Schematic eye

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Schematic eye

  1. 1. Gauri S Shrestha, M.Optom, FIACLE Schematic Eye
  2. 2. Schematic eye in general <ul><li>A schematic eye is a mathematical or physical model that represents the basic optical features of the real eye </li></ul><ul><li>Objective </li></ul><ul><ul><li>To provide a basis for theoretical studies of the eye as an optical instrument </li></ul></ul><ul><li>Complexities of fundamental unimportance is ignored </li></ul>
  3. 4. <ul><li>Simplest reduced version to complex model. </li></ul><ul><li>It permits one to determine </li></ul><ul><ul><li>the retinal image sizes of objects in visual space and </li></ul></ul><ul><ul><li>the dimensions of fundus landmarks such as choroidal nevi and retinal tumors. </li></ul></ul>Models ranges from
  4. 5. History <ul><li>The first physical model of the eye- “real eye”  Christian Huygens (1629-1695) </li></ul><ul><li>Smith in 1738, described Huygens eye; 2 hemisphere, cornea and retina (r 1 =3r 2 ) </li></ul><ul><li>Le Grand, Moser in 1844 was the first to construct a theoretical schematic eye- inaccurate, too hyperopic </li></ul><ul><li>First accurate schematic eye – Listing, 1851 </li></ul>
  5. 6. <ul><li>Helmholtz developed a modified version of Listing’s eye. </li></ul><ul><li>Tschering published a more complex eye that contained the posterior corneal surface, he claimed to measure it first. </li></ul>History
  6. 7. <ul><li>Allvar Gullstrand developed a more improved schematic eye with four surface lens and extra lens complexity. </li></ul><ul><li>Gullstrand’s Noble prize winning work – schematic eyes bear his name </li></ul><ul><ul><li>Invented slit-lamp & improved Helmholtz’s ophthalmoscope </li></ul></ul>History
  7. 8. <ul><li>Also presented a simplified version having one corneal surface and the lens had zero thickness. </li></ul><ul><li>Emsley modified Gullstrand’s simplified eye with thickness of Gullstrands exact eye, and bringing change in refractive index. </li></ul><ul><li>Le Grand simplified model consists a single corneal surface and a lens of Zero thickness. </li></ul>History
  8. 10. Schematic Vs Real eye <ul><li>Schematic eye models are approximations to real eyes </li></ul><ul><ul><li>use only spherical surfaces and </li></ul></ul><ul><ul><li>lenses of constant refractive index, </li></ul></ul><ul><ul><li>known as paraxial models. </li></ul></ul><ul><li>Real eyes have aspheric surfaces and a lens with a gradient index. </li></ul>
  9. 11. <ul><li>Accuracy of schematic eyes can be improved by </li></ul><ul><ul><li>aspherising one or more spherical surfaces or </li></ul></ul><ul><ul><li>using a gradient refractive index lens or </li></ul></ul><ul><ul><li>both. </li></ul></ul><ul><ul><li>They are called ‘finite aperture’ or ‘wide angle’ schematic eyes. </li></ul></ul>Schematic Vs Real eye
  10. 12. Paraxial Schematic Eyes <ul><li>Classification of paraxial schematic eyes </li></ul><ul><ul><li>Exact eyes </li></ul></ul><ul><ul><li>Simplified schematic eyes </li></ul></ul><ul><ul><li>Reduced schematic eyes </li></ul></ul>
  11. 13. Exact eyes <ul><li>Parameters that closely match the mean values of real eyes- </li></ul><ul><ul><li>surface radii of curvature, </li></ul></ul><ul><ul><li>surface separations and </li></ul></ul><ul><ul><li>refractive indices </li></ul></ul><ul><li>Most have four refracting surface, </li></ul><ul><ul><li>two for the cornea and </li></ul></ul><ul><ul><li>two for the lens. </li></ul></ul>
  12. 14. <ul><li>Eyes that fall in this category- </li></ul><ul><ul><li>The Gullstrand exact eye, and </li></ul></ul><ul><ul><li>The Le Grand full theoretical eye. </li></ul></ul>Exact eye
  13. 16. Simplified schematic eyes <ul><li>Cornea is reduced to single refracting surface  posterior corneal surface less power </li></ul><ul><li>The lens has two surfaces and a single uniform refracting index. </li></ul><ul><li>Corneal radius of curvature does not represent the mean value of real eyes  slightly smaller. </li></ul>
  14. 17. Reduced schematic eyes <ul><li>Cornea represented as the only source of refractive power of the eye. </li></ul><ul><li>Lens is completely neglected. </li></ul><ul><li>Results from putting P & P’ and N & N’ at the same location. </li></ul><ul><li>Must have smaller radius. </li></ul><ul><li>Apart from refractive index, </li></ul><ul><ul><li>corneal curvature and length do not represent the values of the real eye  both smaller </li></ul></ul>
  15. 19. <ul><li>Types of this eyes: </li></ul><ul><ul><li>Listing’s reduced eye </li></ul></ul><ul><ul><li>Emsely’s reduced eye </li></ul></ul><ul><ul><li>Donder’s reduced eye </li></ul></ul><ul><ul><li>Bennett and Rabbetts’ reduced eye. </li></ul></ul>Reduced eye
  16. 20. Single Surface Reduced Eyes Distance from the anterior corneal surface 5.00mm 5.73mm 5.55mm Radius of equivalent surface 4/3 4/3 Refractive index +22.0mm +22.9mm +22.22mm Second focal point F’ -13.0mm -15.7mm - 16.67mm First focal point F +7.0mm +7.2mm +5.55mm Nodal Point N +2.0mm +1.5mm +0.0mm Principal point P Donder’s Listing’s Emsley’s
  17. 21. Applications <ul><li>Serve as a frame work for studying the Gaussian properties for e.g. equivalent power and positions of the cardinal points. </li></ul><ul><li>Calculations of retinal image sizes. </li></ul><ul><li>Magnifications </li></ul><ul><li>Retinal illumination </li></ul><ul><li>Entrance and exit pupil positions and diameters. </li></ul><ul><li>Surface reflections (Purkinje images) and some of the causes and effects of refractive errors. </li></ul>
  18. 22. <ul><li>Effect of accommodation on the above quantities. </li></ul><ul><li>Paraxial models accurately predict chromatic aberration. </li></ul>
  19. 23. Limitations <ul><li>Approximation of real eyes that are: </li></ul><ul><ul><li>Constructed with rotationally symmetric spherical surfaces. </li></ul></ul><ul><ul><li>Refractive index assumed to be constant </li></ul></ul><ul><ul><li>Construction parameters- mean of many individual values, called as “average eye” </li></ul></ul><ul><ul><li>Fovea assumed to be on the optical axis, so visual and optical axes are coincident. </li></ul></ul><ul><ul><li>Very poor predictors of monocular aberrations. </li></ul></ul>
  20. 24. Finite Schematic eyes <ul><li>Regarded as improved paraxial schematic eyes </li></ul><ul><ul><li>optical structure closely resembles to those of real eyes. </li></ul></ul><ul><li>Should have aspherised refracting surfaces, a gradient index and a curved retina. But there are no models of such ideality. </li></ul>
  21. 25. <ul><li>Lotmar (1971) </li></ul><ul><ul><li>Spherical aberration and peripheral astigmatism of desired one </li></ul></ul><ul><li>Kooijman (1983)- </li></ul><ul><ul><li>light distribution in retina </li></ul></ul><ul><li>Navarro & colleagues (1985)- </li></ul><ul><ul><li>having same spherical and longitudinal chromatic aberration as the typical real eye. </li></ul></ul><ul><li>Pomerantzeff & co-workers (1984)- </li></ul><ul><ul><li>designed to have same spherical aberration, aspheric lens with 200 or more extremely thin layers with diff. n. </li></ul></ul>
  22. 26. Applications <ul><li>Framework for calculations of </li></ul><ul><ul><li>retinal image sizes </li></ul></ul><ul><ul><li>Magnifications </li></ul></ul><ul><ul><li>Retinal illumination </li></ul></ul><ul><ul><li>Entrance and exit pupil positions & diameters </li></ul></ul><ul><li>Aberration analysis </li></ul><ul><li>Light level distribution at the retina </li></ul><ul><li>As a model for the design of visual optical instruments. </li></ul><ul><li>Analysis of intra-ocular lenses. </li></ul>
  23. 27. Schematic eye in future <ul><li>Schematic eye with both </li></ul><ul><ul><li>Gradient refractive index & </li></ul></ul><ul><ul><li>Aspherical surfaces not published yet. </li></ul></ul><ul><li>Gross attempts to present a ‘mean’ adult eye. </li></ul><ul><li>Neglects effects of age and gender. </li></ul><ul><li>Things need to be modeled </li></ul><ul><ul><li>Lens thickness </li></ul></ul><ul><ul><li>Surface radii of curvatures </li></ul></ul><ul><ul><li>Gradient refractive index distribution </li></ul></ul>
  24. 28. <ul><li>Effects of refractive correction on eye: </li></ul><ul><li>It alters the image as </li></ul><ul><ul><li>Monocular: </li></ul></ul><ul><ul><ul><li>The size/shape of the retinal image. </li></ul></ul></ul><ul><ul><ul><li>The amount of accommodation for near vision. </li></ul></ul></ul><ul><ul><li>Binocular: </li></ul></ul><ul><ul><ul><li>The ocular rotations needed to place the retinal image </li></ul></ul></ul><ul><ul><ul><li>Relation between accom. and fovea. </li></ul></ul></ul>
  25. 31. <ul><li>Thank you </li></ul>

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