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.
Gullstrand-LeGrand Eye Model
|
|
|
Anterior Cornea |
Posterior Cornea |
Anterior Lens |
Posterior Lens |
Retina |
||||
|
R (mm) |
|
7.8 |
|
6.5 |
|
10.2 |
|
-6 |
|
-13.4 |
|
-φ (mm-1) |
|
-0.04835 |
|
0.006108 |
|
-0.0081 |
|
-0.014 |
|
|
|
t (mm) |
Infinity |
|
0.55 |
|
3.05 |
|
4 |
|
16.59655 |
|
|
n |
1 |
|
1.3771 |
|
1.3374 |
|
1.42 |
|
1.336 |
|
|
t/n (mm) |
|
|
0.39939 |
|
2.280544 |
|
2.816901 |
|
12.42257 |
|
|
y (mm) |
|
1 |
|
0.980691 |
|
0.884095 |
|
0.744614 |
|
0 |
|
nu (rad) |
0 |
|
-0.04835 |
|
-0.04236 |
|
-0.04952 |
|
-0.05994 |
|
|
yc (mm) |
|
-0.30376 |
|
-0.25796 |
|
0 |
|
0.31862 |
|
1.668325 |
|
nuc (rad) |
0.1 |
|
0.114686 |
|
0.11311 |
|
0.11311 |
|
0.108649 |
|
Cardinal Points & Pupils
- Principal Planes – conjugate planes that have unit magnification. Can be used to generate effective lens.
- Focal Points – points where collimated beams come to focus.
- Nodal Points – 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 – conjugate planes that are the entrance and exit ports of the optical system.
Principal Planes
Similarly, the front principal plane P is located 1.595 mm from corneal
vertex.
Total Power
Φ = n’ / P’F’
Φ = 1.336 / 22.28896 mm = 0.05994 mm-1= 59.94 D
Total Power Φ = 1 / PF, PF = -16.683 mm or the front focal point is –15.089 mm from corneal vertex (about where your spectacles sit).
Pupils
Nodal Points
PN = P’N’= (nvit – nair) / Φ = 0.336 / 0.05994 = 5.605 mm
Front Nodal Point N is 7.200 mm from corneal vertex
Rear Nodal Point N’ is 7.513 mm from corneal vertex
Angular Subtense
Typically, 1 minute of arc is stated as the eye’s limit of resolution. This leads to y ~ 5 microns (two points separated by 5 microns on the retina can just be resolved.
