The availability of a complete patient-specific eye model would provide many key advantages in vision science and ophthalmology. For example, the model could be used as a theoretical basis for vision correction of higher-order aberrations in laser refractive surgery or with corrective lenses, since classical devices only measure and correct for basic refractive errors (i.e., defocus and astigmatism). Accurate determination of optical parameters in normal and abnormal eyes could also be valuable in developing data bases for clinical diagnosis of pathologies, while measurements of ocular surface misalignments would be useful after implantation of intraocular lenses in cataract surgery [1
]. Moreover, knowledge of the refractive index distribution in the lens may be beneficial in optical coherence tomography, which is based on interferometric reflectometry and index changes [4
]. It could additionally lead to a substantial improvement in retinal imaging. For instance, current adaptive-optics ophthalmoscopes incorporating a Shack-Hartmann wavefront sensor (WFS) and wavefront corrector conjugated to a single surface of the eye offer high resolution [6
], but over a very limited field-of-view (FOV) [8
] due to a form of anisoplanatism involving aberrations of the eye. Aberrations collected over different field positions on the retina result from the passage through different parts of the ocular media so that the adaptive-optics correction is valid only over a certain field area, referred to as the isoplanatic patch. One solution is to conjugate multiple wavefront sensors and correctors to various refractive surfaces in the eye, thereby increasing the isoplanatic patch size and enabling wide-field measurements, but choice of the optimal planes at which to conjugate the correctors would be facilitated by knowing the real eye structure of the individual.
In addition to improvements in vision correction and retinal imaging, the availability of patient-specific parameters could facilitate a broad range of ongoing vision science studies. Of significant interest is the in vivo
gradient-index (GRIN) distribution and lenticular geometry of the human crystalline lens as a function of both age and accommodation [3
], but this information has been difficult to obtain, and reliable measurements are scarce [4
]. While previous studies suggested that aspheric surfaces in the anterior segment and an effective refractive index for the lens are sufficient to model spherical aberration, lack of knowledge regarding the GRIN distribution precludes both the prediction of off-axis aberrations and study of dispersion in the lens, so that experimental data are limited [9
]. A complete mapping of the human eye could also be used to evaluate intersubject variability and statistical variations, as well as vision performance and image quality in the central and peripheral visual fields [11
], which could be enhanced by accurate measurement of the retinal curvature [13
]. Another fundamental study in physiological optics is how individual ocular components factor into the overall performance of the human eye [15
] and how such performance would change if one or more surfaces are altered, a critical element in surgical procedures. While schematic eyes have been extremely useful for that purpose, they often lack asymmetry such as decentration of the lens or pupil, which manifest in the fovea as aberrations of non-axisymmetrical systems (e.g., coma, astigmatism, and transverse chromatic aberration) and may have a significant impact on ocular performance [16
]. We believe that a patient-specific mapping of the entire eye, including nonaxially symmetric components, would enable further investigations that have been previously unapproachable.
We are developing a new method for studying the human eye, either for clinical ophthalmology or for basic research. In our approach, we estimate patient-specific parameters of the eye, including surface curvatures, conic constants, tilts, decentrations, thicknesses, refractive indices, and graded-index distributions. The data consist of the raw detector outputs from a Shack-Hartmann wavefront sensor (WFS), a device that measures the phase distortions of a wavefront and provides useful information about aberrations in an optical system. Once we have the data, the parameters in the eye model are estimated via maximum-likelihood (ML) estimation using an optical design program. This process is the opposite of traditional optical design, where the lens parameters at each iteration are fixed and data on one or more output planes are computed. Here the WFS data are given, and the lens parameters are estimated, so we refer to the method as inverse optical design
. It should be noted that this is a nonlinear estimation problem, since the data depend nonlinearly on the parameters. Similar methods have been applied in astronomy and optical shop testing [18
]. In astronomy, image data are used to estimate optical prescription parameters (i.e., first-order geometrical parameters), a process referred to as prescription retrieval
. In optical shop testing, coefficients in an arbitrary wavefront expansion (e.g., Zernike coefficients) are estimated to characterize aberrations in a test element. However, this is a linear estimation problem in contrast to our method.
Our method of inverse optical design using wavefront sensing could provide an in vivo
, non-invasive, and complete mapping of the human eye, including dozens of parameters that are essential to an accurate representation of the eye and its aberrations. Existing in vivo
methods supply a small subset of ocular parameters. For example, a common technique in phakometry uses Purkinje images of the back reflections from the anterior and posterior surfaces of both the cornea and crystalline lens, providing basic curvatures, tilts, and decentrations [2
]. However, one difficulty in this approach is that insufficient knowledge of the refractive index distribution of the lens leads to significant measurement errors in the lens posterior radius [20
]. Scheimpflug slit imaging is increasingly being used to obtain sharp cross-sectional images of the anterior eye segment, imparting surface shapes, misalignments, and intraocular distances, although accurate determination of these parameters relies on the correction of optical distortions in the imaging system and within the eye itself [2
]. Distortion due to the geometry of the Scheimpflug camera can be corrected analytically with relative ease, but correction of distortion due to refraction at intermediate ocular surfaces is much less approachable. Measurements of a particular surface are subjected to refraction at all successive surfaces [3
] and traversal through media of individually varying thickness and curvature. Hence, arbitrary quantification errors in one surface are propagated throughout the system [22
]. Conversely, magnetic resonance imaging has recently been used for in vivo
visualization of structures in the anterior segment, which eliminates the distortion dilemma [21
], but suffers from low resolution, signal-to-noise ratio (SNR) constraints, and eye motion artifacts due to longer acquisition times [23
]. On the other hand, corneal topography is a rapidly developing technique that provides very detailed and reliable measurements regarding corneal curvature [24
], including astigmatism and surface irregularities, although it does not provide information about the remaining ocular surfaces. However, such accurate corneal information could be used to supplement or validate the parameter estimates acquired with our system, or even used as input to inverse optical design to narrow the high-dimensional parameter space.
In this paper, we will discuss some of the obstacles that must be overcome to make the system practical and reliable for clinical use. For instance, we discovered strong coupling between the ocular parameters and a complex likelihood surface. Therefore, the crux of future research will involve the development of an efficient global search algorithm as well as rapid processing techniques.