Optimized Gaussian model for non-uniform heating compensation in pulsed thermography

Jorge Erazo-Aux; Jorge Erazo-Aux; H. Loaiza-Correa; H. Loaiza-Correa; A. D. Restrepo-Giron; A. D. Restrepo-Giron; W. Alfonso-Morales; W. Alfonso-Morales

doi:10.1364/AO.388173

Applied Optics
Vol. 59,
Issue 14,
pp. 4303-4313
(2020)
•https://doi.org/10.1364/AO.388173

Optimized Gaussian model for non-uniform heating compensation in pulsed thermography

Jorge Erazo-Aux, H. Loaiza-Correa, A. D. Restrepo-Giron, and W. Alfonso-Morales

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Jorge Erazo-Aux, H. Loaiza-Correa, A. D. Restrepo-Giron, and W. Alfonso-Morales, "Optimized Gaussian model for non-uniform heating compensation in pulsed thermography," Appl. Opt. 59, 4303-4313 (2020)

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Abstract

This paper presents a new, to the best of our knowledge, methodology for the thermal compensation of background heating in thermograms of composites. The technique analyzes the spatial data of the thermal images obtained from a pulsed thermography inspection and automatically calculates the optimal parameters of a predefined objective function. These parameters are obtained by curve fitting using the least squares method and model the temperature distribution of the image background using the proposed objective function. To verify the methodology, we use real and synthetic images of a sample of carbon-fiber-reinforced plastic (CFRP) with defects, with diameter/depth ratios that range between 15.0 and 75.0 and between 1.7 and 90.0, respectively. The performance of the method is tested using a local and a global definition of the signal-to-noise ratio (SNR) and is statistically validated by analysis of variance. The average performance values obtained were $55.0\;\text{dB}$ and $7.0\;\text{dB}$ on synthetic images and real images, respectively. The proposed method provides superior and statistically significant differences compared to techniques reported in the literature for contrast enhancement [e.g., differential absolute contrast (DAC) and background thermal compensation by filtering (BTCF)]. Unlike contrast normalization (CN), the proposed technique stands out since it does not need to predefine variables, select reference regions, have prior knowledge of the partial (or complete) state of the material, or analyze totally (or partially) the temporal evolution of the temperature or any characteristic derived from it.

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Material	Conductivity ( $x = y = z$ direction) $[W / m \cdot K]$	Calorific Capacity $[W \cdot s / K g \cdot K]$	Density ( $ρ$ ) $[K g / m^{3}]$
CFRP	0.7	1200	1600
Teflon	0.25	1050	2170
Air	0.07	928	1.3

Pulse Width [s]	Energy Density $[W / m^{2}]$	Acquisition Frequency [Hz]	Time Window [s]
$1260 \times 10^{- 5}$	$1 \times 10^{5}$	157	9

			Processing Conditions
S (mm)	${SNR}_{avg}$ (dB)	Value	Raw Seq.	CN	DAC	BTCF	BTCOp	BTCOpN
3	L	Min	−16.8	27.2	−13.1	−2.0	29.3	24.3
		Max	4.8	28.1	4.1	14.5	31.6	26.6
	$RDI \to$		4.50	0.03	4.01	1.13	0.07	0.09
	G	Min	−9.2	77.1	−4.3	10.7	46.9	45.1
		Max	19.6	89.5	18.7	28.2	68.9	65.7
	$RDI \to$		1.46	0.14	1.30	0.65	0.32	0.31
9	L	Min	0.1	24.1	11.1	16.9	24.0	23.9
		Max	13.8	24.3	21.9	28.2	24.2	24.3
	$RDI \to$		0.99	0.01	0.49	0.41	0.01	0.02
	G	Min	8.1	73.8	14.5	35.1	52.9	54.4
		Max	28.2	83.6	33.8	39.9	59.7	63.4
	$RDI \to$		0.71	0.11	0.57	0.12	0.11	0.14
	$RDI \to$		$\geq 0.37$ higher dispersion			$< 0.37$ lower dispersion

			Processing Conditions
S (mm)	${\bar{SNR}}_{avg}$ (dB)	D (mm)	Raw Seq.	CN	DAC	BTCF	BTCOp	BTCOpN
3	L	0.1	−7.5	25.3	−9.7	6.6	28.2	23.4
		0.4	−2.5	37.0	1.9	14.0	35.2	35.2
		1.8	−11.6	27.5	−9.6	0.8	21.5	21.6
9		0.1	3.9	11.2	3.6	16.0	18.8	11.2
		0.4	9.6	24.2	14.9	20.9	24.1	24.1
		1.8	−6.7	16.4	−2.2	8.1	14.8	15.1

Material	Conductivity ( $x = y = z$ direction) $[W / m \cdot K]$	Calorific Capacity $[W \cdot s / K g \cdot K]$	Density ( $ρ$ ) $[K g / m^{3}]$
CFRP	0.7	1200	1600
Teflon	0.25	1050	2170
Air	0.07	928	1.3

Jorge Erazo-Aux	https://orcid.org/0000-0003-2692-9654
H. Loaiza-Correa	https://orcid.org/0000-0001-7206-7333
A. D. Restrepo-Giron	https://orcid.org/0000-0001-7891-1064
W. Alfonso-Morales	https://orcid.org/0000-0002-3091-6082

Abstract

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Equations (17)

Applied Optics