The Advanced Human Eye Model (AHEM): A Personal Binocular Eye Modeling System Inclusive of Refraction, Diffraction, and Scatter

The Advanced Human Eye Model (AHEM): A Personal Binocular Eye Modeling System Inclusive of Refraction, Diffraction, and Scatter William Donnelly III, PhD ABSTRACT PURPOSE: To present a commercially available software tool for creating eye models to assist the development of ophthalmic optics and instrumentation, simulate ailments or surgery-induced changes, explore vision research questions, and provide assistance to clinicians in planning treatment or analyzing clinical outcomes. METHODS: A commercially available eye modeling system was developed, the Advanced Human Eye Model (AHEM). Two mainstream optical software engines, ZEMAX (ZEMAX Development Corp) and ASAP (Breault Research Organization), were used to construct a similar software eye model and compared. The method of using the AHEM is described and various eye modeling scenarios are created. These scenarios consist of retinal imaging of targets and sources; optimization capability; spectacles, contact lens, and intraocular lens insertion and correction; Zernike surface deformation on the cornea; cataract simulation and scattering; a gradient index lens; a binocular mode; a retinal implant; system import/export; and ray path exploration. RESULTS: Similarity of the two different optical software engines showed validity to the mechanism of the AHEM. Metrics and graphical data are generated from the various modeling scenarios particular to their input specifi cations. CONCLUSIONS: The AHEM is a user-friendly commercially available software tool from Breault Research Organization, which can assist the design of ophthalmic optics and instrumentation, simulate ailments or refractive surgery induced changes, answer vision research questions, or assist clinicians in planning treatment or analyzing clinical outcomes. [J Refract Surg. 2008;24: xxx-xxx.] V ision technology has become highly advanced and continues to evolve. There are many reasons to model the eye including, but not limited to, clinical optometry; ophthalmic diagnostics and refractive surgery; intraocular lens (IOL), spectacles, and contact lens design; optical instrumentation; and bio-optical engineering, vision research, and education. The goal of modeling the eye is to input whole eye optical properties for a complete custom virtual eye model. Paraxial eye models have existed for a long time. However, they are simplified versions of the eye, do not work well off-axis, and consist of parameters generalized over populations. 1 Refractive calculations, such as for spectacles and contact lens fitting and IOL implants, are based on simplified paraxial eye models. There is some uncertainty involved in their use. 1 In addition to paraxial eye models, aberrometry can be used to produce eye models to yield realistic refractive results, useful for LASIK procedures and other wavefront applications. 2 However, these models have limitations in quantifying transmission losses from absorption, diffraction, dispersion, Fresnel reflections, and surface and volumetric scatter. Also, wavefront refractive models are typically single surface phase-based, 2 whereas the eye consists of multiple surfaces and elements. In some instances, it is important to consider the entire eye s geometry for the research application. Other existing eye models are sequentially traced where a ray must trace to the next sequential surface programmed into the model. Sequential ray-tracing is suitable for refraction; however, it is not suitable when assessing multiple surface scattering and back reflections. Non-sequential ray-tracing accounts for rays traced in any direction without a predisposed surface ordering. Furthermore, most commercially available From Breault Research Organization, Tucson, Ariz. The author is an employee of Breault Research Organization and has a proprietary interest in the technology. The author is also a research lecturer at the Department of Ophthalmology, University of Arizona, Tucson, Ariz. Presented at the 9th International Congress of Wavefront and Presbyopic Refractive Corrections; February 14-17, 2008; San Francisco, Calif. Correspondence: William Donnelly III, PhD, 6400 E Grant Rd, Ste 350, Tucson, AZ 85715. Tel: 520.721.0500; Fax: 520.721.9630; E-mail: wdonnelly@breault.com 2 journalofrefractivesurgery.com JRSS1108DONNELLY.indd 2 10/21/2008 1:09:27 PM

Figure 1. Advanced Human Eye Model (AHEM) input screens. Only two input screens are required to describe the default model, a simple refractive model. More complex models will prompt the user with additional input screens. The basic input screen (left) describes initial setup. The second input screen (right) describes parameters particular to the lens choice and other eye geometry. optical modeling software is not very eye friendly, eg, certain tricks, such as dummy surfaces, are required to make the model look like an actual eye. 3,4 Instrumentation is available to acquire detailed biometry for the eye. For instance, ocular wavefront aberrometry describes whole eye aberrations, 5,6 corneal topography describes corneal surfaces, Scheimpflug systems such as the Pentacam (Oculus Optikgërate, Wetzlar, Germany) describe scatter and anterior segment geometry, and ultrasound systems and optical coherence tomography can measure axial length. 7 By accepting biometry in its various forms and creating a personalized eye model, the user can get closer to modeling realistic retinal image quality. A versatile software tool is presented that has been developed to assist researchers, clinicians, and engineers to model the eye for their specific applications without the need for becoming proficient on ray-tracing software or the computer programming of optical phenomena. MATERIALS AND METHODS An optical software engine was chosen to drive the developed eye model. A proven optical software engine Journal of Refractive Surgery Volume 24 November 2008 provides integrity to an eye model because optical phenomena do not require additional core programming. The software engine should be capable of importing external geometry and data from other software, exporting to other software, accounting for scattering and reflections in multiple directions (non-sequential), be capable of design optimization, and provide a variety of useful optical metrics. The software engine chosen was ASAP, the Advanced Systems and Analysis Program from Breault Research Organization (Tucson, Ariz). The eye modeling system developed to interface with the ASAP optical software engine is called the Advanced Human Eye Model (AHEM). There are two modes of the AHEM, design and optimization modes. The user begins in design mode to build an eye model. The design mode steps through screens, prompting for input relevant to the modeling task. In the optimization mode, a preliminary design is complete, inclusive of design variables. The user performs optimization of any of these design variables to obtain design objectives. Optimized design variable values are produced, and the user inserts these values back into the AHEM in the design mode. 3 JRSS1108DONNELLY.indd 3 10/21/2008 1:09:28 PM

Upon launching the AHEM in design mode, the user is prompted on whether to use the default model or a previously designed and saved model. Ocular media details, such as refractive indexes, are stored in a user accessible library. Multiple refractive indexes for media can be assigned to polychromatic wavelengths (for dispersion and chromatic aberration), which can be photopically or scotopically weighted. Upon choosing the default model, a basic input screen appears and a refractive eye model is loaded using settings from the AZ Accommodative Eye Model (Fig 1). 1 Default settings displayed in the input screen can be modified. Source options include monochromatic or polychromatic wavelengths that can be weighted, and coherency or incoherency. An object target may be selected, such as an eye chart or user bitmap. Other options include refractive correction with spectacles, contact lenses, or IOLs; scattering and reflections; ametropia; corneal Zernike surface deformation; a gradient index lens with adjustable index profiles; pupil size; retinal window size; and system insertion such as an instrument, additional lenses, or a retinal prosthesis. Systems are inserted as ASAP native script files. These script files can be written by the user in ASAP or automatically translated from computer aided design (CAD) files, or other optical software such as ZEMAX (ZEMAX Development Corp, Bellevue, Wash), Code V (Optical Research Associates, Pasadena, Calif), or OSLO (Sinclair Optics, Pittsford, NY). If a new best focus is created from optical changes, the retina can either be displaced axially to meet the new best focus (simulating emmetropization) or stay fixed at the initial focus for subsequent refractive corrections. A ray history file can be saved for isolating and analyzing specific ray paths. Models with additional complexity branch to additional input screens relevant to the application. The basic input screen controls most of the branching. For example, if two eyes had been selected, subsequent input screens for eye 1 and eye 2 are displayed. If a correction is selected, a screen prompts for relevant spectacles or contact lens information. If scattering and reflections are selected, a screen prompts for scatter and reflection parameters, which include ray split and scatter levels for individual surfaces, mean free path and particle size for cataract simulation parameters, and retinal reflection percentage. The AHEM is a software tool designed for research applications, and is not a research question itself. The following results describe various scenarios of the use of the AHEM. The AHEM will first be run using the default settings and compared with a ZEMAX model using the same parameters. Next, the results of an optimization of sphere and cylinder for a refractive 4 spectacle correction will be shown. Simulated cataract scatter and its effect on the retinal image will follow. The AHEM s gradient index lens and binocular mode capabilities are summarized, and finally a brief description is given of file import/export and ray path exploration. RESULTS The AHEM accepts parameters that describe virtually any human eye geometry and media. To illustrate validity to the AHEM, the same basic refractive model eye was created from two different lens design programs, ZEMAX and ASAP (with AHEM). Parameters of the AZ Accommodative Eye Model from the Field Guide to Visual and Ophthalmic Optics 1 were used for both systems. These parameters consisted of eye surface geometry, refractive indexes, source, wavelength, and pupil diameter. Ray traces were run, and retinal encircled energy was the comparison metric produced. The programs yielded similar results, differing by only a micron or less (a negligible difference) of radius at any point on the encircled energy graph (Fig 2). It is difficult to assess which modeling program is more precise; however, the results are similar, which is reassuring. A few metric output examples of the default eye model are shown as retinal image point spread functions (PSF) and a three-dimensional PSF containing a volume of field energy showing 0.4 mm of axial through-focus at the retina. Dissecting planes can be positioned anywhere and data can be extracted (Fig 3). Any optical metric, analysis, or graphic that ASAP produces is available to the user. The user can also post process original data to acquire tabular processed data, additional image quality metrics, Fourier analysis, and graphics. The original data are always retained as well. Optimization is the ability to specify design objectives and allow the computer to automatically adjust design variables until the design objectives are met. Optimization can be used with the AHEM and is summarized in this scenario. The AHEM can include combinations of spectacles, contact lenses, IOLs, or any optical hardware. A spectacle lens correction was found using sphere and cylinder as design variables for an optimization. A deformation was applied to the corneal first surface of the default eye model using Zernike coefficients to create an aberrated eye with oblique astigmatism and defocus. Full Width at Half Maximum (FWHM) of the retinal image PSF was driven towards zero as an optimization design objective. The optimization is performed in quarter diopter steps arriving at a spectacle prescription of 0.75 0.75 135. Figure 4 shows the corrected eye model with a spectacle lens automatically modeled with the prescription. journalofrefractivesurgery.com JRSS1108DONNELLY.indd 4 10/21/2008 1:09:30 PM

Figure 2. Comparative validity of the Advanced Human Eye Model (AHEM). Retinal encircled energy plots are overlain from two different lens design programs, ZEMAX and ASAP, using the eye model parameters of the AZ Eye Model. Differences in the plots are minimal with the maximum radius difference slightly over one micron. Figure 3. Retinal image point spread function (PSF) of coma. Examples of several graphics and optical metrics output from the Advanced Human Eye Model. Some coma aberration results from deforming the anterior corneal surface. A source is traced into the eye and refracts to the retina. Top left) Aerial PSF view. Top right) Isometric PSF view. Bottom) Through-focus threedimensional PSFs are shown. Slice planes may be placed anywhere within the specified volume. Numerical data for all complex field components are accessible at any position. In reality, retinal imaging includes contrast loss from light scatter at ocular surfaces. Scatter properties of a surface are characterized by its Bi-directional Scatter Distribution Function (BSDF). The BSDF is acquired by measuring a surface sample with a scatterometer where a detector is swept in a hemisphere detecting reflected flux from a source at various incident angles to the surface normal. Ocular surfaces tend to be smooth Journal of Refractive Surgery Volume 24 November 2008 and Harvey BSDF models (used particularly for smooth surfaces) and user-defined BSDF functions, such as measured scatter data from an IOL, may be applied to surfaces in the AHEM. Conveniently, ASAP has a utility for fitting a BSDF function to measured scatter data. Furthermore, Lambertian or partial Lambertian scatter models may be assigned to the retina. Retinal reflection can be simulated as a percentage of scatter for par- 5 JRSS1108DONNELLY.indd 5 10/21/2008 1:09:30 PM

Figure 4. An aberrated eye with spectacle correction. Top) Left to right shows retinal image point spread functions of the aberrated eye, the eye with correction using optimization of sphere and cylinder in 0.25-diopter steps, and an emmetropic eye. Bottom) Left to right shows the respective retinal encircled energy plots. 6 ticular wavelengths. 8 Cataract, a result of volumetric small particle scattering in the eye lens, 9 is modeled with a Rayleigh-Mie volumetric scatter model. Figure 5 displays the results of an AZ eye model combined with simulated cataract in the lens. Scatter and PSF degradation are consistent with the literature. 10,11 A gradient index (GRIN) lens may be chosen for the eye model. The lens is composed of hyperbolic cosinebased geometry and is made up of 13 onion-layered shells. 12 Different refractive indexes are applied to each layer. The GRIN profile may be modified by the user. The lens may be scaled, stretched, or compressed to simulate aging and/or accommodation. Different scattering properties can also be applied on different lens layers, ie, for nuclear cataract, layers in the embryonic nucleus will contribute more scatter than layers in the cortex, and vice versa for cortical cataract. 13 The user may import CAD files into the eye model via ASAP s CAD translator. The user may desire to integrate CAD files of a retinal implant, custom contact lenses, aphakic or pseudophakic IOLs, a pair of binoculars, fashion eyewear, a microscope, a LASIK system, a retinal scanning system, etc. Figures 6A through 6C illustrate some imported and optimized systems in the AHEM. After insertion, the user can position and scale lenses or systems manually or automatically through optimization. Upon design completion, the eye model, including any imported systems, can be saved and integrated into other ASAP optical systems. One command line can recall the entire assembly into another system. The reverse is also possible. The entire system or any individual components of the eye model such as an optimized IOL, spectacles, or contact lens, may be exported as CAD files perhaps for manufacturing specifications. The binocular mode of the AHEM allows two eyes to be modeled, which is useful for binocular or biocular instrumentation design or other applications in- journalofrefractivesurgery.com JRSS1108DONNELLY.indd 6 10/21/2008 1:09:32 PM

Figure 5. Eye model inclusive of Rayleigh- Mie volumetric scatter. Top left) Aerial retinal image point spread function is shown with veiling luminance from particle scatter. Top right) Log relative Mie volumetric forward scatter and backscatter as a function of angle. Mie scatter is modulated by altering particle size and/or mean free path (concentration). Bottom) Graphic of the eye model inclusive of scattering rays. Figure 6. Various Advanced Human Eye Model applications. A) The imported system is a retinal prosthesis implanted in the vitreous on top of the retina. A corrective lens corrects for the implant s thickness. B) An intraocular lens was imported from a CAD file and optimized for retinal image quality using scaling and position variables. C) A toric contact lens is shown on the cornea. D) Two eyes fixate and converge on a point source target. Journal of Refractive Surgery Volume 24 November 2008 7 JRSS1108DONNELLY.indd 7 10/21/2008 1:09:34 PM

Figure 7. Application of the Path explorer ASAP utility: Advanced Human Eye Model merged with a Shack-Hartmann wavefront sensor. A) All ray paths are shown. B) Paths shown reflect and scatter from the retina, pass through the system, and end on the detector. C) Paths shown are only scattered by the cornea onto the retina. volving two eyes. Interpupillary separation and target location are specified. The eyes will rotate and converge while fixated on the target that may be placed at various locations (Fig 6D). The user can manually alter vergence of eyes independently, ie, to simulate exotropia and then correct with a prism optic. Ray tracing is performed and stereo retinal image pairs are generated. Two different retinal images are created corresponding to vergence and independent eye parameters. The user may combine the two retinal images or analyze them separately. ASAP contains several built-in utilities. A utility that can be used in conjunction with the AHEM is called the Path explorer (PX). The PX renders a three-dimensional interactive visualization of specifically selected ray trajectories, or paths, computed in the course of the 8 AHEM simulations. This feature is useful for isolating particular ray paths, such as those scattering or ending on selected objects. Ray paths can be isolated that start from objects, divide at objects, split a number of times, or hit objects a number of times. Ray paths of specific scattering levels and generations of splitting also can be isolated. Ray paths can also be found with intersections of objects or volumes (Fig 7). DISCUSSION The AHEM is designed to be a flexible software tool. The user interface is configured for speed and ease of use. The user is prompted for data that are relevant to the task being modeled. Data can be input into a model, saved, and reloaded as a complete system later. The user is not required to be proficient on the use of a journalofrefractivesurgery.com JRSS1108DONNELLY.indd 8 10/21/2008 1:09:38 PM

complex ray-tracing engine, such as ASAP. However, familiarity with ASAP allows the user to fully exploit the AHEM applications. Optometrists, ophthalmologists, vision researchers, teachers, and optical engineers can benefit from such a versatile and user-friendly system. A small sampling of applications has been described. Additional applications can be found at http://www.breault.com/ahemjrs. These discussions include visual appearance modeling of IOL haptic reflections observed at the cornea, a GRIN lens model, more IOLs, a bionic retina, spectacles, contact lenses, more optimization, and other applications. Future directions of the AHEM may include developing an advanced retina, inclusive of individual absorption, scattering, and reflection properties of the various retinal layers and the waveguide properties of the photoreceptors. Apodization of a source on the retina could be used to model a Stiles-Crawford effect. Biomechanics of the cornea and tears could also be simulated. Ocular trauma and advanced surgical procedures could be modeled. Development of the AHEM is customer- and potential customer driven. However, the user can continue independent development as well. The AHEM will interface with other user ASAP files as well as other mainstream CAD and optical software files. Limitations of optical modeling include the complexity of the model and the ability to obtain and describe all necessary parameters. However, optimization can help fill in some of the blanks. Dynamic biomechanical properties of the eye are difficult to model in real time; however, compilations of multiple models at various stages are possible. Other limitations are tracing enough rays to avoid noise, the time required to trace those rays, computing power, and software engine ray-trace speed. ASAP is an extremely fast raytrace engine and can trace very complex models in a short time. The AHEM driven by ASAP is a unique, versatile, and powerful eye modeling tool. REFERENCES 1. Schwiegerling J. Field Guide to Visual and Ophthalmic Optics. Bellingham, Wash: SPIE Press; 2004. 2. Donnelly WJ III, Roorda A. Optimal pupil size in the human eye for axial resolution. J Opt Soc Am A Opt Image Sci Vis. 2003;20:2010-2015. 3. Donnelly WJ III. Improving imaging in the confocal scanning laser ophthalmoscope [master s thesis]. Houston, Tex: University of Houston College of Optometry; 2001. 4. ZEMAX. San Diego, Calif: Focus-Software; 2007. 5. Thibos LN, Hong X. Clinical applications of the Shack-Hartmann aberrometer. Optom Vis Sci. 1999;76:817-825. 6. Liang J, Grimm B, Goelz S, Bille JF. Objective measurement of wave aberrations of the human eye with the use of a Hartmann- Shack wave-front sensor. J Opt Soc Am A Opt Image Sci Vis. 1994;11:1949-1957. 7. Donnelly WJ III. Measuring and modeling intraocular light scatter with Shack-Hartmann wavefront sensing and the effects of nuclear cataract on the measurement of wavefront error [doctoral thesis]. Houston, Tex: University of Houston College of Optometry; 2005. 8. Delori F, Pflibsen K. Spectral reflectance of the human ocular fundus. Appl Optics. 1989;28:1061-1077. 9. Gilliland KO, Freel CD, Johnsen S, Craig Fowler W, Costello MJ. Distribution, spherical structure and predicted Mie scattering of multilamellar bodies in human age-related nuclear cataracts. Exp Eye Res. 2004;79:563-576. 10. Cox MJ, Atchison DA, Scott DH. Scatter and its implications for the measurement of optical image quality in human eyes. Optom Vis Sci. 2003;80:58-68. 11. Donnelly WJ III, Pesudovs K, Marsack JD, Sarver EJ, Applegate RA. Quantifying scatter in Shack-Hartmann images to evaluate nuclear cataract. J Refract Surg. 2004;20:S515-S522. 12. Kasprzak HT. New approximation for the whole profile of the human crystalline lens. Ophthalmic Physiol Opt. 2000;20:31-43. 13. Hemenger RP. Light scatter in cataractous lenses. Ophthalmic Physiol Opt. 1990;10:394-396. Journal of Refractive Surgery Volume 24 November 2008 9 JRSS1108DONNELLY.indd 9 10/21/2008 1:09:42 PM