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A ray (single arrow) emerging from a retinal point passing through the exit pupil at a radius r crosses the principal ray (double arrows) from the same point a distance k ͑ r ͒ . The transverse aberration, t ͑ r ͒ , is a measure of the emerging ray intercept position from the principal ray intercept in a plane perpendicular to the optical axis at a specified distance l from the exit pupil.
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A geometrical-optical analysis is developed to predict the reflex observed in retinoscopy. The analysis can be expanded to explain the reflex for an eye with aberrations. The succession of reflexes across the pupil for each position of the retinoscope is represented in a contour plot. The plots demonstrate that retinoscopy can be considered a measu...
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... the monochromatic aberrations of the eye. If the aberrations are known, we can predict what the retinoscopic reflex will be. Our technique uses computer algorithms to trace many rays through the eye. We used this technique to predict successfully intensity profiles in eccentric photorefraction for any degree of aberration. 21,22 Previously we modeled the optics of eccentric photorefraction, using a source whose position was fixed with respect to the camera aperture. 23,24 The camera aperture was assumed to be large. In adapting the model to analyze the optics of retinoscopy, two major changes had to be made. First, we allowed for the motion of the source with respect to the sight hole induced by tilting the retinoscope, and second, we had to consider the finite limits of the small sight-hole aperture. Furthermore, the retinoscopist typically uses corrective lenses to neutralize the reflex, whereas eccentric photorefraction is more rapid by allowing for image analysis of a single pupillary light reflex, although the use of corrective ophthalmic lenses is possible. 25,26 The unique feature of our model is that it explicitly considers the double-pass nature of the formation of the reflex and it can be used for any general aberration in the eye. The analysis is performed in two steps, the first for light entering the eye and the second for light leaving the eye. Because, in most cases, retinoscopy is performed along the principal astigmatic meridians, our analysis is limited to measurements along these meridians. In our current study, our optical model is tested em- pirically. We investigate the possibility of determining the transverse aberration of the eye by using a hand-held retinoscope and also use a CCD-based retinoscope to provide a more quantitative comparison of the experimental and predicted results. A standard retinoscope has a source located in the handle of the instrument. The light from the source reflects from a mirror oriented 45 ± from vertical, forming a virtual image of the source behind the mirror. The retinoscopist views the pupil of the subject through a small sight hole in the center of the mirror. The retinoscopist directs the divergent beam from the virtual source toward the subject’s pupil and drives it across the pupil by tilting the retinoscope. Hereafter we refer to the driving of the beam as scoping. Tilting the retinoscope causes the virtual image of the light source to shift its eccentricity from the sight hole in the center of the mirror (Fig. 1). The changing eccentricity of the source with respect to the sight hole causes the appearance of the reflex to change, depending on the refractive state and aberrations in the eye. The retinoscopist uses motion and brightness of the reflex to determine the refractive state of the eye. We present a simplified model that will qualitatively explain the phe- nomenon of reflex motion. This model illustrates how the presence of defocus and aberrations affect the waist of rays returning to the retinoscope and predicts the resulting retinoscopic reflexes (Fig. 2). As shown in Fig. 1, one normally tilts the retinoscope and causes a movement of the virtual source of light with respect to the aperture. To simplify the ray diagrams in Fig. 2, we use a frame of reference in which the sight-hole aperture moves with respect to the source as the retinoscope is tilted. The simplified model considers only the second pass through the optics. We assume that there is a small spot projected onto the retina that diffusely reflects, thereby acting as a secondary source of light. The light from the spot on the retina emerges from the subject’s pupil into a fan of rays whose intercepts are determined by the defocus and aberration of the eye. The principle of the origin of the reflex is that, if a ray from a particular point in the subject’s pupil enters the sight-hole aperture, then that point on the pupil will appear luminous. One observes the succession of reflexes by moving the aperture across the fan of rays that emerges from the subject’s pupil. The simplified model offers a quick and intuitive expla- nation for the origin of the reflex based on the waist of rays at the retinoscope and the relative change in source- aperture eccentricity. This model is easy to visualize and is usually sufficient to explain effects of defocus and aberrations in retinoscopy because the retinoscopist generally concentrates on the motion of the retinoscopic reflex. For a complete description, however, we must consider the extended blur on the retina from the first pass through the optics. The ray tracing model uses the same theory that was previously used to predict eccentric photorefractive intensity profiles. 22 In our analysis the eye is modeled as a single refracting surface, where the function k ͑ r ͒ defines the aberrations in the eye. This function repre- sents the change in the far point of the eye as a function of the radius from the geometrical center of the pupil (Fig. 3). In other words, k ͑ r ͒ defines the distance to the intersection point of a ray emerging at radius r with the principal ray ͑ r 0 ͒ . This function can be derived from measurements that use either objective 28,29 or psychophysical 30,31 techniques. The function k ͑ r ͒ can define both symmetric (e.g., spherical) and asymmetric (e.g., coma) aberrations. A constant value of k represents a simple defocus error for which the far point is the same for all radii. The refractive state of the eye is the reciprocal of this value; K 1 ͞ k . By conven- tion, for distances measured perpendicular to the optical axis, temporal is positive and nasal is negative. Also, k ͑ r ͒ is negative for distances measured in front of the eye and positive for distances measured behind the eye. The aberration commonly measured experimentally is the transverse aberration. The transverse aberration, t ͑ r ͒ , is a measure of the general ray intercept position from the principal ray intercept in a plane perpendicular to the optical axis. The conversion from t ͑ r ͒ to k ͑ r ͒ can be calculated by geometrical optics and is given ...
Citations
... 180 Therefore, refraction methods that employ a known pupil location, repeatable across time, are preferred. For example, eccentric photorefraction and retinoscopy can have their results affected by aberrations in the pupil margins, 181,182 while participantive refractions are biased toward the pupil center. 183 Objective methods that employ a known measure-ment aperture that can be repeatedly located in (or close to) the pupil center are recommended. ...
The evidence-basis based on existing myopia control trials along with the supporting academic literature were reviewed; this informed recommendations on the outcomes suggested from clinical trials aimed at slowing myopia progression to show the effectiveness of treatments and the impact on patients. These outcomes were classified as primary (refractive error and/or axial length), secondary (patient reported outcomes and treatment compliance), and exploratory (peripheral refraction, accommodative changes, ocular alignment, pupil size, outdoor activity/lighting levels, anterior and posterior segment imaging, and tissue biomechanics). The currently available instrumentation, which the literature has shown to best achieve the primary and secondary outcomes, was reviewed and critiqued. Issues relating to study design and patient selection were also identified. These findings and consensus from the International Myopia Institute members led to final recommendations to inform future instrumentation development and to guide clinical trial protocols.
... Swaine used a simple model to predict further pupil size influence and the intensity profile of the reflex [19][20][21][22]. Higher order aberration that is normally considered a difficulty in retinoscopy interpretation has been investigated more carefully in recent years [23,24]. Rather than the spot retinoscopy, Smith included the consideration of streak orientation and brightness change in the presence of astigmatism [25]. ...
Realistic simulation of ophthalmic measurements on normal and diseased eyes is presented. We use clinical data of ametropic and keratoconus patients to construct anatomically accurate three-dimensional eye models and simulate the measurement of a streak retinoscope with all the optical elements. The results show the clinical observations including the anomalous motion in high myopia and the scissors reflex in keratoconus. The demonstrated technique can be applied to other ophthalmic instruments and to other and more extensively abnormal eye conditions. It provides promising features for medical training and for evaluating and developing ocular instruments.
... From a theoretical point of view, several analyses of retinoscopy can be found in the literature (see for example [3]). Most of them only consider refractive errors and the global effect of aberrations on this technique was not considered until the work of Roorda and Bobier [7]. They use a geometrical-optics approach to analyze the retinoscopic reflex for a reduced eye model with aberrations. ...
... Thus, to analyze a complete scope along one of the eyeÕs meridians different optical axes must be defined, one for each source position. In order to simplify the analysis we use an alternative frame of reference (as in [7]) in which the sight-hole aperture moves with respect to the fixed source. Although this approach is not fully equivalent to conventional retinoscopy, it is even simpler to implement experimentally. ...
The influence of optical aberrations on the retinoscopic reflex is theoretically analyzed from a geometrical point of view. The relationship between the wave aberrations to the ray aberrations is applied to explain the appearance of the retinoscopic patterns for different types of ocular aberrations. Several schematic models of the human eye are tested numerically, showing that a careful retinoscopic examination can detect the usual eye aberrations.
... 13 Aberrations also influence the retinoscopic measure. 14 An increase with age of the error between subjective refraction and autorefraction has been found, 15 which could arise from the fact that higher-order aberrations increase with age. 16,17 Some autorefractors may somehow incorporate the effect of higher-order aberrations by, for example, maximizing the contrast of a target imaged on the retina. ...
We explored the impact of the eye's higher-order aberrations on subjective refraction comparing two classes of methods for estimating refractive state, one based directly on the wave aberration defined in the pupil plane and another based on the retinal image plane. The method defined in the pupil plane chose the sphere and cylinder that either minimized the wave aberration root mean square or minimized the sum of all the spherical and cylindrical components in the wave aberration. The method defined in the image plane chose the sphere and cylinder that optimized an image-quality metric such as the Strehl intensity ratio, the entropy and the intensity variance of the point-spread function, the volume under the modulation transfer function, or the volume under the contrast-sensitivity function. All these methods were compared in a population of six eyes for which we measured both the wave aberration with a Shack-Hartmann wavefront sensor and the subjective refraction under identical conditions. Pupil plane methods predicted subjective refraction poorly. The mean absolute error of the prediction, in spherical equivalent, was about 0.5 D (range, 0.1 to 0.8 D) and increased with increases in higher-order aberrations. However, for all the retinal image plane methods, the mean error between predicted and subjective refraction was about 0.1 D (range, 0 to 0.25 D). The reliability of the method based on the image-quality optimization was further confirmed in a large population of 146 eyes. In conclusion, higher-order aberrations influence the amount of sphere and cylinder required to correct vision. The results indicate that subjective refraction can be predicted from the eye's optics alone by optimizing computed retinal image quality.
Purpose:
We tested the hypothesis that changes in accommodation after instillation of Phenylephrine Hydrochloride (PHCl) observed in some studies could be caused by changes in optics.
Methods:
We performed two experiments to test the effects of PHCl on static and on dynamic accommodation in 8 and 6 subjects, respectively. Objective wavefront measurements were recorded of the static accommodation response to a stimulus at different distances or dynamic accommodation response to a sinusoidally moving stimulus (between 1 and 3 D of accommodative demand at 0.2Hz). The responses were characterized using two methods: one that takes into account the mydriatic optical effects on the accommodation produced by higher-order aberrations of the eye and another that takes into account only power changes paraxially due to the action of the ciliary muscle and regardless of the pupil size.
Results:
When mydriatic optical effects were taken into account, differences in responses before and after PHCl instillation were 0.51±0.53 D, and 0.12±0.15, for static and dynamic accommodation, respectively, and were statistically significant (p<0.039). When mydriatic optical effects were not taken into account, the differences in responses before and after PHCl instillation were -0.20±0.51 D, and -0.05±0.14, for static and dynamic accommodation, respectively, and were not statistically significant (p>0.313).
Conclusions:
The mydriatic effect of the PHCl causes optical changes in the eye that can reduce the objective and subjective measurement of accommodation.
Aberrations of the human eyes in the horizontal visual field were measured with modified Hartmann-Shack wave front sensor. The characteristic of third to tenth order Zernike aberration rms both temporally and nasally out to 50° is as follows: considerable differences occur among subjects in the pattern of aberrations, particularly for the dominating second-order aberrations; the third to tenth order Zernike aberrations increase with the visual angle, but the increscent magnitude decreases as the Zernike order increases; in despite of imperfect symmetry, the increscent magnitude is the same on the whole; the third-order Zernike aberrations increases up to 2 times from 0° to ±50° visual angle, the forth-order up to 1.8 times, and the fifth to tenth order up to 1.7-1.3 times.
The Wigner distribution is used to model the PSF of an aperture mask at different defocus planes. Algorithmic methods of determining an optimal mask pattern for a desired set of impulse responses are investigated.
Many fish and some terrestrial animals have multifocal lenses that compensate for
chromatic aberration by a mechanism unique to biological optical systems. We describe
four optical methods for the study of such lenses. Significantly improved methods
(focal-area imaging, schlieren photography, and laser scanning) are explained in
full detail. One method (photorefractometry) was only slightly modified over
earlier versions and is illustrated in brief. Portable equipment is available for
photorefractometry, schlieren photography, and laser scanning. With our methods
we could for the first time directly illustrate chromatic correction by multifocal
lenses and detect a number of previously unknown optical features of fish lenses.
The ultimate stage in most optical imaging systems is the formation of an image on the retina, and the design of most optical systems takes this important fact into account. For example, the light output from optical systems is often limited (or should be limited) to the portion of the spectrum to which people are most sensitive (i.e., the visible spectrum). The light level of the final image is within a range that is not too dim or bright. Exit pupils of microscopes and binoculars are matched to typical pupil sizes, and images are often produced at a suitable magnification, so that they are easily resolved. One even incorporates focus adjustments that can adapt when the user is near‐ or farsighted. Of course, it is understandable that a man‐made environment is designed to fit within sensory and physical capabilities. But this process is not complete. There is still much to know about the optical system of the human eye, and as understanding of the eye increase better ways to present visual stimuli and to design instruments are learned.
This article focuses on the way images are formed in the eye and the factors in the optical system that influence image quality.
