Multifocal diffractive lens design in ophthalmology

Aizhong Zhang

doi:10.1364/AO.403554

Applied Optics
Vol. 59,
Issue 31,
pp. 9807-9823
(2020)
•https://doi.org/10.1364/AO.403554

Multifocal diffractive lens design in ophthalmology

Aizhong Zhang

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Aizhong Zhang, "Multifocal diffractive lens design in ophthalmology," Appl. Opt. 59, 9807-9823 (2020)

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- Medical Optics, Microscopy, and Biotechnology
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About this Article
History
- Original Manuscript: July 31, 2020
- Revised Manuscript: September 27, 2020
- Manuscript Accepted: September 28, 2020
- Published: October 26, 2020

Abstract

Multifocal diffractive lenses are used widely in ophthalmology. This paper provides a general mathematical formula to summarize various multifocal diffractive lens designs and introduces a novel, design: the subzonal multifocal diffractive (SMUD) lens. Analytical and numerical methods of SMUD lens design are elaborated in detail. A number of trifocal and quadrifocal SMUD lens designs of high diffraction efficiency are presented. Fresnel zone spacing factors are introduced to take into account the incidence of a converging or diverging beam and the curvature of the substrate on which the diffractive surface is created. Apodization and ophthalmic astigmatism correction related to diffractive lenses are also discussed.

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#	$γ$	$β_{1}$	$β_{2}$	$η_{0}$	$η_{1}$	$η_{2}$	$η_{e f f}$	SS
1	0.50	0.68	1.31	28.18%	28.43%	27.68%	84.29%	$8.7 \times 10^{- 5}$
2	0.50	1.32	0.69	27.68%	28.43%	28.18%	84.29%	$8.7 \times 10^{- 5}$
3	0.51	0.73	1.32	27.21%	29.32%	28.19%	84.71%	$6.7 \times 10^{- 4}$
4	0.51	1.27	0.68	28.19%	29.32%	27.21%	84.71%	$6.7 \times 10^{- 4}$
5	0.44	0.47	1.28	27.10%	27.09%	27.20%	81.39%	$2.3 \times 10^{- 6}$
6	0.44	1.53	0.72	27.20%	27.09%	27.10%	81.39%	$2.3 \times 10^{- 6}$

#	$γ$	$β_{1}$	$β_{2}$	$η_{0}$	$η_{1}$	$η_{2}$	$η_{e f f}$	SS
7	0.50	1.08	0.57	41.54%	20.95%	21.35%	83.83%	$5.3 \times 10^{- 5}$
8	0.50	1.04	0.56	42.85%	21.54%	19.89%	84.28%	$5.1 \times 10^{- 4}$
9	0.49	1.05	0.56	43.33%	21.33%	19.63%	84.30%	$7.2 \times 10^{- 4}$
10	0.43	1.27	0.60	40.80%	20.50%	20.50%	81.81%	$1.9 \times 10^{- 6}$
11	0.56	0.56	1.28	40.95%	20.37%	20.45%	81.77%	$2.0 \times 10^{- 6}$

#	$γ_{1}$	$γ_{2}$	$β_{1}$	$β_{2}$	$β_{3}$	$η_{0}$	$η_{1}$	$η_{2}$	$η_{3}$	$η_{e f f}$	SS
12	0	0.5	–	0.5	2.5	21.1%	22.5%	22.5%	21.1%	87.2%	0.00083
13	0	0.5	–	2.5	0.5	21.1%	22.5%	22.5%	21.1%	87.2%	0.00083
14	0	0.6	–	2.3	0.4	23.1%	23.4%	21.6%	18.5%	86.5%	0.0060
15	0	0.6	–	0.7	2.6	18.5%	21.6%	23.4%	23.1%	86.5%	0.0060
16	0.4	0.7	2.1	0.9	0.8	23.9%	23.6%	22.1%	18.8%	88.5%	0.0066
17	0.4	0.7	0.9	2.1	2.2	18.8%	22.1%	23.6%	23.9%	88.5%	0.0066
18	0.4	0.8	2.2	0.9	0.8	21.8%	22.7%	21.5%	21.5%	87.5%	0.00040
19	0.4	0.8	0.8	2.1	2.2	21.5%	21.5%	22.7%	21.8%	87.5%	0.00040

$Φ > 0$ , $t > 0$ , $d > 0$	$- n t + n^{'} d + j λ_{0} = n^{'} \sqrt{d^{2} + r_{j}^{2}} - n \sqrt{t^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{- n d + n^{'} t}$
$Φ > 0$ , $t < 0$ , $d > 0$	$- n t + n^{'} d + j λ_{0} = n^{'} \sqrt{d^{2} + r_{j}^{2}} + n \sqrt{t^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{- n d + n^{'} t}$
$Φ > 0$ , $t < 0$ , $d < 0$	$- n t + n^{'} d + j λ_{0} = - n^{'} \sqrt{d^{2} + r_{j}^{2}} + n \sqrt{t^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{- n d + n^{'} t}$
$Φ < 0$ , $t > 0$ , $d > 0$	$n t - n^{'} d + j λ_{0} = - n^{'} \sqrt{d^{2} + r_{j}^{2}} + n \sqrt{t^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{n d - n^{'} t}$
$Φ < 0$ , $t > 0$ , $d < 0$	$n t - n^{'} d + j λ_{0} = n^{'} \sqrt{d^{2} + r_{j}^{2}} + n \sqrt{t^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{n d - n^{'} t}$
$Φ < 0$ , $t < 0$ , $d < 0$	$n t - n^{'} d + j λ_{0} = n^{'} \sqrt{d^{2} + r_{j}^{2}} - n \sqrt{t^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{n d - n^{'} t}$

$Φ > 0$ ( $d > 0$ )	$- n s_{j} + n^{'} d + j λ_{0} = n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{1}{n^{'} + (n - n^{'}) d / R}$
$Φ < 0$ ( $d < 0$ )	$n s_{j} - n^{'} d + j λ_{0} = n^{'} \sqrt{{(s_{j} - d)}^{2} + r_{j}^{2}}$
	$ζ = \frac{1}{- n^{'} - (n - n^{'}) d / R}$

$Φ > 0$ , $t > 0$ , $d > 0$	$- n t + n^{'} d + j λ_{0} = n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}} - n \sqrt{{(t - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{n^{'} t - n d + (n - n^{'}) t d / R}$
$Φ > 0$ , $t < 0$ , $d > 0$	$- n t + n^{'} d + j λ_{0} = n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}} + n \sqrt{{(t - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{n^{'} t - n d + (n - n^{'}) t d / R}$
$Φ > 0$ , $t < 0$ , $d < 0$	$- n t + n^{'} d + j λ_{0} = - n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}} + n \sqrt{{(t - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{n^{'} t - n d + (n - n^{'}) t d / R}$
$Φ < 0$ , $t > 0$ , $d > 0$	$n t - n^{'} d + j λ_{0} = - n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}} + n \sqrt{{(t - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{- n^{'} t + n d - (n - n^{'}) t d / R}$
$Φ < 0$ , $t > 0$ , $d < 0$	$n t - n^{'} d + j λ_{0} = n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}} + n \sqrt{{(t - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{- n^{'} t + n d - (n - n^{'}) t d / R}$
$Φ < 0$ , $t < 0$ , $d < 0$	$n t - n^{'} d + j λ_{0} = n^{'} \sqrt{{(d - s_{j})}^{2} + r_{j}^{2}} - n \sqrt{{(t - s_{j})}^{2} + r_{j}^{2}}$
	$ζ = \frac{t}{- n^{'} t + n d - (n - n^{'}) t d / R}$

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Equations (80)

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