How to Model the Human Eye in Zemax

Introduction

Accurate simulation and modeling of the human eye can be tricky. Entire volumes have been written on the subject, and it is a subject that continues to spur new developments. In this study, we will create model of a human eye in Zemax using the Liou & Brennan 1997 eye model. 

Human Eye Model

set the System|General|Units Lens Units to “Millimeters”. Next you’ll want to set the Wavelengths (found in the System section) to “F, d, C (Visible)” as shown below: 

Next, go to System|General|Aperture and set the Aperture Type to “Float By Stop Size” and then go to System|General|Glass Catalogs and add the catalog “MISC” to your Glass Catalogs. Set just one Field, of Type “Angle(Deg)” with an X-Field value of 5: 

Now insert 3 surfaces before the STOP and insert another 3 surfaces after the STOP. Below is a step-by-step guide to setting up all the surfaces, one at a time. 

Surface 0 

This surface is not actually labeled Surface 0 in the Zemax Lens Data Editor, it’s labeled “OBJ” and it’s the object surface. Below are the settings for Surface 0 (note that any settings not mentioned here should be left with their default values): 

Surf:Type = Standard 

Comment = Object 

Radius = Infinity 

Thickness = 1.00E+009 

Surface 1 

The first surface (after the Object) is just a dummy plane, and we use it to make our layout drawings easier to understand. Below are the settings for Surface 1: 

Surf:Type = Standard 

Comment = Input Beam 

Radius = Infinity 

Thickness = 50.0 

Surface 2 

This is the outer cornea surface. Below are the settings for Surface 2: 

Surf:Type = Standard 

Comment = Cornea 

Radius = 7.77 

Thickness = 0.55 

Glass = Model; 1.376, 50.23 

Semi-Diameter = 5.00 

Conic = -0.18 

Note: to set these glass parameters you will need to right-click the Glass cell, select “Model” as the Solve Type from the drop down list, and then type in the values like this: 

Surface 3 

This is the interface between the cornea and the aqueous humor. Below are the settings for Surface 3: 

Surf:Type = Standard 

Comment = Aqueous 

Radius = 6.4 

Thickness = 3.16 

Glass = Model; 1.336, 50.23 

Semi-Diameter = 5.00 

Conic = -0.60 

Surface 4 

This surface is not actually labeled Surface 4 in the Zemax Lens Data Editor, it’s labeled “STO” and it’s the aperture stop of the system. This is our eyemodel’s pupil plane. Below are the settings for Surface 4: 

Surf:Type = Standard 

Comment = Pupil 

Radius = Infinity 

Thickness = 0.00 

Glass = Model; 1.336, 50.23 

Semi-Diameter = 1.25 

Surface 5 

This is the anterior (front) portion of our model’s crystalline lens. Below are the settings for Surface 5: 

Surf:Type = Gradient 3 

Comment = Lens-front 

Radius = 12.4 

Thickness = 1.59 

Semi-Diameter = 5.00 

n0 = 1.368 

Nr2 = -1.978E-003 

Nz1 = 0.049057 

Nz2 = -0.015427 

Surface 6 

This is the posterior (rear) portion of our model’s crystalline lens. Below are the settings for Surface 6: 

Surf:Type = Gradient 3 

Comment = Lens-back 

Radius = Infinity 

Thickness = 2.43 

Semi-Diameter = 5.00 

n0 = 1.407 

Nr2 = -1.978E-003 

Nz2 = -6.605E-003 

Surface 7 

This is the rear surface of the crystalline lens (that is, it is the interface between the crystalline lens and the vitreous body of the eye). Below are the settings for:

Surface 7: 

Surf:Type = Standard 

Comment = Vitreous 

Radius = -8.1 

Thickness = 16.23883 

Glass = Model; 1.336, 50.23 

Semi-Diameter = 5.00 

Conic = 0.96 

Surface 8 

This surface is not actually labeled Surface 8 in the Zemax Lens Data Editor, it’s labeled “IMA” and it’s the image surface. This is the retina of our model. Below are the settings for Surface 8: 

Surf:Type = Standard 

Comment = Retina 

Radius = -12.0 

Semi-Diameter = 5.00 

This is the Liou & Brennan (1997) eye model. At this point, your Lens Data Editor should look like this: 

Change the Settings on the 3D Layout so that Rotation Z = 90, and set it so that the First Surface is Surface 1 (input beam) and you’ll see the top-down view of the model, complete with offset pupil and off-axis field 

Here is the resulting Diffraction Image Analysis diagram:

You’ll see below that the thickness from the back of the eyeglass lens to the coordinate break (at the eyeball’s center) is 28mm (that’s 15mm from eyeglass to cornea plus 13mm from cornea to center of eyeball). Then, after the coordinate break, there is a thickness of negative 13mm, to get back to the cornea surface. 

Surface 2 

This is the front surface of the eyeglass lens. 

Surf:Type = Even Asphere 

Comment = glasses-front 

Radius = 100.0 

Thickness = 3.0 

Glass = POLYCARB 

Semi-Diameter = 20.0 

Surface 3 

This is the rear surface of the eyeglass lens. 

Surf:Type = Extended Polynomial 

Comment = glasses-back 

Radius = 100.0 

Thickness = 28.0 

Semi-Diameter = 20.0

Surface 4 

This is the coordinate break located at the center of the eyeball. 

Surf:Type = Coordinate Break 

Comment = center of eye 

Thickness = -13.0 

Here is a 3D Layout plot showing the system from a side view for the 3 configurations 

Prepare to Optimize

Insert two new operands at the beginning of the Merit Function. Below are the settings to use for these two new operands: 

First new operand 

Type = XNEG 

Surf1 = 2 

Surf2 = 3 

Zone = 0 

Target = 1 

Weight = 1 

Second new operand 

Type = XXEG 

Surf1 = 2 

Surf2 = 3 

Zone = 0 

Target = 6 

Weight = 1 

Optimizing The PAL 

Summary

We used Zemax to model a human eye using realistic parameters, including a gradient refractive-index crystalline lens, pupil, curved retina, and off-axis field angle. We then provided for a realistic rotation of this model and used this rotating eye model to design a progressive addition lens (PAL)