R _hv(75°) = 0.0170 ± 0.0008	R _hv(75°) = 0.0119 ± 0.0006
	R _hh(75°) = 0.43 ± 0.02	R _hh(75°) = 0.45 ± 0.02
	K _vve(75°) = 0.0087 ± 0.0004	K _vve(75°) = 0.0035 ± 0.0002
Initial guess	n = 2.0	n = 2.0
	k = 1.0	k = 1.0
	x = 0.15	x = 0.3
	N _p = 20	N _p = 10
Number of iterations	6	7
Converged data and uncertainty corresponding to measurement errors	n = 1.70 ± 0.04	n = 1.60 ± 0.01
	k = 0.71 ± 0.05	k = 0.60 ± 0.04
	x = 0.30 ± 0.01	x = 0.20 ± 0.01
	N _p = 10 ± 1	N _p = 20 ± 2
Actual values	n = 1.70	n = 1.60
	k = 0.70	k = 0.60
	x = 0.30	x = 0.20
	N _p = 10	N _p = 20

Set Number	Pairing Set	Minimum Inversion Uncertainty (%) of
Set Number	Pairing Set	n	k	x	N _p
1	R _vv(15°), R _hv(130°), K _vve(165°), R _hh(80°)	1.9	5.0	3.7	5.1
2	R _vv(15°), R _hv(15°), K _hhe(75°), R _hh(85°)	2.3	4.2	3.2	4.8
3	R _vv(15°), R _hv(15°), K _hve(65°), R _hh(80°)	1.8	5.4	4.7	5.0

x	N _p	Optimum Angles				Uncertainty (%) of
x	N _p	R _vv	R _hv	K _vve	R _hh	n	k	x	N _p
m = 1.7 + i 0.7
0.15	10	15	165	15	80	7.8	11.1	8.7	8.1
0.2	10	15	165	15	80	5.8	8.3	5.9	4.8
0.3	10	15	130	165	80	1.9	5.0	3.7	5.1
0.3	5	15	165	50	80	6.5	11.0	7.5	7.5
0.3	15	15	90	90	80	1.9	4.8	3.7	6.6
0.3	20	15	110	100	70	2.2	5.9	3.9	8.1
m = 1.6 + i 0.6
0.15	10	15	165	15	80	6.7	11.7	8.1	7.9
0.2	10	15	165	15	80	5.0	8.7	5.5	5.0
0.3	10	15	140	165	80	1.8	5.2	3.6	5.2
0.3	5	15	165	25	85	6.2	11.2	7.4	6.9
0.3	15	15	165	85	80	1.8	5.0	3.7	6.5
0.3	20	15	105	100	75	1.6	5.6	3.5	9.3

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Applied Optics