Estimates of the ocular wave aberration from pairs of double-pass retinal images

We apply a computational technique to retrieve the wave aberration of the eye from the point-spread function obtained from pairs of double-pass retinal images. The method consists of an adapted pyramidal version of a nonlinear least-squares fitting procedure to a wave aberration expressed as an expansion in Zernike polynomials. Although the procedure provides accurate estimates of the wave aberration, it presents several drawbacks that are discussed in detail. In particular, since a great deal of computational time is necessary to retrieve a single wave aberration, this technique is not useful for real-time applications. We present results of wave aberrations in five normal subjects in the fovea for a 4-mm-pupil diameter. In every case there is a clear presence of comalike aberrations, while the third-order spherical aberration is usually smaller than previous estimates. The root-mean-square error in the retrieved wave aberration, when defocus and astigmatism were corrected, ranges from 0.24 to 0.5 wavelength. The particular values of the aberration coefficients present a large intersubject variability.     

Comparison of the eye's wave-front aberration measured psychophysically and with the Shack-Hartmann wave-front sensor

The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack-Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of approximately lambda/2 and approximately lambda/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack-Hartmann wave-front sensor for measuring the optical quality of the human eye.     

Measurement of the wave-front aberration of the eye by a fast psychophysical procedure

We used a fast psychophysical procedure to determine the wave-front aberrations of the human eye in vivo. We measured the angular deviation of light rays entering the eye at different pupillary locations by aligning an image of a point source entering the pupil at different locations to the image of a fixation cross entering the pupil at a fixed location. We fitted the data to a Zernike series to reconstruct the wave-front aberrations of the pupil. With this technique the repeatability of the measurement of the individual coefficients was 0.019 micron. The standard deviation of the overall wave-height estimation across the pupil is less than 0.3 micron. Since this technique does not require the administration of pharmacological agents to dilate the pupil, we were able to measure the changes in the aberrations of the eye during accommodation. We found that administration of even a mild dilating agent causes a change in the aberration structure of the eye.     

Influence of Stiles-Crawford effect apodization on spatial visual performance

The Stiles-Crawford effect is often invoked by vision scientists when predictions of the effects of aberrations and defocus on spatial visual performance are not borne out experimentally. Modeling the Stiles-Crawford effect as an apodization, we investigated the expected influence that it would have on spatial visual performance in the presence of 1-diopter primary spherical aberration at the edge of a 6-mm-diameter centered pupil. The changes in refraction produced by a high Stiles-Crawford effect, according to various criteria, were small at approximately 0.10 diopter. The Stiles-Crawford effect has only a small capability to compensate for defocus and spherical aberration. These results indicate that the Stiles-Crawford effect has little influence on spatial visual performance in the case of centered pupils. We suggest that the faith that has often been placed in the Stiles-Crawford effect to account for discrepancies between experimental results and expected results is not justified, at least for well-centered pupils and Stiles-Crawford effects.     

Why is the eye round?

By an unsophisticated experiment, published data on the anatomy of the eye, wave theory of light, and the laws of geometrical optics the author tries to prove that a spherical concave screen is the optimal variant of a screen on which spherical wave front is projected, formed by a single lens. The shape of the wave front and of the concave screen are in complete agreement. Such optical imperfections as the field curvature, distortion, coma (partially), and astigmatism of the oblique light beams are compensated for. These optical drawbacks are undetectable on a concave screen, and hence they are proposed to be the shortcomings of a flat screen. The author compares this to a spherical shape of the eye, the posterior wall of which represents a concave screen, an indisputable fact, and assumes that the before-named optic imperfections are completely compensated for in human eye due to concavity of the posterior optic wall. Based on the anatomy and practical results of using aspherical refracting surfaces in artificial optic devices, the author draws a parallel with the anatomical structures of the eye possessing aspherical refracting surfaces in order to demonstrate that higher and lower-order spherical aberrations (Zeidel's aberrations) are fully compensated for in human eye, as are the position and enlargement chromatism. Analysis of published data permitted the author to assert that the eye of man is characterized by a method for compensation of spherical aberrations, which has no analogs in man-made practice. Hence, the Nature has imparted the eye with such a collection of compact, universal, and highly effective methods for compensation of optic imperfections, which is not to be found in any of the man-made devices of today.     

Predicting the effects of optical defocus on human contrast sensitivity

We used diffraction modulation transfer functions and model eyes to predict the effect of defocus on the contrast sensitivity function (CSF) and compared these predictions with previously published experimental data. Using the principle that optically induced changes in the modulation transfer function should be paralleled by identical changes in the CSF, we used the modulation transfer function calculations with the best-focus CSF measurements to predict the defocused CSF. An aberration-free model predicted the effects of defocus well when the CSF was measured with small pupils (e.g., 2 mm) but not with larger pupils (6-8 mm). When the model included average aberrations, prediction of the defocused CSF with large pupils was better but remained inaccurate, failing, in particular, to reflect differences between individual subjects. Inclusion of measured aberrations for individual subjects provided accurate predictions in the shape of the monochromatic CSF of two of three subjects with hyperopic defocus and good predictions of the polychromatic CSF of two subjects with hyperopic defocus. Prediction of the effects of myopic defocus by use of measured individual aberrations of one subject were less successful. Hence a diffraction optics model can provide good predictions of the effects of defocus on the human CSF, given that one has knowledge of the individual ocular aberrations. These predictions are dependent on the quality of the aberration measurements.     

Generation of third-order spherical and coma aberrations by use of radically symmetrical fourth-order lenses

We have extended the method of Alvarez [J. Am. Optom. Assoc. 49, 24 (1978)] to generate a variable magnitude of third-order spherical and/or coma aberration by using a combination of fourth-order plates with a magnification system. The technique, based on the crossed-cylinder aberroscope, is used to measure the wave-front aberration generated by the plates. The method has been applied to correct the third-order spherical aberration generated by an artificial eye as well as the coma produced by a progressive addition ophthalmic lens. The simplicity of the method and its relatively low cost make it attractive for partial correction of the aberrations of the eye.     

Use of the astigmatism correction device on the Zeiss fundus camera for peripheral retinal photography

High quality photographs of the peripheral retina are made possible by the proper positioning of the astigmatism correction device on the Zeiss fundus camera. Using a plus cylinder, axis perpendicular or a minus cylinder, axis parallel to that around which the eye is rotated will eliminate the astigmatism induced by viewing the retina obliquely through the optical surfaces of the eye, resulting in a sharply focused image at the film plane. Proper use of this instrument can be helpful in evaluating and diagnosing retinal lesions that occur in the peripheral fundus.     

Average optical performance of the human eye as a function of age in a normal population

PURPOSE: To determine the average optical performance of the human eye, in terms of the modulation transfer function (MTF), as a function of age. METHODS: An apparatus was constructed to measure the ocular MTF, based on the recording of images of a green, 543-nm laser-point source after reflection in the retina and double pass through the ocular media. MTFs were computed from the average of three 4-second-exposure double-pass images recorded by a slow-scan, cooled charge-coupled device camera. The ocular MTF was measured for three artificial pupil diameters (3 mm, 4 mm, and 6 mm) with paralyzed accommodation under the best refractive correction in 20 subjects for each of three age categories: young subjects aged 20 to 30 years, middle-aged subjects aged 40 to 50 years, and older subjects aged 60 to 70 years. The selected subjects passed an ophthalmologic examination, excluding subjects with any form of ocular or retinal disease, spherical or cylindrical refractive errors exceeding 2 D, and corrected visual acuity lower than 1 (0.8 in the older age group). RESULTS: The average MTF was determined for each age group and pupil diameter. A two-parameter analytical expression was proposed to represent the average MTF in each age group for every pupil diameter. The ocular MTFs declined as age increased from young to older groups. The SD of the MTF results within age groups was lower than the differences between the mean for each group. CONCLUSIONS: The average optical performance of the human eye progressively declines with age. These MTF results can serve as a reference for determining mean ocular optics according to age.     

Image formation by the crystalline lens and eye of the rainbow trout

The image of a distant unresolved point (point image or PI) and modulation transfer function (MTF) of the eye and lens of the trout were recorded with high spatial (0.3 micron) and dynamic (4096 grey levels) resolution for various entrance aperture sizes and focal positions in monochromatic light, and in broadband light simulating sunlight absorbed by a retinal cone pigment. The PI is irregular, with streaks, wisps and speckle, as a result of lens structural irregularity and diffraction of light scattered within the lens and cornea. Maximum diameter of a diffraction-limited aperture area of the eye is about 0.3 mm. Axially spaced multiple foci are caused by irregular and discontinuous zonal spherical aberration. Lens substance dispersion causes strong longitudinal chromatic aberration, resulting in a broadband PI with concentric coloured haloes. Incident linearly polarized light is slightly depolarized in the PI. The nature of the image is discussed relative to lens and cornea structure, optical modelling and vision. Human subjective entoptic phenomena analogous to those observed objectively in the trout are described.     

Brain folates and DNA methylation in rats fed a choline deficient diet or treated with low doses of methotrexate

Photorefractive keratectomy (PRK) with the ArF excimer lasers in current use usually approximates the intended corneal curvature by a mean of a delicate step-type pattern that is smooth off afterwards by reepithelialization and tear film. The present study was based on a model eye with axial myopia of -6 D but otherwise the optical and geometric properties of the Gullstrand model eye and was designed to investigate to what extent. (1) corneal step patterns can reduce retinal image contrast and (2) smoothing effects can restore such a loss. METHODS. The corneal surface resulting from PRK in the case of a myopia of -6 D (optical zone diameter 6 mm) is calculated for the parameters of the model eye. The retinal image contrasts of bar patterns are calculated by PSF (point spread function) analysis: varying size of pupil, wavelength, bar width, ablation step height and degree of smoothing. RESULTS. Step height influences retinal image contrast crucially. With step heights above 0.4 micron a massive loss of retinal image contrast must be expected, which can, however, be corrected to a useful extent by surface-smoothing effects. CONCLUSION. This study indicates that PRK with excimer lasers should be performed with low fluence and correspondingly low corneal step heights.     

Small incision single-suture-loop pupilloplasty for postoperative atonic pupil

In this small incision technique to correct postoperative atonic pupil in the aphakic or pseudophakic eye, the pupil is sutured and constricted with a 10-0 polypropylene loop through 3 1.0 mm stab incisions. The surgery is easier to perform than previous methods, appears safe and reproducible, and requires little special equipment. Although the pupil's shape may become slightly irregular, its size is fairly easy to regulate. This new method should be useful in correcting postoperative atonic pupil, and the small incision technique will likely minimize surgical trauma and induced astigmatism.     

Magnification characteristics of fundus imaging systems

OBJECTIVE: To compare the magnification properties of 11 different fundus cameras (including 1 stereo fundus camera), a Rodenstock (infrared) scanning laser ophthalmoscope (SLO), the Heidelberg Laser Tomographic Scanner (LTS), and the Heidelberg Retina Tomograph (HRT). DESIGN: A cross-sectional study of the relationship between the true size of a fundus feature and its photographic-computer image in 14 different fundus imaging devices. This relationship was evaluated for each instrument using a model eye adjusted for axial ametropia between +11 diopter (D) and -14 D. To simulate refractive ametropia, the "crystalline lens" was removed to render the model eye aphakic, and the axial length was adjusted to give aphakic ametropia from emmetropia to +20 D. MAIN OUTCOME MEASURES: A correction factor (p) was calculated for each instrument, which can be used in calculations for determining true retinal size. RESULTS: The following were found to be of telecentric construction, Zeiss Oberkochen (WS240 Heidelberg), Zeiss Oberkochen (UK), Zeiss Oberkochen (Cologne), Nikon NF505, Kowa RCXV, SLO prototype (UK), LTS, and the HRT, and each exhibited a constant relationship between p and degree of ametropia of the model eye. The Canon CF6OU, Canon CF6OS, Canon CR4-45NM, Nidek 3-DX, Olympus GRCW, and Carl Zeiss Jena Retinophot were found not to be telecentric and exhibited a linear relationship between p and degree of ametropia of the model eye. For all instruments, p remained unchanged for axial and refractive ametropias of the same degree. CONCLUSIONS: The study has shown that not all fundus imaging systems are telecentric, so the use of a single magnification correction value may not be appropriate. These findings have important implications for the way in which true retinal size calculations are performed. Examples are given to show how the tabulated values of correction factors can be used for both telecentric and nontelecentric cameras in image size calculations.     

Variations in photoreceptor directionally across the central retina

Cones show a differential sensitivity to light coming from different portions of the pupil, typically being most sensitive to light from the center of the pupil. We measured the directional properties of the cones across the central 6 deg of the retina, using an optical imaging technique. We find that the cones in the center of the fovea have the broadest tuning. The width of the angular tuning changes rapidly from 0 deg to 1 deg retinal eccentricity, with cones at 1 deg being much more narrowly tuned that the cones in the center of the fovea. Directional tuning of the cones remains relatively constant from 1 deg to 3 deg retinal eccentricity. Receptoral disarray contributes minimally to the measured directional properties of the foveal cones, and there is no evidence of asymmetry between horizontal and vertical retinal locations. There are only small differences among the five subjects in the change in angular tuning of the cones with retinal location. We find that at the foveal center the directional tuning of the cones is limited by the diameter of the cone apertures.     

视线追踪中一种新的由粗及精的瞳孔定位方法

基于图像处理的方法,采用了由粗及精的瞳孔定位思想,提出了一种高精度的瞳孔定位算法。该算法首先利用瞳孔区域的直方图,采用改进的最大类间方差法自适应地分割瞳孔区域,实现粗略定位,然后利用瞳孔灰度的梯度特性来精确定位瞳孔边缘点,最后在像素级瞳孔边缘点的基础上,采用亚像素定位方法,更精确地求得亚像素级瞳孔边缘点,并通过椭圆拟合的方法来精确确定瞳孔的中心位置。另外,针对瞳孔被遮挡的情况,本文提出了一种等距离补偿瞳孔的方法。多次实验结果证明了该算法对遮挡瞳孔的定位有较强的鲁棒性,可以准确地定位瞳孔的位置。      

Evaluating diffusion of light in the eye by objective means

PURPOSE: The authors have developed an index of diffusion that describes the relative spread of light inside and outside the region of image focus of the living human eye. It provides in numerical terms a measure of light scatter and can be used to characterize the optical deficit in eyes with age- and disease-related abnormalities of the anterior segment. METHOD: An improved version of the double-pass method of examining the aerial image formed by reflection of the retinal image of a point source is employed, together with a new way of analyzing the image. Experimental estimation shows the contaminating effect of back scatter from the media and corneal reflection to be negligible. Measurements are objective and do not require any responses on the part of the patient. Data become available practically on-line. RESULTS: Index of diffusion values were obtained on 13 patients and varied from 0.22 to 1.04, strongly tending to increase with age. They are rather robust to pupil size, exposure duration, and small amounts of defocus. CONCLUSION: The index appears to provide a promising measure of optical performance of the media of the anterior segment of the eye, which might be useful in studying the effect of aging, injury, and disease.     

Human oculomotor system accounts for 3-D eye orientation in the visual-motor transformation for saccades

A recent theoretical investigation has demonstrated that three-dimensional (3-D) eye position dependencies in the geometry of retinal stimulation must be accounted for neurally (i.e., in a visuomotor reference frame transformation) if saccades are to be both accurate and obey Listing's law from all initial eye positions. Our goal was to determine whether the human saccade generator correctly implements this eye-to-head reference frame transformation (RFT), or if it approximates this function with a visuomotor look-up table (LT). Six head-fixed subjects participated in three experiments in complete darkness. We recorded 60 degrees horizontal saccades between five parallel pairs of lights, over a vertical range of +/-40 degrees (experiment 1), and 30 degrees radial saccades from a central target, with the head upright or tilted 45 degrees clockwise/counterclockwise to induce torsional ocular counterroll, under both binocular and monocular viewing conditions (experiments 2 and 3). 3-D eye orientation and oculocentric target direction (i.e., retinal error) were computed from search coil signals in the right eye. Experiment 1: as predicted, retinal error was a nontrivial function of both target displacement in space and 3-D eye orientation (e.g., horizontally displaced targets could induce horizontal or oblique retinal errors, depending on eye position). These data were input to a 3-D visuomotor LT model, which implemented Listing's law, but predicted position-dependent errors in final gaze direction of up to 19.8 degrees. Actual saccades obeyed Listing's law but did not show the predicted pattern of inaccuracies in final gaze direction, i.e., the slope of actual error, as a function of predicted error, was only -0. 01 +/- 0.14 (compared with 0 for RFT model and 1.0 for LT model), suggesting near-perfect compensation for eye position. Experiments 2 and 3: actual directional errors from initial torsional eye positions were only a fraction of those predicted by the LT model (e. g., 32% for clockwise and 33% for counterclockwise counterroll during binocular viewing). Furthermore, any residual errors were immediately reduced when visual feedback was provided during saccades. Thus, other than sporadic miscalibrations for torsion, saccades were accurate from all 3-D eye positions. We conclude that 1) the hypothesis of a visuomotor look-up table for saccades fails to account even for saccades made directly toward visual targets, but rather, 2) the oculomotor system takes 3-D eye orientation into account in a visuomotor reference frame transformation. This transformation is probably implemented physiologically between retinotopically organized saccade centers (in cortex and superior colliculus) and the brain stem burst generator.     

Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method

A recent study has shown that the double-pass method provides a good estimate of the ocular modulation transfer function (MTF) but that it does not yield the phase transfer function (PTF) [J. Opt. Soc. Am. A 12, 195 (1995)]. Therefore, one cannot recover the true retinal point-spread function (PSF). We present a modification of the double-pass method to overcome this problem. The key is to break the symmetry between the two passes. By using an unexpanded Gaussian input beam, we produce a diffraction-limited PSF for the first passes. Then, by using a large exit pupil, we get an aberrated PSF for the second pass. The double-pass aerial image is the cross correlation of both PSF's, so that the Fourier transform of such an aerial image directly provides the true retinal PTF, up to the cutoff frequency of the effective (small), diffraction-limited entrance pupil. The resulting double-pass aerial image is a blurred version of the true retinal PSF. Thus it shows the effect not only of even symmetric aberrations but also of odd and irregular aberrations such as coma. We have explored two different ways to retrieve the true retinal PSF: (a) deblurring of the aerial image and (b) PSF reconstruction combining PTF data with conventional double-pass MTF. We present promising initial results with both artificial and real eyes.     

Heading detection using motion templates and eye velocity gain fields

Eye or head rotation would influence perceived heading direction if it were coded by cells tuned only to retinal flow patterns that correspond to linear self-movement. We propose a model for heading detection based on motion templates that are also Gaussian-tuned to the amount of rotational flow. Such retinal flow templates allow explicit use of extra-retinal signals to create templates tuned to head-centric flow as seen by the stationary eye. Our model predicts an intermediate layer of 'eye velocity gain fields' in which 'rate-coded' eye velocity is multiplied with responses of templates sensitive to specific retinal flow patterns. By combination of the activities of one retinal flow template and many units with an eye velocity gain field, a new type of unit appears: its preferred retinal flow changes dynamically in accordance with the eye rotation velocity. This unit's activity becomes thereby approximately invariant to the amount of eye rotation. The units with eye velocity gain fields from the motion-analogue of the units with eye position gain fields found in area 7a, which according to our general approach, are needed to transform position from retino-centric to head-centric coordinates. The rotation-tuned templates can also provide rate-coded visual estimates of eye rotation to allow a pure visual compensation for rotational flow. Our model is consistent with psychophysical data that indicate a role for extra-retinal as well as visual rotation signals in the correct perception of heading.