General error model for analysis of laser-induced incandescence signals

Timothy A. Sipkens; Paul J. Hadwin; Samuel J. Grauer; Kyle J. Daun

doi:10.1364/AO.56.008436

Applied Optics
Vol. 56,
Issue 30,
pp. 8436-8445
(2017)
•https://doi.org/10.1364/AO.56.008436

General error model for analysis of laser-induced incandescence signals

Timothy A. Sipkens, Paul J. Hadwin, Samuel J. Grauer, and Kyle J. Daun

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Timothy A. Sipkens, Paul J. Hadwin, Samuel J. Grauer, and Kyle J. Daun, "General error model for analysis of laser-induced incandescence signals," Appl. Opt. 56, 8436-8445 (2017)

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Related Topics
Table of Contents Category
- Remote Sensing and Sensors
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Aerosol detection (010.1100)
- Inverse problems (100.3190)
- Noise in imaging systems (110.4280)
- Combustion diagnostics (120.1740)
- Nanomaterials (160.4236)
- Flow diagnostics (280.2490)

About this Article
History
- Original Manuscript: August 14, 2017
- Revised Manuscript: September 15, 2017
- Manuscript Accepted: September 17, 2017
- Published: October 18, 2017

Abstract

This paper presents a novel error model for TiRe-LII signals and illustrates how the model can be used to diagnose a detection system, quantify uncertainties in TiRe-LII, and characterize fluctuations in the measured process. Noise in a single TiRe-LII measurement shot obeys a Poisson–Gaussian noise model. Variation in the aerosol results in shot-to-shot fluctuations in the measured signals. These fluctuations induce a quadratic relationship between the mean and variance of a set of signals. We show how this model can elucidate aspects of the measurement system and fundamental properties of the aerosol, by comparing the noise model to four sets of experimental data.

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Supplementary Material (1)

Name	Description
Code 1	MATLAB tools for a general TiRe-LII error model.

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Study	Channel or Case	$τ^{2}$	$τ$	$θ$	$γ^{2} {[a.u.]}^{2}$	$γ [a.u.]$	${\bar{s}}_{i}^{*}$ (% of Peak)
Sipkens et al. [8] Iron, aerosolized colloid	Ch. 1, Ne, $λ = 442 nm$	$0.0478 \pm 0.0054$	$0.219 \pm 0.012$	$0.18 \pm 0.43$	$0.1 \pm 1.6$	—	0.39
Sipkens et al. [8] Iron, aerosolized colloid	Ch. 2, Ne, $λ = 716 nm$	$0.0640 \pm 0.0057$	$0.253 \pm 0.011$	$0.31 \pm 0.42$	$0.1 \pm 2.3$	—	0.55
Menser et al. [9] Germanium, plasma synthesized	Ch. 1, $λ = 500 nm$	$0.0005 \pm 0.0040$	$\sim 0.023$	$4.17 \pm 0.30$	$0.00 \pm 0.56$	—	4.18
	Ch. 2, $λ = 500 nm$	$0.0017 \pm 0.0036$	$\sim 0.042$	$4.08 \pm 0.27$	$0.12 \pm 0.51$	—	4.12
	Ch. 3, $λ = 684 nm$	$0.0025 \pm 0.0014$	$0.051 \pm 0.017$	$1.68 \pm 0.10$	$0.00 \pm 0.34$	—	1.68
	Ch. 4, $λ = 797 nm$	$0.0043 \pm 0.0023$	$0.066 \pm 0.021$	$3.55 \pm 0.15$	$0.00 \pm 0.75$	—	3.56
Mansmann et al. [36] Soot, laminar flame	Ch. 1, $λ = 500 nm$	$0.0062 \pm 0.0032$	$0.079 \pm 0.024$	$7.66 \pm 0.25$	$1.15 \pm 2.70$	—	7.86
	Ch. 2, $λ = 500 nm$	$0.0043 \pm 0.0031$	$\sim 0.066$	$7.47 \pm 0.25$	$0.7 \pm 2.7$	—	7.60
	Ch. 3, $λ = 684 nm$	$0.00535 \pm 0.0008$	$0.0731 \pm 0.0057$	$1.731 \pm 0.072$	$2.7 \pm 1.1$	$1.63 \pm 0.34$	2.73
	Ch. 4, $λ = 797 nm$	$0.0001 \pm 0.0015$	$\sim 0.012$	$3.41 \pm 0.13$	$0.0 \pm 2.1$	—	3.42
Hadwin et al. [21] Soot, laminar flame	$λ = 420 nm$	$0.000728 \pm 0.000087$	$0.0270 \pm 0.0016$	$0.174 \pm 0.006$	$0.030 \pm 0.060$	—	0.29
Hadwin et al. [21] Soot, laminar flame	$λ = 780 nm$	$0.000501 \pm 0.000036$	$0.0224 \pm 0.0008$	$0.0689 \pm 0.0031$	$0.000 \pm 0.043$	—	0.07

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