Theme 2: The theoretical eye

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Theme 2 The theoretical eye

• Form and dimensions of the eye
• Optical constants of the eye
• Optical Geometry applied to the eye
• Schematic model of the eye
• Pupils of the eye

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Form and dimensions of the eye

• Sphere of 12 mm radius.
• Transparent anterior cap, fragment of a sphere
  of 8 mm radius.
• Distance between the centers 5mm.

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Form and dimensions of the eye

• Cornea
• Pupil
• Lens (crystalline)
• Retina
• Fovea
• Optical nerve

4
Form and dimensions of the eye

• Anterior chamber. Between the cornea and the
  iris. Contains the aqueous humor.
• Posterior chamber. Between the iris, the ciliary
  body, and the crystalline lens. Contains the
  aqueous humor.
• Vitreous body. Between the crystalline lens and
  the retina. Contains the vitreous humor.

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Optical constants of the eye

• cornea (r1c , r2c)
• crystalline (r1L , r2L, ....)
• Thicknesses
• Cornea (ec)
• Anterior chamber
• Posterior chamber
• Crystalline (eh)
• Vitreous body
• Refractive indices
• Cornea (nC)
• Aqueous humor (nha)
• Crystalline (nL)
• Vitreous humor (nhv)

• The radii of the surfaces curvature

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Geometric optics applied to the eye

• Vergences

Vergence refractive index divided by the distance
xgt0 Xgt0 convergence xlt0 Xlt0 divergence
Unit Diopters
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Geometric optics applied to the eye

• Vergences

Power of an optical system Vergence of the image
focal distance
Power of a spherical dioptric
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Geometric optics applied to the eye

• Vergences

Relationships of conjugation (origin of
principal planes. Gauss equation)
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Geometric optics applied to the eye

Power of a dioptric
The joining of two optical systems
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Geometric optics applied to the eye
Cardinal elements
Principal planes and points
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Geometric optics applied to the eye
Cardinal elements
Focal planes and points
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Schematic model of the eye

• Schematic model of the eye

Representation of the eye as an optical system
working in the paraxial zone within the frame of
geometric optics.
Procedure in order to obtain a schematic model

• Geometric representation of the cornea.
• Geometric representation of the crystalline.
• Geometric representation of the complete eye.
• (Association cornea and crystalline).
• Obtaining the pupils.

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Schematic model of the eye
The cornea Geometric representation
Le Grand model
Cornea Parameters Value
Thickness 0.55 mm
Radius of the first surface 7.8 mm
Radius of the second surface 6.5 mm
Air index 1
Cornea index 1.3771
Aqueous humor index 1.3374
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Schematic model of the eye
The cornea Geometric representation
Power
Power of the first surface
Power of the second suface
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Schematic model of the eye
The cornea Geometric representation
Power
Joining distance
Total power of the cornea
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Schematic model of the eye
The cornea Geometric representation
Cardinal elements
Principal planes and points
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Schematic model of the eye
The cornea Geometric representation
Cardinal elements
Focal distances
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Schematic model of the eye
The cornea Geometric representation
Simplified cornea
The principal planes are very close. Thus, the
cornea can approximate to just one surface
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Schematic model of the eye
The crystalline Geometric representation
Le Grand model
Crystalline parameters Values
Thickness 4 mm
Radius of the first surface 10.2 mm
Radius of the second surface -6 mm
Aqueous humor index 1.3374
Crystalline index 1.42
Vitreous humor index 1.336
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Schematic model of the eye
The crystalline Geometric representation
Power
Power of the first surface
Power of the second surface
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Schematic model of the eye
The crystalline Geometric representation
Power
Joining distance
Total power of the crystalline
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Schematic model of the eye
The crystalline Geometric representation
Cardinal elements
Principal points and planes
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Schematic model of the eye
The crystalline Geometric representation
Cardinal elements
Focal distances
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Schematic model of the eye
The complete eye Geometric representation
Power
Joining distance
Total power of the eye
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Schematic model of the eye
The complete eye Geometric representation
Cardinal elements
Principal points and planes
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Schematic model of the eye
The complete eye Geometric representation
Cardinal elements
Focal distances
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Schematic model of the eye
The complete eye Geometric representation
Eye 1 dioptric SHo1.59 mm?1.75mm SHo1.91
mm?1.75mm
Reduced schematic model (Listing)
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The pupils of the eye
The aperture of the diaphragm (DA) of an optical
system is the orifice that limits the extention
of the beam of light that penetrates it coming
from an object point. The DA limits the passage
of light through the system. The iris is the
diaphragm of the eye.

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The pupils of the eye
Entrance pupil
Entrance pupil Image of the iris through the
cornea Optical system to keep in mind Cornea
The method of calculation that we will use
consists in obtaining the anti-image of the iris
through the cornea.
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The pupils of the eye
Entrance pupil
Position
Size
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The pupils of the eye
Exit pupil

Exit pupil image of the iris through the
crystalline Optical system to keep in mind
Crystalline
Position
Size
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The pupils of the eye
Exit pupil

Entrance pupil 0.56 mm in front of the iris, 13
greater Exit pupil 0.08 mm behind the iris, 4
greater