Open Access
Add to BibSonomyAbstract
A bench-top physical model eye that closely replicates both anatomical and optical properties of an average human eye was designed and constructed. The cornea was sourced from a flouro-polymer with refractive index (RI) of 1.376 and crystalline lenses were made of Boston RGP polymers, EO and Equalens II, with an equivalent RI of 1.429 and 1.423 respectively. These materials served to make crystalline lens components of different age groups and accommodative states. De-Ionized water, with RI of 1.334 represented both aqueous and vitreous humor. The complementary metal-oxide sensor of a PixelLink digital camera with a resolution of 5MP and a 2.2µm pixel pitch, hosted on a motor-base, served as the ‘acting’ retina. The translation and rotary functions of the motor-base facilitated the simulation of different states of ametropia and assessment of peripheral visual function, respectively. We validated one of its configurations to suit normal viewing conditions and results from the on and off-axis optical quality measurements are presented. As a demonstration of potential practical uses, several corrective soft contact lenses were placed on the model eye and their optical performance evaluated.
©2010 Optical Society of America
1. Introduction
The optical characteristics of vision correction devices like spectacles, contact lens (CL) and intra-ocular lenses (IOL) can be assessed with a simple optical bench setup or an interferometer. However, this method cannot mimic the on-eye performance because the lenses are designed in relation to the physiological optics of the eye and not to a test bench. Assessment of corrective lenses in-conjunction with the image-forming capabilities of the human eye provides a more realistic appraisal of their actual performance and is often required in ophthalmic and vision science applications [1].
Schematic eyes or computer generated ray-tracing models are convenient and cost-effective methods for replicating the optical properties of normal eyes and pathologies, and as aids to developing and evaluating refractive corrections that improve image quality on the retina [2]. Several ray-tracing models have come to light over the last century, but only a few are closely similar to an average adult human eye, in both on- and off-axis aspects of optical performance [3–6]. It is arguable that even these cannot be used to directly test ‘off-the-shelf’ commercially available lenses. Instead, the measured or calculated geometry of the lenses is added to the optical schema for the evaluation of their optical performance. It is important to note that such calculations have to make some assumptions, particularly for rotationally asymmetric lenses; and hence the assessment would not always robustly emulate the real world scenario.
Physical model eyes offer the best alternative to address the shortcomings of the schematic models. The known examples of this approach can be divided into three groups based on their utility. First, those which are used to calibrate ophthalmic instruments; secondly, models which are used to exhibit basic eye functions for education and training; and finally, others that attempt to simulate selected optical characteristics of the natural eye either in combination with test lenses or otherwise. The first two groups comprise models which are either greatly enlarged anatomically or optically oversimplified (e.g. reduced eye with single refracting surface). Hence they are unsuited for any realistic evaluation. As the last kind is most optically relevant, they are often used for in-vitro experiments which include the ISO standard eye [7,8], cornea & IOL in a wet-cell type model [9,10]. While they perform well in evaluating IOLs, none are actually capable of testing soft CL due to their anatomic variance.
Recently, Shen and Thibos [11] developed a successor of their reduced physical model eye [12] with additional wide-angle capabilities for assessment of off-axis optical performance. Although this is the only current model with the capability of assessing and analyzing optical performance at a peripheral visual angle it has limitations in terms of its ability to truly represent real world vision due to the simplified geometrical design. In surveying the capabilities and limitations of the various model eyes developed to date, it is apparent that maximum utility will be obtained from a device that has substantially the same key dimensions as a natural, average human eye. Thus, real spectacle, contact or intra-ocular lenses can be fitted in their correct locations and various defects or aberrations accurately simulated, both on and off the optical axis.
With this as our target we set out to fabricate a wide-angle, bench-top, physical, model eye that closely replicates its average, human, adult counterpart, both anatomically and optically. Additionally, we attempted to incorporate variables like age, refractive error, pupil size, and accommodation as well as the possibility of assessing peripheral visual function into the eye model. This manuscript presents the optical design parameters of the developed physical model eye together with results from the on and off-axis optical quality validation. Finally we demonstrate the optical performance of some soft multifocal contact lenses when tested in conjunction with the model eye.
2. Schematic eye modeling
Previous schematic eye models were [3–5] critically reviewed using Zemax [13]. All the models were replicated to examine their aberration characteristics, image quality metrics, and peripheral refraction profiles. The results were compared with published in-vivo data. The finite model eyes proposed by Atchison, Liou-Brennan and Navarro-Escudero were found to closely mimic the average human eye, in terms of both on- and off-axis optical performances [6].
The models proposed by Liou-Brennan [3] and Atchison [5] have incorporated gradient refractive distribution for the lenticular component, as in the real eye. One other recent wide-angle, age-dependent, gradient-index, schematic model eye worth mentioning was proposed by Goncharov and Dainty [14], which proved to be a good starting point for constructing personalized eye models [15]. The fabrication of such a material into a lens imposes a practically complex task. Hence, we considered the Navarro-Escudero model to be our baseline model. Due to the limitations in material choice for manufacturing the refractive elements, and additionally, to account for dependencies like age, accommodative function, refraction and aberration profiles; the baseline model required further fine-tuning of certain parameters, before it took shape of a physical model eye.
Starting from the baseline, age-related, refractive-error dependent, average adult human schematic eyes with discrete levels of accommodation and pupil sizes were remodeled. The remodeling was based on published literature on unaccommodated and accommodated emmetropic eyes [3,4], refractive error dependent models [5], corneal, and lens shapes and their respective changes with age & accommodation [16–21], using the in-vitro lenticular refractive distribution [22] and with information from several peer-reviewed studies on the ocular wavefront aberrations and their changes with age, refractive error & accommodation [23–26].
Although anterior corneal radius is significantly correlated with the level of ametropia, the axial length or vitreous chamber depth is still considered the major cause of refractive error [27]. Hence, our modeling considered the errors to be completely axial in nature. For the cornea, a radius of 7.75 mm was used with asphericity (Q) of −0.25, concurrent with previous studies [16,28]. A value of 6.40 mm was used for the posterior corneal radius. Dubbelman et al [21] have found that the posterior corneal asphericity (Q) flattens with increase in age and based on this work Q values of −0.20, −0.40 were derived for 25- and 45-year old corneas respectively. The central corneal thickness was kept constant at 0.55 mm. The anterior chamber (AC) depth is dependent on age and accommodation. Two AC depths, 3.20 and 3.00 mm, were used for 25- and 45-year old models, respectively; in agreement with previous studies [29,30]. The pupil plane was 0.45 mm in front of the anterior vertex of the lenticular surface with an iris 0.25 mm thick. The space between the back of the iris plane and the anterior vertex of lens was made variable and modeled to linearly compensate for the increase in lens thickness with age and/or accommodation.
It is known that the lens increases its protein concentration with ageing, bringing with it an increase in RI of the lens core. Dubbelman et al [17–20] have studied refractive distribution of the crystalline lens, and proposed that with age, the equivalent RI of the lens decreases slightly, to optically compensate for the reduction of radii of curvature of the lenticular surfaces. An equivalent RI of 1.429 and 1.423, derived from the age-dependent equation proposed by Dubbelman and colleagues and were used for modeling 25- and 45-year old crystalline lenses. The 25-year old eye was modeled to have three accommodative states [0.00, 1.50 and 3.00 D], while the 45 year old had four distinct accommodation levels from 0 to 1.50D in steps of 0.50D.
Spherical aberration (SA) and coma are the most important ocular aberrations after defocus and astigmatism. The distribution of SA and coma in the relaxed eye is in good agreement across all major studies, with mean RMS being about 0.10 μm, for an average 6 mm pupil in each case. It is agreed that the magnitude of SA tends to decrease with increasing accommodation, especially in young eyes less than 20 years of age [24]. Above 35 years however, SA remains relatively constant with accommodation [25]. The 25 year old emmetropic model was modeled to have 0.075 μm, while the 45 year old was aimed to have 0.10 μm of SA at 6 mm pupil. For coma there is no systematic change with accommodation for young adults; but in the elderly it tends to increase, even with the smaller residual amount of accommodation [25]. With the optical axis of the eye shifted to 5° temporal the above model eye acquired horizontal coma of about 0.075 μm. The RMS of higher order aberrations, 3rd to 6th order, were in the magnitude of 0.10 and 0.125 μm for 25- and 45-year old emmetropic models respectively. Due to the discrepancies within the subjects and studies on the change in aberration profiles with accommodation [25,31,32], we have modeled aberration profiles to be constant over the range of accommodative levels.
For every accommodative state described, the standard aberration profile at 6 mm pupil diameter was made the target merit function, for emmetropic state. The lenticular components or surface radii, asphericity and central thickness are largely dependent on age and accommodation [17–20]. Hence, they were considered to be variables in Zemax, for a damped, least-squared optimization algorithm. Furthermore, the values obtained from linear equations proposed by Dubbelman and colleagues were used as the boundary operands [17–20]. Further, the vitreous chamber depth was made variable to include various levels of ametropia, ranging from + 4.00D to −10.00D. This modeling produced an age-related, accommodative and refractive-error dependent model eye, whose generalized description can be seen in Table 1 .
Table 1. Physical model eye configurations as a function of accommodation (A) and refractive error (RE), in diopters.
The measures in square brackets exclusively represent 45 year models; while the remaining parameters are common for both 25- and 45year models. The 25 year old eyes had 3 accommodative states [0, 1.50 & 3.00D], while 45 year ones had 1.50D of partial accommodation, in steps of 0.50D. The linear equation of vitreous chamber depth holds true over a range of refractive errors, −9.00D to + 3.00D. The 25year emmetropic model had 0.075 µm spherical aberration, while 45year ones had 0.10 µm at 6 mm pupil. The fovea, if shifted 5 degrees away from the optical axis induces horizontal coma of 0.075 µm at 6 mm pupil.
Two of the modeled parameters of the schematic eye, namely asphericities of the posterior cornea (−0.40), and anterior lens (−4.50), were found to be slightly larger than the experimental findings [33,34]. Yet these choices could be justified due to the use of a constant refractive index for the lens; because a homogenous lens puts additional constraints on all the surfaces, to provide realistic aberration levels, both on-axis and in the peripheral field.
3. Physical model eye development
Figure 1 illustrates the mechanical layout of the developed physical model eye designed in AutoCAD. All its body parts were machined from aluminum and anodized black to prevent corrosion and minimize stray light reflections. The following sub-sections describe the model eye set-up in detail.
Fig. 1 A simplified mechanical layout of the developed physical model eye presented with three test channels. Channel 1 includes a moveable visual display unit. Channel 2 consists of optical bench set-up for single-pass measurements. The light is first attenuated with neutral density filter (ND), further spatially filtered using a microscopic objective (SF) (8mm EFL), and 50µm pinhole; and collimated with achromatic doublet L1 (250mm EFL). Channel 3 is used for double-pass measurements via COAS aberrometer. A relay system consisting L2 and L3, 125mm EFL each, is used to increase the working distance of aberrometer.
3.1. Description of the physical model eye
The model eye consists of a vertical back plate, rigidly fixed perpendicular to a horizontal base. Two micro-positioning stages, translation (M111.1DG) and rotation (M116.DG), (Physik Instrumente, Karlsruhe, Germany) form the motor base. The rotary stage is mounted onto the vertical back plate with its pivoting axis lying horizontally. The translation stage is mounted on the rotary stage, such that, in its zero position, it provides vertical movement to the photo detector assembly, which is attached via an L shaped bracket. The axis of the rotary stage always passes through the nodal point. This lies at the vertex of the posterior lenticular surface of the model eye irrespective of the eyeball length, which is determined by the linear stage position. The mounting ring (M) holds all the components of the anterior segment (A) and is rigidly attached to the back plate. A removable mirror is mounted just above the anterior segment and optically folds the visual axis to a more convenient horizontal direction.
3.2. The cornea, sclera and lenticular components
The required geometrical shapes of cornea and crystalline lenses were determined from schematic modeling as described in the previous section. The manufacturability was critically analyzed with respect to achievable tolerance levels. The corneas were lathed from a flouro-polymer having RI of 1.376, while the crystalline lenses were diamond turned from commercially available Boston RGP polymers, EO and Equalens II, which had RI’s of 1.423 and 1.429 respectively. These two materials served to model crystalline lenses of the two different age groups. As both the EO and Equalens II materials possess a blue tint, overall light transmission fell by 20%, however with no relative spectral differences. All the polymers selected had less than 1% saline re-absorption. The finished corneas were bonded into lathed scleral rings of 12 mm radial curvature and 18 mm outside diameter, while the crystalline lenses were mounted in metal rings to facilitate handling.
3.3. The aqueous and vitreous chambers
The anterior chamber (A) of the model eye included an optically realistic cornea, iris/pupil and crystalline lens. The ‘back end’ of the model eye did not have a physically accurate vitreous chamber (V), as there was no conventional retinal surface. Instead, the vitreous chamber was formed by a flexible, light-proof, bladder enclosing the entire posterior segment. The bladder was sealed at its top to mounting ring (M) and at its bottom to the horizontal portion of the ‘L’ shaped arm. This allowed the retina to be axially positioned relative to the cornea and lens, while retaining the liquid in the chamber that simulates vitreous humor of the natural eye. The volume and pressure of the entire liquid in the posterior chamber was controlled by a piston pump. De-ionized, purified water, with RI of 1.334, served as aqueous and vitreous humor. The irises of the model eye were machined as thin aluminum discs with a tapered hole in the centre of about 250 µm edge thickness. They were made in 5 pupil diameters, ranging from 2 to 6 mm, in 1 mm steps. The three modular components of the anterior segment are slotted into the mounting ring (M), sealed and secured with a locknut.
3.4. The ‘acting’ retina and ‘virtual’ retinal plane
The monochromatic, complimentary metal oxide semi-conductor (CMOS) sensor of a PixeLink (PL B777F) firewire camera served as the retina. Sensor dimensions were 5.76 x 4.29 mm, and its resolution was 5 mega pixels with 2.2 µm pixel pitch and a bit depth of 12. The pixel pitch is similar to the center-center separation between adjacent foveal cones in the human eye of about 2.4 µm [35]. The sensor is mounted on motorized translation and rotary stages. Linear movement up to 6 mm allowed simulation of ametropia, from approximately + 3.00D to −16.00D. Angular movements, pivoting around the nodal point of the eye, can be used to assess optical performance at any peripheral visual field angle up to 35°, as well different angles kappa of the visual axis. The locus of the selected retinal contour is referred as the ‘virtual’ retinal plane.
3.5 The tracking camera unit
An integrated camera unit (DinoLite AM413TL) was arranged exactly above the model eye in line with the optical axis to record an image of a test CL placed on the cornea. Information about the fit, centration and meridional orientation of the test CL can be obtained in this way. This is of particular advantage where test lenses have significant power variations across their optical zones, such as concentric and translating bifocal, multifocal, or toric CL. The folding mirror would normally be removed when using the tracking camera unit.
3.6. The humidifying chamber
The anterior segment (A) of the model eye is covered by a flat glass window (H). This acts as a humidity chamber to minimize the evaporation rate of soft contact lenses. To prevent condensation and fogging of the window, a heating coil was integrated into the glass window to warm it up to around 50°C. A magnified overview of the anterior chamber of the model eye shows the humidity chamber, cornea and sclera can be seen in Fig. 2 .
Fig. 2 A snapshot of the constructed physical model eye. A magnified overview of the anterior chamber of the model eye shows the humidity chamber, cornea and sclera. The individual elements including cornea and crystalline lens are also shown in highlighted subsection.
3.7 Software development and working of the model eye
The Matlab platform was used to develop the complete control software. This custom-written software features a graphical user interface to control all functions of the instrument, such as 2D positioning of the photo-active device, operations of both tracking and retinal camera, collection and analyses of image data, and storage of the results in the user selected database.
3.8. The methods of optical quality assessment
The assessment of optical performance of either a model eye configuration or a test lens in conjunction with the eye can be studied in detail using both single and double-pass techniques. The performance via single-pass can be predicted in two ways, as shown in the model eye work-station (first two channels of Fig. 1).
The first method emulates standard visual acuity testing using a logMAR chart. This is presented on a visual display unit positioned at a given distance from the model eye. Light from the chart is directed by the folding mirror axially into the eye, generating the image on the retinal plane. 10 such image frames are averaged, subtracted from background image and normalized. The resultant images can further be considered for detailed analysis to predict the expected acuity.
The second method (channel 2, Fig. 1) quantitatively analyses the optical function using an optical bench set-up. Light from the laser source (HeNe 632.8 nm) is first attenuated with neutral density filter (ND), further spatially filtered using a microscopic objective (8mm EFL) and 50 µm pin hole and the collimated laser beam (using achromat L1 of 250mm EFL) is projected into the eye. The spot image is captured (average of 10 frames), transformed and analysed in the Fourier domain to obtain the optical transfer function. The object vergence can be varied by placing additional lenses into the system. In both cases, the retinal detector and the model eye can be rotated away from the on-axis position for analyzing the optical performance at any peripheral visual angle up to 35°.
By placing a diffuse reflecting surface in the retinal plane, evaluation of the model eye, or any test lens, can also be performed by the double-pass technique, with the addition of an auto-refractor or wavefront aberrometer positioned in front of the eye, as depicted in channel 3 of Fig. 1. This approach is particularly useful to cross-validate measurements with those from human eyes, as the same instrument can be used to obtain results on lower and higher order aberrations.
4. Optical quality of the developed model eye
The developed physical model eye was successful in retrieving single-pass images of the real world objects and also permitted double-pass analysis using a COAS wavefront aberrometer (Wavefront sciences, Inc.). The validation of the model eye was performed, for all configurations with different combinations of pupil sizes and accommodation levels. However, for brevity, we select and present the optical quality of one subset configuration of the model eye (unaccommodated 25 year old) in the subsequent sections.
4.1 Gaussian properties of the selected configuration
The total power of the selected configuration was about + 62.00D with an axial length of 24.3 mm. With the effective corneal power close to + 45.00D; the magnification of the entrance pupil was about 1.13 times physical size and about 0.35mm ahead of its actual position. The change in refractive error for a 1mm change in vitreous chamber depth was approximately 2.85D, although this was not perfectly linear for large amounts of myopia (>6.00D). The angle subtended in the object space by every pixel on the ‘acting’ retina was about 0.4 arc minutes.
4.1 On-axis monochromatic aberrations
Although the initial aim was to make a completely rotationally symmetric system, low levels of astigmatism of up to 0.50D were seen in this configuration. The topographies of the individual surfaces suggest that this was mainly caused by the anterior cornea. Engravings on the cornea and lens holders assisted in improving the repeatability of rebuilding the system so that the cylindrical axis remained constant. With a maximum astigmatism of less than 0.50D, we generally worked at the position of the smallest circle of confusion for our performance evaluation.
Although spherical aberration and horizontal coma were the only two Zernike aberrations modeled for all the configurations of the model eye, the actual aberration profiles were found to have other higher order terms. These included vertical C (3,1), secondary coma C(5, ± 1) and secondary spherical aberration C (6,0), but, as illustrated in Fig. 3 , all were less than 0.025 µm at a 6 mm pupil.. The expected RMS of HOA for a 6 mm pupil was 0.09 µm compared with 0.17 µm in the actual device. Although double the modeled value, the measures are well within the range commonly seen for an average adult eye.
Fig. 3 Wavefront aberration contour plots of a subset configuration a) the expected model eye and b) the actual physical model eye built.
4.2 On-axis chromatic aberrations
The change in refraction as a function of wavelength and longitudinal chromatic aberration profile (LCA) for the selected configuration of the developed model eye is shown in Fig. 4 . Physical model eye measures were compared with previous schematic model eyes and some real eye data. Calculations were performed at a reference wavelength of 580 nm.
Fig. 4 Chromatic shifts in refraction (D) relative to a reference wavelength of 580 nm for the physical model eye, selected schematic models and real eyes.
The measures for Navarro-Escudero, Liou-Brennan and Atchison schematic eye models were reproduced from a previous report [6]; while the real eye profile was derived from the data of Bedford & Wyszecki [36]. The chromatic refraction of the physical eye was performed using interference filters of known wavelength and bandwidth in conjunction with a while light source.
The in-focus measures of the white light target as viewed by the photo-active sensor of the physical model eye configuration through four filters [430, 510, 630 and 700 nm], were objectively assessed. These values were use to extrapolate the overall trend over the entire visible spectrum from 420 nm to 760 nm.
The Navarro-Escudero and Atchison models produced LCA of about 2.00, and 2.50 D respectively, in agreement with the real eye data [36]. Liou-Brennan assumed that all ocular media have similar dispersive properties to water and their model predicted a lower LCA of approximately 0.75 D. The physical model eye produced about 1.45D of longitudinal chromatic aberration, slightly lower than the designed 2.25D for this particular age configuration.
4.2 Through-focus point spread function and Fourier domain analysis
We measured the image quality of the selected configuration using point spread and modulation transfer functions (MTF), at a pupil diameter of 4mm. As expected, the results, shown in Fig. 5 , reveal a consistent decrease in MTF as a function of both directions of defocus. Interestingly, for some spatial frequencies the MTF obtained on the hyperopic defocus is slightly better than the same magnitude of myopic defocus. The PSF of the in-focus state subtended 5 arc min in visual space while that of defocused eye spread up to 30 min of arc.
Fig. 5 Through-focus point spread functions captured at the retinal plane by photoactive sensor and their respective radially averaged modulation transfer functions of one subset configuration of the model eye (unaccommodated 25 year old), at 4 mm pupil diameter.
4.2 Off-Axis point spread and modulation transfer functions
Image quality of the selected model eye configuration was also analysed as a function of various retinal eccentricities for a 5mm pupil. The PSF’s, portrayed in Fig. 6 , show the increasing influence of horizontal coma in the peripheral retina (eccentricity ≥15°). This may partly be due to the relative misalignment of the pupil. The PSF on the optical axis was about 7 arc minutes in size; while the measures obtained at 30 degrees of peripheral retina was 33 arc minutes wide. A consistent increase in the PSF area and corresponding decrease in area under the MTF curve, as a function of retinal eccentricity can be observed in Fig. 7 .
Fig. 6 Point spread functions of the 25-year old unaccommodated model eye configuration captured in the ‘virtual’ retinal space (imaged by photoactive sensor) for retinal eccentricities from 0° to 30°, at 5mm pupil diameter.
Fig. 7 Radially averaged modulation transfer functions of the 25-year old unaccommodated model eye configuration calculated in the ‘virtual’ retinal space for retinal eccentricities from 0° to 30°, at 5mm pupil diameter.
4.3 Optical performance with multifocal contact lens designs
To illustrate a potential use of the developed physical model eye, we performed some preliminary analysis on several marketed soft CL. Four test lenses: a single vision CL (Rx: −2.00 D), two center-near and one center-distant type multifocal CL’s (Rx: −2.00 D / + 2.50 D add) were used to correct −2.00 D of axial myopia at 4 mm pupil diameter. Although evaluation was performed by using both the optical transfer function and visual acuity charts, the obtained retinal images of the vision chart provide a more realistic measure and appreciation of the problems associated with multifocal CL wear and only those results are presented.
In Fig. 8 , the images captured by the CMOS sensor at the retinal plane are shown for a target visual acuity chart presented at 40 cm test distance. All the lenses were well centered except for 8 (E), which was deliberately decentered horizontally by 0.5 mm, as guided by the tracking camera. The last line of the chart is 6/6 Snellen equivalent.
Fig. 8 Images of the visual acuity charts presented at 40 cm, captured at the retinal plane of the model eye configured as a −2.00 D (myope with no accommodation) with 4-mm pupil diameter. The first column (A) of the image montage was obtained from the uncorrected myopic model; while the rest were obtained via CL correction (B) well-centered single vision CL (−2.00 D) (C) well centered, center-near, high-add ( + 2.50 D) multifocal CL 2 (D) well centered, center-near, high-add ( + 2.50 D) multifocal CL 3 (E) a center-distant, high-add ( + 2.50 D) multifocal CL 4, decentered by 0.50 mm.
The physical model eye was able to differentiate the performance of the different multifocal CL tested. In spite of the fact that 8(C) and 8(D) of the resultant image montage were obtained with center-near, multifocal CLs with same add power, a difference can be visually detected in the magnitude of contrast loss within the designs, 8 (D) suffered higher contrast loss than 8 (C). On careful observation, a halo effect can be perceived with 8 (D) and ghosting of the individual letters with 8 (E) when the CL was deliberately decentered. Both haloes and ghosting are often reported as visually disturbing experiences by multifocal CL wearers [37].
5. Discussion
We have designed, and developed, an anatomically and optically equivalent bench-top model eye, that is representative of the average human adult eye and suitable for testing of the on- and off- axis performance of contact, spectacle and intraocular lenses. All the parameters of the model eye are substantially life size. The developed model eye has been validated for a range of configurations, with different pupil sizes and accommodative states and has presented in detail the on and off-axis optical quality of one subset configuration, including its on-axis chromatic aberration profile.
The finished model eye has slightly higher levels of astigmatism and coma than expected, but is still well within the range of an average adult eye. A slight toricity in the cornea is cause for the astigmatism, while the higher order aberrations are due to inaccuracies in the alignment and centration of all the optical elements.
Dehydration of soft contact lenses can quickly lead to distortions in shape and degradation of the optical imaging quality. To evaluate the efficacy of the humidity chamber (HC), we measured the optical performance of three different CL’s with and without use of the HC. A time-dependent change in the MTF was considered as a gauging factor. The average time period lapse before an optically significant change occurred was approximately 8-12 seconds and this increased to 24-30 seconds with the HC. Minor differences were seen between the lens types and materials tested. The humidity chamber was successful in retaining the moisture within and around the contact lens. The integrated heating prevented fogging of the window.
When working with contact lenses, the tracking camera was useful and indispensable to confirm centration or deliberate decentration. Attempts to automatically detect the edge of the contact lens failed due to the low contrast of the lens edge against the dark sclera background. Instead, a manual method was implemented whereby the lens center was calculated from several points along a projected image of the lens edge that were selected by the operator.
It is debatable whether the use of a plane surface (photoactive device) in generating the virtual retinal arc leads to significant error. However, it is important to bear in mind that only a very small area (< 500x500 µm) of the detector is used when assessing either the optical transfer function or wavefront aberrations. Thus the utilized region of the sensor is closely planar. Assuming an average retinal curvature of 12 mm, the sag difference is only 2.6 µm.
If only rotation about the nodal point of the eye is used for the evaluation of the peripheral optical performance, then the radius of curvature of the virtual retina cannot be controlled, and will always be dependent on the distance from nodal point to the image sensor plane. However, one could simulate any desired retinal locus with specific radius of curvature and asphericity, by using the translatory stage as another degree of freedom, facilitated by its compensatory linear movements.
It should be remembered that real eyes are not centered systems. The visual axis connects the fovea and the object of regard through the nodal points, and it is usually tilted away from the pupillary axis (i.e. line normal to the cornea and passing through center of the entrance pupil) by about 5° temporally; commonly referred as angle ‘kappa’ [38]. Although we included this in our initial modeling in order to induce normal levels of coma-like aberrations, minor misalignments caused during the manufacturing processes caused the developed eye to already have higher order aberrations than the modeled horizontal coma and spherical aberration. Hence, angle ‘kappa’ was not incorporated in our actual measurements.
As a practical application, the optical performance of several soft multifocal CL was evaluated on the model eye in single pass mode. Not only was the performance within the different lens designs successfully differentiated, but common problems experienced and often reported by wearers, such as haloes and ghosting, were discernibly represented among the output data. Although it is inevitable that image contrast is lost with any simultaneous multifocal design, wearers may have individual preferences for, or tolerances to, particular types of optical compromise and would benefit from this detailed analysis. Being able to visualize the image as it would appear on the retina of a typical eye when projected through a particular vision correction device provides a bridge between predictions of performance based on optical theory and the actual visual experience. Design provisions in the current device allow similar evaluations to be made with other ophthalmic correction modalities, such as spectacle and intra ocular lenses. However, it is necessary to bear in mind that the built physical model eye only mimics the optical performance. The actual psychophysical effects contributing to the visual performance have to be included only via assessing the neural transfer function [39].
With the recent increased interest in the role of peripheral visual stimuli in the progression of myopia [40–46], we envisage that the ability of this model eye to assess the optical performance in off axis positions will be a useful attribute. Peripheral refraction can be performed out to +/− 35° in the peripheral retina. In the more commonly used visual field angle terminology this is approximately equivalent to +/− 40°. Using the single pass PSF method, tangential and sagittal focus planes can be accessed easily and accurately to assess the effectiveness of the “myopia control” design features of the corrective lenses.
6. Limitations of the physical model eye
The current model eye has reproduced the expected levels of optical performance relative to an average human adult eye, and demonstrated potential as an excellent tool to gauge performance characteristics of various vision correction devices. However, there are a few drawbacks associated with its use, as discussed below.
- a) Unlike in the physical model eye, the wavelength selective photoreceptors reside at different locations of the retina in a real eye. This dissimilarity would directly affect the longitudinal chromatic aberration measurements. This is of particular importance for the accurate evaluation of diffractive intra-ocular lenses with intrinsic chromatic aberration with use of the developed model eye.
- b) While evaluating performance at various retinal eccentricities, the use of channels 2 and 3 should be preferred to channel 1, because imaging extended objects, like visual acuity charts, on a flat detector is likely to induce defocus in the periphery due to the lack of field of curvature.
- c) The current physical model eye has been proved suitable for generic test cases that give a broad idea of the optical performance characteristics with various vision correction devices. Nevertheless, they could still be considered inferior to the concept of having personalized (subject-specific) physical model eyes may be more rigorous in situations where it is desired to test ‘off-the-shelf’ lenses.
7. Conclusion
In summary, we developed and constructed an age-related, refractive error dependent, average human physical model eye having discrete amounts of accommodation, over a range of pupil sizes. This bench-top model eye closely replicates both anatomical and optical properties of the average, real, human eye. We validated all the available configurations to suit normal viewing conditions, and presented in detail the on- and off axis optical quality of one of its subset configurations. Subsequently we demonstrated its potential use in testing commercially available contact lenses. The vision chart images produced by the model eye reflect aspects of visual experiences described by contact lens wearers and allow differentiation between the optical performances of various lens types.
Acknowledgements
This research was supported by postgraduate scholarships from the University of NSW, Sydney, Australia and the Brien Holden Vision Institute, Sydney, Australia to the first author (RCB). RCB was also a recipient of William. C. Ezell fellowship from the American Optometric Foundation and postgraduate research awards from the Cornea and Contact Lens Society of Australia. The authors sincerely thank Mr. Colm Dolphin for his assistance in manufacturing the fragile, miniature components of the model eye. Parts of this work have been presented at SPIE BiOS, San Jose, USA in 2009. The intellectual property of the model eye is protected with a provisional patent application (PCT/AU2009/000791).The authors would like to extend their thanks to the anonymous reviewers, for their valuable comments on the earlier version of the manuscript.
References and links
1. S. Patel, M. Fakhry, and J. L. Alió, “Objective assessment of aberrations induced by multifocal contact lenses in vivo,” CLAO J. 28(4), 196–201 (2002). [PubMed]
2. W. Donnelly 3rd, “The Advanced Human Eye Model (AHEM): a personal binocular eye modeling system inclusive of refraction, diffraction, and scatter,” J. Refract. Surg. 24(9), 976–983 (2008). [PubMed]
3. H. L. Liou and N. A. Brennan, “Anatomically accurate, finite model eye for optical modeling,” J. Opt. Soc. Am. A 14(8), 1684–1695 (1997). [CrossRef]
4. I. Escudero-Sanz and R. Navarro, “Off-axis aberrations of a wide-angle schematic eye model,” J. Opt. Soc. Am. A 16(8), 1881–1891 (1999). [CrossRef]
5. D. A. Atchison, “Optical models for human myopic eyes,” Vision Res. 46(14), 2236–2250 (2006). [CrossRef] [PubMed]
6. R. C. Bakaraju, K. Ehrmann, E. Papas, and A. Ho, “Finite schematic eye models and their accuracy to in-vivo data,” Vision Res. 48(16), 1681–1694 (2008). [CrossRef] [PubMed]
7. ISO11979–2, “Ophthalmic implants-Intraocular lenses-Part 2: optical properties and test methods,” (International Organization for Standardization, 1999).
8. S. Norrby, P. Piers, C. Campbell, and M. van der Mooren, “Model eyes for evaluation of intraocular lenses,” Appl. Opt. 46(26), 6595–6605 (2007). [CrossRef] [PubMed]
9. P. G. Gobbi, F. Fasce, S. Bozza, and R. Brancato, “Optomechanical eye model with imaging capabilities for objective evaluation of intraocular lenses,” J. Cataract Refract. Surg. 32(4), 643–651 (2006). [CrossRef] [PubMed]
10. S. Pieh, W. Fiala, A. Malz, and W. Stork, “In vitro strehl ratios with spherical, aberration-free, average, and customized spherical aberration-correcting intraocular lenses,” Invest. Ophthalmol. Vis. Sci. 50(3), 1264–1270 (2008). [CrossRef] [PubMed]
11. J. Shen and L. N. Thibos, “Measuring ocular aberrations and image quality in peripheral vision with a clinical wavefront aberrometer,” Clin. Exp. Optom. 92(3), 212–222 (2009). [CrossRef] [PubMed]
12. L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31(19), 3594–3600 (1992). [CrossRef] [PubMed]
13. ZEMAX, “Focus Software Inc,” (Bellevue, WA, USA, 2009).
14. A. V. Goncharov and C. Dainty, “Wide-field schematic eye models with gradient-index lens,” J. Opt. Soc. Am. A 24(8), 2157–2174 (2007). [CrossRef]
15. A. V. Goncharov, M. Nowakowski, M. T. Sheehan, and C. Dainty, “Reconstruction of the optical system of the human eye with reverse ray-tracing,” Opt. Express 16(3), 1692–1703 (2008). [CrossRef] [PubMed]
16. M. Dubbelman, V. A. Sicam, and G. L. Van der Heijde, “The shape of the anterior and posterior surface of the aging human cornea,” Vision Res. 46(6-7), 993–1001 (2006). [CrossRef]
17. M. Dubbelman and G. L. Van der Heijde, “The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox,” Vision Res. 41(14), 1867–1877 (2001). [CrossRef] [PubMed]
18. M. Dubbelman, G. L. van der Heijde, and H. A. Weeber, “The thickness of the aging human lens obtained from corrected Scheimpflug images,” Optom. Vis. Sci. 78(6), 411–416 (2001). [CrossRef] [PubMed]
19. M. Dubbelman, G. L. Van der Heijde, and H. A. Weeber, “Change in shape of the aging human crystalline lens with accommodation,” Vision Res. 45(1), 117–132 (2005). [CrossRef]
20. M. Dubbelman, G. L. Van der Heijde, H. A. Weeber, and G. F. Vrensen, “Changes in the internal structure of the human crystalline lens with age and accommodation,” Vision Res. 43(22), 2363–2375 (2003). [CrossRef] [PubMed]
21. M. Dubbelman, H. A. Weeber, R. G. van der Heijde, and H. J. Völker-Dieben, “Radius and asphericity of the posterior corneal surface determined by corrected Scheimpflug photography,” Acta Ophthalmol. Scand. 80(4), 379–383 (2002). [CrossRef] [PubMed]
22. C. E. Jones, D. A. Atchison, R. Meder, and J. M. Pope, “Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI),” Vision Res. 45(18), 2352–2366 (2005). [CrossRef] [PubMed]
23. I. Brunette, J. M. Bueno, M. Parent, H. Hamam, and P. Simonet, “Monochromatic aberrations as a function of age, from childhood to advanced age,” Invest. Ophthalmol. Vis. Sci. 44(12), 5438–5446 (2003). [CrossRef] [PubMed]
24. H. Cheng, J. K. Barnett, A. S. Vilupuru, J. D. Marsack, S. Kasthurirangan, R. A. Applegate, and A. Roorda, “A population study on changes in wave aberrations with accommodation,” J. Vis. 4(4), 272–280 (2004). [CrossRef] [PubMed]
25. H. Radhakrishnan and W. N. Charman, “Age-related changes in ocular aberrations with accommodation,” J. Vis. 7(7), 11–21, 1–21 (2007). [CrossRef] [PubMed]
26. L. N. Thibos, X. Hong, A. Bradley, and X. Cheng, “Statistical variation of aberration structure and image quality in a normal population of healthy eyes,” J. Opt. Soc. Am. A 19(12), 2329–2348 (2002). [CrossRef]
27. N. A. McBrien and D. W. Adams, “A longitudinal investigation of adult-onset and adult-progression of myopia in an occupational group. Refractive and biometric findings,” Invest. Ophthalmol. Vis. Sci. 38(2), 321–333 (1997). [PubMed]
28. S. A. Read, M. J. Collins, L. G. Carney, and R. J. Franklin, “The topography of the central and peripheral cornea,” Invest. Ophthalmol. Vis. Sci. 47(4), 1404–1415 (2006). [CrossRef] [PubMed]
29. D. A. Atchison, E. L. Markwell, S. Kasthurirangan, J. M. Pope, G. Smith, and P. G. Swann, “Age-related changes in optical and biometric characteristics of emmetropic eyes,” J. Vis. 8(4), 29–1–20 (2008). [CrossRef] [PubMed]
30. M. Dubbelman, R. G. van der Heijde, and H. A. Weeber, “Comment on “Scheimpflug and high-resolution magnetic resonance imaging of the anterior segment: a comparative study”,” J. Opt. Soc. Am. A 22(6), 1216–1218, discussion 1219–1220 (2005). [CrossRef]
31. N. López-Gil, V. Fernández-Sánchez, R. Legras, R. Montés-Micó, F. Lara, and J. L. Nguyen-Khoa, “Accommodation-related changes in monochromatic aberrations of the human eye as a function of age,” Invest. Ophthalmol. Vis. Sci. 49(4), 1736–1743 (2008). [CrossRef] [PubMed]
32. S. Plainis, H. S. Ginis, and A. Pallikaris, “The effect of ocular aberrations on steady-state errors of accommodative response,” J. Vis. 5(5), 466–477 (2005). [CrossRef] [PubMed]
33. V. A. Sicam, M. Dubbelman, and R. G. van der Heijde, “Spherical aberration of the anterior and posterior surfaces of the human cornea,” J. Opt. Soc. Am. A 23(3), 544–549 (2006). [CrossRef]
34. G. Smith, D. A. Atchison, D. R. Iskander, C. E. Jones, and J. M. Pope, “Mathematical models for describing the shape of the in vitro unstretched human crystalline lens,” Vision Res. 49(20), 2442–2452 (2009). [CrossRef] [PubMed]
35. C. W. Oyster, The Human Eye; Structure and Function (Sinauer Associates, Sunderland, MA 1999). [PubMed]
36. R. E. Bedford and G. Wyszecki, “Axial chromatic aberration of the human eye,” J. Opt. Soc. Am. 47(6), 564–565 (1957). [CrossRef] [PubMed]
37. E. S. Bennett, “Contact lens correction of presbyopia,” Clin. Exp. Optom. 91(3), 265–278 (2008). [CrossRef] [PubMed]
38. D. A. Atchison, and G. Smith, Optics of the Human Eye (Butterworth-Heinemann, Oxford, 2000).
39. E. Dalimier and C. Dainty, “Use of a customized vision model to analyze the effects of higher-order ocular aberrations and neural filtering on contrast threshold performance,” J. Opt. Soc. Am. A 25(8), 2078–2087 (2008). [CrossRef]
40. D. A. Atchison, N. Pritchard, S. D. White, and A. M. Griffiths, “Influence of age on peripheral refraction,” Vision Res. 45(6), 715–720 (2005). [CrossRef] [PubMed]
41. R. C. Bakaraju, K. Ehrmann, A. Ho, and E. B. Papas, “Pantoscopic tilt in spectacle-corrected myopia and its effect on peripheral refraction,” Ophthalmic Physiol. Opt. 28(6), 538–549 (2008). [CrossRef] [PubMed]
42. R. Calver, H. Radhakrishnan, E. Osuobeni, and D. O’Leary, “Peripheral refraction for distance and near vision in emmetropes and myopes,” Ophthalmic Physiol. Opt. 27(6), 584–593 (2007). [CrossRef] [PubMed]
43. W. N. Charman and J. A. Jennings, “Longitudinal changes in peripheral refraction with age,” Ophthalmic Physiol. Opt. 26(5), 447–455 (2006). [CrossRef] [PubMed]
44. W. N. Charman, J. Mountford, D. A. Atchison, and E. L. Markwell, “Peripheral refraction in orthokeratology patients,” Optom. Vis. Sci. 83(9), 641–648 (2006). [CrossRef] [PubMed]
45. J. Tabernero and F. Schaeffel, “Fast scanning photoretinoscope for measuring peripheral refraction as a function of accommodation,” J. Opt. Soc. Am. A 26(10), 2206–2210 (2009). [CrossRef]
46. J. Tabernero, D. Vazquez, A. Seidemann, D. Uttenweiler, and F. Schaeffel, “Effects of myopic spectacle correction and radial refractive gradient spectacles on peripheral refraction,” Vision Res. 49(17), 2176–2186 (2009). [CrossRef] [PubMed]
