IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L.22 (3) 2009 Computer Analysis Of A simplified Eye Model T.A. Abdul Nabi, K.A. Mohamme d ,H. H. Mohamme d Ministry of Education Deparement of Physics, College of Education, Ibn Al-Haitham, Unive rsity of Baghdad Ministry of Sciences and Technology Abstract Computer analysis of simple eye model is p erformed in the p resent work by using the Zemax op tical design soft ware 2000E . The most imp ortant op tical p arameters of the eye were calcu lated such as t he effective focal len gth (EFL) , the image sp ot size at the retina and found to be in a reasonab le agr eement with the values needed for the laser r etinal treatment .The p resent eye model leads to an effective wavelen gth and we found the image sp ot diagram at the surface of the retina and the wavefront error whi ch are p rovided at zero field angle. This gives a good evidence of the validity of the model in one hand, and can be used to determine the comp atibility of any optical design intended for visual app lications. By using the p ulse frequency doubled Nd:YAG laser 532 nm can be used for the to treatment the retina. Introduction In an optical p oint of view, the human ey e is considered as a comp lex imaging sy st em. Ut ilizing comp uter analysis of a simplified eye model, allows us to bett er understand the basics of the eye functions and the limits of visual resolution (1). Recently , much interest was devoted to design and analysis by using Zemax soft ware 2000E of a diffraction limited cat ’ s eye retroreflector (2,3) because of its applications in sp atial light modulators. The recent resear ches were concentrated in the field of scannin g laser op thalmoscopy to measure and correct t he high ord er ab errations of the human eye and to calculate the op timal p up il size in the human ey e for axial resolution (4,5). M ost imaging sy stems are well describ ed by a sequential list of surfaces, each of which defin es the boundary between one media and the next. They are traced from the object surface to each surface in a sp ecific sequ ential order. The Zemax op tical design p rogram is a comp rehensive soft ware tool for op tical design and is used in the p resent work for the comp uter analysis of the simple eye model. Materials and Methods The eye model The ey e, as an op tical device , may be thou ght as a sy st em of optical components, of about one inch in diameter, filled water like f luid. The transp arent surface through which light enters the eye is called the cornea. The convex outer surface of the cornea p rovides the majority of optical p ower to be transmitted through the ey e. At a few millimeters behind the cornea, there is a relatively thick double convex lens, the ey e lens. Just in front of the eye lens, there is an op aque disk with an op ening at its center which is referred to as the iris. The ey e lens focuses the light entering the eye at the back of the eye, the retina. The r etina is the most imp ortant p ortion of the eye that resolves the detail of the image or the visual resolution. By using the Zemax op tical design soft ware 2000E, the most important optical p arameters of the eye were calcu lated such as t he effective fo cal len gth (EFL) and the image sp ot size at the retina. IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L.22 (3) 2009 Results and Discussion Fig. (1) shows the model of the ey e developed in this work by using the optical design Zemax soft ware 2000E.The radius of curvature, thickness, diameter and glass information is p rovided in Table (1). All surfaces are sp herical. The light originates from the second harmonic generation of the Nd: YAG laser emitting at the wavelength of 532 nm. It was mentioned in (1) that the st andard p oint of maximum accommodation is at an object distance of 254 mm. This distance is often ref erred to as the close p oint of a typical eye. In the p resent model and for the p urp ose of making the lens nearly equiconvex, the valu e of 10 mm is taken into consideration. The p resent eye model leads to the effective wavelen gth ( EFL)of 16.3406 mm. This value is in an excellent agreement with the corresp onding value of 16.7 mm obtained in ref. (1) at t he object distance of 6.2 mm. The slight difference is due to the difference in the object dist ance between the case presented in the p resent work and the value used for the p urp ose of the model p resented in (1). Furt hermore, the image sp ace numerical aperture NA is found to be 0.2756169, while the object space NA is 0.7071068 . The image sp ot at t he retinal surface is shown in Fig. (2). The central diameter of the ima ge is found 184 μm, while the blur circle outside this central image sp ot is due to aberration . This value of the central sp ot diameter can be consid ered reasonable for the case of the fr equency doubled Nd:YAG laser at t he eye retina, since it is within the range of the laser sp ot size needed by the surgeons for the laser retinal treatment. Plots of wavefront error are p rovided at z ero field angle, in Fig. (3).The aperture coordinates are relative and the scale of the optical p ath difference runs fro m 100 to 100 waves. T he similar ity of the incident and existing wavefront is the most imp ortant single f igure of merit for t he validity of the present model. Conclusions 1- The p resent ey e model is suitable for comp uter analysis by using modern op tical design soft ware. 2- The present data for the eye model can be used as a reference whi ch can b e used to d etermine the compatibility of any optical design intended for visual app lications. 3- The effective focal len gth ( EFL) of the eye sy stem p rovided in the p resent work can be considered as one of the imp ortant Figure of merit for t esting the validity of the p resent model. 4- The sp ot size provided by the p resent work is in areasonable agreement with t he value needed for the laser retinal treatment. T his gives furt her evidence of the validity of the model Re ferences 1- Walker, B.H. ( 2000) SPIE Web, OE R eport: 166-185. 2-Dorronsoro, C.; Barbero, S.; Llorent ,L. and M arcos, S. (2003) Op tometry and vision science 80:115-122. 3- Biermann, M .L.; Rabinovich, W.S. ; M ahon, R. and Gilbreath, G.C. (2002), Opt. Eng., 41:1655-1660. 4- Boorda, A. ; Borja, F.R.; Donelly , W.J .; Queener, H. ; Herbert, T.J.and Compbell M .C.W. (2002),Opt .Exp ress ,10: 405-415. 5- Donnelly , W.J. and Boorda, A. (2003), J.Op t .Soc.Am.A20:2010-2015. 6- Thibos, L.N. and Bradely , A. (1999) ,M odeling the refractive and neuro –sensor sy st ems of the Eye: CH.4 in Visual Inst rumentation, M cgraw – Hill .Inc.,New York (p p 101-159). IBN AL- HAITHAM J . FO R PURE & APPL. SC I VO L.22 (3) 2009 Table (1) : The surface data for the Zemax software 2000 E(6) Surf. Comment Radius of curvature, mm Thickness mm Glass typ e Diameter, mm OBJ - infinity 10 Air - STO - infinity - Air 20 2 CORNEA 7.98 1.15 M gF2 10.96213 3 AQUEOUS 6.22 2.39 SEAWATER 10.86602 4 LENS 10.2 4.08 CaF2 10.90885 5 VITREOUS -6.17 17.15 SEAWATER 10.9355 6 - infinity 0 - 3.32571 IMA. - infinity - - 3.32571 2009) 3( 22مجلة ابن الهیثم للعلوم الصرفة والتطبیقیة المجلد نموذج مبسط للعینإاستخدام الحاسوب لتحلیل حسن حمادي محمد ، قاسم عزیز محمد تغرید عبد االمیر عبد النبي الحمیري، ةوزارة التربی جامعة بغداد ،ابن الهیثم – ةكلیة التربی ،قسم الفیزیاء وزارة العلوم والتكنلوجیا لخالصةا قدم في هذا البحث باستخدام برنامج التصمیم قد نموذج مبسط للعینال وبالحاسبأستخدام التحلیل ن إ Zemax softيالبصر ware 2000E .مثل للعین ةالمهم ةالمقایس البصری قد حسبت و)EFL ( ،الطول الموضعي المؤثر لعین قاد نموذج المستخدم لاال. عالج الشبكیة باللیزرى لاالمحتاجة وكذلك وجد توافق معقول مع القیم. حجم الصورة في الشبكیة يذالنبضي Nd:YAGلیزر باستخدام ةالى معرفة الطول الموجي المؤثر وقد تمكنا من ایجاد صورة بقعة اللیزر على الشبكی .ةیمكن استعماله لمعالجة الشبكیالذي 532nm لمضاعفالتردد ا نموذج من جهة ومن جهة أخرى یمكن استخدامه اال على امكانیة تطبیق هذا اواضح دلیالت هذه النتائج أعط وقد . لیحدد تطابق أي تصمیم بصري یحتاج الى التطبیقات البصریة