According to early examination (Vojnikovi}, 1978) estimated, that the index of refraction for aqueous and vitreous is not the sum (1.33 or 1.66), than is for aqueous n = 1.334, and for vitreous N = 1.336. This measurements are made with Abbe’s refractometer, by temperature of 33 °C for aqueous, and 36 °C for vitreous, as it’s in human eye. In the principle of these results, the authors calculated the new values of cardinal points for the eye, and compared with Gullstrand’s optical schematic eye. So, the refractive power for the eye F= 59.98 D, first focal length f1= – 16.67 mm and second focal
length f2 = + 22.27 m

Božo Vojniković

Ettore Tamajo

English

Hrčak - Portal of scientific journals of Croatia

Coll. Antropol. 37 (2013) Suppl. 1: 41–45Original scientific paperGullstrand’s Optical Schematic System of the Eye– Modified by Vojnikovi} & TamajoBo`o Vojnikovi} and Ettore TamajoVelika Gorica University of Applied Sciences, Velika Gorica, CroatiaA B S T R A C TAccording to early examination (Vojnikovi}, 1978) estimated, that the index of refraction for aqueous and vitreous isnot the sum (1.33 or 1.66), than is for aqueous n = 1.334, and for vitreous N = 1.336. This measurements are made withAbbe’s refractometer, by temperature of 33 °C for aqueous, and 36 °C for vitreous, as it’s in human eye. In the principle ofthese results, the authors calculated the new values of cardinal points for the eye, and compared with Gullstrand’s opti-cal schematic eye. So, the refractive power for the eye F= 59.98 D, first focal length f1= – 16.67 mm and second focallength f2 = + 22.27 mmKey words: optical schematic eye, modified the position of the cardinal pointsIntroductionKepler was the first to introduce in 1611. the term of»Dioptrice«, and later, in 1704. Newton first describedthe dioptric system of the eye1. Thomas Young 1801. Es-timated the astigmatism of the eye and two meridians,major and minor, and first measurements the several op-tical constants of the eye. The progress of the study of op-tical eye system was litle. Not earlier than 1841. Gaussintroduce the six cardinal points (F1, F2, P1, P2, N1, N2) ofthe optical system of the eye, published in »DioptrischeUntersuchungen«, and 1853. Gauss calculated the firsttheoretical optical schematic eye, »Dioptrik des Auges«.1This work of Gauss stimulated a further intensive studyof the eye optics, and then Helmholtz was modified andadopted the Gaussian schematic eye, so that all laterworks are based on this Helmholtz publication 1856.»Physiologischen Optik«. Only 1856. And than continu-ity, the next pioneers: Donders 1864., Tscherning 1898.,Javal, and than appear Gullstrand 1911. with the work:»Einfihrung in die Methoden d. Dioptrik d. Auges d.Menschen«. For this work Gullstrand received a NobelPrize in 1911.1. As yet today, the Gullstrand’s schematiceye exist, sometimes with modification because the dif-ferent values of optical and anatomical of the eye(indexof refraction of optical eye media, radius curvature ofcornea and lens, axial length of eye globe). Our study andreason for modification of standard Gullstrand schema-tic eye, is our work on measured the index of refractionthe aqueous and vitreous.Materials and MethodsOur earlier study2,3 establishes the truth of differentvalues of index of refraction for aqueous and vitreous.Measurements of index of refraction »n« of aqueous andvitreous were carried out respecting strictly determinedconditions of examination. The first, very important, isconsidered the fact that these measurements were per-formed at a definite temperature of 33 °C for aqueous and36 °C for vitreous (33 °C as the usually temperature ofaqueous, and 36 °C for vitreous), and by means of mono-chromatic sodium yellow light line N=589.3 mu. Thesemeasurements are made with Abbe’s refractometer.In this examination was estimated the means of indexof refraction for aqueous = 1.334, and for vitreous =1.336. In Gullstand schematic eye the index of refractionfor both of aqueous and vitreous is 1.336. In our calcula-tion for new optical schematic eye4–6, the optical and ana-tomical means of the eye was identity, except the meansof index of refraction of vitreous, »n« is 1.33441Received for publication June 20, 2012U:\coll-antropolo\coll-antro-(Suppl 1)-2013\08 Vojnikovic Tamajo.vp2. travanj 2013 13:11:18Color profile: Generic CMYK printer profileComposite  150 lpi at 45 degreesMean refractive indices:ear . . . . . . . . . . . . . . . . . . . n0 . . . . . . . . . . . 1.000cornean . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . 1.376aqueousn . . . . . . . . . . . . . . 2 . . . . . . . . . . . . 1.334crystalline core- lens . . . . . n3 . . . . . . . . . . . 1.386crystalline nucleus lens . . . n4 . . . . . . . . . . . 1.406vitreous . . . . . . . . . . . . . . . n5 . . . . . . . . . . . 1.336Radii of curvature:Cornea anterior surface. . . . . . . . r1 = +7.70 mm.. position: 0.00 mm – d1Cornea posterior surface. . . . . . . r2 = +6.80 mm.. position:+0.50 mm – d2Lens anterior surface. . . . . . r3 = +10.00 mm.. position:+3.60 mm – d3Lens nucleus anterior surfacer. . . . . . . r4 = +7.91 mm.. position: +4.15 mm – d4Lens nucleus posterior surfacer. . . . . . . r5 = –5.76 mm.. position: +6.57 mm – d5Lens posterior surfacer. . . . . . . r6 = –6.00 mm.. position: +7.20 mm – d6ResultsCalculation the power of anterior surface of cornea:Fc1 = (n1 – n0)/r1 = (1.376 – 1.0)/0.0077 = +48.8312 DCalculation the power of posterior surface of corneaFc2 = (n2 – n1)/r2 = (1.334 – 1.376)/0.0068 = –6.1765 DEquivalent power of cornea:Fc = Fc1 + Fc2 – (r1 – r2)/n1*Fc1*Fc2 = 48.8312 – 6.1765 –(0.0077 – 0.0068)/1.376*48.8312*(– 6.1765) = +42.8520 DReduced cornea thickness:c =d dn2 110 005 0 01 376−=−=. ..0.000363372 m = 0.3634 mmFinal power of cornea:F = Fc1 + Fc2 – c*F1*F2F = +48.8312 –6.1765 – 0.000363372*48.8312*(–6.1765) =F = +42.7643 DFocal length of the cornea:111 20 21 00 11 001 21fn nn rn nn rn nnn nn=−−−−− −( )*( )*( )*( )*( )*d dr r2 11 2−=11f= – 6.17647 – 48.83117 + 0.10959 = –54.89805 Df1 = –0.018215584 mf2 = –nn20* f1 = +0.0243 mPosition of the 1. cardinal plane of the cornea:A1 Hc = –( )** * ( )n nn rf d d1 21 21 2 1−−A1 Hc = –( . . ). * ( . )* ( . )1 376 1 3341 376 0 0060 018216−−− * (0.0005 – 0.0)= 0.000040883 m = 0.0409 mmB. Vojnikovi} and E. Tamajo: Gullstrand’s Optical Schematic – Modified, Coll. Antropol. 37 (2013) Suppl. 1: 41–4542Fig. 1. Shows the Gullstand’s means of optical schematiceye. The difference is in value of index of refraction foraqueous, N=1.334.Fig. 2. Represent the schematic optical values of the eye,for Gullstand’s and for modified schemtaic eye in ourexamination (red marked).U:\coll-antropolo\coll-antro-(Suppl 1)-2013\08 Vojnikovic Tamajo.vp2. travanj 2013 13:11:20Color profile: Generic CMYK printer profileComposite  150 lpi at 45 degreesPosition of the 2. cardinal plane of the cornea:A2 Hc = –( )** * ( )n nn rf d d1 01 12 2 1−−A2 Hc = –( . . ). * .* ( . )* ( . . )1 376 1 01 376 0 00770 0243 0 0005 0 0−− =–0.000431176 m = –0.4312 mmPosition of the nodal points of the cornea:N1 = 1201 21 22 1 1− +−−=nnn nn rd d f( )** ( ) *= 11 3341 01 376 1 3341 376 0 00680 0005 0− +−−−..( . . ). * ( . )* ( . .0)* (–0.01822) == 0.006126372 m = 6.13 mmN2 = 1021 01 12 1 2− +−−=nnn nn rd d f( )** ( ) *= 11 01 3341 376 1 01 376 0 00770 0005 0 0− +−−..( . . ). * ( . )* ( . . )* ( . )0 0243= 0.005652931 m = 5.65 mmRefractive power of the anterior cortex lens:F3 =( ) ( . . )..n nr3 231 386 1 3340 015 2−=−= + DRefractive power of anterior nucleus lens :F4 =( ) . ...n nr4 341 406 1 3860 007912 528445−=−= + DReduced the latitude of anterior lens cortex:C =( ) ( . . ).d dn4 330 00415 0 00361 386−=−=0.000396825 m = 0.3968 mmFinal refractive power of anterior lens cortex:F = F3 + F4 – C*F3*F4 =+5.2 + 2.52845 – 0.0003968*5.2*2.52845 = +7.72323 DFocal length of anterior cortex lens133 42 63 22 33 223 43fn nn rn nn rn nnn nn=−−−−− −( )*( )*( )*( )*( )*d dr r4 33 6−=–6.40195778 Df3 = – 0.156202217 mf4 = − = − −nnf4231 4061 334015620*..* ( . ) =0.164630584 mPosition of the 1. principal plane of lens cortex:A3 Hac =( )** * ( )n nn rf d d3 43 63 4 3−− =0.000217768 m = 0.218 mmPosition of the 2. principal plane of lens cortex:A4 Hac = –( )** * ( )n nn rf d d3 23 34 6 5−− =–0.000389132 = –0.389 mmPosition of nodal points anterior lens cortex:N3 = 1423 43 64 3 3− +−−=nnn nn rd d f( )** ( ) *= 11 4061 3341 386 1 4061 386 0 0060 00415 0− +−−..( . . ). * ( . )* ( . . )0036* (–0.1562022)= 0.008224085 m = 8.22 mmN4 = 1243 23 36 5 4− +−−=nnn nn rd d f( )** ( ) *= 11 3341 4061 386 1 3341 386 0 010 0072 0 006− +−−..( . . ). * .* ( . . 57)* (0.164632921)= 0.008041719 m = 8.04 mmRefraction power of posterior lens nucleus:F5 =( ) ( . . )..n nr3 451 386 1 4060 005763 4722−=−−= + DRefraction power of posterior lens cortex:F6 =( ) ( . . )..n nr5 361 336 1 3860 0068 3333−=−−= + DReduced the latitude of posterior lens cortex:C =( ) ( . . )..d dn6 530 0072 0 006571 3860 000454545−=−= m = 0.455 mmRefraction power of posterior lens cortex:F = F5 + F6 – C*F5*F6 =+3.4722 + 8.3333 – 0.0004545*3.4722*8.3333 =+11.792348 DFocal lengths of posterior lens cortex:15f=( )*( )*( )*( )*(n nn rn nn rn nnn nnd3 54 33 44 63 443 536− −−−− − − dr r53 6)*=1.18000776 Df6 = –nnf5451 3361 4060 847452*..* ( . )= − = – 0.805260273 mB. Vojnikovi} and E. Tamajo: Gullstrand’s Optical Schematic – Modified, Coll. Antropol. 37 (2013) Suppl. 1: 41–4543U:\coll-antropolo\coll-antro-(Suppl 1)-2013\08 Vojnikovic Tamajo.vp2. travanj 2013 13:11:21Color profile: Generic CMYK printer profileComposite  150 lpi at 45 degreesPosition of 1. principal plane of posterior lens cortex:A5 Hpc =n nn rf d d3 53 65 6 5 0 00321−− = −** * ( ) . m = –3.21 mmPosition of 2. principal plane of posterior lens cortex:A6 Hpc = –( )** * ( )n nn rf d d3 43 36 6 5−− = –0.000732 m = –0.732 mmPosition of nodal points of posterior lens cortexN5 = 1543 53 66 5 5− +−−=nnn nn rd d f( )** ( ) *= 11 3361 4061 386 1 3361 3860 0072 0 00657− +−−..( . . ). ** ( . . )* ( . )0 847452054= 0.038981735 m = 38.98 mmN6 = 1543 43 36 5 6− +−−nnn nn rd d f( )** ( ) * == 11 3361 4061 386 1 4061 386 0 010 0072 0 006− +−−..( . . ). * .* ( . . 57 0 80526027) * (– . )= – 0.040823249 m = – 40.82 mmEquivalent power of lens (cortex + nucleus):F = Fanterior-cortex + Fposterior-cortex –C * Fanterior-cortex * Fposterior-cortexF = 7.72323 + 11.792348 – 0.000838642*7.723*11.792 =+ 19.43919867 DReduced the latitude of lens:C =[ ]A H d d A Hnac pc4 5 4 54+ − +( )= 0.000838642 mRefracting power of complete system of the eye:F = Fcorneas + Fwhole lens – C * Fcorneas * Fwhole lensF = 42.7643 + 19.43919867 – 0.002667784*42.764*19.439 =+ 59.9857599 DF = +59.98576 DReduced the latitude of the eye:C =[ ]A H d A Hnc pc2 6 52+ +=C =[ ]− + −−0 0004312 7 20 10 0 003211 3343. . ..= 2.667783 mmPosition of the 1. Principal plane of thy eye:A1Heye =n c FF0 3⋅ ⋅eye= 0.00146 mPosition of the 2. principal plane of the eye:A2H'eye =n cFF5 corneaeye= 0.00172900 m1. focal length of the eye:f1 =nF0eye=1 059 98576..= –16.670623 mm2. focal length of the eye:f2 = –nF5eyen= –1 33659 98576..= +22.271952 mmPosition of nodal points of the eye:N1 = 1543 53 66 5 5− +−⋅⋅ −⋅nnn nn rd d f( )( ) = 7.66 mmN2 = 1543 43 36 5 6− +−⋅⋅ −⋅nnn nn rd d f( )( ) = 7.88 mmPosition of the retinal fovea = 24.0 mmDiscussion and ConclusionDifference between Gullstrand calculation in opticalschematic eye and our calculation is the mean of refrac-tive index for aqueous. Historically, all included authorsgives the same means of refractive indices for aqueous andvitreous: 1.333 and 1.336 (1, Essential part in this exami-nation were carried out respecting strictly determinedconditions of testing the refractive index for aqueous andvitreous of human eye2,3. As particularly important is con-sidered the fact that these measurements were performedat a definite temperature (33 °C for aqueous and 36 °C forvitreous, as in human eye) and by means of monochro-matic sodium yellow light line: N = 589, 3 mu. Sometimesis very difficulty discussion about optical calculation forthe eye, because the means of optical and anatomical ele-ments of the eye are not the same. Consequently, the dif-ferent of refractive index of aqueous of 1.334 and that isnot the same as vitreous, 1.336, we can conclude:1. The 1. principal plane H = 1.46 mm (Gullstrand (G)=1.35 mm)2. The 2. principal plane H’ = 1.73 mm (G = 1.60 mm)3. The 1. nodal point N1 = 7.66 mm (G = 7.08 mm)4. The 2. nodal point N1 = 7.88 mm (G = 7.46 mm)5. The 1. focal length f1 = – 16.67 mm (G = –17.05 mm)6. The 2. focal length f2 = + 22.27 mm (G = 22.78 mm)7. Refracting power of complete system of the eye F =59.985 D (G1 = 58.640 D, G2 = 60.48 D)B. Vojnikovi} and E. Tamajo: Gullstrand’s Optical Schematic – Modified, Coll. Antropol. 37 (2013) Suppl. 1: 41–4544U:\coll-antropolo\coll-antro-(Suppl 1)-2013\08 Vojnikovic Tamajo.vp2. travanj 2013 13:11:21Color profile: Generic CMYK printer profileComposite  150 lpi at 45 degreesR E F E R E N C E S1. DUKE-ELDER S, System of Ophthalmology, Vol. V, OphthalmicOptics and Refraction, Henry Kimpton, London (1970). — 2. VOJNIKO-VI] B, DOOH, Zagreb, 2 (1978). — 3. VOJNIKOVI] B, LUTTENBER-GER I, Jug. oftalm. arhiv, 3–4 (1979). — 4. STONER E D, PERKINS P,Optical formulas tutorial, Buttenworth-Heinemann, Boston (1997). — 5.ATCHINSON D A, SMITH G, Optics of the Human Eye (Butterworth--Heinemann, Oxford 2000.). 6 – PEDROTTI L S, PEDROTTI S L, Opticsand Vision. ISBN: 0132422239.B. Vojnikovi}Velika Gorica University of Applied of Sciences, Zagreba~ka cesta 5, 10410 Velika Gorica, Croatiae-mail: decv@decv.comGULLSTRAND-ovo OPTI^KI SHEMATSKO OKO – MODIFIKACIJA PO VOJNIKOVI] I TAMAJOS A @ E T A KNa osnovu ranijih mjerenja indeksa loma »n« (Vojnikovi}, 1970) opti~kih medija oka, sobne vodice i staklastog tijela,pod odre|enim uvjetima: kod temperature od 33 °C za sobnu vodicu = 1.334 i 36 °C za staklasto tijelo = 1.336, autori supristupili izra~unu opti~kih vrijednosti oka. U literaturi se uvijek susre}u identi~ne vrijednosti indeksa loma za sobnuvodicu i staklasto tijelo (1.333 i 1.336). Izra~un pokazuje odre|ene razlike od prvog Gullstrandova izra~una, za kojegmu je i dodijeljena Nobelova nagrada 1911. Tako npr. refrakcijska vrijednost ~itavog oka iznosi 59, 98 D, prednja `ari{nadaljina f1= –16, 67mm, stra`nja `ari{na daljina f2 = +22, 27 mm. Promjene su tako|er nastupile i u vrijednostimaostalih kardinalnih to~aka: P1, P2 i N1, N2. Zaklju~uje se kako bi ove vrijednosti trebalo koristiti u opti~kom ra~unu urefraktivnoj kirurgiji oka.B. Vojnikovi} and E. Tamajo: Gullstrand’s Optical Schematic – Modified, Coll. Antropol. 37 (2013) Suppl. 1: 41–4545U:\coll-antropolo\coll-antro-(Suppl 1)-2013\08 Vojnikovic Tamajo.vp2. travanj 2013 13:11:21Color profile: Generic CMYK printer profileComposite  150 lpi at 45 degrees

Gullstrand’s Optical Schematic System of the Eye – Modified by Vojniković & Tamajo

Abstract

Similar works

Full text

Available Versions

Hrčak - Portal of scientific journals of Croatia

HRČAK - Portal of Croatian Scientific and Professional Journals