Adjustable-focus ultracompact endoscopic lens design with ultrahigh optical performance

Yu-Shan Chang; Long Hsu; Kuang-Lung Huang

doi:10.1364/AO.57.001091

Applied Optics
Vol. 57,
Issue 5,
pp. 1091-1099
(2018)
•https://doi.org/10.1364/AO.57.001091

Adjustable-focus ultracompact endoscopic lens design with ultrahigh optical performance

Yu-Shan Chang, Long Hsu, and Kuang-Lung Huang

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Yu-Shan Chang, Long Hsu, and Kuang-Lung Huang, "Adjustable-focus ultracompact endoscopic lens design with ultrahigh optical performance," Appl. Opt. 57, 1091-1099 (2018)

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Table of Contents Category
- Optical Design and Fabrication
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About this Article
History
- Original Manuscript: November 21, 2017
- Revised Manuscript: January 5, 2018
- Manuscript Accepted: January 5, 2018
- Published: February 6, 2018
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 13, Iss. 4

Abstract

An internally focusing design is developed for a compact endoscopic lens to have optical performance close to the diffraction limit. When changing the working distance from infinity to a predetermined short distance, the overall system length and the field of view remain constant. It is numerically demonstrated that the diffraction-limit-like performance is maintained over a wide range of working distances, showing a novel capability of adjustable focuses. The design concept is numerically proven to be feasible and can enable very high-resolution examination for doctors checking the positions of biological entities through the immediate capture of clear images at different working distances. The corresponding lens configuration, PNN, is shown to be useful in achieving the high-resolution performance once the number of lens elements is four, where P and N are used to denote positive and negative optical power, respectively, for the lens groups. A corresponding tolerance analysis is also presented.

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Lens	Material	Refraction Index $n_{d}$ (589.3 nm)	Abbe Number $V_{d}$
First lens	OKP4HT	1.632	23
Second lens	PMMA	1.49	55.3
Third lens	PC	1.586	29.9
Fourth lens	PMMA	1.49	55.3

Parameters	Specifications
Optical format	$1 / 18^{''}$
Pixel size	$2.5 μm \times 2.5 μm$
Resolution	$320 \times 240$
Image area	$820 μm \times 625 μm$
Chroma	RGB Bayer
Nyquist frequency ( $f_{x y}$ )	$100 lp / mm$

Parameters	Specifications
Wavelength (nm)	486.1
	587.6
	656.3
Effective focal length (mm)	$< 1$
Working distance (mm)	Config. 1 : Infinity
	Config. 2 : 50
	Config. 3 : $< 20$
Working f-number	$≦ 3.5$
FOV (degree)	$> 50$
Chief ray angle (CRA) (degree)	$< 25$
Image height (mm)	0.5
Relative illumination@1.0F (%)	$> 50$
Distortion (%)	$< 2.5$
MTF@ $f_{x y}$ @full object point	$> 0.4$

Lens	Material	Refraction Index $n_{d}$ (589.3 nm)	Abbe Number $V_{d}$
First lens	OKP4HT	1.632	23
Second lens	APEL	1.543	56
Third lens	PMMA	1.49	55.3
Fourth lens	PMMA	1.49	55.3

Items	Conf.1	Conf.2	Conf.3
Object height (mm)	Infinity	23.6349	8.3500
Working distance (mm)	Infinity	50	16.7480
Max. aperture radius (mm)	0.3350
Overall lens length (mm)	1.1997
Effective focal length (mm)	0.6966	0.6575	0.4025
Working f/#	3.1	2.9	2.8
FOV(degree)	$25.5 ° \times 2 = 51 °$	$25.3 ° \times 2 = 50.6 °$	$26.5 ° \times 2 = 53 °$
CRA(degree)	$< 23 °$	$< 23 °$	$< 24 °$
MTF@ $f_{x y}$ @ all object points	$> 0.61$	$> 0.58$	$> 0.44$
Strehl ratio @ 1.0F (%)	98.7	89.7	99.5
Distortion (%)	$< 1.75$	$< 1.75$	$< 2.5$
Relative illumination @ 1.0F(%)	$> 70$

Surface Number	Radius	Axial Distance (mm)	Aper. Radius(mm)
0 (Aperture stop)	0	0.024627	0.1200
1 (First surface of the first lens)	0.5132	0.124853	0.1750
2 (Second surface of the first lens)	0.8541	0.023498	0.1750
3 (First surface of the second lens)	0.3523	0.167066	0.2177
4 (Second surface of the second lens)	−0.4418	Conf. 10.008270	0.2177
		Conf. 20.017054
		Conf. 30.123935
5 (First surface of the third lens)	−0.4106	0.112164	0.2512
6 (Second surface of the third lens)	0.4875	Conf. 10.345112	0.2512
		Conf. 20.336328
		Conf. 30.229447
7 (First surface of the fourth lens)	−0.3685	0.119517	0.3350
8 (Second surface of the fourth lens)	−1.4654	0.274564	0.3350
9 (Image plane)	0	0	0.5024

Surface Number	Aspheric Surface Data
1 (First surface of the first lens)	$A_{2} = - 0.1042811004002$ ;
	$A_{4} = - 13.5501713334843$ ;
	$A_{6} = - 20.0089704372565$ ;
	$A_{8} = 4013.8635465436141$ ;
	$A_{10} = - 3.2666874833 e + 05$ ;
	$A_{12} = - 9.5000113836 e + 06$ ;
	$A_{14} = 8.9210853641 e + 08$ .
2 (Second surface of the first lens)	$A_{2} = 1.0917774737528$ ;
	$A_{4} = - 12.8172856906831$ ;
	$A_{6} = - 223.752178712082$ ;
	$A_{8} = 7820.7160921591194$ ;
	$A_{10} = 56143.34665316977$ ;
	$A_{12} = - 9.0192450789 e + 06$ ;
	$A_{14} = 1.2156939662 e + 08$ .
3 (First surface of the second lens)	$A_{2} = - 0.5763185383361$ ;
	$A_{4} = - 5.973673927703$ ;
	$A_{6} = - 314.0272165941342$ ;
	$A_{8} = 6283.2349797019397$ ;
	$A_{10} = - 11603.354616334545$ ;
	$A_{12} = - 4.2470372233 e + 06$ ;
	$A_{14} = - 2.7556666691 e + 07$ .
4 (Second surface of the second lens)	$A_{2} = - 0.4079331178343$ ;
	$A_{4} = - 3.6744488752962$ ;
	$A_{6} = - 19.8242308292766$ ;
	$A_{8} = - 2246.3356346112209$ ;
	$A_{10} = 58803.397567070293$ ;
	$A_{12} = - 8.0394277075 e + 05$ ;
	$A_{14} = - 1.5506160115 e + 07$ .
5 (First surface of the third lens)	$Conic const. = 0.3869117362135$ ;
	$A_{2} = 1.2009085623858$ ;
	$A_{4} = - 0.8687550583437$ ;
	$A_{6} = 6.9153987529104$ ;
	$A_{8} = 755.6725606021659$ ;
	$A_{10} = 7563.6674329613907$ ;
	$A_{12} = - 6.0654843726 e + 05$ ;
	$A_{14} = 3.8260462715 e + 06$ .
6 (Second surface of the third lens)	$Conic const. = - 1.0004522511508$ ;
	$A_{2} = - 0.8304173829212$ ;
	$A_{4} = - 2.9165924434496$ ;
	$A_{6} = - 19.115467176761$ ;
	$A_{8} = 812.676263897395$ ;
	$A_{10} = - 5945.575287125007$ ;
	$A_{12} = - 85803.10790635251$ ;
	$A_{14} = 1.3243838608 e + 05$ .
7 (First surface of the fourth lens)	$A_{2} = - 1.9869399141874$ ;
	$A_{4} = 0.1166950779962$ ;
	$A_{6} = - 1.8031466201199$ ;
	$A_{8} = 456.2672747721405$ ;
	$A_{10} = - 17296.255161489506$ ;
	$A_{12} = 2.5814640285 e + 05$ ;
	$A_{14} = - 2.4782583362 e + 05$ .
8 (Second surface of the fourth lens)	$A_{2} = - 2.1255555138927$ ;
	$A_{4} = 4.0223260252782$ ;
	$A_{6} = - 54.4515476377582$ ;
	$A_{8} = 1138.0081392435752$ ;
	$A_{10} = - 12373.190936663696$ ;
	$A_{12} = 63824.152638895714$ ;
	$A_{14} = - 59510.416895497263$ .

		MTF@100 lp/mm@ All Object Points
Working Distance (mm)	Config. #	Meridional	Sagittal
16.748	3	$> 0.4450$	$> 0.5150$
30	3	$> 0.4820$	$> 0.4989$
40	2	$> 0.5526$	$> 0.5910$
50	2	$> 0.5814$	$> 0.6263$
60	1	$> 0.5603$	$> 0.6184$
70	1	$> 0.5724$	$> 0.6328$
100	1	$> 0.5901$	$> 0.6531$
150	1	$> 0.6001$	$> 0.6635$
200	1	$> 0.6040$	$> 0.6671$

Object : On Axis		Object : 0.8F		Object : 1.0F
Focus Shift (mm)	MTF	Focus Shift (mm)	MTF	Focus Shift (mm)	MTF
−0.034	0.3872	−0.034	Meridional 0.3983	−0.032	Meridional 0.3948
−0.033	0.4013	−0.033	Meridional 0.4108	−0.031	Meridional 0.4063
$+ 0.037$	0.4080	$+ 0.035$	Sagittal 0.4098	$+ 0.035$	Sagittal 0.4006
$+ 0.038$	0.3944	$+ 0.036$	Sagittal 0.3967	$+ 0.036$	Sagittal 0.3880

Shift (mm)	Axial Distance 4 (mm)	Axial Distance 6 (mm)	MTF@100 lp/mm@ All Object Points
0	0.00827	0.345112	Meridional $MTF > 0.6131$
0	0.00827	0.345112	Sagittal $MTF > 0.6647$
−0.00827	0	0.353382	Meridional $MTF > 0.6211$
−0.00827	0	0.353382	Sagittal $MTF > 0.6727$
$+ 0.0821$	0.09037	0.263012	Meridional $MTF > 0.4001$
$+ 0.0821$	0.09037	0.263012	Sagittal $MTF > 0.4221$

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Applied Optics