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

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Figures & Tables(16)

Fig. 1. Schematic of PINN model for solving the partial differential equation of progressive addition lenses

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Fig. 2. ConvNet used for solving the partial differential equation model of progressive addition lenses

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Fig. 3. Mean curvature distribution matrix

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Fig. 4. Solution of partial differential equation for progressive addition lenses. (a) Lens 1; (b) lens 4; (c) relative error distribution of lenses 1 and 4; (d) lens 2; (e) lens 5; (f) relative error distribution of lenses 2 and 5; (g) lens 3; (h) lens 6; (i) relative error distribution of lenses 3 and 6

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Fig. 5. Simulation results of lenses 1 and 4. (a) Optical power distribution of lens 1; (b) optical power distribution of lens 4; (c) astigmatism distribution of lens 1; (d) astigmatism distribution of lens 4

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Fig. 6. Simulation results of lenses 2 and 5. (a) Optical power distribution of lens 2; (b) optical power distribution of lens 5; (c) astigmatism distribution of lens 2; (d) astigmatism distribution of lens 5

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Fig. 7. Simulation results of lenses 3 and 6. (a) Optical power distribution of lens 3; (b) optical power distribution of lens 6; (c) astigmatism distribution of lens 3; (d) astigmatism distribution of lens 6

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Fig. 8. Six groups of PALs

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Fig. 9. Optical power measurement results of lenses 1 to 6. (a) Lens 1; (b) lens 4; (c) lens 2; (d) lens 5; (e) lens 3; (f) lens 6

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Fig. 10. Astigmatism measurement results of lenses 1 to 6. (a) Lens 1; (b) lens 4; (c) lens 2; (d) lens 5; (e) lens 3; (f) lens 6

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Table 1. General design parameters of progressive addition lenses
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Table 1. General design parameters of progressive addition lenses
Parameter Refractive index Radius of curvature of front surface /mm Base curve /D ADD /D CT /mm
Value 1.56 139.75 3.95 2 2.3

Table 2. Specific parameters of lenses 1‒6
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Table 2. Specific parameters of lenses 1‒6
Lens No. Method Distance vision zone optical power /D Near vision zone optical power /D
1 Explicit finite difference 0 2
2 Explicit finite difference 1 3
3 Explicit finite difference 2 4
4 PINN 0 2
5 PINN 1 3
6 PINN 2 4

Table 3. Comparison of simulation results for lens 1 and lens 4

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Table 3. Comparison of simulation results for lens 1 and lens 4

Lens No.	Distance vision zone optical power	Distance vision zone astigmatism	ADD	Near vision zone optical power	Near vision zone astigmatism	Peripheral maximum astigmatism
1	-0.02	-0.03	1.90	1.88	-0.02	-1.60
4	-0.02	-0.02	2.04	2.02	-0.02	-1.80

Table 4. Comparison of simulation results for lens 2 and lens 5

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Table 4. Comparison of simulation results for lens 2 and lens 5

Lens No.	Distance vision zone optical power	Distance vision zone astigmatism	ADD	Near vision zone optical power	Near vision zone astigmatism	Peripheral maximum astigmatism
2	1.30	-0.03	1.85	3.15	-0.03	-1.30
5	1.02	-0.02	1.90	2.92	-0.02	-1.60

Table 5. Comparison of simulation results for lens 3 and lens 6

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Table 5. Comparison of simulation results for lens 3 and lens 6

Lens No.	Distance vision zone optical power	Distance vision zone astigmatism	ADD	Near vision zone optical power	Near vision zone astigmatism	Peripheral maximum astigmatism
3	1.50	-0.04	2.08	3.58	-0.02	-1.40
6	1.95	-0.04	2.05	3.85	-0.02	-1.60

Table 6. Viewing zone angles and widths of progressive lenses

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Table 6. Viewing zone angles and widths of progressive lenses

Lens No.	Distance vision zone field of view /（°）	Near vision zone field of view /（°）	Distance vision zone width /mm	Channel width /mm	Near vision zone width /mm
1	133	81	25.14	5.18	6.92
2	128	73	18.98	4.58	9.92
3	145	82	21.25	5.87	12.18
4	122	81	24.87	4.35	6.45
5	129	76	19.46	5.22	9.88
6	139	60	20.68	6.65	13.58

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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

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