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of one year to adulthood, ocular dimensions continue to grow to their final values but at a much reduced rate. After adulthood, the outer dimension and the shape of the eye ball are invariable, while the lens shape and positions continue to change. For infants, the anterior lens surface is much steeper. With growth, it becomes flatter, until maturation, and afterwards, the anterior lens surface will become steeper again. Similarly, the posterior lens surface becomes steeper after adulthood. The thickness of the lens continues to increase at a varying rate through life. Infants have shorter VCD. During the growth period, the VCD increases; it then decreases in older age.

Although many studies have investigated the correlation between the ocular biometric parameters and age, no age-dependent eye model has been published. The age-dependent eye modeling can be performed in three age groups: infants (newborn to 12 months old), children (approximately 1–16 years old), and adults (16 years old and over). As in the accommodative and the ametropic eye modeling, the validation of the models is required via optical optimization and proper selections of the free variables necessary to achieve the targeted ocular optics.

13.2.2.4. Modeling for disease development

Eye modeling can be used to study ocular disease and its development. One such example is the keratoconus (KC) eye modeling based on the statistical description of the disease biometry conditions. KC is a degenerative noninflammatory disorder of the eye for which structural changes occur within the cornea and result in the thinning of the cornea and a change to a more conical shape than its normal gradual surface curvature. KC can cause a substantial distortion of vision in multiple images, streaking, and sensitivity to light. One purpose of KC modeling is to study and understand the influence of the properties of the KC cone(s) on the optical performance of human eyes. With the general KC eye models, the effects and visual impacts of different parameters of the KC cone, such as the cone location, volume, and shape, were investigated. The research results of this subject have been published in Ref. 16.

13.2.3. Validation of Eye Models

Patient vision performance is usually used to confirm the modeling success. The refractive errors and the WFA are normally guaranteed in the modeling

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process using optical optimization. Further validation with VA and street vision in the day or night conditions can also be examined after the eye modeling is complete.

13.2.3.1. Point spread function and modulation transfer function

The size and shape of the PSF, which is the image of a point source, provide an indication of VA. In general, the real image on the retina can be calculated by the spatial convolution of the PSF with the object in the object space. Knowing the PSF of one eye model, we can estimate the subject VA by the degree of concentration of the PSF. The dimension and the profile of the PSF can be compared with the clinicalVA report to evaluate the degree of success of the model. The PSF can be directly obtained in the ZAMAX analysis. Notice that the PSF depends on the object distance and the field angle that are assigned in the lens editor. For a 20/20 visual acuity, the PSF should be comparable to a spot size of 5 µm on the retina. A similar way of this measure is the modulation transfer function that represents spatial resolution in frequency domain. A well resolved 20/20 Snellen VA corresponds to a frequency of 100 cycle/mm.

13.2.3.2. Letter chart simulation

The PSF can be used to infer how well the subject can see a point source, but using the parameter alone is neither straightforward nor reliable to describe the subjective vision alone. Before calculating the PSF, we must first set a pupil sampling number of ray tracing (i.e. the size of the grid of rays to trace to perform the computation). Higher sampling densities yield more accurate results at the cost of longer computation times. Second, the PSF depends on the location of the point source in the field of view. When the subject looks at an object, especially a large object, calculation of PSF over a large field angle range is required for accurateness. Third and most importantly, the PSF is a 2D function, which is difficult to directly quantify or directly show correspondence to the single parameter VA. A single index that is derived from PSF, such as the FWHM or STR, does not directly correspond to VA, especially when the PSF profile is far from a Gaussian or Lambertian type of symmetric shape. For these reasons, the

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Fig. 13.6. Input letters (left) and the best-corrected Snellen chart vision of an astigmatism patient (middle) and a KC patient (right).

best way to validate the personalized eye models is to simulate the subject’s vision of an extended object, using, for example, a Snellen letter chart.

ZEMAX geometric image analysis (GIA), rather than PSF convolution, is used to provide such vision simulation. GIA is based strictly upon geometrical ray tracing. It can be used to model extended (light) sources, analyze useful resolution, represent the appearance of imaged objects, and provide intuition as to image rotation. A perfect alphabetic letter E, for example, is assigned as the object image (or the light source) at the desired distance. Figure 13.6 shows the input Snellen letter chart at 20 feet and the resulting retinal images of a hyperopic eye and a KC eye using the customized eye models. Each letter in the letter chart is simulated individually with its corresponding resolution. A letter E at 20/20 line corresponds to 0.873 cm at 6 m and ideally forms a reversed image of 24 µm on retina.

13.2.3.3. Night/day vision simulation

The human vision is different in daylight than in a nighttime environment because light, or the lack, thereof causes a change in pupil size. In the darkness, the pupil is naturally dilated to include more light signals. In nature, the human visual procedure and correction are designed and adapted for

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