Class Note for OPTI 510L at UA
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Date Created: 02/06/15
Schematic Eyes Introduction Curvatures spacings and indices of the ocular components lead us to raytracing the surfaces to determine the imaging properties of the eye Many schematic eye models exist of varying complexity Cardinal points are a first priority aberration analysis is a more sophisticated analysis GullstrandLeGrand Eye Model Anterior Cornea Posterior Cornea Anterior Lens Posterior Lens Retina R mm 78 65 102 6 134 mm 391 004835 0006108 0 0081 0 014 t mm In nity 055 305 4 1659655 n 1 13771 13374 142 1336 tn mm 039939 2280544 2816901 1242257 y mm 1 0980691 0884095 0744614 0 nu rad 0 004835 004236 004952 005994 yc mm 030376 025796 0 031862 1668325 nuc rad 01 0114686 011311 011311 0108649 Cardinal Points amp Pupils Principal Planes 7 conjugate planes that have unit magni cation Can be used to generate effective lens Focal Points 7 points where collimated beams come to focus Nodal Points 7 a ray passing through the front nodal point at a given angle leaves the rear nodal point at the same angle Entrance and Exit pupils 7 conjugate planes that are the entrance and exit ports of the optical system Principal Planes P9 Fa 0059941336 1 L P F 72228896 PaFa or 1908 mm from corneal vertex Similarly the front principal plane P is located 1595 mm from corneal vertex Total Power Total PowerqD n P F d 1336 2228896 mrn 005994 mm l 5994 D Total Power d3 l PF PF l6683 mm or the front focal point is 715089 mm from corneal vertex about where your spectacles sit Entrance Pupil Exit Pupil VE 01080491336 031862 030376quot 39 VE3038 mm VE 3682 mm Nodal Points PN P N nvit nalI d3 0336 005994 5605 mm Front Nodal Point N is 7200 mm from corneal vertex Rear Nodal Point N is 7513 mm from corneal vertex Angular Subtense mmINN N F9 y 16684 tan Typically 1 minute of arc is stated as the eye s limit of resolution This leads to y N 5 microns two points separated by 5 microns on the retina can just be resolved Accommodation releases tension on pulls zonules taut an attens crystalline lens zom es and crysmlhne lens bulges Relaxed emery muscle Constnct cihaiy muscle Accommodated Gullstrand Model R mm n t mm Anteiior 78 13771 55 Comea Posteiior 65 13374 265 Comea AnteIior Lens 60 14270 450 Posteiior Lens 55 13360 16497 Presbyopia Your ability to accommodate A iquot quot quot reduees steadily with age g Warm Typically you don39tnouce the effects urmi r affects your ability to read comfortably This re presbyopia Nvarvn Definitions 7 Refractive Error Myopia e nearsightedness P re in front of retina because eye rs too long orpowens too mgr H F Hyperopraefaresrgmedness F39isbehmdretmabecauseeyeistoo short orpowenstool w kij Emmetxopia 7 perfect vision r39 at retina Definitions Far Point 7 point conjugate to the retina when eye is unaccommodated Myopia Hyperopia Near point 7 point conjugate to the retina when the eye is fully accommodated Schematic Eye Models 1924 Gullstrand made a siX surface eye model crystalline lens with a high index core and a lower index shell Later reduced to four surfaces since raytracing is time consuming 1952 Emsley made a single surface model for simplicity and speed of raytracing Today computers can quickly raytrace eye models so sophistication is ok Big Problem with early models is that the surfaces are all spherical Therefore the paraxial properties Cardinal Points are accurate but aberrations do not look like clinical findings Schematic Eye Models 1971 Lotmar JOSA Vol 61 p 1522 made anterior cornea a polynomial based on clinical measurements and made posterior lens a parabola to give clinical levels of spherical aberration 1983 and 1985 Kooijman JOSA Vol 73 p 1544 and Navarro JOSA A Vol 2 p 1273 Added aspherics to all four surfaces of their models Kooijman model is based on light distribution on the retina Navarro added dispersion for chromatic effects Arizona Eye Model Radius Conic Index Abbe Thickness 78 mm 025 Cornea 1377 571 055 mm 65 mm 025 Aqueous 1337 613 tZiq Rant Kant Lens n39lens 519 tlens Vitreous Rm 1 1336 611 16713 mm 134 mm 000 Retina Rant 2 120 04A Kant 7518749 1285720A Rpost 6224557 02A 12mg 2 1353971 0431762A tall I 297 004A tlenS 3767 004A nlens 142 000256A 000022A2 Conic Section 1 2 R z sag of surface Z 2 r2 X2 yz 1 1 K 1 r R radius of curvature R2 K conic constant K lt 1 Hyperboloid K 1 Paraboloid 1 lt K lt 0 Prolate Spheroid Ellipsoid K 0 Sphere K gt 0 Oblate Spheroid Ellipsoid Ellipsoids Cornea is prolate meaning that it attens towards the periphery By adjusting the conic constant the spherical aberration can be controlled without changing paraXial properties Conic Section Alternatives 2 1 1R2 Klr2 K 1 2E z sag of surface 12 K 1 r2 X2 yz Z 2 Q 39 R radius of curvature 2R K conic constant Schematic Eyes Spectral Sensitivity Relative Spectral Sensitivity Photopic Scot0pic oooooooo mwsmmumon o o 680 480 580 780 anelength nm w 00 o Scotopic Low light level Peak around 505 nm Photopic High light level Peak around 555 nm Mesopic In between To include in raytracing code weight wavelengths by appropriate curve StilesCrawford Effect 1933 Stiles and Crawford found an effect where light striking photoreceptors with a low angle of incidence has a higher efficiency than light striking at a high angle of incidence Full Effect gt Reduced Effect Retinal m Photoreceptors Minimal Effect Schematic Eye Model Reduce intensity of ickeiing beam until it is not detected StilesCrawford Effect The StilesCrawford effect acts like an apodizing lter Most raytracing problems allow for apodization g M Efficiency of peiipheral ray m H fall to about 20 for 8 mm 4 Z D Z pupil Pupil Entry Point m m Lr CXp01051 2 Apodization Halo Reduction in Apn izzd Phase Conhast Apodization is routinely used in microscopy and astronomy to reduce diffractive halos Figure 3 l Astronomical Apodization No Apodization Sonine Apodization A hexagonal apodizing lter is used in this case to shi the location of the diffracted light to reveal a stellar companion StilesCrawford Effect The StilesCrawford effect is phototropic ie the retinal photoreceptors realign themselves With the light source m gh om39nP Eye Axes Since the eye is not rotationally symmetric ie the centers of curvature of each surface do not lie on a common axis several axes can be de ned which all collapse to the optical axis in rotationally symmetric systems Visual Axis The Visual axis connects the xation point to the front nodal and the rear nodal to the fovea Usually denoted by angle on measured from optical axis Typically 4 S on S 8 The fovea is usually displaced temporally and slightly inferior Pupillary Ax1s The pupillary axis strikes the cornea at right angles and passes through the center of the entrance pupil It is equivalent to the chief ray Pupillary Axis Line of Sight The LOS connects the xation point to the center of the entrance pupil and the center of the exit pupil to the fovea Usually denoted by angle K measured from pupillary axis Typically K S on Pupillary
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