Theoretical model and optimization of diffractive optical elements with aspheric substrates in&#x00A0;ophthalmology

Bo Dong; Ying Yang; Yue Liu; Chao Yang; Changxi Xue

doi:10.1364/AO.480515

Applied Optics
Vol. 62,
Issue 3,
pp. 826-835
(2023)
•https://doi.org/10.1364/AO.480515

Theoretical model and optimization of diffractive optical elements with aspheric substrates in ophthalmology

Bo Dong, Ying Yang, Yue Liu, Chao Yang, and Changxi Xue

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Bo Dong, Ying Yang, Yue Liu, Chao Yang, and Changxi Xue, "Theoretical model and optimization of diffractive optical elements with aspheric substrates in ophthalmology," Appl. Opt. 62, 826-835 (2023)

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Related Topics
Table of Contents Category
- Diffraction and Gratings
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: November 8, 2022
- Revised Manuscript: December 23, 2022
- Manuscript Accepted: December 29, 2022
- Published: January 19, 2023

Abstract

Diffractive optical elements (DOEs), which can produce arbitrary light distribution, are widely applied in ophthalmic lens design with spheric substrates. However, diffraction substrates tend to be designed as aspheric surfaces to eliminate aberrations. In this case, the diffraction theory of plane substrates is no longer accurate, which affects the diffraction performance. Therefore, a diffraction theory of aspheric diffraction substrates is proposed in this paper. Using the range of common parameters for aspheric substrates in ophthalmology, the influence of the substrate diopter and the aspheric surface parameters on the period radius and phase delay is analyzed. Then, through a design example of a diffraction intraocular lens (IOL), an optimization equation is proposed and discussed. The results show that the diffraction theory of aspheric substrates and the optimization equation model can analyze and reduce the effect of aspheric diffraction substrates. This research can be used in DOE design with aspheric substrates in ophthalmology.

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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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Surface	Radius	Conic	Thickness	Refractive Index
1	7.77	−0.18	0.5	1.376
2	6.40	−0.60	3.16	1.336
3	12.40	−0.94	1.59	Grad A^a
4	Infinity		2.43	Grad B
5	−8.10	0.96	16.27	1.336

Parameter	Specification
IOL refractive index	1.46
Diameter of IOL (mm)	6
Front surface diopters (D)	15.5
Front surface conic	−12.2767
Front surface fourth-order aspheric coefficient	0.003877
Phase delay ( $λ$ )	0.5, 1.5
Step height (um)	2.2379, 6.7137

	Phase Delay 0.5				Phase Delay 1.5
Diffraction Ring	1	2	3	4	1	2	3	4
$J$ th true phase delay	0.5161	0.5188	0.5221	0.5261	1.5484	1.5565	1.5662	1.5783
True diffraction	$m = 0$		$m = 1$		$m = 1$		$m = 2$
efficiency	37.45%		43.69%		31.52%		50.14%
$σ$	7.60%		7.80%		22.23%		23.71%
$h_{o p t, j}$	2.1679	2.1566	2.1433	2.1269	6.5038	6.4699	6.4299	6.3806
${\bar{h}}_{o p t}$	2.1551				6.4654

Surface	Radius	Conic	Thickness	Refractive Index
1	7.77	−0.18	0.5	1.376
2	6.40	−0.60	3.16	1.336
3	12.40	−0.94	1.59	Grad A^a
4	Infinity		2.43	Grad B
5	−8.10	0.96	16.27	1.336

Parameter	Specification
IOL refractive index	1.46
Diameter of IOL (mm)	6
Front surface diopters (D)	15.5
Front surface conic	−12.2767
Front surface fourth-order aspheric coefficient	0.003877
Phase delay ( $λ$ )	0.5, 1.5
Step height (um)	2.2379, 6.7137

Abstract

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Figures (12)

Tables (4)

Equations (31)

Applied Optics