**Purpose.**:
The purpose of this study was to quantify accommodation-induced changes in the spherical aberration of cynomolgus monkey lenses.

**Methods.**:
Twenty-four lenses from 20 cynomolgus monkeys (*Macaca fascicularis*; 4.4–16.0 years of age; postmortem time 13.5 ± 13.0 hours) were mounted in a lens stretcher. Lens spherical aberration was measured in the unstretched (accommodated) and stretched (relaxed) states with a laser ray tracing system that delivered 51 equally spaced parallel rays along 1 meridian of the lens over the central 6-mm optical zone. A camera mounted below the lens was used to measure the ray height at multiple positions along the optical axis. For each entrance ray, the change in ray height with axial position was fitted with a third-order polynomial. The effective paraxial focal length and Zernike spherical aberration coefficients corresponding to a 6-mm pupil diameter were extracted from the fitted values.

**Results.**:
The unstretched lens power decreased with age from 59.3 ± 4.0 diopters (D) for young lenses to 45.7 ± 3.1 D for older lenses. The unstretched lens shifted toward less negative spherical aberration with age, from −6.3 ± 0.7 μm for young lenses to −5.0 ± 0.5 μm for older lenses. The power and spherical aberration of lenses in the stretched state were independent of age, with values of 33.5 ± 3.4 D and −2.6 ± 0.5 μm, respectively.

**Conclusions.**:
Spherical aberration is negative in cynomolgus monkey lenses and becomes more negative with accommodation. These results are in good agreement with the predicted values using computational ray tracing in a lens model with a reconstructed gradient refractive index. The spherical aberration of the unstretched lens becomes less negative with age.

^{1–4}The changes in lens and ocular aberrations with accommodation are of special interest because they impact retinal image quality and are therefore factors in determining the best focus position of the eye. Changes in ocular spherical aberration with accommodation could also play a role in the development of refractive error and in determining the optical accommodative response.

^{5–9}

^{1–4,10–15}It is difficult to obtain direct in vivo spherical aberration measurements of the lens due to its position behind the cornea and iris. The aberrations of the lens can be estimated by measuring whole-eye aberrations and subtracting the aberrations of the anterior and posterior corneal surfaces.

^{16,17}In a study by Smith et al.,

^{18}the spherical aberration of in vivo human lenses was predicted by measuring the aberrations of the whole eye and subtracting those of the anterior corneal surface, based on the measured anterior corneal radius of curvature and asphericity, and the predicted posterior corneal surface, based on the estimated posterior corneal radius of curvature and asphericity. The mean spherical aberration of the lens was found to be negative over a wide range of possible posterior corneal surface values. With the availability of commercial devices that measure the posterior corneal surface, it is now possible to calculate in vivo lens spherical aberrations more accurately, using ocular biometry and aberrometry combined with optical modeling.

^{12,13,19–22}With these devices, it is possible to directly measure the spherical aberration of the lens and its changes with simulated accommodation. The techniques used thus far to measure lens spherical aberration have their respective limitations. Glasser and Campbell

^{12}measured the longitudinal spherical aberration of 27 human lenses in a lens stretcher by using a laser ray tracing (LRT) system. The lenses were placed in a tank filled with saline and an HeNe laser delivered multiple beams along the lens. Drops of paint were added to scatter the light, and a side-facing camera was used to capture images of the beams projected along the lens. Their results showed that lens spherical aberration becomes more negative with accommodation and more positive with age. This study demonstrated the principle of LRT to measure lens spherical aberration and provided insight into the general behavior of the lens. However, this photographic LRT technique is subject to measurement uncertainty because it is difficult to quantify the path of the rays in the paraxial region. This makes it challenging to determine the paraxial focal length of the lens and therefore to quantify the spherical aberration with high precision. In a more recent study by Roorda and Glasser,

^{13}the technique was refined to produce a three-dimensional wavefront measurement of the lens by using two cameras and measurements of the wavefront slopes rather than the intersections of the rays along the optical axis. However, lens spherical aberration data were reported only for one macaque monkey lens.

^{23}In that study, the lens shape and GRIN were reconstructed from optical coherence tomography (OCT) images.

^{24,25}A numerical ray trace was performed through the reconstructed lens to predict the spherical aberration. The study found that the lens spherical aberration becomes more negative with accommodation, similar to previous findings.

^{23}which serves to validate the GRIN reconstruction technique.

*Macaca fascicularis*; ages 4.4–16.0 years; postmortem time 13.5 ± 13.0 hours). In the four cases where the left and right eyes were measured in the same monkeys, there was a high degree of similarity between eyes. Power and spherical aberration data were averaged for the analysis in the case where both eyes were measured. All experiments adhered to the Association for Research in Vision and Ophthalmology Statement for the Use of Animals in Ophthalmic and Visual Research. The eyes were obtained from the Division of Veterinary Resources at the University of Miami as part of a tissue-sharing protocol and were used in accordance with Institutional Animal Care and Use Guidelines. The eyes were enucleated immediately after monkeys were euthanized and wrapped in gauze and stored in a closed container. No animals were euthanized for the sole purpose of this study. Upon arrival at the laboratory, all eyes were either prepared for stretching experiments or refrigerated at 4°C.

^{26}

^{19,20}In summary, the whole globe was bonded to eight scleral shoes to preserve the globe's shape during the dissection and stretching experiments. Once the shoes were bonded to the sclera, the posterior pole was sectioned, and the cornea and iris were removed. Incisions were made between the sclera of adjacent shoes to create eight independent segments for stretching. Following the dissection, the tissue preparation, consisting of the ciliary body, zonular fibers, crystalline lens, and segmented sclera, was mounted into the lens stretcher. In the present study, the effective power and spherical aberration of lenses in the unstretched and fully stretched states (shoes displaced radially by 2.5 mm) were measured with a laser ray tracing system.

^{22,27}The OCT system uses a superluminescent diode with a central wavelength of 825 nm and a bandwidth of 25 nm.

^{27}The beam delivery system is mounted on a 3-axis translation stage to allow precise centering of the beam in the transverse direction. The beam was aligned on the crystalline lens apex prior to stretching experiments by visualizing the central OCT A-line signal intensity in real-time and adjusting the position of the delivery optics until the signal peaks corresponding to the anterior and posterior lens surfaces were maximized.

**Figure 1**

**Figure 1**

*y*. Figure 2 shows the measured ray heights plotted as a function of entrance ray height for a typical cynomolgus monkey lens. These graphs were generated for each axial position,

*z*, of the camera and fitted with a third-order polynomial, where

*y*is a constant term (mm),

_{0}*B(z)*is a measure of paraxial ray path,

*D(z)*is a measure of the lens third-order spherical aberration (mm

^{−2}),

*h*is the entrance ray height (mm), and

*h*is an offset value that counts for lens decentration relative to the input ray trace (mm). Because the rays travel in a straight line,

_{0}*B(z)*and

*D(z)*are linear functions in terms of the axial position

*z*. The slope and intercept of

*B(z)*and

*D(z)*are determined by performing a linear fit versus

*z*(Fig. 3). The effective lens power,

*P*(diopter [D]), was calculated from the slope,

_{L}*m*, of the linear fit of

_{B}*B(z)*versus

*z*(Appendix 1):

**Figure 2**

**Figure 2**

**Figure 3**

**Figure 3**

*D(z)*at the paraxial focus of the lens (where

*z = z*). The Zernike spherical aberration coefficient

_{focus}^{28}where

*a*is the pupil radius (3 mm),

*P*is the effective lens power, and

_{L}*D(z*is the value of the function at the focal point of the lens. Equation 3 is derived in Appendix 2.

_{focus})*P*< 0.0001), whereas the stretched lens power was relatively constant.

**Figure 4**

**Figure 4**

*P*= 0.002).

**Figure 5**

**Figure 5**

^{29}In addition, it is possible that the lens stretcher could induce unexpected high-order aberrations. The current system was limited to measurements of spherical aberration along a single meridian and did not allow us to reconstruct complete two-dimensional aberration maps and quantify these effects.

^{30}humans become presbyopic at approximately 40 to 50 years of age, so the equivalent monkey presbyopic age is 13 to 17 years old. A linear regression was performed with the lens spherical aberration versus age to determine if there was a statistically significant age dependence. However, more data are required over a broader age range and with a more uniform distribution in order to verify if the age dependency is linear or if it follows a more complex nonlinear behavior.

^{12}and from the preliminary results obtained with a macaque monkey lens by Roorda and Glasser.

^{13}Our results cannot be directly compared with those of Glasser and Campbell

^{12}because in their study the lens spherical aberration was presented as the longitudinal spherical aberration calculated for a normalized lens diameter in diopters. However, the general behavior of the cynomolgus monkey lenses in our study is similar to that of human lenses.

^{23}Seven of the cynomolgus monkey lenses used in the present study were also used in the GRIN reconstruction study by de Castro et al.

^{23}In that study, the lens shape and GRIN were reconstructed from OCT images. A numerical ray trace was performed through the reconstructed lens for a 6-mm pupil diameter (101 rays, ray spacing of 30 μm) to estimate the spot diagrams at the same

*z*positions as the LRT experiment. The spot diagrams for the reconstructed GRIN lens were simulated based on the ray trace for lenses at the corresponding camera positions,

*z*, in the unstretched and stretched states. The simulated spot diagrams are in close agreement with the measurements acquired with the LRT in the present study (Fig. 6). Moreover, the predicted lens spherical aberration based on the reconstructed GRIN lens model

^{23}is in good agreement with the measured spherical aberration using LRT for the seven lenses. Figure 7 shows the predicted spherical aberration versus the measured spherical aberration (Fig. 7, left), and the Bland-Altman analysis for the two different methods (Fig. 7, right). Difference between the two methods fell within ±2 SD for all lenses, and the mean difference was −0.51 μm. The close agreement between experimental data and model predictions using these two independent methods serves to validate the method for reconstructing the lens GRIN from OCT images of crystalline lenses.

**Figure 6**

**Figure 6**

**Figure 7**

**Figure 7**

^{13}

*B(z)*in Equation 1. Another potential source of error in the LRT system is that the posterior window of the tissue chamber may contribute to the measured spherical aberration. To quantify the potential error introduced by the window, a ray trace analysis was performed using ray tracing software (OSLO; Lambda Research Corp, Littleton, MA, USA). Analysis showed that the window contributes approximately 2% error to the spherical aberration coefficient (−0.4325 μm with the window compared to −0.4234 μm without) compared to the crystalline lens spherical aberration, which averaged −6.08 ± 0.79 μm in the unstretched position and −2.57 ± 0.52 μm in the stretched position. The window contribution was therefore not taken into account.

**B. Maceo Heilman**, None;

**F. Manns**, None;

**A. de Castro**, None;

**H. Durkee**, None;

**E. Arrieta**, None;

**S. Marcos**, None;

**J.-M. Parel**, None

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*Adaptive Optics for Vision Science: Principles, Practices, Design and Applications**z*, of the camera. Each plot was fitted with a third-order polynomial:

*B(z)*and

*D(z)*are linear functions where

*B*and

_{0}*D*(mm

_{0}^{−2}) are constant terms,

*m*(mm

_{B}^{−1}) and

*m*(mm

_{D}^{−3}) are the slopes of the linear fits, and

*z*is the position of the camera (mm). To simplify the description, we assumed

*h*= 0, because

_{0}*h*is a term included to take into account lateral offset in the experiment.

_{0}*y*is the measured ray height on the camera (mm),

*θ′*=

*dy/dz*is the output ray slope,

*d*is the distance between the posterior surface of the lens and the anterior surface of the tissue chamber window (mm),

_{p}*P*is the measured effective power of the lens (D),

_{L}*n*is the refractive index of the medium (

_{a}*n*= 1.336),

_{a}*d*is the thickness of the glass window (mm),

_{w}*n*is the refractive index of the window (

_{w}*n*= 1.510),

_{w}*h*is the entrance ray height (mm), and

*θ*is the incident angle (°). In our experiments, the incident angle is equal to zero (

*θ*= 0). In this case, Equation A7 can be simplified to

**Figure A1**

**Figure A1**

*z*that gives

*y*= 0 in Equation A5a, independent of

*h*, which gives

*D(z*, measured with the LRT system with previously published data, the values were converted to Zernike spherical aberration coefficients. Higher-order aberrations other than spherical aberration were assumed to be negligible.

_{focus})^{28}: where Δ

*y*is the ray aberration equivalent to the spot shift on the camera (mm) at the paraxial focus of the lens,

*h*is the entrance ray height (mm), and

*D(z*is the value of the function

_{focus})*D*at the lens focus (mm

^{−2}). The contribution of spherical aberration to the Zernike wavefront aberration

^{31,32}is where

*W*is the wavefront aberration (μm),

*h*is the input ray height (mm), and

*a*is the pupil radius (mm).

^{31,32}is where

*R*is the radius of the reference wavefront and

*n′*is the refractive index of the image space. In our case, for rays entering the lens parallel to the axis,

*R*is the effective focal length,

*f′*, of the lens.