Wavefront aberration measurement of freeform spectacle lens–eye system

Journal Pre-proof Wavefront aberration measurement of freeform spectacle lens–eye system Jing Yu, Weiwei Jiang, Chengli Wang, Xiaoyan Shen

PII:

S0030-4026(19)31358-0

DOI:

https://doi.org/10.1016/j.ijleo.2019.163460

Reference:

IJLEO 163460

To appear in:

Optik

Received Date:

3 September 2019

Revised Date:

23 September 2019

Accepted Date:

23 September 2019

Please cite this article as: Yu J, Jiang W, Wang C, Shen X, Wavefront aberration measurement of freeform spectacle lens–eye system, Optik (2019), doi: https://doi.org/10.1016/j.ijleo.2019.163460

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.

Wavefront aberration measurement of freeform spectacle lens– eye system Jing Yu *, Weiwei Jiang, Chengli Wang and Xiaoyan Shen School of Metrology and Measurement Engineering, China Jiliang University, ZheJiang HangZhou 310018, China *

Corresponding author: [email protected]

Abstract: We establish a spectacle lens–eye system and measure its wavefront aberrations with Shack-Hartman wavefront sensor. In order to analysis the image quality of the freeform spectacle lens. In addition, we compare the wavefront aberrations of the eye system and different spectacle lens–eye systems in the distance, progressive corridor, near, and blending zones. The results show that the piston, tilt, and defocus are the main wavefront aberrations of the lens–eye system. A freeform spectacle lens with

ro of

a progressive inner surface may exhibit lower wavefront aberrations. For the human eye model, selecting a suitable spectacle lens can help reduce wavefront aberrations.

Keywords: spectacle lens-eye system；freeform spectacle lens；wavefront aberration; Physiological characteristics

1.Introduction

Jo

ur

na

lP

re

-p

The human eye is not only an important biological organ but also a precision optical imaging instrument [1]. The best method of correcting ametropia is to wear corrective spectacle lenses [2]. Recently, there have been some studies on human eye by optical simulation [3-6]. A lens and an eye can be treated as an optics image system assembled with lens and a group of lenses. The optical parameters of a spectacle lens are set to correct the optical defects of eyes to obtain an excellent imaging system. Thus, the optical design of a spectacle lens should be related to the actual physiological parameters of the pupil. Since the last few decades, freeform spectacle lenses have been widely used for this purpose owing to the development of freeform manufacturing technology [7,8]. These lenses are designed with more than two refractive powers on the entire surface. Moreover, they provide continuous vision at all distances, instead of the predetermined working distances of bifocal and trifocal lenses. The most typical application is the progressive addition lens (PAL) for presbyopia. Such lenses can be used to achieve the distance and near through one lens. For the progressive addition lens (PAL), the refractive power distribution on the entire surface cannot be used to detect if the lens suitable for the wearer or not. The common methods of measuring refractive parameters include Hartmann measurement [9,10], the Moiré method [11,12], the Ronchi test [13-15], fringe transmission measurement [16-18], and the point diffraction interferometer [19-21]. These methods obtain the refractive distribution of a spectacle lens surface by analyzing the image of a fringe through the spectacle lens. However, refractive parameters cannot be used to evaluate the quality of freeform spectacle lenses comprehensively. Hence, image quality parameters have been proposed to evaluate freeform spectacle lenses. In recent years, a few researchers have suggested measuring spectacle lenses by considering wearing the spectacle lens [22,23]; image parameters are applied in optometry[24]. In this context, we first establish a combined lens–eye optical system and subsequently measure and analyze the wavefront aberration of the system. In this work, we provide the theoretical and experimental basis for evaluating the image quality of freeform spectacle lenses. 2. Measurement theory

Wavefront aberration has been introduced to optometry and ophthalmology in recent years. The wavefront aberration of the human eye is the position deviation of the actual wavefront from the ideal wavefront. It can be divided into two categories. One is low-order aberrations including defocus and astigmatism, which are the main reason for ametropia, and the other is high-order aberrations including spherical aberration and coma [24]. The primary method of measuring human eye aberration is the Shack–Hartmann wavefront technology. In this study, the Shack–Hartman wavefront sensor (SHWS) is used to measure the lens–eye system. For the human eye, low-order aberrations are typically corrected using spectacle lenses and high-order

aberrations must be corrected through refractive surgery [25]. However, a spectacle lens leads to other aberrations because its optical axis is not completely in accordance with the optical axis of the eye. Chromatic aberration is one of the aberrations introduced by spectacle lenses [26], and it is determined by the various material. We establish a spectacle lens –eye system and measure its wavefront aberration. The Hartmann test is one of the simple and effective tests for determining the wavefront shape of an optical system [27]. The principle of the test is illustrated in Fig. 1. A screen with a rectangular array of holes or a microlens array is set up on a measuring system. The core component of the SHWS is the microlens array, which is placed close to the entrance or exit pupil of the system under test. The square array of holes on the Hartmann screen is frequently defined with one of the holes at the center of the screen, as shown in Fig. 1(a). The wavefront is calculated by integrating the transverse aberrations measured on the Hartmann plate shown in Fig. 1(b) [28]. Wavefront deformations, W(x,y), are calculated using the measurements of transverse aberrations TAx and TAy. These aberrations and the wavefront deformations are related as x w  x, y  y





TA x  x, y  r TA y  x, y  r

 θ x  x, y  (1)

ro of

w  x, y 

 θ y  x, y 

(2)

lP

re

-p

where r is the distance from the wavefront at the exit pupil to the Hartmann plate where the spots are recorded. The linear transverse aberrations are TAx and TAy, and the angular transverse aberrations are 𝜃𝑥 and 𝜃𝑦 . The phase distribution of the wavefront can be calculated by the integral of the wavefront slope. The wavefront aberration, refractive distribution, and Modulation Transfer Function(MTF)curve can be calculated using wavefront reconstruction. The Zernike polynomial is used to express wavefront aberrations because the aberrations are independent of each other. All aberrations correspond to the classical Seidel aberrations, where each coefficient represents different aberrations[29]. Table 1 shows the Zernike polynomials from the zero to the fifth order. The wavefront aberration, W (ρ,θ), is broken down into the sum of the Zernike polynomials, and it is given by the following formula: W  ρ,θ   Cmn Zmn  ρ,θ   C00 Z00  C11 Z11  C11Z11  C22 Z22  C02 Z02  C22 Z22  nm

(3)

ur

3.Results and discussion

na

The WFS10-7R Shack-Hartman Wavefront Sensor (SHWS)provided by Thorlabs is used to measure the wavefront aberration of the lens–eye system. A 37× 29 micro lens arrays with a pixel size 4.65 μm, a diameter of 150 μm, and a focal length of 6.7 mm is employed. The resolution the CCD camera is 1280 × 1024 pixels, and the size of its aperture 5.59 × 4.76 mm2.

Jo

According to the physiological parameters of the human eye, a camera lens with a focal length of 12–40 mm and an aperture ranging from F2.8 to F22 is used to simulate the human eye. We set up and adjust the optical layout and ensure that the laser is on the optical axis without deviation. We adjust the focal length of the eye model to be 18 mm. The diopter of the eye is 55.56D. Fig. 2 shows the optical layout of the wavefront sensor. We use a single mode fiber coupled output laser; the diameter of the light beam of the laser is 2.2 mm. L1 is a collimator, and L2 and L3 are expanding systems with a beam expansion ratio of 2:1, L4 is the freeform spectacle lens, and L5 is the eye model. The SHWS is placed after L5, and it shows wavefront aberrations. First, we measure the wavefront without L4; the results show the wavefront aberration of the eye model. Subsequently, we measure the wavefront aberrations of the lens–eye system with different spectacle lenses. There are three types of spectacle lenses, and Table 2 lists their diopters and gradual sides. The central thickness of the lenses ranges between 2 mm and 3 mm, and the diameter of the optical area reaches up to 70 mm. The PALs are composed of resin lenses with a refractive index of 1.56 and an Abbe number of 41. We measure the wavefront aberrations of the spectacle lens–eye system in the distance, near, progressive corridor, and blending zones. Then, we analyze the corrective effect of the freeform spectacle lens. 3.1. Distance

-p

ro of

First, we measure the wavefront aberration of the spectacle lens–eye system without the spectacle lens. Then, we measure the lens-eye system in the distance with three different spectacle lenses. Fig. 3 shows the results of the freeform spectacle lens in the distance. The results show that the wavefront aberration of the eye model is different from others. This indicates that wearing correct spectacle lenses can help humans achieve better vision. The refractive parameter of sphere is one of the most important parameters of the human eye model, in addition to wavefront translation and tilt. Wavefront translation and tilt decrease after correction in the case of the three different spectacle lenses. The sphere is the main influencing factor for wavefront aberration. But the three spectacle lens got different refractive parameter distribution. The quantified measurement results, i.e., the PV, RMS, and wRMS values of the wavefront aberration and the low-order Zernike coefficients are shown in Table 3 and Fig. 4. The results show that after correction, the PV and RMS values of the spectacle lens–eye system reduce. This indicates that the distance of all three spectacle lenses can correct aberration effectively. The PV and RMS values of lens 1 are larger than those of lens 2. This indicates that the inner surface is better than the outer surface. The PV and RMS values of lens 3 are less than those of lenses 1 and 2. This indicates that the larger sphere achieves better correction for high myopia. This is in agreement with the fact that distance can correct myopia for the freeform spectacle lens. 3.2. Progressive corridor We perform measurements at the same positions of the three spectacle lenses in the progressive corridor. The results of the wavefront aberrations of the eye model and spectacle lens–eye model are shown in Fig. 5. The results indicate that the uncorrected human eye model is different from the corrected spectacle lens–eye model. The sphere, wavefront translation, and tilt are evidently present in the wavefront aberration. After correction, lens 3 is better than lenses 1 and 2. Lens 3 exhibits lower wavefront aberrations. The low-order Zernike coefficients and the PV, RMS, and wRMS values are shown in Fig. 6 and Table 4.

Jo

ur

na

lP

re

Table 4 and Fig. 6 illustrate that the main wavefront aberrations are the piston, tilt on the X-axis, tilt on the Yaxis, and defocus. The Zernike coefficients of lenses 1 and 2 change slightly after correction. In addition, the PV and wRMS values change slightly, and the RMS value is higher than that for the eye model. This indicates that the correction effect of the progressive corridor is not sufficient. Lens 3 exhibits lower PV, RMS, and wRMS values. This indicates that lens 3 achieves a better correction effect in the progressive corridor. The main reason for these results is that the refractive powers of the spectacle lenses are different. The refractive powers of lenses 1 and 2 in the progressive corridor are approximately -0.25D; however, the refractive power of lens 3 in the progressive corridor is approximately -1.25D. 3.3.Near We perform measurements at the same positions of the three spectacle lenses in the near. Subsequently, we measure the wavefront aberrations of the eye model and the corrected spectacle lens–eye model. The results of the wavefront aberrations of the eye model and spectacle lens–eye model are shown in Fig. 7. The results indicate that the uncorrected human eye model is different from the corrected spectacle lens–eye model. The sphere, wavefront translation, and tilt are evidently present in the wavefront aberration. After correction, lens 3 is better than lenses 1 and 2. The three lenses exhibit lower wavefront aberrations. The low-order Zernike coefficients and the PV, RMS, and wRMS values are provided in Fig. 8 and Table 5. The results indicate that the main wavefront aberrations are the piston, tilt on the X-axis, tilt on the Y-axis, and defocus. After correction, the Zernike coefficients and the PV and RMS values of lenses 1 and 2 are higher. This indicates that these lenses do not correct the eye model, and the wavefront aberration is higher. For lens 3, the piston, tilt on the X-axis, and astigmatism are lower after correction, defocus changes slightly, and the PV, RMS and wRMS values decrease. This implies that lens 3 can correct the eye model. As the refractive powers of lenses 1 and are positive, the correction effect is poor. The refractive power of lens 3 is negative but small. Thus, the correction effect is not significant. 3.4. Blending zone We perform measurements at the same positions of the three spectacle lenses in the blending zone. Subsequently, we measure the wavefront aberrations of the eye model and the corrected spectacle lens–eye model. The results of the wavefront aberrations of the eye model and the spectacle lens–eye model are shown in Fig. 9. The results indicate that the sphere, wavefront translation, and tilt are evident in the wavefront aberration. After

correction, the wavefront aberrations of all three spectacle lenses change slightly. The low-order Zernike coefficients and the PV, RMS, and wRMS values are shown in Fig. 10 and Table 6. The results indicate that the main wavefront aberrations are the piston, tilt on the X-axis, tilt on the Y-axis, defocus, and the astigmatism on the X-axis and Y-axis. The low-order Zernike coefficients and the PV, RMS, and wRMS values of lens 1 increase slightly, those of lens 2 change slightly, and those of lens 3 decrease slightly. These results indicate that the correction effect of the blending zone is not significant. However, after correction, the astigmatism of all three spectacle lenses improves substantially. This is because the blending zone can correct astigmatism in the human eye. 4. Conclusion

ro of

Considering the physiological characteristics of the human eye, we established a spectacle lens–eye system and discussed the wavefront aberrations of this system. We measured and compared the wavefront aberrations the eye model and the spectacle lens–eye model with different lenses. We compared the wavefront aberrations in different zones of the spectacle lenses, i.e., the distance, progressive corridor, near, and blending zones. The results showed that the piston, tilt on the X-axis, tilt on the Y-axis, and defocus were the main wavefront aberrations of the lens–eye system. Typically, the freeform spectacle lens with an inner progressive surface may achieve lower wavefront aberrations. For the human eye model, selecting a suitable spectacle lens can help reduce wavefront aberrations. This study can help a wearer in selecting the appropriate spectacle lens to correct eye defects. Acknowledgements

-p

This work was supported in part by the National Natural Science Foundation (Grants No. 61605193, 51875543). Reference

J. Yu. Study on Evaluation Method of Freeform Spectacle Lenses, Tianjin University, 2015. (in Chinese)

2.

Jalie M. Ophthalmic lenses and dispensing, Butterworth-Heinemann, 2003.

3.

S. Yeh, T. Chen, R. Lin, K. Su, C. Horng and Hsiang-Chen Wang, Contact lens with peripheral refractive correction,

re

1.

4.

lP

Optik,185 (2019)223-231.

W. Fan, C. Chang, C. Horng, H. Yao, H. Sun, S. Huang and H. Wang. Human eye cataract microstructure modeling and its effect on simulated retinal imaging, Optics Communication, 385 (2017)59-65. H. Sun, Y. Chiang, S. Yeh, S. Huang, C. Horng and H. Wang, Rainbow glare by retinal imaging, Optics Communications, 370 (2016)160-167.

6.

H. Sun, H. Wang and S. Yang, Vision correction via multi-layer pattern corneal surgery, Optics Communications, 300 (2013) 293-298.

7.

F. Fang, X. Zhang and X. Hu, Cylindrical coordinate machining of optical freeform surfaces, Optics Express, 16

ur

(2008)7323-7329. 8.

na

5.

Y. Cheng, F. Fang and X. Zhang, Design and manufacture of off-axis optical reflective integrator with faceted structure, Optical Engineering, 51(2012)094001-09004 C. Zhou, W. Wang, K. Yang, X. Chai and Q. Ren, Measurement and comparison of the optical performance of an ophthalmic

Jo

9.

lens based on a Hartmann-Shack wavefront sensor in real viewing conditions, Applied optics ,47(2008)6434-6441. 10. Marcano O, Salas-Peimbert D, Trujillo-Schiaffino G, Malacara-Hernandez D, Malacara-Doblado D, and Almazan-Cuellar S, Ophthalmic lenses measurement using Hartmann test, 5th Iberoamerican Meeting on Optics and 8th Latin American Meeting on Optics and Their Applications, 5622 (2004) 102-106. 11. Sheedy JE, Campbell C, King-Smith E and Hayes JR, Progressive powered lenses: the Minkwitz theorem, Optometry & Vision Science,82(2005) 916-922. 12. Sheedy JE, Hardy RF and Hayes JR, Progressive addition lenses—measurements and ratings, Optometry-Journal of the American Optometric Association, 77(2006)23-39. 13. Arasa J, Royo S and Tomas N, Simple method for improving the sampling in profile measurements by use of the Ronchi test, Applied Optics, 39(2000)4529-4534.

14. Arasa J, Caum J, Royo S, and Cifuentes A, Progressive addition lenses power map measurement using Ronchi test techniques. Optical Metrology, International Society for Optics and Photonics,5144(2003) 0277-773. 15. Royo S, Arasa J and Pizarro C, Profilometry of toroidal surfaces with an improved Ronchi test,Applied Optics, 39(2000)5721-5731. 16. L. Jiang.

Study on measurement method of optical freeform surfaces based on fringe deflectometry, Tianjin unversity,

2017.(in Chinese) 17. Knauer MC, Kaminski J and Häusler G, Phase measuring deflectometry: a new approach to measure specular free-form surfaces, Optical Metrology in Production Engineering. International Society For Optics and Photonics, 2004. 18. H. Guo, P. Feng, T. Tao, Specular surface measurement by using least squares light tracking technique,Optics and Lasers in Engineering ,48(2010)166-1671. 19. Acosta E, Chamadoira S and Blendowske R, Modified point diffraction interferometer for inspection and evaluation of ophthalmic components, JOSA A, 23(2006)632-637. interferometry, Ophthalmic and Physiological Optics, 29(2009)235-246.

ro of

20. Acosta E, Vázquez D and Castillo LR, Analysis of the optical properties of crystalline lenses by point‐diffraction 21. Chamadoira S, Blendowske R and Acosta E, Progressive addition lens measurement by point diffraction interferometry, Optometry & Vision Science, 89(2012)1532-1542.

22. L. Qin. Study on simulation method and optimization design of ophthalmic freeform lenses, Suzhou University, 2014. (in Chinese)

23. Arroyo R, Crespo D and Alonso J. Scoring of progressive power lenses by means of user power maps, Optometry and

-p

Vision Science, 89(2012)489-501.

24. Y.Wang, Reserch on visual and optical quality evaluation based on wavefront aberration and Moudualation Transfer Function (MTF) before and after corneal refractive surgery, Tianjin medical university,2009. (in Chinese)

re

25. Salas-Peimbert DP, Trujillo-Schiaffino G, González-Silva JA, Almazán-Cuellar S and Malacara-Doblado D. Simple Hartmann test data interpretation for ophthalmic lenses,Review of scientific instruments, 77(2006)043102-043105.

lP

26. Jansonius NM. Tool to estimate optical metrics from summary wave-front analysis data in the human eye, Ophthalmic & physiological optics : the journal of the British College of Ophthalmic Opticians, 33(2013)35-41. 27. Salas-Peimbert DP, Malacara-Doblado D, Durán-Ramírez VM, Trujillo-Schiaffino G and Malacara-Hernández D. Wavefront retrieval from Hartmann test data, Applied optics, 44(2005)4228-4238.

na

28. X. Yin, X. Li, L. Zhao and Z. Fang. Automatic centroid detection for Shack-Hartmann Wavefront sensor, Advanced Intelligent Mechatronics, ASME International Conference on IEEE, 2009. 29. Villegas EA, Artal P. Comparison of aberrations in different types of progressive power lenses, Ophthalmic and Physiological Optics,24(20045):419-426.

ur

30. McAlinden C, McCartney M and Moore J. Mathematics of Zernike polynomials: a review,Clinical & experimental

Jo

ophthalmology, 39(2011)820-827.

Figure captions

re

-p

ro of

(a) Hartmann screen without aberrations (b) Hartmann screen with aberration Fig. 1. Principle of Shack–Hartmann wavefront sensor

Jo

ur

na

lP

Fig. 2. Optical layout of the wavefront sensor

(a)

(b)

lP

re

-p

ro of

(c) (d) Fig. 3. Wavefront aberration measurement results in the distance. (a) wavefront of the eye model (b) wavefront of lens 1 (c) wavefront of lens 2 (d) wavefront of lens 3

Jo

ur

na

(a) (b) Fig. 4. Bar chart of the measured results in the distance. (a)Low-order Zernike coefficients (b) PV, RMS, and wRMS values

(a)

(b)

re

-p

ro of

(c) (d) Fig. 5. Wavefront aberration measurement results in the progressive corridor. (a) wavefront of the eye model (b) wavefront of lens 1 (c) wavefront of lens 2 (d) wavefront of lens 3

Jo

ur

na

lP

(a) (b) Fig. 6. Bar chart of the measured results in the progressive corridor. (a)Low-order Zernike coefficients (b) PV, RMS, and wRMS values

(a)

(b)

re

-p

ro of

(c) (d) Fig. 7. Wavefront aberration measurement results in the near. (a) wavefront of the eye model (b) wavefront of lens 1 (c) wavefront of lens 2 (d) wavefront of lens 3

Jo

ur

na

lP

(a) (b) Fig. 8. Bar chart of the measured results in the near. (a)Low-order Zernike coefficients (b) PV, RMS, and wRMS values

(a)

(b)

(c)

(d)

re

-p

ro of

Fig. 9. Wavefront aberration measurement results in the blending zone. (a) wavefront of the eye model (b) wavefront of lens 1 (c) wavefront of lens 2 (d) wavefront of lens 3

Jo

ur

na

lP

(a) (b) Fig. 10. Bar chart of the measured results in the blending zone. (a)Low-order Zernike coefficients (b) PV, RMS, and wRMS values

Table Table 1. Zernike polynomials from zero to fifth order and description with regard to their relation to classical Seidel aberrations[30]

m (frequency) 0 1 0 -3 1 -4 0

0 1 2 3 3 4 4 4

n (order) 1 2 2 3 3 4 4

Description Piston Tilt (about y-axis) Spherical defocus Trefoil (base on x-axis) Coma (along y-axis) Tetrafoil Spherical aberration

4

m (frequency) -1 -2 2 -1 3 -2 2

Description Tilt (about x-axis) Astigmatism (axis 45°, 135°) Astigmatism (axis 0°, 90°) Coma (along x-axis) Trefoil (base on y-axis) Secondary astigmatism Secondary astigmatism

Tetrafoil Table 2. Lens parameters

No. 1 2 3

Diopter BASE-1.0D+ADD1.5D BASE-1.0D+ADD1.5D BASE-2.0D+ADD1.5D

ro of

n (order)

Progressive surface outer surface inner surface outer surface

Z2 Tilt ( X-axis)

Eye model Lens 1 Lens 2 Lens 3

9.268 7.356 8.294 5.776

-4.906 -2.858 -3.788 -2.421

Z3 Tilt (Yaxis) -2.257 -1.367 -1.576 0.049

Z4 Z6 Z5 Spherical Spherical PV RMS wRMS defocus aberration aberration 0.04 -3.059 0.01 29.807 6.252 6.958 0.08 -3.354 0.035 29.016 6.081 6.449 0.062 -3.361 0.035 27.949 5.986 6.349 -0.007 -3.696 -0.048 26.206 5.679 5.996

re

Z1 Piston

lP

No.

-p

Table.3 Measurement data in the remote area

Table 4. Measured data in the progressive corridor

Eye model Lens 1 Lens 2 Lens 3

9.268 9.024 8.669 3.309

Z2 Tilt ( Xaxis) -5.006 -3.876 -2.689 0.907

Jo

Z3 Tilt (Yaxis) -2.257 -2.104 -2.916 -0.69

na

Z1 Piston

ur

No.

Z4 Z6 Z5 Spherical Spherical PV RMS wRMS Defocus aberration aberration 0.04 -3.059 0.01 29.807 6.252 6.958 -0.02 -2.984 0.026 29.066 6.595 7.145 0 -3.101 0.044 28.094 6.903 6.717 -0.08 -3.009 0.089 24.429 5.316 5.517

Table 5. Measured data in the near

No.

Z1 Piston

Z2 Tilt ( Xaxis)

Z3 Z4 Z6 Z5 Tilt (Y- Spherical Spherical Defocus axis) aberration aberration

Eye model

9.268

-5.006

-1.257

0.04

-3.159

0.01

Lens NO.1 Lens NO.2 Lens NO.3

10.012 9.321 8.312

-5.391 -5.103 2.879

-1.353 -1.575 -0.313

0.05 0.009 -0.058

-3.223 -3.095 -2.953

0.016 0.026 -0.004

PV 29.807

RMS wRMS 6.252

6.958

29.929 6.497 29.861 6.396 28.495 5.757

7.187 7.098 6.128

Table 6. Measured data in blending zone

No.

Z3 Tilt (Yaxis) -2.257 1.353 -1.304 -2.613

Z4 Z6 Z5 Spherical Spherical Defocus aberration aberration 0.04 -3.059 0.01 0.046 -3.143 0.142 0.032 -2.998 -0.018 -0.033 -3.028 0.01

PV 29.807 31.625 29.981 29.329

RMS wRMS 6.252 6.568 6.007 5.852

6.958 7.386 7.714 5.495

Jo

ur

na

lP

re

-p

ro of

Eye model Lens NO.1 Lens NO.2 Lens NO.3

Z2 Z1 Tilt ( XPiston axis) 9.268 -5.006 9.512 -5.991 9.193 -5.245 8.094 -2.245