Optical Eye Modeling and Applications

iteration, the three variables are optimized to produce the sharpest retinal image from a point source at infinity.

One important issue that deserves much attention in the refractive error optimization is the pupil diameter. With the presence of aberration, the refractive error always varies with the pupil size. A typical example of such variation is the existence of (positive and negative) spherical aberration (SA) that induces (myopic and hyperopic) refractive error in the periphery. As the pupil size increases (which occurs in darkened environments and night vision), the eye tends to be shifted myopically (or hyperopically). For this reason, when performing the optimization in either step for refractive error, a reasonable pupil size of 3–4 mm, which is about the condition for typical reading or eye examinations should be assigned before the iteration. When the pupil diameter is set as 3.0 mm, the entrance pupil will be approximately 3.33 mm due to the magnification from the anterior chamber and cornea. In clinical language, the pupil size means the “pupil appearance,” which is the entrance pupil in the optical system, not the physical pupil size. After the two-step optimization is performed, the correcting Gaussian thin lens in front of the cornea should be removed. An eye model with appropriate refractive error is then obtained.

13.2.1.2. Optimization to the wavefront measurement

In the recent years, the WFA map is available in clinics. WA provides not only the second-order aberration, but also the aberration information to the sixth or seventh-order. If the WFA measurement of the eye is available, this clinical vision assessment could be used for the final targeted merit functions. Variables will be assigned in the initial personalized model for iteration to obtain the optical quality target values given by the merit function. If the WFA map is obtained from the patient eye, it will be assigned as the merit function in the final optimization. A backward eye model will be used and the wavelength (typically infrared) of the wavefront aberrometer should be assigned. If the wavefront data are available, the second optimization for cylindrical refractive error is not required. The optimization for axial length is still sensible if it is not a known condition. At the beginning of the optimization, the type of anterior lens surface should be selected as the Biconic Zernike and the Zernike coefficients will be assigned as free

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variables for iteration. In this step, the merit function will be changed from SRX to Zernike coefficients. The optimization target is to approach the measured WFA, which is reported in the Zernike polynomial format. The merit function will require the optimization operand “ZERN.” The parameters may be set as Term = 1, 2. . . in the order of Zernike coefficients in ZEMAX, Wave = 1 (only one wavelength used in each of the calculations), Samp = 2 (pupil sampling = 64 64), field = 1 (only one field set in our calculations), and Type = 1 (Zernike standard coefficient), and Zernike coefficients of the clinical WFA will be input at the column of the “target” values, and the weight of each coefficient will be set equally. Figure 13.5 shows the comparison of the measured and the final wavefront after optimization in a test run. The result reveals a successful determination of a personalized eye model that has the same anterior corneal map and WFA as the individual subject.

13.2.1.3. Tolerance analysis

The method described above has intrinsic uncertainties in the sense that the whole lens geometry is initially unknown. The geometry is then adjusted to fit the clinically measured optical performance with the sole constraint that the result is as close as possible to the initial base model. This uncertainty is an optical design problem, in which it is essential to perform a tolerance

Fig. 13.5. Comparison of measured and reproduced WFA of an eye and eye model.

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