Optical Eye Modeling and Applications

daytime vision. However, since human activities extend long after nightfall, the performance of night vision becomes important and requires more concern. Night vision problems have been the reason for most complaints from LASIK patients. Fortunately, eye modeling can be used to predict a patient’s night vision. The object image, such as the street view, can be entered in ZEMAX at the assigned object distance. The retinal image of the street view can then be obtained by running the image analysis procedure through the desired eye model. Pupil size and accommodation level must be assigned adequately. The day and night vision predictions using ZEMAX BMP Image–Analysis can serve as one way to validate eye modeling.

13.3. Other Modeling Considerations

In the eye modeling work described previously, many ocular conditions are not encountered. Some of these missing conditions will be addressed here.

13.3.1. Stiles Crawford Effect (SCE)

SCE is an optical feature of the eye that is caused by the wave-guide property of the cone photoreceptors of the eye. A photoreceptor acts like an optic fiber on the retina; it captures light that hits it at a narrow angle from its normal. As a result, the rays of light passing through the periphery of the pupil are more oblique to the cone. The acceptance angle of a cone is narrow, approximately 5◦; rods have larger acceptance angles. SCE reduces the disadvantageous effects of aberration and the light scatter on the retina at photopic levels. A number of mathematical functions have been used to describe the SCE, the most popular of which is a Gaussian distribution as first used by Stiles and Crawford in 1937.17 This function is usually an excellent fit to experimental data out to 3 mm from the peak of the function, and has the additional virtue of simplicity. This SCE function Le(r) is described as Le(r) = exp(−βr2), where r is the distance in the pupil from the peak of the function. The function is normalized to have a value of 1 at the peak. The Stiles-Crawford co-efficient β describes the steepness of the function, and is assumed to reflect the directionality (variation in alignment) of the photoreceptor population being tested. It may not have

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the same value for measurements in eyes affected by retinal pathology. Measured β coefficients for the large-scale study are given byApplegate and Lakshminarayanan.18 Combining the data across many studies gives a mean value of 0.12. The SCE can be included easily in optical modeling of the eye as an apodization effect, which means that it can be treated as an optical filter of variable density attenuation placed at the pupil. The apodization filter can be simply added into our model by entering a user-defined surface and loading a “dll-file” to define the surface that represents the equation of SCE.

13.3.1.1. Multiple reflection and scattering of the retina

In some applications of eye modeling, especially the simulation of ophthalmic measurement, the reflection and scattering properties of the retina need to be addressed. Because the human retina is not self-luminous, an external light source is necessary to make the retina visible, and the light reflected from the retina will bring the information behind the cornea to the instrument. Thus, the multiple reflection and scattering properties of the retina should be addressed. Although most layers in the retina are virtually transparent, there are small refractive index variations between cells. Such a deviation from homogeneity will give rise to scattering and reflections. A proper model of any ophthalmic or optometric instrument measurement that uses the double pass reflection must consider the uniqueness and complexity of this retinal reflection. Even if the simplifications of any model are used, the implications of such simplifications should be understood. Up to this point, only sequential ray tracing is described for eye modeling. Rays are always traced from the object surface to the assigned surface numbers in a strict sequential order. Each ray “hits” each surface once and only once in this predetermined sequence. The sequential model is straightforward, numerically fast, and extremely useful and complete for many important cases. However, when multiple scattering/reflection is involved, a nonsequential ray tracing may be required. Nonsequential means the rays are traced in the physical order that they encounter the various objects or surfaces, and not necessarily in the order the objects are listed in the software user interface. Note that rays in a nonsequential trace may hit the same object repeatedly, and entirely miss other objects. Generally, the order in which objects are hit by rays depends upon the object geometry and the

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angle and position of the input ray. Certain types of analysis, such as stray or scattered light effects, are only practical in a completely nonsequential environment. In the ophthalmic simulation, the inclusion of the back scattering from retina and the use of the nonsequential system may well be the only solution in ZEMAX to mimic the multiple reflection and scattering from the retina.

13.3.1.2. Other retinal properties

The spectral properties of retina can be easily handled by assigning the wavelength and weight at the beginning of each of the double path simulations. A birefringent retinal surface can be modeled using the birefringent in/out surface types as described in “Birefringent In and Birefringent Out” in ZEMAX. As to the position-dependent reflectance, a retinal component with schematic layers, using the nonsequential component in ZEMAX and setting the scattering type and parameters of each layer, can be constructed. However, using this multiple retinal layer model to make any simulation could significantly increase the computation time, and the result may not be appreciably different from the calculation based on single-layer retina model.

13.3.1.3. Tear film influence and tear film breakup

The tear film has not been included or discussed in any acknowledged schematic eye models. Although the typical tear film is very thin (3–40 µm) compared to the corneal thickness (greater than 500 µm), vision image quality as well as the ophthalmic measurements can be influenced significantly by the tear film condition. The tear film quality is determined by its structure, composition, and thickness. The tear film possesses a free surface, which is secreted by the lacrimal gland, is lost via evaporation and drainage at the lacrimal ducts at the nasal side, and will eventually breakup in the absence of blinking.

The tear film breakup time (TBUT) is normally greater than 10 second for healthy tears. Pathologies of this film, or its production, are typically responsible for dry eye syndrome that possesses many features that are encompassed by the fluid mechanical and associated solute transport processes of the tear film. Studies in this are far from complete. Recently, the

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