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Abstract
Many myopia control methods based on the peripheral defocus theory have emerged towards applications in recent years. However, peripheral aberration is a critical issue, which is still not well-addressed. To validate the aberrometer for peripheral aberration measurement, a dynamic opto-mechanical eye model with a wide visual field is developed in this study. This model consists of a plano-convex lens representing cornea (f’ = 30 mm), a double-convex lens representing crystalline lens (f’ = 100 mm), and a spherical retinal screen with a radius of 12 mm. To optimize the quality of spot-field images from the Hartman-Shack sensor, the materials and surface topography for the retina are studied. The model has an adjustable retina to achieve Zernike 4th item (Z4 focus) ranging from -6.28 µm to +6.84 µm. As for mean sphere equivalent, it can achieve -10.52 D to +9.16 D at 0° visual field and -6.97 D to +5.88 D at 30° visual field with a pupil size of 3 mm. To realize a changing pupil size, a slot at the back of the cornea mount and a series of thin metal sheets with 2, 3, 4, and 6 mm holes are generated. Both on-axis aberrations and peripheral aberrations of the eye model are verified by a well-used aberrometer and the eye model to mimic a human eye in a peripheral aberration measurement system is illustrated.
Published by Optica Publishing Group under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
1. Introduction
An opto-mechanical eye model, namely opto-mechanical artificial eye model, imitates the basic structure or basic imaging function of the human eye. It mainly consists of an artificial cornea, crystalline lens, an aperture as pupil, and a posterior retinal surface. The corneal lenses can be “on-shelf” optics for simplification or customized for a realistic imaging effect [1,2]. In some eye models for intraocular lens (IOL) testing, the crystalline lens can be replaced by a chamber filled with refractive index-matching liquid [3–5]. For retina, imaging sensor can be used alternatively for evaluating correction methods [2,6]. The appearance of eye models can be close to the real human eye [7,8], while others may be more like a system composed of various peripheral devices [2,9]. This is determined by physiological authenticity and functionality.
The applications of artificial eye model can be divided into three main categories. (1) The model can be used to evaluate vision correction through contact lenses [2,10–13], IOLs [14–17], and spectacle lenses [18–20] or even refractive surgery [21]. This kind of eye models generally incorporates an image sensor serving as a retina. Quantitively, point spread function and modulation transfer function can be calculated. Qualitatively, the imaging quality can be illustrated and analyzed. (2) It can be standards for calibration of ophthalmic instruments, such as aberrometers [22–25], retinal cameras [26–29], corneal topographers [30] and optical coherence tomography (OCT) [31]. (3) It is also an effective approach for demonstration, like eye movement [32] or education [33]. To obtain a continuous refraction or test the refractive dynamic range of ophthalmic instruments, the artificial eye model is expected to be dynamic. Two commonly used methods to achieve dynamic refractions are an adjustable axial length or a tunable crystalline lens. Tunable crystalline lenses are usually achieved by squeezing the liquid in a polymer film to change the shape of the lens [34,35]. In addition, dynamic focal lengths can also be realized by directly extruding solid polymers [36], and directly using liquid crystal lenses [37].
As the theory of myopia control based on peripheral defocus has been widely recognized in the industry in recent years, a new category of aberrometers designed for measuring peripheral aberrations has attracted a significant attention [38]. By far, three systems for peripheral aberration measurement are relatively accepted comparing with other lab-based apparatus, which are achieved in three approaches. Whole-field peripheral refraction scanning within a large eyepiece (WPRS) [39], multi-meridian scanning of peripheral refraction in multi-optical channels (SPR) [40], and fast peripheral wave-front sensor mounted on a scanning arm (FSWS) [41]. At validation phrase of the three instruments, WPRS used the trail lenses rather than a specially designed eye model. The trail lenses were set in a dedicated holder that allow itself to rotate to align the eccentric measurement. In contrast, SPR and FSWS have eye models to assess the accuracy. The eye model used by FSWS is a dynamic eye model for adaptive optics testing [37]. SPR employed an eye model with custom-designed peripheral refractions. However, both of the eye models need adjustment every time being measured at different angles [42]. All the three scanning instruments were not scanning when validation. Thus, a dynamic eye model with designed peripheral refraction that allow the instrument to scan when validation is demanded, thereby improving the efficiency of instrument validation.
In this study, a novel artificial eye model with dynamic refraction both on-axis and off-axis is proposed. This eye model can effectively validate aberrometers designed for peripheral refraction scanning. In addition, a retina surface manufacturing process is developed for a stable and reliable spot-field image captured by Hartmann-Shack (HS) wavefront senor, which assures the compatibility with all commercial aberrometers based on HS principle. The performance of the eye model is tested, which meets the requirements of wavefront sensing at peripheral visual field.
2. Optical and opto-mechanical design
2.1 Optical design
To design the eye model, three technical requirements were set in advance. (1) The refraction of the central visual field should be dynamic, and the mean spherical equivalent (M) range should cover -10 D to +10 D. Hence the aberrometer can be validated in a large dynamic range; (2) The peripheral field of view should range from -30° to +30°; (3) The size of the model should be comparable with the real human eye so that a commercial aberrometer can fit it for validation. To meet the above three requirements, this eye model allows a variable distance from the posterior surface of the lens to the retina to achieve dynamic diopter. As the retina moves, not only is the diopter of the central visual field dynamic, but the peripheral visual field also changes. However, the design is only for the central field of view, and the diopter of the peripheral field of view is derived accordingly. To make the model as correct as possible to the real physiological structure of the human eye, the Navarro schematic eye model is used as a blueprint [43], and then select the cornea and lens according to the optical component suppliers’ stock components and the feasibility of opto-mechanical assembly.
The optical components of the eye model include cornea, pupil, crystal lens and retina. The two optical elements in the model are cornea and crystalline lens. The cornea is a convex-plano lens selected from Edmund optics (Stock No. 63-523, VIS-NIR Coated). The NIR coating avoids cornea reflection when calibrating with an aberrometer. The crystalline lens is a dual-convex lens with 100 mm FL (Stock No. 63-670, VIS-NIR Coated). The distribution of refractive power between the cornea and the lens is close to that of the real human eye, and the cornea contributes 2/3 of the total refractive power. The overall optical power of the eye model is 41.67 D that is quite different from schematic eye power (58-70 D), due to the material difference (Schott NBK-7, n = 1.5168). The R.I. of these lenses are different from the cornea (n ∼ 1.3771) and crystal lens (GRIN) [17]. The reason why the lenses with the identical power with the real eye components cannot be chosen is that the power of the eye is variable, and the value is not integral. Most importantly, the optical media in the eye is the aqueous (n = 1.3374) and vitreous humor (n = 1.3360), which is like de-ionized, purified water (n = 1.334), rather than air (n = 1). In fact, this difference is not negligible for evaluating eye care products but does not affect the performance of the eye model used for aberrometer calibration.
The pupil is placed at 0.5 mm from the posterior surface of the cornea, which is close to 0.55 mm in Navarro’s theoretical eye and equal to 0.5 mm in Gullstrand schematic eye [44]. The diameter of the pupil was simulated with 3 mm, 4 mm, and 5 mm, corresponding to 3.27 mm, 4.36 mm, and 5.45 mm exit pupil size (It is the entrance pupil diameter of the human eye. However, the retina is the object surface, and the light is traced from the inside out in the simulation. Hence it is the exit pupil of the model). The three selected pupil diameters cover diameter variation range of the pupil of the human eye in daily life.
According to the Navarro’s schematic eye, a 12 mm retina radius is used for a guarantee of a large visual field. It moves within a 12.46 mm distance, changing the eye length from 22.325 mm to 34.785 mm. The variable eye length allows a dynamic M ranging from -10 D to +10 D in 3-5 mm pupil size. The geometry parameters of the eye model are shown in Figure 1. And all the parameters about the optical layout of the model are given in Table 1.
Fig. 1. Geometry parameters of the eye model. (a) Ray tracing in eye model from 0° to 30°, (b) The optical layout of the eye model.
Table 1. Optical Parameters of the Eye Model
Refraction simulation accompanies the entire design phase. In ophthalmic optics, refractive error is described by combination of “sphero-cylinder” (S, C × β), or rectangular Fourier form [M, J0, J45] [45]. These two descriptions can be converted into each other through Eqs. (1) to (6). In this study, M is used to simulate refraction error and compare at different angles. For Zemax, the Zernike aberrations of the eye model at exit pupil plane can be directly accessed in order of Zernike coefficient. And the Fourier form refractive error is derived from the Zernike coefficient by the Eqs. (7) to (9).
Zernike aberrations with 37 polynomial terms were simulated and the three main components of mean spheric equivalent, the coefficients of Z4, Z12, and Z24, were studied. However, while Z12 and Z24 were simulated, the coefficients of them were almost zero (10−14) at the 0° field of view. Therefore, $c_4^0$ and $c_6^0$ are not plotted. The ranges of distance from the crystaline lens to retina at selected pupil sizes are slightly different from each other. It is because the range is correponding to the distances that secure a range of M from -10 D to +10 D. Varying pupil size causes this distance to vary slightly. As shown in Fig. 2, with an increase in axial length, $c_2^0$ gradually changed from negative to positive, and M became negative. In line with the real situation of the human eye, the eye changes from hyperopia to myopia as the axial length of the eye changes from short to long.
Fig. 2. Change in 4th Zernike coefficient (defocus) with the moving retina. (a) 3 mm pupil size, (b) 4 mm pupil size, (c) 5 mm pupil size.
To investigate the peripheral aberration of the eye model, $c_2^0$, $c_4^0$ and $c_6^0$ at 0° to 30° field angle at 0.55 µm wavelength are taken. Figure 3 gives that the eye model exhibits myopic peripheral defocus, with M increasing in the negative direction as the field angle increases. This represents one of several peripheral refraction patterns existing in human eye. At the meantime, it can also be seen that the change of aperture has a significant effect on aberration. At 0° field angle, $c_2^0$ is zeroed by adjusting axial length under different pupil sizes. Subsequently, 30° field angle is taken and then get $c_2^0$ equals to 0.589 µm under 3 mm pupil size, 1.066 µm under 4 mm pupil size, and 1.704 µm under 5 mm pupil are obtained. However, the effect on refractive power is not obvious ideally. They are -1.53 D, -1.55 D, and -1.59 D.
Fig. 3. Change in $c_2^0$, $c_4^0$ and $c_6^0$ with the visual field angle, when M = 0 D at 0° visual field. (a) 3 mm pupil size. (b) 4 mm pupil size, (c) 5 mm pupil size.
In addition to the individual coefficients, the entire wavefront of the eye model was simulated. For on-axis wavefront aberrations, the wavefront always maintains rotational symmetry regardless of the axial length of the eye, as shown in Fig. 4. Meanwhile, wavefront aberration increases with pupil size. At peripheral field angle, the wavefront is more like a saddle surface. These are shown in Fig. 5. However, at eccentric visual field, the shape of pupil changes from a circle to an ellipse, and the length of minor axis is determined by $D^{\prime} = D\ast cos(\theta )$. $\theta $ is the visual field angle, and D is the diameter of pupil. Zemax stretches the ellipse in the direction of minor axis to form a circle. Thus, the wavefront is a unit circle and can be fitted by Zernike polynomials. However, this deformation affects the gradient of the wavefront and then the refractive power as well as the aberrations.
Hartmann-Shack aberrometers measure elliptical pupil in a different way from Zemax. The HS aberrometer (VX 130+, Luneau Technology, France) used in this study deals with non-circle pupil by applying a circular sub-aperture and fit Zernike polynomial within it. If measured results are needed to be comparable to simulation results, the stretched wavefront from Zemax should be “compressed” back to elliptical shape, inscribe a sub-aperture with a fixed size aperture, and perform Zernike fitting within it. After this process, simulation results and measurement results can be compared with each other. To allow the inscription to be at the highest angle (30°), the diameter of the sub-aperture should be larger than the minor axis length. 3 mm is chosen as sub-aperture diameter because the aberration of this size can be directly measured by the aberrometer. The whole process is accomplished by MATLAB (The MathWorks, Inc., USA). The stretched and inscribed results are shown and compared in Table 2. Figure 6 visualizes the difference between M of stretched 4 mm pupil, 3 mm pupil, and 3 mm inscribed pupil at peripheral visual field. For the stretched wavefront, if the axial length is fixed, the change of M is trivial and almost constant from 0.06 to 0.08 D no matter how field angle is changed. The gap between M derived from inscribed wavefront and that from stretched wavefront is exaggerated by increased eccentricity. Therefore, the trend of the refractive power is dependent on the data processing. If the wavefront sources to be studied are different, it is necessary to unify the data processing methods before making comparisons. In this study, inscribed wavefront is used for eye model validation.
Fig. 6. Difference between M of stretched 4 mm pupil, 3 mm pupil, and 3 mm inscribed pupil at peripheral visual field.
Table 2. M of stretched 4 mm pupil, 3 mm pupil, and 3 mm inscribed pupil at peripheral visual field
2.2 Opto-mechanical design
A rendering of the assembly and photo of the finished eye model are shown in Fig. 7. The parts design and assembly are performed using Inventor (Autodesk Inc., USA). The mechanical eye model consists of a base, corneal lens mount, pupil frame, pupil sheet, crystalline lens mount, retina, and two linear motion guides that work with two micrometer heads (Mitutoyo, Japan). The optical mounts, pupil frame, and the base are fabricated using a precision lathe. They are made from 6061 aluminum alloy, and post-processed with mesh 100 sand blasting as well as black anodization. The corneal lens mount is the front face of the model. To make the model compatible with both commercial HS aberrometers and the laboratory-based optical apparatus, two series of featured holes are designed. These holes match Thorlabs 16 mm and 30 mm cage system respectively. The optical axis is automatically aligned once the model is connected to the cage system. As for pupils, four 0.5 mm thick aluminum sheets with 2, 3, 4, and 6 mm diameter apertures were made. A pupil frame for pupil sheet is screwed on the back of the corneal lens mount, so that the pupil sheet can be easily replaced. To allow the precise linear motion of retina, 13.00 mm travel range micrometer heads are purchased from the market and serves as the motion actuators. The travel range covers the designed change of axial length. The crystalline lens mount is also made moveable laterally. The original points of the retina and the crystalline lens mount are calibrated by a coordinate measurement machine (VideoCheck HA 400 3D CNC, Werth Messtechnik GmbH, Germany).
Fig. 7. Artificial eye model that consists of four functional parts: corneal mount, pupil, crystalline lens mount and retina. (a) The rendering of the 3D assembly, (b) Image of the real eye model.
In addition to the cage system, the method to mount the model in front of an aberrometer also needs to consider. Three types of eye model bases were designed. (1) A base with two extendable clamps that can hold the side pillars of the aberrometer chin rest. (2) To make the eye model suitable for various aberrometers whose chin rests are special shaped by injection molding but can be clamped, an elevated base with two slots that can be fixed by chin rest bolts is made. (3) For the chin rest has no feature that can be clamped, a camera tripod is used to hold the eye model. A carriage with 1/4-20 UNC thread hole that can be screwed together with a tripod is fabricated. However, due to the separation of the eye model and the aberrometer, the alignment takes longer time in this way.
2.3 Retina fabrication process
The most challenging part of the eye model is the retina. The design and fabrication of retina determines whether the eye model can obtain a spot-field image that can be solved when measured by the HS aberrometer. Initially, a retina of white ABS is machined and subsequently polished. In a certain exposure time range of HS sensor, moderate energy density and uniform energy distribution were found to be the prerequisites for the normal operation. When the energy is low, the poor signal-to-noise ratio and the long exposure time make the solution of the spot-field very difficult. When the energy is too high, the saturated spots overflow their assigned sub-apertures, making it difficult to determine the relationship between the spot centroid and the sub-aperture, which in turn leads to distortion in the slope calculation. A control of the retinal refraction is needed. The reflection of a surface has specular reflectance and diffuse reflection [46]. It can be expressed as Eq. (10):
Fig. 8. Spot-field image of HS sensor and eye model. (a) The spot-field image of human eye, (b) The spot-field image of the eye model with polished white ABS retina, (c) Eye model with polished white ABS retina, (d) The spot-image of P60 sandpaper, (e) The spot-image of P240 sandpaper, (f) The spot-image of P320 sandpaper, (g) The spot-image of P600 sandpaper, (h)The spot-image of P1200 sandpaper, (i) The spot-image of P2500 sandpaper.
Three retinas from a wide range of materials, off-white ABS, black ABS, and clear PMMA were additionally fabricated, as shown in Fig. 9(d). All the surfaces are post-processed with sand blasting with grain size P300. The surface roughness is Ra 10.32, which is measured with surface roughness tester (SJ-210, Mitutoyo, Japan). The spot-field image obtained from black ABS retina is of the best quality, as shown in Fig. 9(a). It is selected as the ideal material for our retina manufacturing. All the experiments are conducted using the same retina.
Fig. 9. Spot-field image of the custom-machined retina and eye model with replaceable retina. (a) The spot-field image of P300 sandblasted black ABS retina, (b) The spot-field image of P300 sandblasted off-white ABS retina, (c) The spot-field image of P300 sandblasted clear PMMA retina, (d) The eye model and the retinas made from black ABS, white ABS, off-white ABS, 6061 aluminum alloy, and clear PMMA.
3. Experiments
The experimental study includes reflectance validation, on-axis refraction validation and peripheral refraction validation. Reflectance validation is used to verify if the reflectance of the artificial retina is alike human retina reflectance to guarantee the energy match. Therefore, moderate exposure of HS sensor is assured. The on-axis and peripheral validation are to examine the refraction consistency between the eye model and the design objectives. Because of the deviation from the design, the eye model was calibrated to the scale of the micrometer head. The feasibility of aberrometer validation was also investigated.
3.1 Reflectance validation
To compare the reflectance of the eye model with that of real human eye retina, the first step is to measure the reflectance of the eye model. As shown in Fig. 10, an optical path was set up. It consists of the eye model, an 850 nm laser module (LDM850, Thorlabs, USA), a beam splitter plate (BSW11R, Thorlabs, USA) mounted in a cage cube, a pair of relay lens to conjugate the pupil plane onto the wavefront sensor, and a wavefront sensor (WFS20-5C, Thorlabs, USA). The alignment is automatically achieved by cage rods, which is not depicted in Fig. 10. To measure the reflectance of the eye model, five measurements were done in four positions with optical power meter (PM160, Thorlabs, USA). The test order followed ①, ②, ③, ④ with eye model on, ④ without eye model. The results are P1, P2, P3, P4on and P4off, respectively. Firstly, the optical power meter is placed at ① to measure the overall optical power emitted from the laser module. Next, before mounting the eye model into the setup, the power at ② and ③ are measured to calculate ratio of transmittance and reflectance of the beam splitter. Then, the optical power at ④ is tested to acquire the background optical power in experiment environment. Finally, the eye model is mounted into the setup with the cage rods. And the power at ④ is tested again. The result reveals the power of the light reflected from the eye model plus background optical power. Each result is the average of three measurements.
Fig. 10. The setup to test the reflectance of the eye model. The optical power meter measurement order follows ①, ②, ③, ④ without eye model, ④ with eye model on.
3.2 On-axis refraction validation
The refraction validation is to measure the refraction of the eye model with a commercial HS aberrometer, VX130+ (Luneau Technology, France), as shown in Fig. 11. The eye model is mounted in front of the aberrometer, and the alignment is achieved by the three-dimensional motorized stage embedded in the aberrometer. The whole alignment is under the monitor of the aberrometer pupil camera. By adjusting the micrometer head that modulates the axial length, 7 different retina positions that were correspondingly simulated to be -10 D, -5 D, -2.5 D, 0 D, + 2.5 D, + 5 D, and +10 D are measured. The pupil sheet we used is of 4 mm diameter. M was calculated from the S and C measured within a 3 mm diameter sub-aperture (automatically applied by aberrometer).
3.3 Peripheral refraction validation
Peripheral refraction validation is decisive to its core function, the validation of scanning peripheral HS aberrometer. The test method of peripheral refraction and axial refraction are basically the same. The difference is that the orientation of the eye model needs to be manually adjusted every time before the measurement at a certain angle, since the aberrometer to validate the eye model is designed only for on-axis aberration measurement rather than efficiently scanning of global visual field. The scale of the micrometer was 4.58 mm when the measurements were performed. At this position, the refraction at 0° under 4 mm pupil size was simulated to be 0.00 D. Due to different wavefront construction methods between the aberrometer and Zemax, the 0° refraction was 0.15 D after applying a 3 mm sub-aperture and recalculation.
4. Results
In reflectance validating experiment, the reflectance of the eye model is calculated from the following equation:
where P1 was 4.36 mW, P2 2.11 mW, P3 1.87 mW. P4on and P4off were 20.42 µW and 15.53 µw. Transmittance of beam splitter plate varies with wavelength. $\frac{{{P_3}}}{{{P_1}}}$ gives the transmittance at the wavelength of 850 nm. P4off is the optical power in the environment, which needs to be removed to reveal the reflection from the eye model.The reflectance of anti-reflection coating (VIS-NIR coating) of the lenses is around 0.25%. To avoid mixing the corneal reflection with the retina reflection, a wavefront sensor was used to monitor the reflection, instead of capturing the wavefront. The images with and without corneal reflection are shown in Fig. 12. To calculate the reflectance of retina accurately, the spot-field image without corneal reflection was assured. The retinal reflectance of the eye model was 0.54%, which is highly consistent with the human retina reflectance, 10−3 to 10−4 [47].
Fig. 12. Spot-field images of the eye model. (a) The retina reflection, (b) The retina reflection mixed with the corneal reflection.
In the experiment of measuring on-axis refraction, Fig. 13 shows the results obtained from the on-axis refraction measurement. M changed from -10.52 D to +9.16 D, which is designed to be from -10.00 D to +10.00 D. The curve was fit to three-term polynomials, given by $M = A{x^2} + Bx + C$, where A, B, C equal to 0.05643, -2.33882, + 10.323, and x is the micrometer head position in mm, M is the mean spherical equivalent in D. The refraction of the eye model can be predicted by using this polynomial.
The measured M was 0.04 D lower than the design values on average, ranging from 0.02 D to 0.07 D.
Fig. 13. Difference between measured M and simulated M at specific micrometer head positions. The average difference of measured value is -0.43 D. Each measured value is the average of three measurements. The maximum standard deviation of each value is 0.07 D, 0.04 D in average, which shows the excellent repeatability of VX130 + .
Figure 14 shows the measured M under 3 mm pupil size at different visual field angles and the simulated M calculated within the 3 mm sub-aperture. M drops from 0.13 D at 0° to -1.52 D at 30°. The measured curve was fitted by three-term polynomials,
where x denotes the field angle in degree, and M is the mean spherical equivalent in D.Fig. 14. Change of peripheral refraction at different visual field angle. The averages difference of measured value is 0.03 D. Each measured value is the average of 3 measurements.
Figure 15 shows the spot-field images captured by the commercial aberrometer. They are in well accordance with the theorical changing while the eye model is viewed from eccentric angles. The visual field angle of the model can be derived from the ratio of the long axis and the short axis.
5. Discussion
In contrast to the combination of a lens and a diffuser, the conventional way to calibrate HS sensor in an optical setup, a new type of eye model with a designed wide visual field is proposed. This eye model can meet the emerging demand of validating scanning peripheral aberrometers. The advantage of this model is that, while performing a scanning measurement at a series of locations, no human intervention or realignment of the eye model is needed.
In the reflectance validating experiment, the fabrication and the post-processing of retina are investigated and energy match to acquire the optimal spot-field image is achieved. From the Francois’ study, the reflectance of the fovea varies from 0.23% to 10.37%, depending on the wavelength [47]. In the study, the reflectance is not strictly precise to a specific wavelength. In the study, we focus on whether the wavefront sensor can capture a high-quality spot-field image and accurately reconstruct the wavefront. The reflectance validation experiment shows that the reflectance of the human eye matches the reflectance of the model. It explains the similarity between the spot-field image obtained from the eye model and the one from real human eye.
Alignment was another barricade. For human eye, subject can stare at the fixation target. It can be a house or a hot balloon at the infinite point of a country road. Then, by centering the iris at pupil camera monitor, the line of sight is aligned with the optical axis of the aberrometer. For eye model, it cannot actively look at some point. It is planned to judge the alignment by Purkinje images [48]. The source of the Purkinje image is the illuminated Placido disc inside the aberrometer. Then, like aligning human eye, the head of the aberrometer could be adjusted to center the artificial iris. However, the anti-reflection coating not only controls the corneal vertex reflection of the probe laser beam, but also eliminates the Purkinje image that can be used to aid alignment. Thus, the symmetricity of the shadow left by illuminating LEDs on both sides can was used as an auxiliary reference.
To make the adjustment easy, an aberrometer with manual control focusing option is preferred. VX130 + is a fully automated examine platform without manual focusing. The algorithm of focusing is not designed to bring the axis of a tilted pupil plane into focus, which makes the measurements cumbersome. It always took three or four times to get a satisfactory focus. If not, the mis-conjugation results in deviant values. However, though focused many times before measuring, the focus was not as accurate as on-axis measurement with servo-focusing algorithm, due to visual inspection. To explore the focus mechanism and improve success rate of focus, it is assumed that the surface texture similarity of the retaining ring and pupil sheet gave the focus algorithm two peaks, as shown in Fig. 16(a). The two peaks were at different depths. Therefore, plasticene was used to cover the retaining ring to differentiate the retaining ring from pupil sheet. Plasticene has smooth surface, and the pupil sheet is coarse, as shown in Fig. 16(b). For on-axis measurement, the successful rate of auto-focus on pupil plane was increased. For peripheral measurement, it was still hard to focus. Thus, for the manufacturing of the eye model that works with autofocus aberrometer, the post processing methods of corneal lens mount and pupil sheet should give them different surface characteristics. For example, the corneal lens mount can be polished to 0.2 µm in Ra, and the pupil sheet sandblasted to 3.2 µm in Ra. When a human eye is focused, the reflection of the Placido disk is always sharp, and the image of the Placido disk and the entrance pupil plane are almost at the same depth, as shown in Fig. 16(c). Therefore, to explore the focusing strategy of the aberrometer, the VIS-NIR AR coated corneal lens was changed to the same lens without any AR coating (Stock No.63-475, Uncoated, Edmund Optics), as shown in Fig. 16(d). As expected, the reflection of the Placido disk can also be sharply focused on. However, unlike the human eye, the image plane of the Placido disk and the entrance pupil do not coincide in our model, which resulted in measurement error. In the meantime, different angular magnifications can also be observed, due to the radius of curvature discrepancy between the corneal lens (15.5 mm) and the human cornea front surface (7.7-7.8 mm) [43]. Therefore, the focusing mechanism of the auto-focusing aberrometer should be thoroughly studied before the approval of the eye model.
Fig. 16. Images of eye model and human eye taken from pupil monitor: (a) Front surface of the eye model viewed from the commercial aberrometer. (b) front view of the corneal lens mount covered by plasticene. (c) Human eye viewed from the aberrometer. (d) Eye model with uncoated corneal lens.
The results of the on-axis refraction validation show a high coincidence between the simulated results and measured results. The measured M was 0.04 D below the design values on average. This represents the model is more myopic. It indicates the real products meet the design parameters. Though this deviation gives the refraction an offset from the designed range, it doesn’t influence the function of aberrometer validation. Extending the hyperopic limit was considered by moving the retina further forward. However, the mechanical collision between the crystalline lens mount and the edge of the retina constrained this movement. This presents if the target range is -10.00 D to +10.00 D refraction, the design parameter should be set to -10.50 D to +10.50 D, or even larger. Thus, target range can be guaranteed should there any deviation.
The peripheral refraction measurement shows that the eye model has a myopic peripheral defocus, which is one of the five peripheral refraction types of human eye [49,50]. Unlike the on-axis measured results, the deviation of the measured data is not consistent in direction. Two possible reasons are alignment error and focusing error. The alignment error is estimated to be ±1°. For the following reasons: (1) The repeatability of the eye model is within the standard deviation and refractive measuring precision of the commercial aberrometer or other autorefractometers, 0.2 D and ±0.5D respectively [51,52]. (2) The alignment error is within the alignment tolerance of aberrometers and autorefractometers [53,54], this eye model is more than sufficient as a verification standard.
In mechanical design, to make the eye model compact, an open rail was designed to guide linear motion of the retina. The repeated positioning accuracy is ±0.03 mm, which is measured by micrometer gauge. The linear motion accuracy can be further improved by using miniature cross roller linear bearing and changing the coupling method between the micrometer head and the retina - adding preload spring for backlash elimination.
The chosen design of eye model can be further upgraded to integrate more functions to validate cornea topographer, anterior chamber by replacing the corneal lens with an uncoated lens. It should have a specifically designed shape that is like human corneal contour [48]. Figure 17 shows the corneal reflection of Placido disk when measuring the corneal topography. The result is 15.30 mm that is close to the nominal radius of the corneal lens, 15.50 mm. Schiempflug imaging was also tried to reconstruct the anterior corneal surface. However, the result was not ideal because: (1) The corneal lens is much thicker than the human cornea. (2) The radius of curvature of the front surface (15.50 mm) is quite larger from the radius of curvature of the front surface (7.7 mm) of the human eye. (3) Compared with the human eye, the position of the corneal lens in the eye model is not prominent. Retina camera would also be validated by attaching USAF resolution target on the retina plane [55]. Moreover, pseudorandom movement could be mechanically added to the model for testing eye tracker of retina imaging [32,56]. Thus, due to the versatility of the model, it can be extended to serve various kinds of ophthalmic instruments as a standard.
6. Conclusion
This opto-mechanical eye model is proposed that can be effectively used for aberrometer validation on the measurement of on-axis aberrations as well as the peripheral aberrations. The retina of the eye model is studied, designed, and manufactured for working with Hartmann-Shack wavefront sensor to guarantee a credible quality of spot-field image. The movable retina allows this model to test the dynamic range of aberrometer within a wide range. The further improvement for this model is being developed to validate corneal topographer and anterior segment analyzer.
Funding
Science Foundation Ireland (15/RP/B3208); Enterprise Ireland (CF20221894), Irish Research eLibrary.
Acknowledgment
The authors extend their appreciation to Qing Li for the help for the reflectance study, Mingyue Shen for surface roughness metrology, Chenghao Chen for being eye test subject, and Quanyue Li for the images of high quality. Open access funding provided by Irish Research eLibrary.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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