1. Introduction

The sense of sight is normally presumed by us all. However, its value is quickly appreciated as soon as we detect varying degrees of its deterioration that affect our daily functions. Timely diagnosis and correction by ophthalmic specialists are usually sought. For children, and particularly the very young and pre-schoolers, the challenge of recognition and importance of poor vision is not only different from adults but its importance is magnified. The ability to detect and quantify vision problems of young children is more difficult than for adults and because good vision is so important for childhood development, the ability to do so is crucial. Early detection and subsequent treatment are estimated to be beneficial for as many as twenty per cent of infants and preschool children [1, 2]. Further, as many as five per cent of children in this country suffer from amblyopia, which presents as a unilateral vision impairment that is caused by uncorrected large refractive abnormalities, lens opacity, or strabismus. Treatment for this disorder is recommended by the age of six [1-4]. It is recognized that the large majority of young children do not visit eye specialists, and great reliance is placed on pediatricians and general practitioners for detection of these abnormalities and referral to appropriate specialists. Moreover, young children who are medically underserved will not, in general, be examined. There is clearly an impetus to perform vision screening on large populations of children to address these needs, and since as many as eighty per cent of children are normal, it is surely desirable to concentrate limited medical resources on those children who are in need of specialists’ services. To achieve the dual objectives of the improvement of the quality of care and simultaneously the decrease of the medical cost per child, vision screening is recommended for infants, toddlers, and preschool and school children.

There are many technical requirements that must be satisfied by any practical method of vision screening of young children. Of course, it must be medically useful and quantitative, but foremost in practicality, it must be easy to use by personnel who are not medical specialists. Further, the method should be non-mydriatic, and the results must be capable of interpretation by trained but non-specialist persons. For a range of vision abnormalities, including amblyopia and strabismus but excluding astigmatism, photorefraction (PR), or photoretinoscopy, has been advocated for the past decade [5, 6]. The favored specific method is off-axis, or eccentric, photorefraction for which an image of the subject’s pupil is obtained using a camera that is aligned eccentric to a flash-lamp illumination source. Similar to the ordinary retinoscope reflex, the geometric form and irradiance of pupil image will be dependent upon the subject’s pupil size, refractive errors, staring angle, other properties of the eye, and the design parameters of the optical measurement system. As shown by Choi and coworkers [7], a significant advantage of the eccentric photorefraction compared with the autorefractors and retinoscopes that are used in routine clinical eye exams is its ability to perform binocular measurements. This, of course, enables the same accommodative state in both eyes and measurably improves the ability to detect amblyopia and strabismus. A second advantage of note is the ability to make measurements of young and often not cooperative children at a comparatively large distance from the child’s eyes so that the complications of the effects of cycloplegia are eliminated.

The examination results of a typical eccentric photorefractive examination consist of images of the eye observed at the pupil. Analysis, or diagnosis, is obtained from the geometric features and the spatial intensity profiles of these images. Some groups [7–15] have derived predictions of these results for specific ocular conditions by using first-order optical calculations of model eyes for which the ray tracings are performed only for tangential rays. Either the size and orientation of the crescent or the slope of intensity across the vertical center of pupil is used to determine the refractive state of the eye. When the theory is applied to the measurement, even though repeatable, it is found that calibration is required for individuals to achieve accuracy. Therefore, the majority of photorefraction vision screening programs currently relies on empirical studies for analysis and interpretation of the subjects’ images. To date, there is not an entirely satisfactory optical theory that quantitatively explains the intensity gradient in the image of the pupil of a human eye. In this paper, we perform three-dimensional ray-tracing simulation using schematic eye models that include all essential optical parts of human eyes. The optical performance of the combined photorefraction measurement system and the human eye is far from the refractive limit, which allows geometric ray tracing to produce accurate results. The use of schematic eye models in the simulation makes possible the evaluation of performance of the photorefractive instrument over a broad range of operational parameters.

Numerous eye models have been developed to study the optical performance of the human eye. The first-order eye models that are used most frequently are those of Gullstrand [16], Von Helmholtz [17], and Le Grand-Gullstrand [18]. The Gullstrand model contains six surfaces, two of which describe the core of lens with higher refractive index, and is anatomically accurate to the first order. This model is sufficient when the pupil size is small and the spherical aberration value isn’t influential. To match the measured aberration values, Lotmar [19] introduced asphericities for the anterior surface of cornea and the back surface of the lens in the Le Grand-Gullstrand model. Navarro and associates, using values determined from the average of clinical measurements, introduced asphericities to all surfaces [20–22]. The Indiana eye model has a smaller sized eyeball, which includes no crystalline lens, and produces image quality that matches the clinical measurements [23]. Al-Ahdali and El-Messiery [24] and Liou and Brenan [25] incorporated into the model the gradient refractive index of the lens. Considering the various characteristics of the schematic eye models, it is necessary to select a suitable model for simulating measurements of a specific optical instrument. Previously, we have compared the photorefractive images [26] using several models, including the Gullstrand model [16], the Australia Liou model [25], Navarro’s model [20–22], and UC San Diego model [27]. Since many groups indicate that analysis of photorefraction images are not possible when the pupil diameter is less than 3 mm [28, 29], this method is normally performed in a dimmed room to ensure the pupils are naturally dilated. Therefore, the eye models that emphasize accurate paraxial performance and ignore the aberrations may not be suitable for the nonmydriatic photoretinoscope. For this reason, in this paper we consider only the Navarro [21, 22], Arizona [30], and Liou [25] models. Using an optics code, we have demonstrated the methodology for computing the relative spatial irradiance at the detector plane of a photorefractive instrument. To do this, a photorefractive device that is currently used for ocular screening was selected, and with its optical design parameters, the monochromatic spatial irradiance at its detector plane was computed for these three optical models for a range of refractive conditions.

2. Simulation

The Navarro [21,22], Arizona [30], and Liou [25] eye models were selected for this study. A commercial optics computer code, Zemax^™ (ZEMAX Development Corporation, San Diego, CA, USA), was used for the subsequent calculations, and the published eye model parameters were incorporated into the structured computer code. For all three models, radius and conic constants are used to describe the anterior and posterior cornea and crystalline lens surfaces. The optical parameters and surface constants used in these models are based on the measured anatomic parameters and were adjusted to approach the published measurement of monochromatic and chromatic aberrations in human eyes. Different from other models, the Liou model uses a gradient index of refraction for the crystalline lens, which is more realistic for the actual human eye, but its use greatly increases the complexity of the optical calculation. Among all the published eye models, the Navarro model was developed with regard to off-axis aberrations for a field angle up to 60 degrees. The parameters used in these 3 models are listed in Table 1. Optical computations were performed using the assembled models, and the aberration results presented in the original papers were reproduced. The results of the longitudinal spherical aberration (LSA) and chromatic aberration (LCA) of these 3 model eyes, along with Gullstrand model, are shown in Fig. 1.

Table 1. Parameters used in the construction of the three eye models along with Gullstrand model.

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In the simulation, the significant eye and system parameters, such as the pupil diameter, the eye location and its orientation with respect to the camera and light source, the size and shape of the light source, and the entrance pupil of camera, are included in the computational model. After the standard eye models are created for the normal human eye, the effect of various eye conditions as observed by the measurement instrument can be evaluated by the adjustment of the ocular parameters. For example, the degree of spherical aberration can be varied by changing the asphericity or conic constant of the cornea or lens surfaces, and adjusting the dispersive power of the index of refraction varies the degree of chromatic aberration. Refractive errors can result, however, from one or more anatomical irregularities. As an example, for a myopic eye the cause of the condition could be an over-powered curvature in any surface of the cornea or lens, a stronger index of refraction gradient in lens, or an increase in the length of the eyeball. The evaluation of the diagnostic method for different abnormalities can be performed. To synthesize different degrees of refractive error of the subjects in this paper, we introduce a virtual paraxial lens at the location of the iris in each of the model eyes. With a small pupil diameter of 3.0 mm, we iterate the power of the virtual lens to approach the far point position from the front of the cornea for a target refractive error. Since this condition is nearly paraxial, the required powers for the virtual lens using these 3 eye models appear, as expected, to vary nearly linearly with the target refractive error. As shown in Fig. 2, these values for the three models are nearly equal. This virtual lens introduces a constant refractive power across the pupil area without changing other optical parameters of the eye, which is ideal for isolating and evaluating a single effect.

 

Fig. 1. Longitudinal spherical aberration (LSA) and chromatic aberrations (LCA) in different eye models. The reference wavelength in the LCA plot is 589 nm.

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One of the assumptions in the model eye construction for the photorefraction simulation is the nature of scattering from the retinal surface. Most of previous theoretical works assume the retina to be a perfect diffusive surface and treat the illumination of light source upon retina as a new light source. Campbell and Roorda [8–10] use an attenuation factor to incorporate the directional property of retina. This attenuation factor decreases the intensity in the periphery of the retina reflex and produces a photorefraction slope profile that matches the experimental result. In this paper, we assume a spherical Lambertian retinal surface instead of the plane surface used by other theoretical works. How significantly the retinal property affects photorefraction requires further analysis. The retinal property, as well as other parameters used in any eye models, depends on at least the age, gender, and race of the subjects and varies from individual to individual. If the statistical variance of a parameter is known, the corresponding measurement uncertainty can be evaluated.

 

Fig. 2. Power of the virtual lens used to produce refractive prescription of model eye.

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The light source used in the photorefraction method is either a point (such as visible or IR LED source) or an extended source (one- or two-dimensional). Normally the size of extended source is less than a few prism diopters (cm per meter working distance) in either dimension when viewed from the subject in the eccentric arrangement, and the light source is normally located near the camera lens with an off-axis distance that is smaller than a few prism diopters from the eye. This eccentric distance and the aperture size and shape of camera determine the sensitive range of refractive detection. In the calculation, the eccentric distance can be set from zero to an arbitrary distance, and the camera focus can be set to any location to produce predictions for co-axial photorefraction or eccentric photorefraction. For specific comparison purposes, most of parameters of the optical system are chosen to be appropriate to the iScreen Digital photoretinoscope [29]. The distance between the subject and the camera is 800 mm, and the eccentric, or off-axis, distance is 11 mm. This instrument uses as a light source a broadband white photographic flash lamp with a size of 10 mm by 3 mm, and the camera entrance pupil is 25 mm diameter and is shielded at the flash location. For our computations for each image calculation, one hundred million (10⁸) source rays are traced toward a constant entrance pupil of 8 mm diameter of subject, and we assumed a monochromatic source of 555 nm to demonstrate the optical irradiance features of the models.

3. Simulation results and discussion

Figure 3 shows the simulation results of the iScreen eccentric digital photoretinocope using the published Navarro eye model [21] with synthetic refractive prescriptions from +10 diopters hyperopia (left) to of -10 diopters myopia (right). The pupil diameter, which is indicated with a reference circle in each image, ranges from 3 mm to 7 mm. The wavelength of 555 nm, which is most sensitive to human eye, is used. The false-color levels are scaled according to the maximum illumination, or irradiance, in each row of data, and they decrease from 100% to about 70, 50, 30, and 16%, which roughly correspond to the ratios of the total input irradiance at the pupil.

The first row of images in Fig. 3 (7 mm pupil diameter) shows a typical simulation result. For the nearly emmetropic eye (~0 diopter), the irradiance across pupil space of the PR image is very dark. For a mildly myopic (hyperopic) eye, the bright crescent appears at the lower (upper) corner of pupil. As the refractive error increases, the crescent size (or the FWHM of the irradiance) increases monotonically until about ±4 diopters. For an eye with higher degree of refractive errors, the crescent shapes become more circular and the change in shape and irradiance become less sensitive. The dark center area where the photorefraction method is insensitive is called the dark zone (DZ) or dead zone. The sensitive detection ranges are between the boundary of dark zone and ~±4 diopters. Depending on the detection range of interest, the sensitive range can be extended outward to the higher refractive error regions by increasing the eccentric distance of the system (or, normally, the vertical distance between camera and light source) and /or the entrance pupil diameter of the camera. From the second to the fifth row in Fig. 3, the simulation results of smaller pupil sizes are presented. The dark zone areas increase toward the myopic side when the pupil sizes are smaller. The sensitive ranges move toward higher refractive errors which characterize an ever decreasing population. In addition to the reduction of total signal intensity for smaller pupil sizes (16% at 3 mm pupil compared to 100% at 7 mm pupil), many photorefraction vision screening programs claim a detection minimum limit of 3 mm pupil diameter. Therefore the screenings are usually performed in a darkened environment to ensure larger pupils.

In photorefraction, the center of dark zone (CDZ) is a very important parameter since it represents the baseline of symmetry of crescent size or slope profile (ignoring the opposite in vertical orientation). However, as the results show, the center of dark zone moves and the dark zone width decreases with the pupil enlargement. Without knowledge of the pupil effect, the reading of refractive status is questionable.

 

Fig. 3. Simulated photorefraction images with pupil diameters from 7 mm to 3 mm (top to bottom). From left to right, the refractive errors are indicated at the bottom.

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The basic optical concept of photorefraction (or retinoscopy) is that the light rays from a distant source enter the eye, are reflected from the retina, and are then collected by the detection camera (or examiner’s eye), which is near the location of the light source. For a normal eye, the light rays from the far zone are focused or imaged onto the retina into the smallest size. The reflected (or scattered) light rays from retina are then focused by the eye in the second pass and form a converging (if myopic) or diverging (if hyperopic) cone, symmetric to the axis that connects the eye and light source. Normally, the signal light cone from an emmetropic eye has the smallest solid angle. The solid angle of the reflection light cone increases with the degree of refractive error. When the light cone reaches the detector plane, the eccentric distance comes into play. Since the camera is located off-axis, the dark zone is created when the camera aperture cannot capture signals of the light cone of near-emmetropic eyes due to the eccentric alignment. When the refractive error increases slightly so that the corner of the light cone barely reaches the pupil of the detector (or camera aperture), a thin crescent appears. As the refractive error increases, the projection of light cone on the detector plane increases and the crescent size increases accordingly. When the refractive error continuously increases so that the light cone projection covers the whole detector aperture, the crescent become more circular. For refractive errors greater than this value, the change in irradiance profile becomes less sensitive, or saturated. This determines the sensitive range of detection of the optical instrument. The aperture of the camera, therefore, affects the sensitive range in photorefraction. The converging cones in the myopic case reverse the orientation of light distribution from the pupil plane to the detection plane. This results in a crescent appearance for myopic eye that is opposite to that of the hyperopic eye in photorefraction.

The visual acuity (VA) is a measure of the ability of the eye to recognize detail. VA is defined and measured for a pupil diameter of approximately 3 to 4 mm. When the pupil diameter is smaller than 2 mm, which occurs for very bright illumination conditions, diffraction effects become significant. When the pupil size is larger than 5 mm, which occurs in the darkened environments, the spherical aberration near the periphery can be very strong (see Fig. 1). In both cases, the acuity performance is degraded. In a normal clinical setting for the routine measurement of the spherical and cylindrical refractive errors, the brightness of environment is such that the pupil size is within the proper range. In the 3mm pupil diameter case in Fig. 3, if we examine the center of dark zone (CDZ) location numerically, it is clearly seen that its location of -1.25 diopter marks the reciprocal of the location of light source (0.8 meter in iScreen instrument) in photorefraction, and this value is verified for computations of all eye models used. Because the light source is not at infinity, the corresponding myopic eye (-1.25 D in this case) will image the light source onto the retina and will produce a smallest light cone projection on the detection plane. Therefore, for a 3 mm-diameter pupil, the center of the dark zone can be determined as the reciprocal of the distance (in meter) between the eye and the light source.

When the light source with wavelength other than 555 nm is used, the chromatic effect of human eyes is of concern. The refractive power difference of human eyes from the red at 700 nm to the blue at 400 nm is as large as 2.3 diopters (see Fig. 1). With the wavelength correction, the CDZ for a 3 mm pupil can be expressed as: CDZ_3mm-pupil=-(1/d)-LCA, where d is the working distance between eye and the light source and the LCA term is the longitudinal chromatic aberration correction. The CDZ for the 3 mm pupil can be treated as a constant since the LCA term is a very stable function of wavelength among the population [31–35]. Figure 4 shows the simulation result of the CDZ shift with wavelength at 3-mm pupil diameter. The precision of this set of simulation data is 0.1 diopter instead of the 1 diopter step shown in Fig. 3. The longitudinal chromatic aberration (LCA) of the Navarro model along with 4 published ocular measurements of LCA are compared. When a broadband light source such as a white flash lamp is used in photorefraction, the resulting irradiance is an integral over wavelength of the source spectral irradiance. In some cases, the red crescent appears on the top with the blue crescent at the bottom in the PR images when a white flash lamp is used. Because of the significant LCA of the human eye and the variation of spectral characteristics of retina, either a narrow-band light source or spectrally filtered detection is suggested for PR measurements

 

Fig. 4. Comparison of CDZ shift in photorefraction with 4 published measurements of ocular chromatic aberration and eye model. All data are adjusted vertically to have a zero value at the reference wavelength of 589 nm.

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As the pupil diameter increases from 3 mm, the center of dark zone can no longer be characterized by the well-defined expression because the spherical aberration (SA), which is a function of pupil radius [31] (also see Fig. 1), exhibits significant individual variation,. As shown in Fig. 1, the Navarro model eye has a LSA value of +2 diopter for a 7 mm diameter pupil. Therefore, the shift of center of dark zone shifts from -1.25 diopter to a positive value (see Fig. 3). It is noted that the intensity distribution of the photorefraction image is the integration of light rays with different ray height and that the CDZ shift cannot exceed the LSA (+2 D) at the periphery of pupil. Figure 5 shows the simulation results of 3 different eye models at 7 mm pupil diameter.

Figure 5 shows the simulation results of 3 different eye models at 7 mm pupil diameter. The Arizona and Navarro models predict the centers of symmetry on the slightly hyperopic side at about +0.5 and +0.25 diopter while the Liou model produces a symmetric center near the myopic location of -0.75 diopter. As described earlier, the center of symmetry at large pupil is shifted by the LSA (see Fig. 1). The LSA at 7 mm diameter are about +2.0, +2.25, and +0.75 diopters, respectively, for the Navarro, Arizona, and Liou model eyes, which are comparable to the shifts of CDZ in Fig. 5. In conclusion, the center of dark zone can be expressed as CDZ(d, λ, r)=-(1/d)-LCA(λ)+fuc(LSA(r)), where fuc(LSA(r)) is a function of LSA, which is a function of pupil radius, r.

The next observation in Fig. 5 is the different widths of dark zones in the simulation result. The Liou model has the widest dark zone about 1 diopter while Arizona model has basically no dark zone. As understood in photorefraction theory, the width of dark zone depends on two parameters: the minimum size of the retinal reflex cone and the eccentric distance between the light source and camera. Since the systematic parameters are fixed in these 3 sets of calculations, the difference is a result of the aberrations of the eyes. Suppose the eye is a perfect optical imaging system; at the CDZ condition, the retinal plane would be the conjugate plane of the light source and camera plane. The minimum size of the reflection cone projection would approach the diffraction limit at the detection plane. With aberrations in the ocular system, the CDZ location shifts to compensate aberrations and to approach a smallest focus on retina. The projection size of retinal reflex on the camera plane is related to the aberrations of the eye. In photorefraction, the spherical aberration is dominant when the eye is well aligned. It is obvious that this minimum size of retinal reflex is affected by the LSA in the simulation of the 3 models. Because the Liou model has a significantly smaller LSA value, it produces the narrowest retinal reflex cone at the CDZ eye condition compared to the other 2 models and therefore the widest range of dark zone.

 

Fig. 5. Simulation results of photoretinoscope images using Navarro, Arizona, and Liou eye models. From left to right are eyes with refractive error of +10 to -10 diopters. The irradiance levels in all calculation results are related.

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The slope intensity profiles across the center or pupil from PR images are shown in Fig. 6. The quantitative signal and intensity profile comparisons of the different eye models show small differences in their shape and magnitude across each image except for the shift of the CDZ and the width of dark zone. The attractive implication of this result is that either the slope or crescent measurement should be a reliable measure for the refractive error once the CDZ and the width of dark zone are determined.

To compare the computations and measurements, a series of eye images from volunteers was obtained in the darkened laboratory using the iScreen digital retinoscope [29]. Contact lenses were used to simulate the required refractive corrections. Shown at the top of Figs. 7 and 8, respectively, are the original photorefraction images of an Asian (BT) and a Caucasian (KP) volunteers. The examinees in the true-color photographs wore contact lenses of -5D and +5D, which produce, respectively, the hyperopic eye on the left and myopic eye on the right in the photograph. A target-finding code was created to locate the irises, pupils, and the white cornea reflections (the first Purkinje image) and to obtain the fitted pupil diameters. In the iScreen photographs, when the retinal reflex is not too strong, the 4^th Purkinje reflection can be observed at the nasal upper side of the first Purkinje point. The positions of these two reflections with respect to the center of iris can be used to identify the gazing angle of the subject to a specified accuracy. Comparing with the calculated results, it is seen that many of the images in the experiment data appear tilted. This results from, in additional to gazing angle variations, the displacement of the location of subject from the optical axis. The following photographs are a row of cropped and target-located images ranging from hyperopic to myopic eyes. The pupil diameters in Fig. 7 are obtained from the fitting, and they are 7.1±0.5 mm, and in Fig. 8 are 7.6±0.2 mm. The spectral images of the series of data using the red (574–730 nm), green (508–584 nm), and blue (400–510 nm) broad-band filters, respectively, are presented in the following three rows. The false- colored scale map is the same as used in Figs. 3 and 5. The minimum and maximum counts, respectively, in the spectral images are 100 (noise and background, presented as blue) and 255 counts (shown as pink) and are limited by the digital camera (8 bits per color per pixel) and iScreen system performance.

 

Fig. 6. Slope profiles from the simulation results of Fig. 5. The forms, or shapes, and the magnitudes of the irradiance profiles are similar within the 3 models’ result except for the shifted in refractive power (CDZ position) and the width of insensitive zone (dark zone). These differences are results from the monochromatic aberrations inherited with the eye models.

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For the Asian’s images in Fig. 7, the blue images contain only the background scattering and noise from the system. None of the blue images shows any sign of a crescent structure. Because of the higher absorption of the human retina at shorter wavelengths, the refractive power information of the eye is too low in the blue region to be observed compared to that of the green and red signals. Although significant retinal property variation exits among a diverse population, the blue signal is always comparably low for normal refractive error conditions.

The green series, 508–584 nm, of iScreen images in Figs. 7 and 8 are comparable with the simulation images in Figs. 3 and 5 at 555 nm. With increase of refractive errors toward both sides, the irradiance of images reduce and the shapes tend to be circular. At the refractive power of +1 diopter in Fig. 7, the red crescent appears at the upper side before the green crescent can be observed due to the chromatic aberration of human eye. The measured chromatic aberration from the center of red (574–730 nm in the camera) to the center of green band is about 0.7 diopter (Fig. 4), which is less than the step size of one diopter in the series of images taken. However, the shift from the center of green to blue (400–510 nm) in human eyes is about one diopter. The green-to-blue CDZ shift in Fig. 8 is more observable.

 

Fig. 7. Experimental data using iScreen photoretinoscope. Upper row: original photographs. The iris, pupil, and the 1^st Purkinje image from cornea in each photograph are circled using a target-finding program. Second to forth row: Intensity distribution of the original data in red (2^nd row), green (3^rd row) and blue (4^th row).

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Fig. 8. Experimental data taken from a Caucasian using iScreen photoretinoscope. Upper row: original photographs. The iris, pupil, and the 1^st Purkinje image from cornea in each photograph are circled using a target-finding program. Second to forth row: Intensity distribution of the original data in red (2^nd row), green (3^rd row) and blue (4^th row).

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When examining CDZ locations in Figs. 7 and Fig. 8, the significant difference of ~ 1.25 diopter appears. The Asian data in Fig. 7 seem to exhibit a stronger spherical aberration that is close to the Arizona model eye, and the Caucasian data in Fig. 8, on the other hand, appear to have a small SA that is closer to the Liou model. Unlike the chromatic aberration, ocular spherical aberration exits large variation among a diverse population.

One of the differences between the data of BT and KP is the signal level in all three colors. Caucasians usually have very high retinal reflectivity in red region. This can be easily observed from daily photographs. In Fig. 8, most of the red images appear to be saturated. A ‘background’ of ~50 counts (over the 150 counts dynamic range of iScreen camera in each color) of red signal exit all over the pupil area throughout all the images in Fig. 8. If the red background signal and the saturation problem of Caucasians’ are not properly solved, the slope profile or crescent size method would be unjustified.

Next, the dark zone width in Figs. 7 and 8 appear to be increasing toward shorter wavelength. The simulation results at different wavelengths do not provide the proof this observation. In the other words, the wavelength of the source does not affect the light cone angle of retina reflex significantly according to the theory considered. Since the optical system and eccentric condition are fixed during the measurements, the cause of different dark zone spans is suggested to lie in the retinal and aberration properties of the two individuals. As described earlier, the wider dark zone indicates a narrower spreading cone of retina reflection signal. The Caucasian’s results compared with that of the Asian may suggest a wavelength-dependent retinal property that we do not include in the simulation. Another possible cause is simply that a series of images of each color is not presented with normalized irradiance. If the signal level in each series is normalized to its maximum and if the camera dynamic range is sufficient for all measurements, the dark zone width may not be different in three colors. If this is true, the retinal variation among a diverse population may not be a difficult issue for photorefraction simulation as we supposed at the outset of this study.

4. Summary

We have presented the theoretical analysis of photorefraction using three-dimensional ray tracing and realistic models of the human eye, and utilizing a commercial digital photoretinoscope, example images were obtained for two subjects of different racial groups. The analysis reconciled the predictions using the different eye models and was employed to develop predictive performance parameters for a practical measurement device. The subjects’ images provided operational data of the commercial device, indicated differences to be found for different racial groups, and served for comparison with the computational predictions. We described the two important parameters in photorefraction: the width of dark zone and the center location of dark zone (CDZ). At small pupil sizes, the center of dark zone is located at the reciprocal of light source distance (in diopter) minus the logitudal chromatic aberration. This parameter is stable from individual to individual since the chromatic aberration of human eyes does not vary within 0.1 diopter throughout the wavelength range, and this value is a constant once the light source position and wavelength are determined. When the pupil size is greater than 3 mm in diameter, spherical aberration contributes significantly to the result, which negates the practical use of the CDZ. Further, the measurement of the crescent size or slope profile is not reliable without correcting the bias of CDZ. The maximum width of the dark zone and the sensitive range of detection are determined by the photorefraction instrumentation, which include the eccentric distance, light source size and shape, and camera aperture and shape. The ocular aberrations reduce the width of the dark zone by increasing the angle of retinal reflex.

Some factors that affect the photorefraction measurements have not been discussed in this paper. For example, the interference effect from the tear film can produce unexpected results. Figure 9 shows three photorefraction images that were taken shortly after blinking of the eyes. From left to right, the eyes in these three images exhibit refractive errors of -1, -2, and +5 diopters. The interference patterns in these images redistribute the brightness around the wavefront of the tear. Occasionally, the image becomes difficult to analyze (as the right image shows). The tear wave could be modeled in the current eye models to produce the prediction of interference patterns. However, the computer decoding of PR photographs with tear-wave interference is still difficult.

 

Fig. 9. Tear waves appeared after blinking eyes may cause interference patterns in photorefraction measurement.

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A second example of a potentially significant parameter is the “red reflex” that appears in almost all Caucasian eyes, some African-American eyes, and almost no Asian eyes. This red reflex can be observed in a great range of gazing angles as long as the pupil size is sufficiently large. As mentioned previously, this signal appears as a constant background in one direction and carries no refractive information. It results from a portion of rays that are scattered/reflected more than once before they leave the pupil. They require to be modeled separately in the simulation. When photorefraction is applied in red or NIR regions where the retina has less absorption, the additional part of modeling and proper background subtraction should be considered.