Translucency measurement system based on a polarized camera

Pei-Yu Lai; Tzung-Han Lin

doi:10.1364/AO.507311

Applied Optics
Vol. 63,
Issue 4,
pp. 1170-1181
(2024)
•https://doi.org/10.1364/AO.507311

Translucency measurement system based on a polarized camera

Pei-Yu Lai and Tzung-Han Lin

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Pei-Yu Lai and Tzung-Han Lin, "Translucency measurement system based on a polarized camera," Appl. Opt. 63, 1170-1181 (2024)

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Abstract

This paper proposes a measurement system capable of estimating the transmittance and haze values of a composite object. The system, comprising a polarized camera, linear polarizer, and backlight, was calibrated to obtain four phase polarization images. Forty-one samples, which covered a wide range of transmittance and haze values, were manufactured to assist in correlating the polarization images and the referenced ground truth from the BKY-Gardner instrument. After the data regression, two linear equations were selected to estimate the transmittance and haze values of transparent objects. The verification experiment for 52 samples demonstrated that the proposed method accurately estimated the transmittance of the samples with a coefficient of determination ($R^2$) as high as 0.96 and an average error of less than 4.1%. The haze estimation had an $R^2$ of 0.94 and an average error of 5.08%. Pseudo color maps were used to present the different transmittance and haze values of a single object. The proposed system can perform image-based translucency measurements and obtain individual values of a composite object.

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Data availability

The data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Case Variable	$Δ I_{90^{\circ}}$	$Δ I_{0^{\circ}}$	$Δ Y_{90^{\circ}}$	$Δ Y_{0^{\circ}}$	$Δ L_{90^{\circ}}^{*}$	$Δ L_{0^{\circ}}^{*}$	DoLP
$T_{1}$	◯	◯
$T_{2}$	◯	◯					◯
$T_{3}$			◯	◯
$T_{4}$			◯	◯			◯
$T_{5}$					◯	◯
$T_{6}$					◯	◯	◯
$T_{7}$	◯
$T_{8}$	◯						◯
$T_{9}$			◯
$T_{10}$			◯				◯
$T_{11}$					◯
$T_{12}$					◯		◯

Case Variable	$I_{90^{\circ}}$	$I_{0^{\circ}}$	$Y_{90^{\circ}}$	$Y_{0^{\circ}}$	$L_{90^{\circ}}^{*}$	$L_{0^{\circ}}^{*}$	$\frac{I_{0^{\circ}}}{I_{0^{\circ}} + I_{90^{o}}}$	$\frac{Y_{0^{\circ}}}{Y_{0^{\circ}} + Y_{90^{o}}}$	$\frac{L_{0^{\circ}}^{}}{L_{0^{\circ}}^{} + L_{90^{o}}^{*}}$	DoLP
$H_{1}$	◯	◯
$H_{2}$	◯	◯								◯
$H_{3}$			◯	◯
$H_{4}$			◯	◯						◯
$H_{5}$					◯	◯
$H_{6}$					◯	◯				◯
$H_{7}$							◯
$H_{8}$							◯			◯
$H_{9}$								◯
$H_{10}$								◯		◯
$H_{11}$									◯
$H_{12}$									◯	◯

Polarized Images	Color Correction Matrix M ( $3 \times 10$ )
0°	[−68.34, −168.34, 36.78, 233.17, 43.11, −76.06, 87.38, 105.48, −1.95, −0.40, −26.59, −22.60, 47.48, 67.19, −49.68, −12.40, 5.06, 228.04, −33.25, 0.22, −67.42, −38.49, 48.47, 138.19, −86.72, −3.33, 17.88, −86.34, 243.24, −0.67]
45°	[−78.07, −188.20, −5.73, 251.62, 96.51, −81.99, 89.17, 95.74, 8.90, 0.01, −38.99, −69.71, −22.52, 106.96, 44.18, −23.33, 6.53, 213.28, −16.68, 0.70, −61.62, −56.02, 46.03, 136.57, −71.31, −5.75, 14.13, −75.91, 236.02, −0.10]
90°	[−56.46, −161.50, 51.82, 215.35, 29.42, −77.53, 88.04, 111.26, −0.85, −0.61, −9.99, −8.04, 56.74, 34.18, −72.94, 1.93, −0.12, 243.63, −33.81, −0.11, −59.64, −28.47, 77.14, 134.37, −113.79, −14.61, 13.66, −86.83, 253.26, −0.39]
135°	[−68.56, −167.84, 44.60, 233.68, 31.18, −74.80, 86.74, 104.55, −2.47, −1.21, −28.01, −34.36, 23.27, 75.21, −22.18, −14.40, 5.87, 221.19, −26.65, −0.88, −60.99, −1.06, 115.10, 105.14, −169.12, 2.22, 19.21, −75.58, 224.03, −1.22]

Case	Regression Equation	MAE	RMSE	$R^{2}$
$T_{1}$	$0.813 Δ I_{90^{\circ}} + 0.063 Δ I_{0^{\circ}} - 6.115$	5.64	7.29	0.92
$T_{2}$	$1.076 Δ I_{90^{\circ}} + 0.045 Δ I_{0^{\circ}} - 29.879 D o L P + 9.425$	4.91	6.22	0.94
$T_{3}$	$0.823 Δ Y_{90^{\circ}} + 0.036 Δ Y_{0^{\circ}} + 0.953$	4.91	6.48	0.94
$T_{4}$	$1.004 Δ Y_{90^{\circ}} + 0.029 Δ Y_{0^{\circ}} - 21.10 D o L P + 12.327$	4.33	5.74	0.95
$T_{5}$	$0.845 Δ L_{90^{\circ}}^{} + 0.058 Δ L_{0^{\circ}}^{} - 23.469$	8.16	10.04	0.84
$T_{6}$	$1.541 Δ L_{90^{\circ}}^{} + 0.006 Δ L_{0^{\circ}}^{} - 72.693 D o L P + 3.506$	5.61	7.01	0.92
$T_{7}$	$0.949 Δ I_{90^{\circ}} + 13.532$	13.19	16.44	0.59
$T_{8}$	$1.478 Δ I_{90^{\circ}} - 70.949 D o L P - 36.901$	73.81	74.39	0.87
$T_{9}$	$0.954 Δ Y_{90^{\circ}} + 19.585$	13.49	16.76	0.58
$T_{10}$	$1.446 Δ Y_{90^{\circ}} - 66.085 D o L P + 44.598$	7.35	10.77	0.82
$T_{11}$	$0.981 Δ L_{90^{\circ}}^{*} - 6.656$	13.12	16.20	0.60
$T_{12}$	$1.597 Δ L_{90^{\circ}}^{*} - 78.14 D o L P + 5.975$	5.57	7.02	0.92

Case	Regression Equation	MAE	RMSE	$R^{2}$
$H_{1}$	$- 0.590 I_{90^{\circ}} + 2.684 I_{0^{\circ}} + 61.004$	9.99	14.04	0.80
$H_{2}$	$- 0.135 I_{90^{\circ}} + 0.965 I_{0^{\circ}} - 96.263 D o L P + 111.073$	5.52	7.06	0.95
$H_{3}$	$- 0.718 Y_{90^{\circ}} + 5.233 Y_{0^{\circ}} + 59.847$	11.69	16.11	0.73
$H_{4}$	$- 0.134 Δ Y_{90^{\circ}} + 1.692 Δ Y_{0^{\circ}} - 102.217 D o L P + 114.946$	5.81	7.36	0.94
$H_{5}$	$- 1.216 L_{90^{\circ}}^{} + 2.573 L_{0^{\circ}}^{} + 76.855$	7.13	10.10	0.90
$H_{6}$	$- 0.417 L_{90^{\circ}}^{} + 1.191 L_{0^{\circ}}^{} - 80.227 D o L P + 106.626$	4.94	6.34	0.96
$H_{7}$	$248.2 \frac{I_{0^{\circ}}}{I_{0^{\circ}} + I_{90^{\circ}}} + 7.378$	7.71	8.71	0.92
$H_{8}$	$- 13.9 \frac{I_{0^{\circ}}}{I_{0^{\circ}} + I_{90^{\circ}}} - 130.932 D o L P + 138.382$	7.71	8.71	0.92
$H_{9}$	$234.7 \frac{Y_{0^{\circ}}}{Y_{0^{\circ}} + Y_{90^{\circ}}} + 19.409$	11.04	12.67	0.84
$H_{10}$	$- 426.9 \frac{Y_{0^{\circ}}}{Y_{0^{\circ}} + Y_{90^{\circ}}} - 337.021 D o L P + 327.998$	3.43	4.38	0.98
$H_{11}$	$267.3 \frac{L_{0^{\circ}}^{}}{L_{0^{\circ}}^{} + L_{90^{\circ}}^{*}} - 9.901$	5.38	6.53	0.96
$H_{12}$	$185.0 \frac{L_{0^{\circ}}^{}}{L_{0^{\circ}}^{} + L_{90^{\circ}}^{*}} - 40.722 D o L P + 35.091$	5.00	5.80	0.97

Abstract

Data availability

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Figures (9)

Tables (6)

Equations (13)

Applied Optics