BRDF modeling and optimization of a target surface based on the gradient descent algorithm

Yanhui Li; Pengfei Yang; Lu Bai; Zifei Zhang

doi:10.1364/AO.506672

Applied Optics
Vol. 62,
Issue 36,
pp. 9486-9492
(2023)
•https://doi.org/10.1364/AO.506672

BRDF modeling and optimization of a target surface based on the gradient descent algorithm

Yanhui Li, Pengfei Yang, Lu Bai, and Zifei Zhang

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Yanhui Li, Pengfei Yang, Lu Bai, and Zifei Zhang, "BRDF modeling and optimization of a target surface based on the gradient descent algorithm," Appl. Opt. 62, 9486-9492 (2023)

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Table of Contents Category
- Physical Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: September 22, 2023
- Revised Manuscript: November 21, 2023
- Manuscript Accepted: November 21, 2023
- Published: December 11, 2023

Abstract

Addressing the current challenges in modeling and optimizing the bidirectional reflectance distribution function (BRDF) for the target surface, an improved six-parameter semi-empirical model is proposed based on an existing five-parameter semi-empirical model. In comparison with the original five-parameter model, the new, to the best of our knowledge, model considers reciprocity, and the results demonstrate that as the incident angle increases, the fitting accuracy of the six parameters gradually surpasses that of the five parameters. Additionally, this paper employs a machine learning optimization algorithm, namely, the gradient descent method, for optimizing the BRDF. The algorithm was comprehensively compared with other optimization methods, revealing that for the same dataset, the gradient descent method exhibited the smallest fitting errors. Subsequently, utilizing this algorithm for fitting experimental data resulted in errors consistently within 3%, confirming the reliability and accuracy of this optimization algorithm.

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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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Material	Model	$k_{b}$	$k_{r}$	$b$	$a$	$k_{d}$	$c$	$E$
		Parameters
	$5 p$	5.74	5.5	−36.1	0.69	−0.036	$\times$	1.15%
Copper	$6 p$	10.06	13.3	−47.8	0.76	−2.55	−8.27	1.07%
	$5 p$	5.69	5.43	−35.6.	0.69	−0.033	$\times$	2.07%
Aluminum	$6 p$	9.9	9.33	−54.1	0.77	−0.13	−15.1	1.22%

Algorithm	$k_{b}$	$k_{r}$	$b$	$a$	$k_{d}$	$c$	$E$
GD	0.14	4.38	−6.14	0.57	0.34	−0.71	0.25%
GA	0.16	4.58	−6.13	0.57	0.34	−0.72	0.41%
SA	0.15	3.98	−6.63	0.52	0.32	−0.82	0.40%
PSO	0.14	4.08	−5.83	0.51	0.36	−0.78	0.41%

Sample	$k_{b}$	$k_{r}$	$b$	$a$	$k_{d}$	$c$	$E$
Aluminum	2.72	26.14	−49.84	0.72	0.36	−0.024	1.66%
Copper	4.31	29.26	−90.88	0.78	0.27	0.012	0.88%
Jade white	1.17	7.78	−42.56	0.38	0.047	−0.69	2.35%
Sea gray	0.385	16.88	−112.2	0.59	0.029	−1.11	2.57%

Sample	$k_{b}$	$k_{r}$	$b$	$a$	$k_{d}$	$c$	$E$
Aluminum	4.13	14.24	−85.01	0.61	0.87	0.11	2.35%
Copper	5.49	14.29	−86.91	0.63	1.25	−0.30	1.63%
S3	0.015	4.39	−6.16	0.58	0.032	0.11	2.93%
S72	0.82	14.52	−24.8	0.81	0.14	0.0068	2.56%

Material	Model	$k_{b}$	$k_{r}$	$b$	$a$	$k_{d}$	$c$	$E$
		Parameters
	$5 p$	5.74	5.5	−36.1	0.69	−0.036	$\times$	1.15%
Copper	$6 p$	10.06	13.3	−47.8	0.76	−2.55	−8.27	1.07%
	$5 p$	5.69	5.43	−35.6.	0.69	−0.033	$\times$	2.07%
Aluminum	$6 p$	9.9	9.33	−54.1	0.77	−0.13	−15.1	1.22%

Abstract

Data availability

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Figures (6)

Tables (4)

Equations (9)

Applied Optics