05.Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens(¹Q

Journal of China University of Science and Technology Vol.47-2011.04

Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens

使用非球面及重量最佳化作精巧型近視眼鏡設計

¢ £ ¤ ¥ ¦ § ¤ ¨ © ¡

Der-Chin Chen 1, Shih-Wen Lee 2, Mei-Hsiu Lee 3

1Department of Electrical Engineering of Feng Chia University 2Department of Electrical Engineering, China University of Science and Technology 3 Heng Chun Primary School

摘要

本文研究目的係使用非球面及重量最佳化設計一精巧型高度近視眼鏡。設計時著重客製化眼鏡設計以適合高度近視眼睛病患的配戴，設計當中並進一步對遠、中、近視場進行優化，使眼鏡也適合看遠、中、近距離。本精巧型高度近視

眼鏡除了可矯正高度近視(-8.00D )之外，還可以使配戴-8.00D 眼鏡之後的眼睛解像 " 率在 30lp/mm ! MTF 值達 0.3 經重量最佳化設計之後，還可以使高度近視眼鏡的

邊緣厚度從 6.16mm 降至 3.98mm "

# $ % & '( )

ABSTRACT

This paper studies the design of the aspheric high power myopic ophthalmic lens by the aspheric surface and the optimizing mass of lens for the minimum edge thickness. The design of myopic ophthalmic lens has considered the effects of myopic eyes and three configurations, named far, middle, and near view fields according to visual action of the human eye. These three configurations have three different view angles for the eye. We have designed a -8.00D aspheric eyeglass lens to correct the myopia. The MTF values have more than 0.3 when spatial

Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens frequency is 30lp/mm.The edge thickness of the lens reduces from 6.16mm to 3.98mm by using this novel technology. Keywords: human eye, diopter, ophthalmic lens, optical design, optimization

I. INTRODUCTION

A lens has two surfaces with a len’s material separated by a finite amount of center or edge thickness. The power of each surface contributes to the total focal power of the lens. In fact, the total focal power of the lens, which is the capacity of a lens to add either convergence or divergence to incident waves of light, is simply the net effect of its two surfaces. The focal power of a lens, in diopters, is therefore given very nearly by:

Focal Power = Front Surface Power + Back Surface Power (1)

Modern ophthalmic lenses are generally meniscus—or "crescent-shaped". This means that they typically have a convex front surface (i.e., positive power) and a concave back surface (i.e., negative power). When the negative (concave) back surface is stronger than the positive (convex) front surface, the net power of the two surfaces is negative and the lens is generally a minus lens. This means that the concave back surface will be the highest surface. Consequently, by necessity, a minus lens will generally be thicker at the edge and thinner at the center. Since the thinnest point on a plus lens occurs at the edge, the edge thickness of a plus lens represents its minimum thickness. Conversely, the thickest point on a plus lens occurs at the center, which represents its maximum thickness as shown in Fig.1. The center thickness is given by:

Center Thickness = Edge Thickness + (Front Sagitta – Back Sagitta) (2)

Since the thinnest point on a minus lens occurs at the center, the center thickness of a minus lens represents its minimum thickness. Conversely, the thickest point on a minus lens occurs at the edge, which represents its maximum thickness as shown in Fig.2. The edge thickness is given by:

Edge Thickness = Center Thickness + Back Sagitta - Front Sagitta (3)

66 Journal of China University of Science and Technology Vol.47-2011.04

The minus lenses are never made to a "zero" center thickness, and plus lenses are very seldom surfaced to a "zero"—or knife-edged—edge thickness. There is always some minimum substance or thickness to the lens.

Fig.1 Relationship of the center thickness and edge thickness of plus lens

Fig.2 Relationship of the center thickness and edge thickness of minus lens

II. THE PRINCIPLE OF OPHTHALMIC LENS

1. MYOPIC OPHTHALMIC LENS The ophthalmic lens is a singlet lens with negative or positive power to correct Myopia and hyperopia respectively. Myopia is due to the incoming parallel light entering the eye’s refraction system in a way that the light is imaged in front of the retina, causing the image is blurred [1-3]. Added a negative lens in front of the eye, it makes the parallel light to be divergent before entering the eye. Then the corrected light will be focused to the retina to get a clear image. In general, the radius of the front surface of ophthalmic singlet is chosen by 200 mm as it is used in optics shop, so the focal power of lens is set up by the back surface power of the lens. The aim of this research is to get a rigorous method to design an ophthalmic lens, i.e., finding the construction parameters of the back surface. The optical model of normal eye can be simulated, and its construction data are listed in Table 1. The design parameters shown in Table 1 are simulated by Zemax lens design software. Note the thickness from vitreous to retina is 16.215mm. According to the rigorous lens making formula, it shows as eq.(4) [4-5],

Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens

 t(n − )1  = 1 = ()−  1 − glass  (4) D nglass 1   f  R front R front Rback nglass 

The t is the thickness of the lens which is 3mm. Then choosing the diopters of the ophthalmic lens, we get the corresponding radius of the back surface of the lens by eq.(4). These diopters of lenses are chosen by practical used in optics shop, due to the variation of thickness of vitreous shown in Table 2. The back surface of ophthalmic lens use aspheric surface. The aspheric surface was defined by following formula:

2 = cr +α 2 + +α 10 + +α 16 z 1r ... 5r ... 8r (5) 1+ 1− 1( +k)cr 2

Where r is the radius of curvature, c is the conic constant, and αn is the aspheric surface coefficient. The formula of the gradient 3 surface is shown in the following equation:

Table 1 Construction data of normal eye

Surface Type Radius (mm) Thickness(mm) OBJ Sphere Infinity 1.00 +09 1 Sphere Infinity 50.00 2 Sphere 7.77 0.55 3 Sphere 6.40 3.16 STO Sphere Infinity 0.00 5 Gradient 3 12.4 1.59 6 Gradient 3 Infinity 2.43 7 Sphere -8.10 16.21 IMA Sphere -12.00

= + 2 + 4 + 6 + + 2 + 3 n n0 nr2r nr4r nr6r nz1z nz2 z nz3z (6)

where r 2 = x 2 + y 2 , n is the index of the lens.

2. OPTIMIZE TOTAL MASS The size of myopic ophthalmic lens will optimize for ultra light and minimum thickness at basic requirement of the structure, resolution, and power. By equation (2) and spherical surface formula, the shape of aspherical back surface, front surface curvature and center thickness have known.

68 Journal of China University of Science and Technology Vol.47-2011.04

The volume of the ophthalmic lens calculated by the following equation:

f (x, y,z)dxdydz = f (X (u,v,w), Y(u,v,w), Z(u,v,w |)) J(u,v,w |) dudvdw (7) ∫∫∫ST ∫∫∫

∂X ∂Y ∂Z   ∂u ∂u ∂u  ∂X ∂Y ∂Z  Where J(u,v,w) =    ∂v ∂v ∂v  ∂X ∂Y ∂Z  ∂w ∂w ∂w

The small size of lens is equal to small mass at fix optical glass material of lens. The ZEMAX design soft program has TMAS to reduce lens lighter and thinner by optimizing.

III. DESIGN EXAMPLE AND RESULT

This research is to design an ophthalmic lens with -8.00D myopic; the procedures are described as follows:

Table 2 Relationship between ophthalmic lens and the length of eye axis

-4.00D -10.00D -1.00D -8.00D Diopter of lens (medium (high (low diopter) (medium diopter) diopter) diopter)

Rback 197.3mm 91.5mm 53.1mm 51.9mm Distance * 16.58mm 17.69mm 19.17mm 19.91mm 1. the distance from Vitreous to retina’s distance is 16.21mm at 0.00D 2.’-‘ means negative lens * The distance of Vitreous to retina

1. SETUP THE OPTICAL EYE MODEL Use ZEMAX optic design software to construct a human eye’s optical model[6]. The human eye responds three main wavelengths of the electromagnetic spectrum. These are the visible light of F, d, and C lines which correspond to three wavelengths 0.486 m, 0.587 m, and 0.656 m, respectively. In this study we use multi-configuration

Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens method to systematically design the myopic ophthalmic lens. The three configurations are shown in Table 3. In the FAR (far) field, the object distance is infinity, and the stop direction is parallel to optical axis, i.e., the visual sight is not rotate about the optical axis. In the MID (middle)and NEAR (near) fields, the object distance is set by 1000 mm, 500 mm, respectively. And the visual sight is rotate about the optical axis by -10 degree, and -20 degree in the MID and NEAR fields as shown in Fig.4.

Table 3 Multi-configuration parameters

FAR MID NEAR Distance(mm) 10 9 1000 500 Angle(°) 0 -10 -20

2. WEARING THE -8.00D OPHTHALMIC LENS MADE BY USING LENS MAKER FORMULA A myopia eye is chosen by diopter (for example:-8.00D). We change the retina distance from 16.214 mm to 19.174 mm. A model with an ophthalmic lens in front of the eye was proposed, the radius of the back surface was setup to 60.7mm with that front surface was fixed at 200mm to accord the ophthalmic lens of -8.00D. The layouts of ophthalmic lens in the three viewing fields are shown in Fig.3.

(a) (b)

To optimize the back surface of myopic ophthalmic lens, we set the variation parameter terms from 4 th -term to the 12 th -term of the aspheric surface and TMAS code

70 Journal of China University of Science and Technology Vol.47-2011.04

of merit function. The design result of the spheric lens with the aspheric lens in the - 8.00D. The center thickness of the spheric lens is 3.05mm and the edge thickness is 6.16mm. The center thickness of the aspheric lens is 1.54mm and the edge thickness is 3.98mm.And we compare the MTF of the spheric lens with the aspheric lens of the Far, middle and near vision as shown in Fig.4, Fig.5, and Fig.6, respectively. The black line show diffraction MTF and blue lines are sagittal and tangential MTF, respectively. The result of the MTF of aspheric lens is larger than the spheric lens. The RMS spot diameter can be reduced from 50 m to 16 m.

IV. CONCLUSION

We find the aspheric surface lens and optimizing mass are better than the spheric surface lens, whether on the thickness or the MTF value. By using above novel technology we not only reduce the lens thickness but also get a better optical performance, for example, MTF and RMS spot size. So, this design example, we can use these to design the ophthalmic lens which has many advantages. Since edge thickness is a function of lens power, centre thickness and curvature of the front and back curves (all inter-related) the edge thickness is influenced by the following features: refractive index of the lens material, centre thickness (e.g. safety lenses have a greater central thickness) and size of the spectacle frame, i.e. larger eye size means a bigger lens. The optimizing total mass has variable parameter in the lens design and is good flexibility technique. There are differences between the design goals and practical design results due to the complexity of the physiological structure of the human eyes. There are some differences for the eyes of any two persons. In this paper, an ideal eye model is used to design the lenses of myopia. If the design results are fit for everyone, it needs to build up more data banks. After finishing the design, there are no advanced processing equipments in Taiwan to prove the test of the design.

Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens

Fig.4 (a) MTF of the spheric surface myopic ophthalmic lens at FAR vision

Fig.4 (b) MTF of the aspheric myopic ophthalmic lens at FAR vision

Fig.5 (a) MTF of the spheric surface myopic ophthalmic at MIDDLE vision

72 Journal of China University of Science and Technology Vol.47-2011.04

Fig.5 (b) MTF of the aspheric surface myopic ophthalmic at MIDDLE vision

Fig.6 (a) MTF of the spheric surface myopic ophthalmic at NEAR vision

Fig.6 (b) MTF of the aspheric myopic ophthalmic lens at NEAR vision

V. REFERENCES

[1] Yung-Feng Shih, Luke L-K Lin,Por-Tying Hung, “ Studies of Ocular Biometry in Taiwan ”, Volume 15, Issue 1, pps 9-18, Elsevier, Journal of Medical Ultrasound, 2007.

Design the Compact Myopic Ophthalmic Lens by Aspheric Surface and the Optimizing Mass of Lens

[2] R. S. Chen, Der-Chin Chen, Shang-Wei Hsieh, “System Design of Myopic Ophthalmic Lens”, Asian Journal of Health and Information Sciences, Vol. 1, No. 1, pps.83-95, June, 2010. [3] Muhammad Nadeem Akram and Muhammad Hammad Asghar, “Wavefront aberrations in the accommodated human eye based on individual eye model”, Applied Optics, Vol. 42, Issue 13, pps.2312-2316, 2003. [4] Warren J. Smith, ‘ Modern Optical Engineering ’, p.42, McGraw-Hill, 2000. [5] George Smith and David A. Atchison, “ The Eye and Visual Optical Instruments ”, Chapter 13, Cambridge University Press, 1997. [6] ZEMAX Development Cooperation, “ZEMAX User Manual ”, Chapter 3,5,7, February 4, 2010.