A method to measure wave aberrations in the isolated crystalline lens is demonstrated. The method employs a laser scanning technique in which the trajectories of narrow refracted laser beams are measured for an array of sample positions incident on the lens. The local slope of the emerging wavefront is calculated for each sample position, and a least squares procedure is used to fit a Zernike polynomial function to define the wave aberration. Measurements of the aberrations of an isolated porcine lens and macaque lens undergoing changes in accommodative state with mechanical stretching are shown. Many aberrations were present, but negative spherical aberration dominated. In the macaque lens, many aberrations underwent systematic changes with accommodation, most notably the 4^{th} order spherical aberration, which became more negative, and the 6^{th} order spherical aberration, which progressed from negative to positive.

*isolated*crystalline lens are essential to implicate the actual sources of the compensation.

*x*(horizontal) and

*y*(vertical) direction. After reflection from the second mirror, the horizontally directed laser beam enters a glass chamber filled with saline. A small quantity of powdered milk in the saline allows the laser beam to be visualized in the solution. A crystalline lens is positioned in the solution in the path of the laser beam either by placing the isolated (pig) lens on a molded putty pedestal or by attaching the partially dissected anterior segment of an eye (rhesus monkey) to a mechanical stretching apparatus (see below). Two CCD video cameras positioned above and to the side of the glass chamber allow the laser beam entering (entrance beam) and exiting the crystalline lens (exit beam) to be imaged simultaneously. The video images are captured by a video capture card (ICPCI, AM-VS, Imaging Technology Inc.) in a personal computer. A macro written for Optimas Image Analysis software (Media Cybernetics) moves the

*x*- and

*y*-translation stages to position the entrance laser beam on the lens. Movement of the stages to a predetermined sequence of positions delivers a specified laser spot pattern onto the anterior surface of the lens. The paths of the laser beams in the solution are digitized, and the slopes and intercepts of the entrance and exit beams are calculated. An alignment procedure ensures that image magnification is identical, that the horizontal and vertical cameras view the same image field, and that the laser beam is passing through the optical axis of the lens (no deviation between entrance and exit beams) in the

*x*and

*y*planes. Minor physiological asymmetries in the lenses limit the precision with which the alignment can be achieved, preventing, for example, alignment of the lens such that the anterior surface is normal to the optical axis laser beam. The scanning procedure moves the stages to position the laser sequentially at each

*x*,

*y*position of the pre-specified spot pattern. At each laser beam position, the laser entrance and exit beams are digitized three times, and the slopes and intercepts of each beam are recorded each time and saved to a file together with the location of the

*x*,

*y*stepper motor positions. The data from the three iterations at each laser beam position are averaged to reconstruct the three dimensional trajectory of each laser beam entering and exiting the crystalline lens. The intersection point of the entrance and exit beam is calculated for each laser beam position to determine the principal plane of the lens. The position in the

*x*and

*y*planes where each exit beam crosses the optical axis is also determined. The mean focal plane of the lens is determined as the average position of intersection of each exit beam with the optical axis. The transverse deviation of each exit beam from the optical axis at the focal plane is calculated. The mean focal length of the lens, the transverse deviation, and the

*x*and

*y*stepper motor positions are saved to a file for subsequent analysis.

*x*and

*y*planes to minimize the deviation of the laser beam as it passes through the lens in both the

*x*and

*y*planes.

*x*axis translation stage is moved by the computer to locate the horizontal edges of the lens. These are determined as the point at which the laser beam is just refracted as it grazes the edge of the lens. These two horizontal edges are recorded and the laser centered again. The

*y*stage is then moved to locate the vertical edges of the lens in the same way. These positions are recorded and the laser centered again. The desired spot pattern is then calculated. This calculation considers the diameter of the lens to scan, the total number of entrance beam positions, and the beam separation. Any number and geometry of sample locations can be used and is limited only by the minimum step size of the stepper motors (1 µm) and the absolute size of the lens. In the tests described here, a grid pattern of 241 equally spaced entrance positions is used such that a circular arrangement of these spots falls within the lens diameter, constituting 17 sample positions across the lens diameter (Figure 6). Once the beam spot pattern is determined, the number of beam positions desired and the scan diameter are entered into the software macro and the scanning begins. For the analysis, three iterations are averaged to obtain one horizontal and one vertical slope and intercept value for each beam position. The number of iterations can be adjusted under software control. The sequence of moving the stages, acquiring the images, digitizing the beam paths three times with both cameras, and storing the data takes approximately 2 s. Thus the duration of the entire procedure can be calculated based on the number of beam positions and iterations chosen. The measurement of a lens with 241 beam positions and three iterations at each beam positions takes approximately 8 min.

*x*and

*y*deviations of each exit beam as it intersects with this mean focal plane are then computed. These

*x*and

*y*deviations are then used to determine the local slopes of the wavefront at each entrance beam position and then to fit the wavefront. The 3D laser-scanning technique allows the wave aberration to be derived from the slope of the wavefront, which is calculated at an array of positions across the aperture (Cubalchini, 1979). The wavefront is calculated at the entrance pupil position that roughly corresponds to the principal plane of the lens. The data analysis is no different than the Shack-Hartmann method (Liang & Williams, 1997) or other ray tracing techniques that measure wave aberrations in human eyes (He, Marcos, Webb, & Burns, 1998). In this method, the derivative of the polynomial describing the wavefront is fit to the data, using a least squares fitting method. The coefficients for the derivative of the polynomial are the same as for the original equation, so the wave aberration can be recovered directly from the fit to its derivative. The wave aberration was fit with the Zernike polynomial series, which was ordered according to the OSA standard for vision science (Thibos, Applegate, Schwiegerling, Webb, & VSIA Taskforce, 2000). Analysis was done with custom software written in Visual C++. The analysis program allows for any number of sample locations and can fit any number of Zernike terms. Many image quality metrics can be calculated once a mathematical representation of the wave aberration has been fit. All metrics shown are derived from the wave aberration.

*x*and

*y*directions at 241 points in an evenly spaced grid pattern that filled the circular aperture of the lens. The wave aberration, analyzed over 19 mm was fit to a 7

^{th}order Zernike polynomial. ZEMAX optical design software (Focus Software Inc.) was used to calculate the wave aberrations of the same glass lens based on its catalog description using the same parameters as defined in the scanning laser software. Figure 3 shows a bar graph comparing the Zernike terms (with

*SD*s from the three measurements) obtained from both techniques. Optical modeling showed that only rotationally symmetric aberrations are present in the lens, mainly 4

^{th}and 6

^{th}order spherical aberration. The experimental results are similar, but also show some additional coma and astigmatism. The presence of these additional aberrations can easily arise with a small amount of decentration of the sampling pattern along with tilt of the lens in the apparatus.

^{th}order. This crystalline lens has a myriad of low- and high-order aberrations. In addition to negative spherical aberration, the next most dominant aberrations are trefoil and a secondary trefoil Z

_{5}

^{−3}, both of which have threefold symmetry. These threefold symmetric terms account for the three lobes that are readily visible in the contour plots of the calculated wave aberration (Figure 5).

^{th}and 6

^{th}order spherical aberration. For the 4

^{th}order spherical aberration, the aberration starts negative and becomes more negative as the power of the lens increases (as stretching deceases). The reverse happens for 6

^{th}order spherical aberration where the coefficient starts negative and progresses to a positive value with accommodation.

Stretch amount (mm) | Focal length (mm) | Focal power (D) | RMS aberration (microns) |
---|---|---|---|

0 | 25.8 | 38.8 | 3.35 |

0.58 | 30.1 | 33.3 | 2.99 |

1.17 | 37.0 | 27.1 | 2.18 |

1.75 | 40.2 | 24.9 | 2.00 |

2.33 | 42.0 | 23.8 | 2.08 |

2.92 | 43.9 | 22.8 | 2.15 |

*SD*of three separate measurements, show that the measurements are consistent. While the measured values show the existence of coma and astigmatism, most likely resulting from tilt of the glass lens, there is also a 1-micron difference in the extent of the spherical aberration. This could be due to slight differences between the actual scan diameter and the calculated scan diameter. In the glass lens, which had a high degree of spherical aberration, ZEMAX modeling demonstrated that only a 3.5% difference (0.65 mm) in the analyzed entrance pupil diameter could account for the difference between the calculated and the measured values. The same change in scan diameter for a 10-mm aperture in the same lens caused in a difference in the spherical aberration coefficient of only 0.07 microns. It is impossible to get a good idea of the variability in this method from the results of different physiololgical lenses. Lenses exhibit considerable variability, so comparisons between different lenses offer little information on variability of the method versus variability of the lenses. The relatively consistent and systematic changes that resulted with the repeated measurements of the monkey lens suggest that the method is reliable. Additional testing underway will consider other approaches to understand the repeatability and reliability of the method.

^{th}order spherical aberration, which became less negative with stretching. The same result was seen in previous studies of human lenses (Glasser & Campbell, 1998) and is also observed in vivo during accommodation in iridectomized rhesus monkey eyes (Vilupuru, Roorda, & Glasser, 2004). In the present study, RMS of all aberrations (excluding defocus) increased as the lens became more accommodated. In the intact human eye, it has been reported that ocular aberrations reduce with accommodation to a point and then increase again (He & Marcos, 2000). These two effects are compatible for the following reason: In the unaccommodated state, the whole eye aberrations are dominated by the positive spherical aberrations of the cornea. With accommodation, the increasing negative spherical aberration of the lens compensates for the cornea until, at some point, the compensation is optimal and the whole eye RMS aberration is at a minimum. Further increases of the negative spherical aberration of the lens from accommodation over-compensate for the cornea and increases the whole eye aberration again.