Non-spherical particle size estimation using supervised machine learning

Chi Young Moon; Aldo Gargiulo; Gwibo Byun; K. Todd Lowe

doi:10.1364/AO.385750

Non-spherical particle size estimation using supervised machine learning

Chi Young Moon, Aldo Gargiulo, Gwibo Byun, and K. Todd Lowe

Applied Optics
Vol. 59,
Issue 10,
pp. 3237-3245
(2020)
•https://doi.org/10.1364/AO.385750

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Chi Young Moon, Aldo Gargiulo, Gwibo Byun, and K. Todd Lowe, "Non-spherical particle size estimation using supervised machine learning," Appl. Opt. 59, 3237-3245 (2020)

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- Instrumentation and Measurements
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About this Article
History
- Original Manuscript: December 12, 2019
- Revised Manuscript: February 28, 2020
- Manuscript Accepted: March 3, 2020
- Published: March 30, 2020

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Abstract

The inverse scattering problem of non-spherical particle size estimation is solved using a series of supervised machine learning models trained on a library of light scattering data. By establishing a large library with spheres and spheroids as fundamental shapes and through optimization of model hyperparameters, the trained models are able to accurately estimate a precise equivalent volume sphere radius of particles from an external database and simulations, with root mean square errors of 2.6% and 1.9% for the external and simulated particles, respectively. It was found that classification via a $ k $-nearest neighbor model and refinement via a trained ensemble regression model performed best for equivalent volume measurements.

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Parameter	Range
Equivalent volume sphere radius ( $r$ )	1 µm–25 µm
Size parameter ( $x$ )	6–300
Aspect ratio (AR)	0.5–3
Refractive index ( $n$ )	1.3–1.7

Name	Formulation
Intensity ratio 1	${I R}_{1} = \frac{I (θ_{1} {= 5}^{\circ})}{I (θ_{3} {= 30}^{\circ})}$
Intensity ratio 2	${I R}_{2} = \frac{I (θ_{2} {= 10}^{\circ})}{I (θ_{3} {= 30}^{\circ})}$
Absolute intensity shift 1	${A I S}_{1} = \| I (θ_{1} = 5^{\circ}) - I_{r e f} (θ_{1} = 5^{\circ}) \|$
Absolute intensity shift 2	${A I S}_{2} = \| I (θ_{2} = 10^{\circ}) - I_{r e f} (θ_{2} = 10^{\circ}) \|$
Absolute intensity shift 3	${A I S}_{3} = \| I (θ_{3} = 30^{\circ}) - I_{r e f} (θ_{3} = 30^{\circ}) \|$

Name	Effective Radius (µm)	Wavelength (nm)	Size Parameter
	Volcanic Ash
Eyjafjallajökull [33]	7.8	647	75.8
St. Helens [34]	4.1	633	40.7
Lokon [35]	7.1	442	100.9
Pinatubo [35,36]	3.0	442	42.7
Puyuhue [33]	8.6	647	83.5
Spurr [34]	14.4	633	142.9
Cosmic Dust Analogs
JSC0 [31]	15.9	488	204.1
JSC-1A [32]	29.5	647	286.5
JSC200 [31]	28.1	647	272.9
Miscellaneous
Fly Ash [37]	3.7	442	51.9
Basalt [31]	6.9	647	67.0
Calcite [31,38]	3.3	448	46.3
Loess [35]	3.9	442	55.4
Quartz [35]	2.3	442	32.7
Sahara Sand [35]	8.2	442	116.6
Water droplet* [29]	1.1	442	15.6

Monodisperse
			Equivalent Volume
Particle #	Aspect Ratio	Refractive Index	Sphere Radius (µm)
1	1.3	1.5	3.1
2	0.7	1.5	12.3
3	2.5	1.5	20.7
Polydisperse
	$μ$	$σ$	$r_{e f f}$ (µm)
	0.1	1.0	13.5

Name	Classification Range (µm)	Regression Estimation (µm)	Reference Radius (µm)
Volcanic Ash
Eyjafjallajökull	6.6–9.6	7.1	7.8
St. Helens	3.5–6.4	4.6	4.1
Lokon	6.6–8.7	7.9	7.1
Pinatubo	2.4–4.5	3.2	3.0
Puyuhue	6.6–9.6	7.5	8.6
Spurr	12.4–15.4	13.9	14.4
Cosmic Dust Analogs
JSC0	14.1–16.4	15.7	15.9
JSC-1A	27.9–30.9	29.5	29.5
JSC200	27.9–30.9	29	28.1
Miscellaneous
Fly Ash	4.5–6.6	4.5	3.7
Basalt	6.6–9.6	6.9	6.9
Calcite	2.5–4.6	3.5	3.3
Loess	2.4–4.5	3.5	3.9
Quartz	2.4–4.5	2.7	2.3
Sahara Sand	6.6–8.7	8	8.2
Water droplet*	0.35–2.4	1.2	1.1

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