Design the Progressive Hard Contact Lens for Myopic Presbyopic

Journal of China University of Science and Technology Vol.50-2012.01

61

Design the Progressive Addition Hard Contact Lens for Myopic Presbyopia

應用於近視性老花眼的多焦點硬式隱形眼鏡設計應用於近視性老花眼的多焦點硬式隱形眼鏡設計應用於近視性老花眼的多焦點硬式隱形眼鏡設計應用於近視性老花眼的多焦點硬式隱形眼鏡設計

�� 1 �� 2 �� 3

Chia-Tsung Hung Der-Chin Chen Shih-Wen Lee �� !� �� "#��1,2Department of Electrical Engineering, Feng Chia University

3Department of Electrical Engineering, China University of Science and Technology

ABSTRACT

The purpose of this study is to design the progressive addition hard contact lens for

myopic presbyopia patients by using the multi-configuration function in ZEMAX

optical design program. The multi-configuration settings consist of four ranges, which

are infinity, 2000mm, 1000mm and 400mm. So, the myopic presbyopia patients are able

to see clearly under the four different fields of view after wearing progressive addition

hard contact lens. Using the methods of multi-configuration and the free form surface;

it could correct the -3.00D at the infinity and -1.0D at the near vision of myopia

presbyopia, and the Modulation Transfer Function (MTF) value can reach above 0.3 at

30lp/mm. And super progressive addition hard contact lenses are designed.

Key Word: Progressive Lens, Myopic presbyopia, Freeform

摘摘摘摘要要要要

本文研究目的係使用自由曲面最佳化設計一近視性老花眼硬式隱形眼鏡。$%&'() *ZEMAX +,-./ 01234 567 89 :2000mm:1000mm:

400mm;4種視場(View Field)進行設計，使近視性老花眼在配戴硬式隱形眼鏡後後

也適合看遠、中、近距離。除了可矯正近視 Myopia(-3.00D)之外，還可以使配戴近

視性老花眼硬式隱形眼鏡之後的視網膜解像率在 30 lp/mm的 MTF 值達 0.3以上。


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I. INTRODUCTION

The crystalline lens in the eye structure looks like camera’s zoom lens, as shown in

Fig.1. The accommodation whereby changes in the dioptric power of the crystalline lens occur

so that an in-focus retinal image of an object of regard is obtained and maintained at the high

resolution fovea for seeing near or far. From far to near is called positive accommodation,

otherwise is called negative accommodation. Donders, Duane and Hofstetter has been

successively in 1864, 1912 and 1947 to do the test that range of amplitude of accommodation

for different age as shown in Table 1 [1-5]. The results for the age of 35 to 40 amplitude of

accommodation over the age of amplitude of accommodation is remaining half of the age of 10,

70 at the age of accommodative power are almost zero. Three scholars chart changes in the

statistics is not much difference, adjust the rate of Amplitude of Accommodation for poor

people, prolonged close work on the eyes is a burden. We had published about the design of

astigmatic eyeglass lenses by ZEMAX optical software in the previous issue of this journal [6].

The designing result of 1.0D astigmatic lens can obviously correct astigmatism and the MTF is

more than 0.3 at 30 lp/mm. This paper studies the design of progressive addition hard contact

lens. The difference of two researches is: the former is to correct astigmatic eye and the latter is

to correct myopic presbyopia eye.


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Fig.1 the structure of the eye


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II. Amplitude of Accommodation with the Range of Clear Vision

The amplitude of accommodation, expressed in diopters, is difference between the far

point and the near point of accommodation with respect to the spectacle plane, the entrance

pupil or some other reference point of the eye. The closest points conjugate to the retina with

exertion of maximal accommodation.

Table 1 Change the value of accommodate

Ages 10 15 20 25 30 35 40 45 50 55 60 65 70

Donders 14 12 10 8.5 7 5.5 4.5 3.5 2.5 1.75 1 0.5 0.25

Duane(mean) 13.4 12.6 11.5 10.2 8 7.3 5.9 3.7 2 1.3 1.1 1.1 0

Hofstetter

(probable) 15.5 14 12.5 11 9.5 8 6.5 5 3.5 2 0.5 0.5 0

@unit Ndiopter

Maximum amount of accommodation represented in space is called near point of

accommodation. The farthest point conjugates to the retina with exertion of minimum

accommodation. Minimum amount of accommodation represented in space is called far point of

accommodation. The equation of amplitude of accommodation isN

AA=(1/ MrS) –(1/ MpS) (1) where AA is amplitude of accommodation, MrS the linear distance of far point of

accommodation to spectacle plane and MpS is the linear distance near point of accommodation

to spectacle plane. James Ware was the first person in the 19th century to understand that far

sight was not necessarily associated with presbyopia as shown in

Fig.2 . In 1855, Stellwag von Carion provided a relatively clear description with an optical

explanation of the differences between hyperopia and presbyopia.

We focused on 40 to 60 years (every 5 years), respectively, hyperopia +3.00 D ~

myopia-3.00D of the people to do the analysis clear horizon, as listed in Table 2. By the formula

(1): amplitude of accommodation formula can change into:

MpS= MrS/(1-AA* M rS), MrSO0 (2)

or MpS=((1/ MrS)-AA)-1 (3)

and when MrS=0, MrS=(-AA)-1 (4)

The AA value use data of Donders’s in Table 2.


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III. The Optical Model of Human Eye

In the book of Introduction to Optics, Frank L. Pedrotti, Leno M. Pedrotti, Leno S. Pedrotti

mentioned the symbols and optical data of model eye in Table 3[7]. The optical layout of model

eye optics is defined more or less differently as illustrated in Fig. 3.The model eye’s parameter

in ZEMAX Software in as Fig.4 shows.

Table 1 The Range of Clear Vision

Ametropia +3.00D +2.00D +1.00D 0.00 -1.00D -2.00D -3.00D

Ages

(Acc.)

F.P.

(P )

N.P.

(P )

F.P.

(P )

N.P.

(P )

F.P.

(P )

N.P.

(P )

F.P.

(P )

N.P.

(P )

F.P.

(P )

N.P.

(P )

F.P.

(P )

N.P.

(P )

F.P.

(P )

N.P.

(P )

40years(

+4.5D)

IBE

33.3

IFE

66.7

IBE

50

IFE

40

IBE

100

IFE

28.6

IFE

∞

IFE

22.2

IFE

100

IFE

18.2

IFE

50

IFE

15.4

IFE

33.3

IFE

13.3

45 years

(+3.5D)

IBE

33.3

IFE

200

IBE

50

IFE

66.7

IBE

100

IFE

40

IFE

∞

IFE

28.6

IFE

100

IFE

22.2

IFE

50

IFE

18.2

IFE

33.3

IFE

15.4

50 years

(+2.5D)

IBE

33.3

IBE

200

IBE

50

IFE

200

IBE

100

IFE

66.7

IFE

∞

IFE

40

IFE

100

IFE

28.6

IFE

50

IFE

22.2

IFE

33.3

IFE

18.2

55 years

(+1.75D)

IBE

33.3

IBE

80

IBE

50

IBE

400

IBE

100

IFE

133

IFE

∞

IFE

57.1

IFE

100

IFE

36.4

IFE

50

IFE

26.7

IFE

33.3

IFE

21.1

60 years

(+1D)

IBE

33.3

IBE

50

IBE

50

IBE

100

IBE

100

IFE

∞

IFE

∞

IFE

100

IFE

100

IFE

50

IFE

50

IFE

33.3

IFE

33.3

IFE

25

F.P.=Far Point; N.P.=Near Point; I.F.E.=in front of eye; I.B.E.=in back of eye


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Fig.2 The range of clear vision with accommodation

Table 3 optical data of eye model

Optical surface

or element

Difining

Symbol

Distance from corneal

vertex(Q )

Radius of curvature

of surface(Q )

Refractive

index

Refractive power

(diopter)

Cornea S1 — +8a — 41.6

Lens(unit) L — 1.45 30.5

Front surface S2 +3.6 +10b — 12.3

Back surface S3 +7.2 -6 — 20.5

Eye(unit) — — — — 66.6

Front focal plane F -13.04 — — —

Back focal plane F' +22.38 — — —

Front principal

plane H +1.96 — — —

Back principal plane H' +2.38 — — —

Front nodal plane N +6.69 — — —

Back nodal plane N' +7.38 — — —

Anterior chamber AC — — 1.333 —

Vitreous chamber VC — — 1.333 —

Entrance pupil EnP +3.04 — — —

Exit pupil ExP +3.72 — — —


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a:The cornea is assumed to be thin.

b:Value is given for the relaxed eye. For the tensed or fully accommodated eye, the radius of curvature of

the front surface is changed to +6mm.

reference : adapted with permission from Mathew Alpern,RThe Eyes and Vision,RTable1,Section 12, in

Handbook of Optics (New York: McGraw-Hill Book Company,1978)

Fig. 2 optical layout of eye model

Fig. 3 The optical data of eye model in ZEMAX optical design software

We simulate four visual ranges, for example: extra far distance (∞), the far distance (2000

mm), middle range (1000 mm) and near (400 mm), so need to use the multi-configuration. In

Fig. 4, THIC in configuration 1 to configuration 4 that represent for distance at (∞), 2000 mm,

1000 mm, 400 mm; CRVT on behalf of lens curvature change; PRAM on behalf of the relative

angle that between visual axis of the eyeball and central axis of the contact lens.


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The solution to optimize the ophthalmic lens is to change the surface type of CL-front from

sphere to free-form surface for giving more freedom of design. Polynomial expansion of

free-form surface as in formula (5) shows, k of the Polynomial expansion will affect the contact

lens to make distorted and the curvature of the distribution.

Fig. 4 setting multi-configuration in ZEMAX optical design software

(5)

Where N is the total number of series in the polynomial coefficients, Ai for the first item

expansion coefficients of the polynomial i, c for the curvature, r is radius, k coefficient for the

quadratic surface. Quadratic surface which is less than -1 for the hyperbolic plane coefficient,

equal to 1 for the parabolic in an ellipse between -1 and 0, equal to 0 for the sphere.

IV. Result and Analysis

This research is to design the progressive addition hard contact lens to correct the -3.00D

far sight and -1.00D near sight myopia, the procedures are as followings:

4.1 Set up the three-dimensional layout (3D Layout)

Fig.6 is a three-dimensional setting layout. First surface represent for the incident beam entering

and the last surface on behalf of the retina for image plane. The other set are default value. The

first surface is the object plane, if the object distance is infinity setting for the graph is blank.

Fig.7 shows the eye of four configurations (from input beam to retina).


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Fig.6 3D layout diagram setting 1

Fig.7 3D eye layout (four configurations)

For understanding the relative included angle between the visual axis of eye and the

central axis of contact lens, we can change the output settings of three-dimensional eye layout.

Figure 8 shows the eye of four configurations (from CL-front to LENS-BACK). The 3D map of

the four configurations shows in figure 9, 10, 11 and 12.


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Fig.8 3D layout diagram setting 2

Fig.9 3D layout configuration 1(infinity) Fig.10 3D layout configuration 2(2000mm)

Fig.11 3D layout configuration 3(1000mm) Fig.12 3D layout configuration 4(400mm)

4.2 Setting Modulation Transfer Function (MTF)

Modulation Transfer Function (MTF) is an important method of describing the performance of

an optical system, and describes the contrast in the image of a spatial frequency presented in the

scene being viewed. The maximum spatial frequency of modulation transfer function set in30 lp


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/ mm for meeting the human eye of need. Figure 13 shows the fast Fourier transform MTF icon

and the modulation transfer function setting of system. The MTF of the four configurations

shows in figure 14, 15, 16 and17.

Fig.13 Setting Modulation Transfer Function

Fig.14 MTF configuration 1(Infinity) Fig.15 MTF configuration 2 (2000mm)

Fig.16 MTF configuration 3(1000mm) Fig.17 MTF configuration 4(400mm)


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The MTF plot for this eye glass, above, shows the contrast ratio for any spatial frequency

up to the maximum that the eye glass can support. In this case, we choose to limit the spatial

frequencies shown to a maximum of 30 cycles/mm. Also shown for reference is the diffraction

limited performance of an aberration-free lens of the same f/# [8].

4.3 Setting Partially Coherent Image Analysis

Partially Coherent Image Analysis can be performed by using the incoherent of transfer

functions and simulates the actual visual image. When generating diffraction images using

incoherent transfer functions, diffraction effects are accounted for, however, each point on the

source is considered to be incoherent with respect to all other points. The partially coherent

transfer functions are characterized using a parametric function, Gamma. The Gamma function

utilized for a particular analysis can be one of two types, Gaussian or Sinc (although others can

be added upon request): S(r)= e (-r*r/ T2) andS(r)=Sinc(x/T)*Sinc(y/T).For the Gaussian

Gamma function, the position vector, r, represents the distance between two points in the

displayed image. For both functions, the parameter α is a scaling parameter defined in lens units.

This parameter sets the effective width of the Gamma function. Use mostly incoherent method

when α is small and Sis narrow. First, let us try a small α value (i.e. 0.025). We know that for

small α values, the resulting Gamma function is narrow and, as such, the results are mostly

incoherent. The narrower the Gamma function, the more incoherent the resulting image will

appear. Figure 18 show partially coherent image analysis settings. Figure 14, 15, 16 and 17

show the image analysis of the four configurations.

Fig.18 Setting Partially Coherent Image Analysis


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Fig.19 PCIA configuration 1(Infinity) Fig.20 PCIA configuration 2(2000mm)

Fig.21 PCIA configuration 3(1000mm) Fig.22 PCIA configuration 4(400mm)

Notice that the resulting image shows the general blurring expected (as a result of

diffraction) in configuration 3 and 4. It is important to note that the image must be sufficiently

sampled to generate accurate partial coherence results. Not all light sources are perfectly

incoherent or perfectly coherent. Some light sources lie somewhere in the middle and, thus, are

partially coherent. The degree of partial coherence is specified by a Gaussian or Sinc Gamma

function.

4.4 Setting Power Field Map

The sag of progressive hard contact lens surface is very complex. Set to show contours at

an interval of 0.25 diopters, we can see the spherical and cylindrical power added by this

surface over the all field of view. This feature computes optical power or focal length as a

function of field coordinate. The method used is to trace a ring of real rays around the entrance


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pupil at each point in the field. Figure 23 is partially coherent image analysis settings. Figure

24, 25, 26 and 27 shows the enlarged map of Power Field Map of four configurations.

Fig.23 Setting Power Field Map

Fig.24 PFM configuration 1 (Infinity) Fig.25 PFM configuration2 (2000 mm)

Fig.26 PFM configuration 3(1000 mm) Fig.27 PFM configuration4 (400 mm)

The feature of PFM can display x or y direction optical power, maximum and minimum

power and spherical power.


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4.5 Result

After designed, the myopic presbyopia eye was corrected by progressive addition hard contact

lens. Fig.28 shows the lens data of progressive addition hard contact lens (from surface 2 to

surface 3), and Fig. 29, Fig.30, Fig.31 and Fig. 32 shows the MTF value after designed at four

visions respectively. The progressive addition hard contact lens can correct myopic presbyopia

and the average of MTF is over than 0.6 at 30 lp/mm spatial frequency.

In Fig.29, Fig.30, Fig.31 and Fig.32, the MTF of tangential plane is superior to the MTF of

saggital plane, because the tangential plane of toroidal surface uses the asphereic surface. The

near vision has blur spot produced by defocusing at about 30 lp/mm spatial frequency so the

MTFS is bad as shown in Fig32. The total MTF is in excess of 0.6 so it still fit performance

requirement of vision.

Fig. 28 the design result of progressive addition hard contact lens

Fig. 29 The MTF at the far vision (infinite) Fig. 30 The MTF at the middle vision (200 mm)


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Fig.31 The MTF at the middle vision (100mm) Fig. 32 The MTF at the near vision (40mm)

The design result is satisfied with the following two specifications of the myopia

presbyopia: -3.00 Diopters at the far (infinite) vision and -1.00 Diopters at the near vision. The

MTF is an important parameter in optical system design. When optimizing on MTF, only the

spatial frequency of interest is computed, this is much faster and requires far fewer rays for a

given level of precision. For conventional eyeglass with large aberrations the Geometric

MTF computes an approximate MTF with great speed. It is a good chose for "roughing in" a

design for best MTF as fast as one can optimize RMS spot radius. Above method is used,

MTF approaches diffraction-limited performance as RMS wave front error goes to zero.

Therefore, initial optimization using the default RMS Wave front merit function is highly

recommended. Also, do not start to optimize on MTF until all the desired spatial frequencies

are within the first minimum of the MFT plot [8].

V. Conclusion

From the result at section IV, we can summarize the system design of progressive addition

hard contact lens. First, test the diopter of the myopic presbyopia eye. Secondly, choose the

suitable diopter of the eyeglass, and it shows the diopter of the eyeglass is weaker than the

expected. Designed the spheric surface to free-form aspheric, we can get a more suitable

eyeglass to prevent to further degrade the myopic presbyopia eye. In this study, we also find the

optical simulation code can be a tool to aid to predetermine the choosing a suitable diopter of

the eyeglass. And we hope to corporate with eye clinical to construct the data base to verify the

validity of weaker eyeglass for myopic presbyopia eye. We can offer innovative design method

to correct myopic presbyopia eye. Based on your statement of myopic presbyopia eye, we


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develop a solution that meets form, fit, and function specifications while satisfying your visual

defect requirement.

VI. Reference

[1] Willian Andrew Keirl and Caroline Christie, “Clinical Optics and Refraction: A Guide for

Optometrists, Contact Lens Opticians and Dispensing Opticians” Baillière Tindall

Elsevier/Butterworth-Heinemann, chapter 13.pp.132-152, 2007.

[2] Yung-Feng Shih, Luke L-K Lin and Por-Tying Hung, “Studies of Ocular Biometry in

Taiwan”, Journal of Medical Ultrasound, Volume 15, Issue 1, pp.9-18, 2007.

[3] Frank L. Pedrotti, Leno M. Pedrotti and Leno S. Pedrotti, “Introduction to optics,” Pearson

Prentice Hall, chapter 19, pp.419-437, 2007.

[4] DarryI J Meister and Scott W Fisher, “Progress in the spectacle correction of presbyopia.

Part 2: Modern progressive lens technologies”, Clin. and Exp. Optom. , Vol.91, No.3,

pp.251-264, May, 2008.

[5] James E. Sheedy, Raymond F. Hardy, “The optics of occupational progressive lenses”,

Journal of Optometry, Vol. 76, Vol. 8, August, 2005.

[6] Der-Chin Chen, Shang-Wei Hsieh and Shih-Wen Lee, “ The Design of Astigmatic Lenses

by ZEMAX Optical Software”, Journal of China University of Science and

Technology,Vol.46, pp.77-86 ,April ,2011.

[7] Frank L. Pedrotti, S.J., Leno M. Pedrotti and Leno S. Pedrotti, “Introduction to Optics”,

chapter 19, pp.433-434, 2007.

[8] http://www.zemax.com/kb/articles/187/1/How-to-Optimize-on-MTF/Page1.html.

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Design the Progressive Hard Contact Lens for Myopic Presbyopic