Designing Progressive Lenses Using Physics-Informed Neural Networks to Solve Partial Differential Equations

Huazhong Xiang; Hui Cheng; Qihui Ding; Zexi Zheng; Jiabi Chen; Cheng Wang; Dawei Zhang; Songlin Zhuang

doi:10.3788/AOS241463

Acta Optica Sinica, Volume. 45, Issue 1, 0122002(2025)

Designing Progressive Lenses Using Physics-Informed Neural Networks to Solve Partial Differential Equations

Huazhong Xiang^1,2、*, Hui Cheng¹, Qihui Ding¹, Zexi Zheng³, Jiabi Chen⁴, Cheng Wang^1,2, Dawei Zhang⁴, and Songlin Zhuang⁴

Author Affiliations

¹Institute of Medical Optics and Optometry, School of Health Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

²Shanghai Engineering Research Center of Interventional Medical Device, University of Shanghai for Science and Technology, Shanghai 200093, China

³School of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

⁴School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

show less

Abstract Get PDF(in Chinese)

References(21)

[1] Pascual E, Gómez-Pedrero J A, Alonso J. Theoretical performance of progressive addition lenses with poorly measured individual parameters[J]. Ophthalmic & Physiological Optics, 43, 244-253(2023).

[2] Legras R, Vincent M, Marin G. Does visual acuity predict visual preference in progressive addition lenses?[J]. Journal of Optometry, 16, 91-99(2023).

[3] Sun H Y, Tsai J D, Nien Y S et al. The use of progressive addition lenses to improve the daily visual function of children receiving topical atropine treatment[J]. Ophthalmic and Physiological Optics, 43, 195-201(2023).

[4] Katz J A, Karpecki P M, Dorca A et al. Presbyopia: a review of current treatment options and emerging therapies[J]. Clinical Ophthalmology, 15, 2167-2178(2021).

[5] Winthrop J T. Progressive addition spectacle lens[P].

[6] Zhan X D, Xiang H Z, Wang Y Q et al. Design of progressive addition lenses based on conic parametric equations[J]. Acta Optica Sinica, 43, 0722001(2023).

[7] Zhang X, Xiang H Z, Ma L F et al. Optimization design of progressive corridor of freeform progressive addition lenses[J]. Acta Optica Sinica, 44, 0822003(2024).

[8] Steele T, McLoughlin H, Payne D. Progressive addition power lens[P].

[9] Loos J, Greiner G, Seidel H P. A variational approach to progressive lens design[J]. Computer-Aided Design, 30, 595-602(1998).

[10] Wang J, Santosa F. A numerical method for progressive lens design[J]. Mathematical Models and Methods in Applied Sciences, 14, 619-640(2004).

[11] Jiang W, Bao W Z, Tang Q L et al. A variational-difference numerical method for designing progressive-addition lenses[J]. Computer-Aided Design, 48, 17-27(2014).

[12] Jian H Y, Zeng H B. Existence and uniqueness for variational problem from progressive lens design[J]. Frontiers of Mathematics in China, 15, 491-505(2020).

[13] Barbero S, González M D M. Admissible surfaces in progressive addition lenses[J]. Optics Letters, 45, 5656-5659(2020).

[14] Xia R S, Fu Y Y, Ma K et al. Surface astigmatism correction using segmented freeform surfaces for a progressive addition lens[J]. Optics Express, 30, 43384-43397(2022).

[15] Santosa F, Wang J, Gulliver R. Analysis of a variational approach to progressive lens design[J]. SIAM Journal on Applied Mathematics, 64, 277-296(2003).

[16] Hsu W Y, Liu Y L, Cheng Y C et al. Design, fabrication, and metrology of ultra-precision optical freeform surface for progressive addition lens with B-spline description[J]. The International Journal of Advanced Manufacturing Technology, 63, 225-233(2012).

[17] Raissi M, Perdikaris P, Karniadakis G E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[J]. Journal of Computational Physics, 378, 686-707(2019).

[18] Luo M L, Lee S S. Inverse design of optical lenses enabled by generative flow-based invertible neural networks[J]. Scientific Reports, 13, 16416(2023).

[19] Xian W, Božič A, Snavely N et al. Neural lens modeling[EB/OL]. https:∥arxiv.org/abs/2304.04848

[20] Park J W, Wagner-Carena S, Birrer S et al. Large-scale gravitational lens modeling with Bayesian neural networks for accurate and precise inference of the Hubble constant[J]. The Astrophysical Journal, 910, 39(2021).

[21] Zheng Q, Zheng C W. NeuroLens: data-driven camera lens simulation using neural networks[J]. Computer Graphics Forum, 36, 390-401(2017).

Tools

Get Citation

Copy Citation Text

Huazhong Xiang, Hui Cheng, Qihui Ding, Zexi Zheng, Jiabi Chen, Cheng Wang, Dawei Zhang, Songlin Zhuang. Designing Progressive Lenses Using Physics-Informed Neural Networks to Solve Partial Differential Equations[J]. Acta Optica Sinica, 2025, 45(1): 0122002

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Optical Design and Fabrication

Received: Aug. 23, 2024

Accepted: Sep. 25, 2024

Published Online: Jan. 17, 2025

The Author Email: Xiang Huazhong (xiang3845242@163.com)

DOI:10.3788/AOS241463

CSTR:32393.14.AOS241463

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology