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Abstract
The link between retinal peripheral defocus, and its influence on myopia development has opened the need for accurate scientific investigations to understand the peripheral mechanisms of action. In such a manner, high-quality peripheral refractometry has become the cornerstone of myopia research. A clinical aberrometer is an efficient and robust instrument for measuring wavefront error for central vision. However, several difficulties prevent standardization in clinical use to measure aberrations in the peripheral field. In this work, we developed a new scanning Shack Hartmann aberrometer using a different economical customized relay telescope and a dual-axis fast steering mirror. The study aims to investigate the characteristics of defocus aberration in the instrument with support of digitalization techniques. Two physical eye models were built and analyzed to show and validate the working principle. The results of this research provide knowledge for remote maintenance and calibration of ophthalmological instruments, remote visual care and telemedicine.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Peripheral vision not only plays a vital role in daily visual tasks, such as locomotion and detection, but there is also the hypothesis that peripheral defocus influences eye growth and myopia development [1,2]. In 1971 Hoogerheide et al. [3] suggested an increased risk for humans to become myopic if the peripheral refractive errors tend to be hyperopic, i.e., showing relative peripheral hyperopia (RPR). Furthermore, other findings suggest that the prolate eye shape is a consequence of and not a cause of the growth of the myopic eye [1,2]. The RPR not only depends on the optical aberration field curvature (due to the oblique incidence of light) but also on the ocular shape [4]. The prevalence of myopia is increasing fast globally, and many research projects attempt to understand the reasons for this increased prevalence and how to slow it down or completely prevent it [5]. Several different optical correction designs have been suggested to induce negative RPR to control myopia progression [6,7], both soft and rigid contact lenses with bi- or multifocal designs, as well as orthokeratology lenses and laser surgery. The fact that it is not yet possible to completely stop the progression of myopia in all children demonstrates the need for a better understanding of the underlying mechanisms for the optical control of eye growth in humans [8]. It is necessary to fully quantify the visual optical quality to judge the worth of a confident correction.
During the last years, several techniques have appeared to evaluate peripheral refraction. One of the gold-standard requirements for evaluating peripheral refraction is that the instrument can analyze the wavefront aberration on a wide range of angles. There are two different objective techniques to assess the wavefront errors of the peripheral eye: the Hartmann–Shack sensor and laser ray tracing. The first wavefront technique used to evaluate the peripheral optical errors was based on laser ray tracing and was first presented by Navarro et al. [9]. Laser ray tracing setups require a longer time to sample the complete pupil than a Hartmann-Shack (HS) aberrometer. In this way, the HS-based devices, which measure the aberrations in a fraction of a second, are the most popular instruments for studying peripheral aberration. The first technique needed the rotation of the eye. Atchison and Scott [10] presented the first lab-based HS sensor developed explicitly for peripheral measurements. Lundström et al. [11] built a new setup and implemented a different post-processing stage approach.
Other devices perform a relatively fast scan using different methodologies in the hardware stage. In 2011, Jaeken et al. [12] introduced a new scanning peripheral wavefront sensor capable of measuring the optical quality over the central 80$^\circ$ horizontal visual field in 1.8 seconds with an angular resolution of 1 degrees. Therefore, to measure both the horizontal and vertical axis, the system combines the automatic horizontal acquisition accompanied by the rotation of the eye on the vertical axis. The first device that performs a fast and wide-field wavefront aberration analysis is built on custom-design lenses and two scanning mirrors that allow scanning the $\pm$15 degrees visual field in a spiral pattern within 7 seconds. This system is named Scanning Shack Hartmann aberrometer (SSHA) (Wei and Thibos 2010) [13]. In addition, the custom-design lenses were optimized to get a balanced afocal system. Last, a recent article has been published that also utilizes a relay telescope and a steering mirror to measure peripheral refraction up to $\pm$25 degrees that has been validated on human participants [14]. The clinical need shows great interest in making the technique simple, cheap, fast, wide-field, and safe. Furthermore, laser intensity levels approved by the safety standard for laser products must be ensured to avoid adverse effects on the patient’s eye [15,16].
This study presents the evaluation of defocus aberration introduced by a different version of SSHA designed in our laboratory. The prototype has a wide field of view, it is compact, built from inexpensive stock lenses, and the speed was improved using a dual-axis fast steering mirror. The current speed scan is 10 points/sec. The advantages of using this apparatus are several. First, the angular magnification of the system is 0.42 so that a slight deflection in the galvanometric mirror produces a more extensive scanning range on the pupil plane. Second, the size of the relay system is about three times smaller than the original SSHA. Third, instead of designing a perfectly optimized afocal system using ray-tracing techniques, we have chosen a set of lenses within the stock market that meets the minimum optimization requirements and reduces our relay telescope’s total cost. The drawback is that the afocal system is slightly unbalanced due to the restriction in terms of cost, so the measurements of the peripheral refraction from the eye on the wavefront sensor may contain additional aberrations. However, this is not an obstacle. And this is where the importance of this study comes from. If the aberrations introduced by the new ophthalmic device are well known, these could be subtracted from the wavefront detected and thus achieve reliability in the eye analysis. Last, thanks to using a X-Y galvanometric mirror, the number of elements used to build the instrument is considerably reduced, thus allowing higher scanning speeds and leading to an even more significant reduction in the system’s total cost. This work aims to study the off-axis defocus and compensate it in two different model eyes. In this work, we also introduce how to use digitization tools to carry out telemedicine and remote maintenance for peripheral refraction studies.
2. Methods
First, we used ray-tracing software (OpticStudio, Zemax, LLC, Kirkland, WA, USA) for characterizing the relay telescopes. The double pass scanning (DPS) system designed by Wei and Thibos can be appreciated in Fig. 1(a). The embodiment was initially built to progressively measure the off-axis wavefront aberrations of the human eye over a $\pm$15 degrees field of view (FoV). The DPS was designed to optimize scanning performance. This design minimizes systematic errors and allows improved measurement on off-axis wavefront aberration around the complete FoV. The detailed characteristics of the DPS lens system are explained in Ref. [17]. However, this level of precision has a high cost in economic terms.
Fig. 1. Two different relay scanning pair. Double pass scanning lens system designed by Xin Wei and Larry Thibos (a) and its peripheral defocus (b). Scanner relay of the new instrument (c) and its peripheral defocus error (d). The parameter for defocus $c(2,0)$ in waves was calculated using the standard Zernike parameter analysis for a 3 mm pupil diameter.
Our new relay telescope, main object of study, is presented in Fig. 1(c) and has several differences from the previous embodiment. It shows that the system is not symmetric since two different telecentric lens sets were used. Such a DPS lens produces an angular magnification of 0.42, allowing the optical beam to be deflected from $\pm$8 degrees in the input plane to $\pm$20 degrees in the output plane (EP). In addition, the axial distance (total track) has been reduced to 1/3 so that the overall system can be compacted into smaller spaces. In the first stage, the distances between the various elements were optimized by Zemax to get the smallest spot size around the whole FoV. Later, the optimized design was replaced by an approximate version and built with lens from the stock market. Unfortunately, although cheaper, the novel relay telescope has lost optimization of scanning performance, and systematic errors must be considered. Figure 1(b-d) shows a comparison between the off-axis defocus aberrations $c(2,0)$ (the defocus component from standard Zernike parameters) from both relays. This parameter is the most important in the evaluation of peripheral refraction.
Our ophthalmic arrangement is depicted in Fig. 2. The system uses an 830nm diode laser source (CPS830S, Thorlabs, Newton, NJ, US). The laser passes through a small aperture, a neutral filter, and a polarized beam splitter before reaching a dual-axis scanning mirror (OSM - Optotune Scanner Mirror) (MR-15-30, Optotune Switzerland AG, Dietikon, Switzerland). The OSM is placed at the input plane of the $\pm$20 degrees relay telescope. The laser beam passes through the DPS following a predefined scanning squared pattern. The model eye is placed behind the relay telescope, and the pupil plane EP is conjugated with the mirror plane. The laser pivots centrally and covers a range of $\pm$20 degrees radius range without vignetting effect. Then, the first stage is responsible for scanning a narrow laser beam along the whole peripheral visual field over a model retina. Next, the second stage collects the information reflected and scattered from the model retina and returns through the opposite direction to a Hartmann-Shack wavefront sensor (HSWS).
Fig. 2. Setup of peripheral refraction wavefront laser scanner by custom designed relay telescope and a dual axis fast steering mirror.
3. Results
3.1 Defocus aberration from the instrument
Two synthetic retinal surfaces for the model eye were designed with Blender (Blender Foundation, Amsterdam, NL). The object file is used to introduce the sample in the virtual environment. Moreover, it is also used to print the synthetic retinal surfaces by inexpensive additive manufacturing. The first one has a flat surface (FS), and the second has a prolate curved surface (CS), typical for myopic eyes. The lens used as an ocular optical system was a simple lens purchased from Thorlabs to which an iris was attached to simulate the pupil aperture.
The videos show the performance of the instrument when the light comes back from the retina to the HSWS using the sequential mode analysis in Zemax Optics Studio. A macro code was prepared in Zemax Optics Studio to obtain the mirror calibration in the virtual environment. A particular harmony can be seen between the movement of the mirror and both working sides. The defocus aberration from the instrument was then obtained experimentally and by simulation (see Visualization 1).
Computing methods finally process the data collected by the HSWS. The result for defocus component can be seen in Fig. 3. The Zernike parameter at the center of the figure is zero. It is because the instrument is well focused at the on-axis level. Then, the cornea and detector plane are conjugated. However, as the system scans towards the periphery, the instrument introduces an unwanted defocus that overlaps with the original information coming from the eye model. If the instrument operation is not well known and the reference is not considered, the data obtained by the device has a small refractive error, and it is equivalent to almost -1D for eccentricities close to 20 degrees radii. Analysis of defocus aberration by the instrument helps to understand the effects of not considering instrumental errors. It is necessary to take the reference measurement in the real environment. A collimated beam must be sent through different angles and both mechanical mirrors must be connected to evaluate the aberrations produced by the instrument on the image plane of the HSWS.
Fig. 3. Reference simulation from the novel peripheral wavefront laser scanner for the defocus Zernike parameter ${c(2,0)}_{sim}^{ref}$ in waves vs. $\pm$20 degrees FoV and a 3 mm pupil diameter. The defocus weight is shown in a 41x41 matrix image.
3.2 Compensation of defocus aberration in model eye
The scan for the FS model eye, a limit case of the oblate morphology, is shown in Visualization 2. The process of scanning and capturing the Zernike parameter was programmed a priori. The result of the simulation is shown in Fig. 4(a). The synthetic retina was placed in the emmetropic plane. That is, the model eye focused well at the on-axis level. It can be seen from Fig. 4(a) that the Zernike parameter for the defocus becomes positive. That means the periphery’s spherical equivalent (M) is negative and tends towards myopic peripheral refraction.
Fig. 4. Simulation and experimental Zernike defocus results from custom designed model eye samples (FS and CS). Ray-tracing simulations of peripheral defocus (a, d). Experimental analysis of peripheral defocus (b, e). Postprocessed values of peripheral defocus after compensating angular magnification and subtracting the reference from whole system (c, f). The Zernike parameters are in waves and were calculated for a 3 mm pupil size.
Lastly, Visualization 3 depicts the scanning process simulation for the CS model eye. The result is reflected in Fig. 4(d). Like the FS eye model, the center of focus is placed on-axis, simulating an emmetropic eye again. The difference is that this surface simulates a pronounced case of a prolate morphology. In addition, the Zernike parameter of defocus tends to be lower than zero in the periphery, and therefore the spherical equivalent informs that such eye model has hyperopic peripheral refraction. Last, the reference mentioned above must be considered in the final evaluation to obtain an optimal peripheral refraction study. The color bars in Fig. 4(c-f) show the quantitative results from the eye (off-axis defocus Zernike parameter) considering the reference. The results indicate that our novel ophthalmic device produces an off-axis myopic shift that must be considered in the final evaluation. If the reference is not counted, eyes with low hyperopic peripheral refraction would be evaluated as low myopic peripheral refraction. Therefore, a clinical study must be supported by high-quality calibrated instrumentation.
3.3 Comparison of experimental and simulation results
The results obtained through the experimental setup mounted on the optical table are illustrated in Fig. 4(b-e). A quantitative study is carried out to verify the results obtained through the experimental system. Figure 4(a, b) and (d, e) are very similar. However, the values of the Zernike parameter obtained by simulation and experiment are different. This is mainly due to the magnification of the system. To check if there is a relationship between the different values, each point of experimental defocus ${c\left (2,0\right )}_{exp}$ is compared in a plot against its analog from the simulation ${c\left (2,0\right )}_{sim}$ (see Fig. 5). The Zernike parameters of defocus for simulation ${c\left (2,0\right )}_{sim}$ and experiment ${c\left (2,0\right )}_{exp}$ were analyzed by fitting polynomials:
where “$\beta$” has an inverse relationship with the square of mean angular magnification “$\alpha$” produced by the ophthalmic device around the whole FoV. Accordingly, the peripheral defocus ${c(2,0)}_{eye}$ from both eye models (FS and CS) follow the Eq. (3) for simulation and the Eq. (4) for experimental setup:Fig. 5. Defocus Zernike parameters from both eye models determined by the experimental setup ${c(2,0)}_{exp}$ (ordinate) plotted against the measurements using ray tracing simulation ${c(2,0)}_{sim}$ (abscissa) and all angular positions (n = 3362 data points).
The “$\alpha$” factor is not constant, but depends on various parameters. On-axis measurements gave a value of 0.42, while off-axis values at 20 degrees gave 0.46. Therefore “$\beta$” and “$\alpha$” also depend on the scanning angle. This detail must be considered to perform a good calibration of the instrument.
3.4 Test with trial lenses
The instrument was tested using trial lenses between -20D and +16D to verify the instrument calibration. In Fig. 6 five plots are shown for different checking angles between 0 and 20 degrees in 5 degrees step. The results offer a good linear fit with parameter $R^2 \approx 1$. The ordinate axis corresponds to the experimental measurements of the sphere made with our instrument. These are of opposite sign since converging lenses cause a focusing of the rays in front of the retina, while diverging lenses cause focusing behind the retina.
Fig. 6. Linear regression of experimental defocus along the positive horizontal direction (0 deg, 5 deg, 10 deg, 15 deg, 20 deg) vs. a set of trial lens between -20D and 16D.
4. Discussion
The mirror calibration was performed in the real setup by projecting the laser on a metric board. The system was calibrated using trial lenses from -20D to 16D. The results can be extended to the whole off-axis wavefront aberration analysis to study other kinds of peripheral aberrations like off-axis astigmatism and coma. Astigmatism is important to validate the spherical component of defocus. Although in this work we study the analysis of defocus aberration by means of Zernike polynomials, in Fig. 7 we show also the capability to get the off-axis astigmatism from our experimental setup in a 100x100 image size. Certain limitations arise in this methodology. For example, although the calibration through model eyes is prioritized to accurately understand the operation of the instrument in static conditions, a complete analysis must include the study in human eyes and thus be able to evaluate the performance of the device in dynamic conditions. The objective of this work solely focused on a static arrangement. Moreover, for a better examination of the myopic or hyperopic defocus the field angle could be extended by a larger telescope. Additionally, corneal reflection and backscattered light from the instrument must be treated. By means of polarization techniques and readjustments in the alignment we could considerably reduce this effect. Once the device was assembled with the built-in model eye, the control of the system was done through a VPN connection. The software was developed and updates were sent to the instrument. Part of the calibration could be done remotely. Thanks to this fact, the device is prepared for remote eye care and telemedicine.
Fig. 7. Off-Axis astigmatism around $\pm$20 degrees from model eye acquired using our experimental device in an 100x100 image size.
An instrument for objective and fast objective measurement of the peripheral refraction in the human eye has been presented recently by Enrique J. Fernandez et al. [14]. The basic operation mode consists of scanning a circular retinal field of 50 degrees of diameter in a rectangular grid with 5-degree steps (30 points/s). Similarities to our present instrument are size reduction, increased scanning speed, and increased scanning range in both X-Y directions. To achieve a greater scanning range, the relay system must be worked on and optimized so that it meets certain requirements. The system can be balanced or unbalanced. Information post-processing is greatly simplified with symmetrical and optimized relay telescope systems, but the disadvantage is that they are usually expensive and bulky. On the other hand, it is possible to dispense with a well-balanced telecope relay system with a minimum of aberrations. Using an unbalanced system it is possible to obtain validation of results by means of calibration and compensation of instrument aberrations. At the same time, the manufacturing cost is low and the scanning range can be greatly increased. One of the important limits is the distance between the output of the relay telescope and the plane of the pupil. Any relay telescope system must consider a minimum of space between these planes to ensure patient comfort or to be able to insert corrective lenses to jointly analyze the results. In our work we have wanted to approach the compensation of the defocus aberration since in previous works this important point is left in the background. Even so, there are limitations in our study since a complete characterization of the wavefront in the entire off-axis field is essential to obtain a full aberration compensation. Future work should expand to whole wavefront aberration compensation and a more detailed study on the effects of angular magnification on the entire field of view. On the other hand, the scanning speed depends on three points: camera exposure time, processing time and angle step time. Reducing the exposure time implies increasing the intensity of the laser beam. This point must be taken into account since the human eye cannot be exposed to any intensity and a compromise between speed and safety needs to be considered. On the other hand, the use of high frame rate cameras could also be considered in order to reduce the exposure time using low and optimal light intensities for measurements in human eyes. Processing times can be improved by using more computation or by using parallel computing tools (GPU). Finally, there are limitations on the speed of angle change. The steering mirror works with two modes: Open loop and closed loop. The closed loop modality was used in our work. Although this is slower, it is more accurate. The speed of angle change can be improved in open loop mode but in this mode the lack of precision should be considered. The best thing would be to avoid sequential measurements that require more complete analysis time and develop a method that could collect the complete off-axis information in a single shot.
5. Conclusion
In summary, a different version of SSHA has been presented. The instrument is wide-field, very compact, fast, and low-cost. The analysis of the peripheral refraction is carried out through a Hartmann-Shack wavefront sensor. The use of simulation tools and remote connection facilitates the calibration of the system remotely, and the use of two model eyes has helped validate the instrument’s reliability decisively. The device is prepared for remote eye care and telemedicine. At the level of vision science, it is shown that the peripheral refractive error is highly dependent on the morphology of the eye. Myopic eyes tend to be prolate, and these, in turn, show a tendency towards hyperopic peripheral refraction. This study aimed to investigate the defocus abberration of our instrument and determine the causes that limit its deployment. This work will offer the scientific community and future clinical studies a reliable method to compensate off-axis aberrations from the instrument. Indirectly, help to improve the quality of myopia control devices, and understand the foundations of myopia development and emmetropization theory.
Funding
Bundesministerium für Bildung und Forschung; Eberhard Karls Universität Tübingen (ZUK 63).
Disclosures
The authors declare that there are no conflicts of interest that could have interfered in the course of this study. S.W. is scientist at the University Tübingen, and S.W. and A.P. are employed by Carl Zeiss Vision International GmbH.
Data availability
Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.
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