Virtually measuring layered material appearance

Kewei Xu; Arthur Cavalier; Benjamin Bringier; Mickaël Ribardière; Daniel Meneveaux

doi:10.1364/JOSAA.514604

Journal of the Optical Society of America A
Vol. 41,
Issue 5,
pp. 959-968
(2024)
•https://doi.org/10.1364/JOSAA.514604

Virtually measuring layered material appearance

Kewei Xu, Arthur Cavalier, Benjamin Bringier, Mickaël Ribardière, and Daniel Meneveaux

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Kewei Xu, Arthur Cavalier, Benjamin Bringier, Mickaël Ribardière, and Daniel Meneveaux, "Virtually measuring layered material appearance," J. Opt. Soc. Am. A 41, 959-968 (2024)

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Abstract

This paper describes the design and the implementation of a virtual gonioradiometer dedicated to the analysis of layered materials BSDF. For a given material sample, interfaces between layers are represented by geometric meshes, associated with elementary reflectances. Light scattering is performed using path tracing. Our system is composed of five hemispherical sensors, whose cells have uniform solid angles, and a close-to-uniform geometry. The upper hemisphere captures the reflected radiance distribution, while the other four collect the light energy lost by the sample sides. Sensor resolutions can be set to gather very fine details of the BSDF. With the proposed system, any type of virtual surface reflection and transmission can be simulated, with several controllable surface layers, and with any type of reflection configuration, including direct reflections, two bounces of reflection, or all contributions. A series of results is provided with several types of layered materials, as well as discussion and analysis concerning the assumptions made with analytical layered BSDF models. We also propose an in-depth study of the side effects that inevitably appear when measuring such (real) material configurations. Finally, our system will be freely available to the community (open source dissemination).

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Supplementary Material (1)

Name	Description
Dataset 1	Additional results.

Data availability

Data underlying the results presented in this paper are available at Dataset 1, Ref. [48].

48. K. Xu, A. Cavalier, B. Bringier, et al., “Additional information for ‘Virtually measuring layered material appearance’,” GitLab (2024), https://gitlab.xlim.fr/virtualgonio-layeredmaterial/additionnal_results_josaa.

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Equations (11)

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$I_{n}$	$n t h$ interface
$σ_{n}$	Roughness of $n t h$ interface (in our case, it is the standard deviation of a Beckmann normal distribution function)
$η_{n}$	Refractive index of $n t h$ medium
$θ_{i}$	Angle between incident light and interface normal
$h_{n}$	Thickness (mm) between $I_{n}$ and $I_{n + 1}$
$Φ_{1}$ , $Φ_{2 +}$	Radiant flux ( $W$ ) captured from single scattering and multiple (excluding the first) scattering
$L_{1}$ , $L_{2 +}$	Radiance ( $W \cdot m^{- 2} \cdot {s r}^{- 1}$ ) captured from single scattering and multiple (excluding the first) scattering
$Φ_{X Z 0}$ , $Φ_{X Z 1}$ , $Φ_{Y Z 0}$ , $Φ_{Y Z 1}$	Radiant flux ( $W$ ) captured from the four boundaries of the material sample (Fig. 5)
$E_{X Z 0}$ , $E_{X Z 1}$ , $E_{Y Z 0}$ , $E_{Y Z 1}$	Radiant exitance ( $W \cdot m^{- 2}$ ) captured from the four boundaries
$L_{X Z 0}$ , $L_{X Z 1}$ , $L_{Y Z 0}$ , $L_{Y Z 1}$	Radiance ( $W \cdot m^{- 2} \cdot {s r}^{- 1}$ ) captured from the four boundaries

	$Φ_{2 +}$
$Φ_{1}$	Position-Free	$h_{1}$ (mm)	Mirror-Tiling	w/o Side Energy
0.020	0.980	0.05	0.980	0.916
		0.2	0.980	0.768
		2	0.979	0.337

$σ_{1}$	$Φ_{1}$	$Φ_{2 +}$	$Φ_{X Z 0}$	$Φ_{X Z 1}$	$Φ_{Y Z 0}$	$Φ_{Y Z 1}$
0.05	0.028	0.244	0.114	0.114	0.433	0.066
0.15	0.029	0.239	0.117	0.117	0.432	0.066
0.25	0.031	0.230	0.119	0.119	0.435	0.066

$σ_{2}$	Substrate BSDF	$Φ_{1}$	$Φ_{2 +}$	$Φ_{X Z 0}$	$Φ_{X Z 1}$	$Φ_{Y Z 0}$	$Φ_{Y Z 1}$
0.15	Perfect mirror	0.028	0.314	0.024	0.023	0.611	0.0
0.25	Perfect mirror		0.288	0.039	0.039	0.606	0.0
0.00	Diffuse ( $ρ = 1$ )		0.244	0.114	0.114	0.433	0.066

$θ_{i} (^{\circ})$	$Φ_{1}$	$Φ_{2 +}$	$Φ_{X Z 0}$	$Φ_{X Z 1}$	$Φ_{Y Z 0}$	$Φ_{Y Z 1}$
15	0.02	0.599	0.093	0.093	0.111	0.085
45	0.028	0.576	0.089	0.089	0.148	0.070
80	0.340	0.376	0.059	0.058	0.128	0.040

Abstract

Supplementary Material (1)

Data availability

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Figures (14)

Tables (5)

Equations (11)

Journal of the Optical Society of America A