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- ZEMAX Models of the Human Eye
ZEMAX Models of the Human Eye
- By Rod Watkins
- Published 18 June 2007
- User Articles , System Modeling
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ZEMAX Tools
ZEMAX has many tools to make eye models more useful by customising them for particular applications.
- Layout: Because of the steep curves of some surfaces and the fact that in a real eye the edges of the sequential surfaces are not actually connected, the layout is often clearer and a better representation of a real eye if the edges are not drawn. However, in some applications it is necessary to turn on the edges. This is controlled in the Lens Data Editor by right clicking the Surface Type and opening the Draw tab.
In the sequential models given here, some edges are drawn while others are not. The anterior hemisphere of the retina is drawn as a separate surface between the cornea and the pupil, so that the eye is represented as a complete retinal globe. If the dummy surface in the anterior chamber is distracting, this surface can be removed and the posterior hemisphere edges drawn to connect with the lens edge. It is possible to also draw the outer surface of the sclera to connect to the front surface of the cornea, to look more like a real eye, but this produces an additional dummy surface in the anterior chamber. In the non-sequential model these dummy surfaces are removed so the sclera is realistically represented, but the corneal edges cannot be turned off.
- Wavelengths: A very useful ZEMAX tool for eye models is the ability to insert either F,d,C visible spectrum wavelengths or photopic (or scotopic) wavelengths with relative luminosity weightings. The F,d,C wavelengths will often be appropriate when looking at the retina (the Eye_Retinal Object model) but the photopic wavelengths will often be appropriate when the eye is looking through an external optical system (the Eye_Retinal Image model). Open the Wavelength Data Editor and click Select.

When wavelength choice is important it is worth noting that transverse chromatic aberration of the eye is very small, since the second principal plane is close to the aperture stop of the system, but longitudinal chromatic aberration is very marked. Measurements in real eyes of about 2.5 diopters of aberration are very similar to the predictions of these model eyes.
- Field angle weighting: When looking at the retina, for example with a fundus camera, it is necessary that the image resolution does not fall away too much over quite large field angles of 30° or more, and the field angles will need similar weighting. On the other hand, when the retina is the image surface the relative visual acuity (where the acuity at the point of highest visual acuity, the fovea, is 1.0) falls to 0.5 at 2.5°, 0.2 at 10°, 0.1 at 20° and 0.025 at the periphery. (The fovea is actually normally located slightly away from the optical axis, but for most eye model purposes it can be considered to be on axis.)
Choosing incorrect weightings when optimising a system can give quite invalid results. Field angle weightings are set in the Field Data Editor.
- Image quality: When the retina is the object surface, the usual aberration and resolution analysis tools (fans, spot diagrams, MTF etc.) are helpful. However when considering what an eye is seeing, ZEMAX has some very powerful additional tools:
a. ZEMAX menu Analysis/ Image Analysis/ Geometric Image Analysis. A number of library image files are available. Particularly useful are the LETTERF.IMA file and the LINEPAIR.IMA file (see Settings/ File), as they can be related directly to visual acuity, but custom image files are also very easy to create. Since normal visual acuity (6/6, 20/20 or 1.0) corresponds to resolution of a five-bar letter such as E that subtends 5 minutes of arc in object space, the retinal image size is 0.024mm. The Eye_Retinal Image model and Geometrical Image Analysis/ Settings/ Image Size shows the significant variation in image quality with wavelength due to longitudinal chromatic aberration. (Enter an image size of the order of 0.024mm and a similar field size.) This is particularly useful when comparing retinal images before and after changes in an optical system, but a good deal of care is needed in drawing conclusions about visual acuity as processing in the neural pathways from the eye to the brain can have a large effect on the perceived acuity. (Also, for this reason, it is not straight forward to relate grating frequency or limiting MTF frequency in a model eye to visual acuity.)
b. ZEMAX menu Analysis/ Image Analysis/ Geometric Bitmap Image Analysis. This allows real scenes to be projected as bitmaps onto the retina. A number of library files are available and custom files can be easily used. (For example, in the Eye_Retinal Image model open Geometric Bitmap Analysis/ Input ALEX200.BMP and select Field Size 1.0, X and Y Pixels 100, X and Y Pixel Size 0.005). This can be a very useful way of estimating differences between what a person will actually see when changes are made to an optical system, although like Geometrical Image Analysis it is hard to make quantitative judgements based on a single image.

- Ray aiming: The entrance pupil of the eye changes shape and position with field angle, so for calculations at even modest field angles and pupil sizes it may be necessary to turn on Ray Aiming. This is done at ZEMAX menu General/ Ray Aiming. Users are encouraged to read the manual to understand the implications of ray aiming. (I have used the term “pupil” in this article and in the models both correctly to mean the entrance pupil of the eye and also incorrectly but in accordance with common practice to mean the physical aperture of the iris. I hope the different meanings are clear from the context.)
- Other useful ZEMAX tools:
a. Toroidal surfaces. Most real eyes have astigmatism due to the cornea being curved more steeply vertically than horizontally. This can be modelled in the Lens Data Editor/ Surface Type/ Toroidal.
b. Eye rotation, surface tilt and decentration: These effects can be modelled using co-ordinate breaks as described in the Knowledge Base article “How to Model the Human Eye in ZEMAX”. In some cases where the eye rotates by a large angle to look into an optical system it is important to realise that there is no fixed centre of rotation. As each of the six extraocular muscles become more or less important at different angles of rotation, the eye translates as it rotates. For small angles, the centre of rotation has been measured to be on average 15.4mm behind the anterior corneal surface and 1.6mm to the nasal side of the geometric centre. However, it is simplest in the model eyes here to locate the co-ordinate break to rotate the eye at the geometric centre of the retinal globe (in these models that is 13mm behind the cornea and on axis) and we have not found a case where that has given significant errors.
c. Biocular Analysis: ZEMAX can analyse the field of view for up to four configurations in a system where two eyes are looking through the same optical system. The manual describes how to use this tool.
d. Tolerancing: Many studies have measured the optical parameters of real eyes and have noted that the distribution of refractive errors that is predicted from the convolution of the individual parameter distributions does not match the measured distribution. ZEMAX tolerancing offers a powerful way of investigating this and matching measured distributions with theoretical ones.