Simultaneous retrieval of the complex refractive indices of the core and shell of coated aerosol particles from extinction measurements using simulated annealing

Carynelisa Erlick; Mitch Haspel; Yinon Rudich

doi:10.1364/AO.50.004393

Applied Optics
Vol. 50,
Issue 22,
pp. 4393-4402
(2011)
•https://doi.org/10.1364/AO.50.004393

Simultaneous retrieval of the complex refractive indices of the core and shell of coated aerosol particles from extinction measurements using simulated annealing

Carynelisa Erlick, Mitch Haspel, and Yinon Rudich

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Carynelisa Erlick, Mitch Haspel, and Yinon Rudich, "Simultaneous retrieval of the complex refractive indices of the core and shell of coated aerosol particles from extinction measurements using simulated annealing," Appl. Opt. 50, 4393-4402 (2011)

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- Atmospheric and Oceanic Optics: Wave-front Sensing
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About this Article
History
- Original Manuscript: February 17, 2011
- Revised Manuscript: June 10, 2011
- Manuscript Accepted: June 14, 2011
- Published: July 27, 2011

Abstract

Simultaneously retrieving the complex refractive indices of the core and shell of coated aerosol particles given the measured extinction efficiency as a function of particle dimensions (core diameter and coated diameter) is much more difficult than retrieving the complex refractive index of homogeneous aerosol particles. Not only must the minimization be performed over a four-parameter space, making it less efficient, but in addition the absolute value of the difference between the measured extinction and the calculated extinction does not have an easily distinguished global minimum. Rather, there are a number of local minima to which almost all conventional retrieval algorithms converge. In this work, we develop a new (to our knowledge) retrieval algorithm that employs the numerical method known as simulated annealing with an innovative “temperature” schedule. This study is limited only to spherical particles with a concentric shell and to cases in which the diameter of both the core and the coated particle are known. We find that when the top ranking particle sizes according to their information content are combined from separate experiments to make up the particle size distribution, the simulated annealing retrieval algorithm is quite robust and by far superior to a greedy random perturbation approach often used.

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Overall Particle Index	Experiment	Core Diameter [ $μm$ ]	Coated Diameter [ $μm$ ]	Information Content Rank
1	1	0.300	0.311	6
2	1	0.300	0.322	11
3	1	0.300	0.334	13
4	1	0.300	0.346	15
5	1	0.300	0.359	17
6	1	0.300	0.372	18
7	1	0.300	0.385	21
8	1	0.300	0.400	23
9	1	0.300	0.429	5
10	1	0.300	0.461	2
11	2	0.250	0.269	8
12	2	0.250	0.289	9
13	2	0.250	0.311	12
14	2	0.250	0.334	14
15	2	0.250	0.359	16
16	2	0.250	0.385	20
17	2	0.250	0.414	22
18	3	0.175	0.195	1
19	3	0.200	0.220	3
20	3	0.250	0.270	7
21	3	0.300	0.320	10
22	3	0.350	0.370	19
23	3	0.400	0.420	4

Starting Index	Greedy Merit Function Final Threshold	Greedy Iterations	Greedy Final Index	Annealing Merit Function Final Threshold	Annealing Iterations	Annealing Final Index
$1.873 + i 0.791$	10	$> 10^{7}$	$1.646 + i 0.243$	$10^{- 4}$	44537	$1.649 + i 0.238$
$1.372 + i 0.546$			$1.406 + i 0.000$			$1.410 + i 0.000$
$1.780 + i 0.134$	1	$> 10^{7}$	$1.642 + i 0.260$	$10^{- 4}$	893809	$1.649 + i 0.238$
$1.605 + i 0.692$			$1.420 + i 0.001$			$1.410 + i 0.000$
$1.523 + i 0.421$	10	$> 10^{7}$	$1.653 + i 0.254$	$10^{- 4}$	753106	$1.649 + i 0.238$
$1.588 + i 0.204$			$1.418 + i 0.003$			$1.410 + i 0.000$
$1.911 + i 0.223$	10	$> 10^{7}$	$1.641 + i 0.210$	$10^{- 4}$	123064	$1.649 + i 0.238$
$1.461 + i 0.351$			$1.399 + i 0.005$			$1.410 + i 0.000$
$1.209 + i 0.010$	1	$> 10^{7}$	$1.651 + i 0.246$	$10^{- 4}$	801779	$1.649 + i 0.238$
$1.244 + i 0.802$			$1.407 + i 0.000$			$1.410 + i 0.000$
$1.197 + i 0.408$	1	$> 10^{7}$	$1.640 + i 0.249$	$10^{- 4}$	582459	$1.649 + i 0.238$
$1.623 + i 0.959$			$1.419 + i 0.009$			$1.410 + i 0.000$
$1.485 + i 0.205$	$10^{- 4}$	459522	$1.649 + i 0.238$	$10^{- 4}$	22740	$1.649 + i 0.238$
$1.906 + i 0.050$			$1.410 + i 0.000$			$1.410 + i 0.000$
$1.379 + i 0.092$	1	$> 10^{7}$	$1.641 + i 0.254$	$10^{- 4}$	942748	$1.649 + i 0.238$
$1.889 + i 0.652$			$1.417 + i 0.005$			$1.410 + i 0.000$
$1.262 + i 0.384$	$10^{- 4}$	369437	$1.649 + i 0.238$	$10^{- 4}$	113736	$1.649 + i 0.238$
$1.767 + i 0.709$			$1.410 + i 0.000$			$1.410 + i 0.000$
$1.565 + i 0.181$	10	$> 10^{7}$	$1.653 + i 0.259$	$10^{- 4}$	77498	$1.649 + i 0.238$
$1.540 + i 0.300$			$1.405 + i 0.004$			$1.410 + i 0.000$

Overall Particle Index	Experiment	Core Diameter [ $μm$ ]	Coated Diameter [ $μm$ ]	Information Content Rank
1	1	0.300	0.311	6
2	1	0.300	0.322	11
3	1	0.300	0.334	13
4	1	0.300	0.346	15
5	1	0.300	0.359	17
6	1	0.300	0.372	18
7	1	0.300	0.385	21
8	1	0.300	0.400	23
9	1	0.300	0.429	5
10	1	0.300	0.461	2
11	2	0.250	0.269	8
12	2	0.250	0.289	9
13	2	0.250	0.311	12
14	2	0.250	0.334	14
15	2	0.250	0.359	16
16	2	0.250	0.385	20
17	2	0.250	0.414	22
18	3	0.175	0.195	1
19	3	0.200	0.220	3
20	3	0.250	0.270	7
21	3	0.300	0.320	10
22	3	0.350	0.370	19
23	3	0.400	0.420	4

Starting Index	Greedy Merit Function Final Threshold	Greedy Iterations	Greedy Final Index	Annealing Merit Function Final Threshold	Annealing Iterations	Annealing Final Index
$1.873 + i 0.791$	10	$> 10^{7}$	$1.646 + i 0.243$	$10^{- 4}$	44537	$1.649 + i 0.238$
$1.372 + i 0.546$			$1.406 + i 0.000$			$1.410 + i 0.000$
$1.780 + i 0.134$	1	$> 10^{7}$	$1.642 + i 0.260$	$10^{- 4}$	893809	$1.649 + i 0.238$
$1.605 + i 0.692$			$1.420 + i 0.001$			$1.410 + i 0.000$
$1.523 + i 0.421$	10	$> 10^{7}$	$1.653 + i 0.254$	$10^{- 4}$	753106	$1.649 + i 0.238$
$1.588 + i 0.204$			$1.418 + i 0.003$			$1.410 + i 0.000$
$1.911 + i 0.223$	10	$> 10^{7}$	$1.641 + i 0.210$	$10^{- 4}$	123064	$1.649 + i 0.238$
$1.461 + i 0.351$			$1.399 + i 0.005$			$1.410 + i 0.000$
$1.209 + i 0.010$	1	$> 10^{7}$	$1.651 + i 0.246$	$10^{- 4}$	801779	$1.649 + i 0.238$
$1.244 + i 0.802$			$1.407 + i 0.000$			$1.410 + i 0.000$
$1.197 + i 0.408$	1	$> 10^{7}$	$1.640 + i 0.249$	$10^{- 4}$	582459	$1.649 + i 0.238$
$1.623 + i 0.959$			$1.419 + i 0.009$			$1.410 + i 0.000$
$1.485 + i 0.205$	$10^{- 4}$	459522	$1.649 + i 0.238$	$10^{- 4}$	22740	$1.649 + i 0.238$
$1.906 + i 0.050$			$1.410 + i 0.000$			$1.410 + i 0.000$
$1.379 + i 0.092$	1	$> 10^{7}$	$1.641 + i 0.254$	$10^{- 4}$	942748	$1.649 + i 0.238$
$1.889 + i 0.652$			$1.417 + i 0.005$			$1.410 + i 0.000$
$1.262 + i 0.384$	$10^{- 4}$	369437	$1.649 + i 0.238$	$10^{- 4}$	113736	$1.649 + i 0.238$
$1.767 + i 0.709$			$1.410 + i 0.000$			$1.410 + i 0.000$
$1.565 + i 0.181$	10	$> 10^{7}$	$1.653 + i 0.259$	$10^{- 4}$	77498	$1.649 + i 0.238$
$1.540 + i 0.300$			$1.405 + i 0.004$			$1.410 + i 0.000$

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Applied Optics