Holographic waveguide based optometer for the quantitative monitoring of ocular refractive error.

Oculomotor disorders are known to have profound impacts on a patients' quality of life. However, current clinical practice lacks the capability to provide simultaneous assessment of three tightly coupled oculomotor control components, i.e. eye movement, lens accommodation, and pupil response. In this study, a holographic waveguide (HW) based benchtop optometer was constructed and evaluated with a model eye. Experimental result and quantitative analysis indicate that a HW can convey high quality retinal images to a camera at an illumination level safe for human subjects and support high accuracy measurements of ocular refractive error over a wide range. Further development of a HW-based system promises a wearable, see-through device for comprehensive assessment of oculomotor control components while the subject is engaged in normal daily activities and thus enable advanced research and clinical management of oculomotor disorders.


Introduction
Three oculomotor components, i.e., eye movement, lens accommodation and pupil response, are functionally coupled to ensure the target of interest is imaged on the retina with optimal sharpness and brightness [1][2][3]. When one shifts gaze from a far target to near, the two eyes converge, the accommodation increases, and the pupils constrict (the near triad). Defects in this routine can cause visual symptoms and visual impairments. Oculomotor disorders are one of the most common encounters in eye care clinics and have profound impacts on the patients' quality of life [4][5][6][7]. However, current clinical practice falls short of providing objective, quantitative and simultaneous assessment of all three components that can guide the diagnosis, prevention and treatment of oculomotor disorders and associated diseases.
Current vision tests and oculomotor assessments often rely on the clinician's subjective observation, usually require a high level of cooperation from the patient and are performed in a setting that can be significantly different from the patient's natural way of eye use [8]. For example, many 2nd and 3rd grade pupils read and write 16-20 cm from the page, usually at a very shallow angle, with non-uniform illumination, varying print size and a gradient blur [9]. In comparison, the standard vision test distance for reading is 40 cm, with optimal illumination and viewing pasture. Such tests may not reveal the visual diffculties young children experience every day, and may not help to understand the correlation between near work and myopia development [10]. Another shortcoming of the current clinical practice is to measure the oculomotor components in isolation. For example, the near point of convergence and the amplitude of accommodation, two measures of how close one can converge and focus, are measured separately in two procedures. Although it is known that some of the high prevalence disorders in convergence and accommodation are associated, such as convergence insufficiency and accommodation insufficiency [11], they are assessed, diagnosed and treated as separate diseases. The problem of lacking instruments for objective, comprehensive oculomotor assessment in clinical practice has recently been recognized [12,13].
An ideal device for clinical practice is a pair of wearable, see-through spectacles that can provide objective and quantitative assessment of all three oculomotor components while patients are engaging in daily activities in their natural environment. While many eye trackers, optometers and autorefractors have been developed [14][15][16], none of them includes all these three features in one device. A key obstacle is to capture the image of the eye right in front it without obscuring the eye's view of the outside world. While this feature is desirable for monitoring eye position, it is mandatory for measuring accommodation because the camera has to be able to collect light reflected from the fundus through the pupil. Although a half mirror can capture the image of the fundus and transmit it to a camera outside the eye's field of view [17][18][19], the size and weight of the optics in front of the eye make it a poor candidate for a wearable device.
A holographic waveguide (HW) is a diffractive component. Optically, it functions like a pair of mirrors but is highly compact and light-weight [20]. Original development of HW is motivated by its potential in wearable, inconspicuous, see-through augmented displays [21][22][23]. We have recognized the potential of using HW to develop a wearable, see-through oculometer, which can monitor all three oculomotor components simultaneously. Placed in front of the eye on the frame of a pair of spectacles, the in-coupler of the HW can capture the images of the anterior segment and the fundus of the eye. The images can be guided to a camera installed on the temple of the spectacle and are coupled out to a camera for computing eye position, pupil size and accommodation status. However, as a diffractive component, a HW may attenuate the incoming light, sensitive to input angle, and introduce color dispersion and distortion. It is thus important to determine if a HW can be used to image the retina with quality high enough for accommodation measurements, at a level of illumination that is safe for potential clinical deployment.
Recently, we have demonstrated that a HW can be used to monitor eye position with good precision and accuracy [24,25]. The purpose of this research is to test the feasibility of measuring the accommodative statue, i.e., the refractive error of the eye, through a HW. Compared to eye tracking, this task is more challenging because the illumination light needs to pass the ocular media twice to image the light reflected from the retina. For this study, we developed a prototype Scheiner optometer [26][27][28] using an existing HW and evaluated its ability to quantify refractive errors of a model eye. Accurate assessment was obtained over a wide range of refractive errors with an illumination level safe for human subjects. Future development of a HW-based, wearable, see-through device will enable comprehensive assessment of all three oculomotor control components while the subject is engaging in normal daily activities, thus to foster near research and improve diagnosis of oculomotor disorders.

Materials and methods
A transmission HW, which was originally designed for display (wavelength 505 nm), was used to construct the prototype optometer ( Fig. 1). Technical details of the HW was described in previous publication [29]. Briefly, it has a 20×60×3 mm flat glass substrate and a pair of 20 × 18 mm in-and out-couplers. The couplers are photopolymer films with holographic fringe patterns which has ~34% diffraction efficiency, 20 μm thickness, 0.04 refractive index modulation, ~ 60° diffraction angle, and are glued on the glass substrate. Incident lights propagate through the glass substrate via total internal reflection. An optical diffractive element with a 40 mm focal length was integrated into the in-coupler to serve as an optical collimator. The HW in this research was used as part of a retinal imaging system [ Fig. 1(a)].
According to the Scheiner Principle [30,31], refractive errors of an eye can be determined by the separations and relative positions of the images of two pinholes reflected back from the retina. The two pinhole images superimpose on each other when the eye is emmetropic (no refractive error). The pinhole images are separated when there is a non-zero refractive error, and the separation should be linearly related to the amount of the refractive error. The pinhole images are on the same or opposite sides of the pinholes depending on hyperopic or myopic condition of the eye [30,31]. In Fig. 1, (a) collimated light from a green LED source illuminated a mask plate with two pinholes to form an image of the pinholes to retinal plane of a commercial model eye built for autorefractor calibration [ Fig. 1(a)]. The two pinholes were 2 mm in diameter and were vertically separated by 4 mm. The mask plate was produced using a mechanical design software and was printed using a high resolution 3D printer (Objet30 Prime, Stratasys). An optical relay system, consisting of lens 1 and 2 (35 mm and 50 mm focal length, respectively), was employed to project pinhole patterns to the eye lens of the model eye. The eye lens, with focal length ~50 mm, focuses the pinhole patterns to the retinal plane of the model eye. The light source, mask, lenses and model eye were carefully aligned to share the same optical axis to minimize vignetting effect.
The pinhole images reflected from the retinal plane passed through the eye lens, lens 2 and were directed to the in-coupler of the HW by the beam splitter. The pinhole images collected by the in-coupler were propagated in the glass substrate, were coupled out of the waveguide by the out-coupler, passed through the lens 3 (60 mm focal length), and were finally focused by the camera lens (25 mm focal length) onto the senor of a CMOS camera (EO-6412C, Edmund optics), as shown in Fig. 1(a). The relative distance and orientation between the waveguide and the camera were carefully adjusted to ensure high diffractive efficiency and image quality. The camera had 3088×2076 pixels (pixel size: 2.4 μm×2.4 μm). A 450×450 pixels region of interest was used to analyze the pinhole images. Trial lenses of different powers were inserted in front of the model eye to introduce different refractive errors.
Three images of the pinholes were acquired for each trial lens, the upper pinhole alone, the lower pinhole alone and both pinholes. Custom software was used to calculate the location of each pinhole image. This was done by estimating the squared center of gravity (SCOG) of each pinhole image [32]. SCOG was selected for this study because it was not sensitive to saturation of the pinhole image luminance distribution and it did not require prior knowledge of the luminance distribution. Computer simulation showed that the algorithm can determine the center of a luminance distribution at subpixel accuracy at moderate levels of saturation and noise. For example, when the luminance distribution (0 to 1.0) was saturated at 0.7 and the Gaussian noise was 0.15, the SCOG distribution center estimation error was 0.05 ± 0.039 pixel. Euclidean distance method was used to calculate the separation between the centers of the two pinhole distribution [33]. The relative positions of the pinhole images were also recorded.
The prototype optometer was calibrated with ±0.5 to ±10 diopter (D) trial lenses at an illumination light intensity of 45 μW. The total range of refractive error measurement was explored using ±16D, 18D and 20D trial lenses. The optometer performance was validated with ±2.5D, 4.5D, and 8.5D trial lenses, which were not used in system calibration. Waveguide efficiency and minimum illumination light intensity for reliable measurement were assessed using ±18D trial lenses and 5.5, 11, 22, and 45 μW light intensities. Optometer readings were obtained by determining the pinhole image separation in pixels and then computing the refractive error using the inverse function of the calibration curve. Measurement error was quantified by the difference between the nominal trial lens power and optometer reading. All measurement was repeated three times at each trial lens power. The mean and standard deviation of the repeated measures were evaluated. The image acquisition sequence of the different trial lenses was randomly chosen to avoid experimenter bias.

Pinhole image separation
The pinhole images were superimposed on each other at 0D (no refractive error, Fig. 2, 0(D)). The separation between the pinhole images increased with increasing amount of refractive error introduced by the trial lenses. Pinhole image contrast and intensity were reduced with increasing refractive error. The pinhole image size and intensity were relatively bigger and higher in positive refractive errors compared to negative errors (Fig. 2).
The relative positions of the pinhole images depended on the type of refractive error. Figure  3 shows pinhole images from a −5D trial lens (upper row) and a +5D trial lens (lower row). The separation between the pinhole images was roughly the same [Figs. 3(a2) and 3(b2)] for both positive and negative trial lenses, but their relative positions were the opposite. When the negative trial lens was placed in front of model eye, the image of the lower pinhole was above the image of the upper pinhole and the upper pinhole image was positioned in lower side on retina plane [Figs. 3(a1), 3(a3) and 3(a4)] and vice versa when the positive trial lens was placed [Figs. 3(b1), 3(b3) and 3(b4)]. The relative positions of our pinhole images are the opposite from the textbook description of a Scheiner optometer [26][27][28]. This is because the relay imaging system had inverted the positions of the pinholes before they entered the eye (Fig. 1).

Optometer calibration and validation
The red line in Fig. 4(a) shows the calibration curve of the prototype optometer over the range of −10D to +10D. This is the typical range for commercial autorefractors calibration. The relationship between the refractive error (nominal trial lens power) and the pinhole image separation was highly linear (linear regression, r 2 =0.9998). The slope is 10.299 pixels/diopter. In other words, a one-pixel separation of the pinhole images corresponded to ~0.1D of refractive error. The range of refractive error measurement was explored with higher power lenses. Reliable measures could be obtained with −20D and +20D lenses [black curves in Fig. 4(a)], which is close to the range of commercial autorefractors. Saturation of optometer responses started to show at these high refractive errors. A polynomial curve fitted the entire range of measurement well (r 2 =0.99991). The mean optometer errors, which is the difference between the nominal trial lens power and optometer reading, and standard deviation were calculated. The mean optometer error was smaller at low refractive errors and increase somewhat with high refractive errors [ Fig. 4(b)]. The standard deviation was larger in high refractive errors and all values were below 0.125D [ Fig. 4(c)].
The measurement accuracy of the prototype optometer was assessed using trial lenses that were not used in calibration. Table 1 shows optometer readings and errors derived from the calibration curve shown in Fig. 4(a). The optometer readings were in good agreement with refractive errors and standard deviations were small. The mean optometer error and mean standard deviation were 0.054D and 0.041D, respectively. This is very accurate, considering the spherical refractive power measurement steps of major commercial autorefractors (Topcon and Huvitz) are 0.12 or 0.25D.

Holographic waveguide efficiency
Optometer readings with ±18D trial lenses under different illumination light intensities were collected to determine the dependence of measurement quality on illumination light. These lenses were chosen because they were close to limit of the measurement range, where the pinhole image signal became weaker and thus the measurement should be more sensitive to reduction of illumination. Three measures were taken at each illumination level and the mean and standard deviation were calculated. As expected, the measurement error and standard deviation increased with decreasing illumination (Fig. 5). However, when the illumination light intensity was higher than 22 μW, the mean measurement error was smaller than 0.25 D, even if measured near the edge of the prototype's measurement range. Because the permissible light exposure limit for continuous illumination is ~390 μW (532 nm) [34,35], the efficiency of HW is high enough to allow reliable refractive error/ accommodation measurements at an illumination light intensity that was well within the safety limit.

Discussions
A HW-based prototype optometer was developed and validated for quantitative measurement of ocular refractive error. The prototype optometer demonstrated high accuracy and precision over a wide range of refractive errors. The prototype is safe for human use because the illumination light intensity used for measurement was one-order lower than established safety limit. This also makes it possible to measure refractive error in patients with mild cataract by increasing illumination light intensity. There are some advantages for small pinhole illumination of a periphery cornea area for the refractive error measurement. The most important optical portion of the eye is the central part, which is about 3-4 mm in diameter. We used a ready-made HW technology without elaborate optimization of waveguide fabrication, eye illumination, image acquisition and image processing. This demonstrates that HW is capable of delivering fundus images with sufficient quality for measuring ocular refractive error. We used a model eye to evaluate the prototype optometer instead of human subjects because our focus in image quality and HW light efficiency. It was also because the prototype operated on visible light, which would interfere with human subject's ability to maintain steady fixation on a visual target. Future research will include developing and fabrication near infrared HW (require different procedures) and testing on human subjects. Moreover, the current bench prototype for feasibility demonstration doesn't consider astigmatism. In future development, a ring of pinholes will be used to provide comprehensive assessment of ocular refractive errors. The shape of the retinal reflection of the pinhole ring will be fitted by a general ellipse function. The direction and magnitudes of any astigmatism will be quantified by the lengths and directions of the major and minor axes of the general ellipse.
There are commercially available clinical instruments to objectively measure accommodation in human patients [36][37][38]. However, these instruments are desktop or handheld devices. The patient either sees real targets through a half mirror or sees a target built in the device. They cannot be used to measure oculomotor responses while the patient is engaged in daily activities in natural environment. Our studies demonstrated that a HW can be used to capture retinal images right in front of the eye for the purpose of measuring eye movement, pupil size [24,25] and refractive error. This study lays the foundation for future development of a wearable see-through binocular oculometer that can have significant impacts on both research (why children get myopia) and clinical practice (how to prevent myopia or reduce convergence insufficiency). Further development of the HW based device can provide a viable platform to enable wearable see-through oculomotor assessment systems.

Funding
National Institutes of Health (NIH R43 EY026265, P30 EY001792, R21EY025760); Research to Prevent Blindness; Richard and Loan Hill Endowment. Schematic diagram (a) and photograph (b) of experimental setup, i.e., a HW-based Scheiner optometer. Light path difference and pinhole image separation introduced by −5D and +5D trial lenses. The separation of the pinhole images is roughly the same (a2 and b2), but their relative positions are opposite. When a negative lens is in front of the model eye, the pinhole images are on the opposite sides as the pinholes (a3 and a4). When a positive lens is in front of the model eye, the pinhole images are on the same sides of the pinholes (b3 and b4). The upper and lower pinhole was blocked in (a3 and b3) and (a4 and b4) to show the relative positions of the pinhole images. Optometer reading using different illumination light intensities at −18D and +18D refractive errors. Mean optometer errors (a) and standard deviations (b) increase with decreasing amount of illumination light. Validation of calibration curve with trial lenses which were not used in calibration procedure.  Optometer readings are obtained by determining the pinhole image separation in pixels and then computing the refractive error using the inverse function of the calibration curve in Fig. 4.