Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error

The description of sphero-cylinder lenses is approached from the viewpoint of Fourier analysis of the power profile. It is shown that the familiar sine-squared law leads naturally to a Fourier series representation with exactly three Fourier coefficients, representing the natural parameters of a thin lens. The constant term corresponds to the mean spherical equivalent (MSE) power, whereas the amplitude and phase of the harmonic correspond to the power and axis of a Jackson cross-cylinder (JCC) lens, respectively. Expressing the Fourier series in rectangular form leads to the representation of an arbitrary sphero-cylinder lens as the sum of a spherical lens and two cross-cylinders, one at axis 0 degree and the other at axis 45 degrees. The power of these three component lenses may be interpreted as (x,y,z) coordinates of a vector representation of the power profile. Advantages of this power vector representation of a sphero-cylinder lens for numerical and graphical analysis of optometric data are described for problems involving lens combinations, comparison of different lenses, and the statistical distribution of refractive errors.

Statistical variation of aberration structure and image quality in a normal population of healthy eyes

A Shack-Hartmann aberrometer was used to measure the monochromatic aberration structure along the primary line of sight of 200 cyclopleged, normal, healthy eyes from 100 individuals. Sphero-cylindrical refractive errors were corrected with ophthalmic spectacle lenses based on the results of a subjective refraction performed immediately prior to experimentation. Zernike expansions of the experimental wave-front aberration functions were used to determine aberration coefficients for a series of pupil diameters. The residual Zernike coefficients for defocus were not zero but varied systematically with pupil diameter and with the Zernike coefficient for spherical aberration in a way that maximizes visual acuity. We infer from these results that subjective best focus occurs when the area of the central, aberration-free region of the pupil is maximized. We found that the population averages of Zernike coefficients were nearly zero for all of the higher-order modes except spherical aberration. This result indicates that a hypothetical average eye representing the central tendency of the population is nearly free of aberrations, suggesting the possible influence of an emmetropization process or evolutionary pressure. However, for any individual eye the aberration coefficients were rarely zero for any Zernike mode. To first approximation, wave-front error fell exponentially with Zernike order and increased linearly with pupil area. On average, the total wave-front variance produced by higher-order aberrations was less than the wave-front variance of residual defocus and astigmatism. For example, the average amount of higher-order aberrations present for a 7.5-mm pupil was equivalent to the wave-front error produced by less than 1/4 diopter (D) of defocus. The largest pupil for which an eye may be considered diffraction-limited was 1.22 mm on average. Correlation of aberrations from the left and right eyes indicated the presence of significant bilateral symmetry. No evidence was found of a universal anatomical feature responsible for third-order optical aberrations. Using the Marechal criterion, we conclude that correction of the 12 largest principal components, or 14 largest Zernike modes, would be required to achieve diffraction-limited performance on average for a 6-mm pupil. Different methods of computing population averages provided upper and lower limits to the mean optical transfer function and mean point-spread function for our population of eyes.

Power vector analysis of the optical outcome of refractive surgery

PURPOSE

To demonstrate the power vector method of representing and analyzing spherocylindrical refractive errors.

SETTING

School of Optometry, Indiana University, Bloomington, Indiana, USA.

METHODS

Manifest and keratometric refractive errors were expressed as power vectors suitable for plotting as points in a 3-dimensional dioptric space. The 3 Cartesian coordinates (x, y, z) of each power vector correspond to the powers of 3 lenses that, in combination, fulfill a refractive prescription: a spherical lens of power M, a Jackson crossed cylinder of power J0 with axes at 90 degrees and 180 degrees, and a Jackson crossed cylinder of power J45 with axes at 45 degrees and 135 degrees. The Pythagorean length of the power vector, B, is a measure of overall blurring strength of a spherocylindrical lens or refractive error. Changes in refractive error due to surgery were computed by the ordinary rules of vector subtraction.

RESULTS

Frequency distributions of blur strength (B) clearly demonstrate the effectiveness of refractive surgery in reducing the overall blurring effect of uncorrected refractive error.

CONCLUSIONS

Power vector analysis also revealed a reduction in the astigmatic component of these refractive errors. Paired comparisons revealed that the change in manifest astigmatism due to surgery was well correlated with the change in keratometric astigmatism. Power vectors aid the visualization of complex changes in refractive error by tracing a trajectory in a uniform dioptric space. The Cartesian components of a power vector are mutually independent, which simplifies mathematical and statistical analysis of refractive errors. Power vectors also provide a natural link to a more comprehensive optical description of ocular refractive imperfections in terms of wavefront aberration functions and their description by Zernike polynomials.

Accuracy and precision of objective refraction from wavefront aberrations

We determined the accuracy and precision of 33 objective methods for predicting the results of conventional, sphero-cylindrical refraction from wavefront aberrations in a large population of 200 eyes. Accuracy for predicting defocus (as specified by the population mean error of prediction) varied from -0.50 D to +0.25 D across methods. Precision of these estimates (as specified by 95% limits of agreement) ranged from 0.5 to 1.0 D. All methods except one accurately predicted astigmatism to within +/-1/8D. Precision of astigmatism predictions was typically better than precision for predicting defocus and many methods were better than 0.5D. Paraxial curvature matching of the wavefront aberration map was the most accurate method for determining the spherical equivalent error whereas least-squares fitting of the wavefront was one of the least accurate methods. We argue that this result was obtained because curvature matching is a biased method that successfully predicts the biased endpoint stipulated by conventional refractions. Five methods emerged as reasonably accurate and among the most precise. Three of these were based on pupil plane metrics and two were based on image plane metrics. We argue that the accuracy of all methods might be improved by correcting for the systematic bias reported in this study. However, caution is advised because some tasks, including conventional refraction of defocus, require a biased metric whereas other tasks, such as refraction of astigmatism, are unbiased. We conclude that objective methods of refraction based on wavefront aberration maps can accurately predict the results of subjective refraction and may be more precise. If objective refractions are more precise than subjective refractions, then wavefront methods may become the new gold standard for specifying conventional and/or optimal corrections of refractive errors.

Standards for Reporting the Optical Aberrations of Eyes

In response to a perceived need in the vision community, an OSA taskforce was formed at the 1999 topical meeting on vision science and its applications (VSIA-99) and charged with developing consensus recommendations on definitions, conventions, and standards for reporting of optical aberrations of human eyes. Progress reports were presented at the 1999 OSA annual meeting and at VSIA-2000 by the chairs of three taskforce subcommittees on (1) reference axes, (2) describing functions, and (3) model eyes.

The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans

New measurements of the chromatic difference of focus of the human eye were obtained with a two-color, vernier-alignment technique. The results were used to redefine the variation of refractive index of the reduced eye over the visible spectrum. The reduced eye was further modified by changing the refracting surface to an aspherical shape to reduce the amount of spherical aberration. The resulting chromatic-eye model provides an improved account of both the longitudinal and transverse forms of ocular chromatic aberration.

Metrics of optical quality derived from wave aberrations predict visual performance

Wavefront-guided refractive surgery and custom optical corrections have reduced the residual root mean squared (RMS) wavefront error in the eye to relatively low levels (typically on the order of 0.25 microm or less over a 6-mm pupil, a dioptric equivalent of 0.19 D). It has been shown that experimental variation of the distribution of 0.25 microm of wavefront error across the pupil can cause variation in visual acuity of two lines on a standard logMAR acuity chart. This result demonstrates the need for single-value metrics other than RMS wavefront error to quantify the effects of low levels of aberration on acuity. In this work, we present the correlation of 31 single-value metrics of optical quality to high-contrast visual acuity for 34 conditions where the RMS wavefront error was equal to 0.25 microm over a 6-mm pupil. The best metric, called the visual Strehl ratio, accounts for 81% of the variance in high-contrast logMAR acuity.

Clinical applications of the Shack-Hartmann aberrometer

The efficacy of the Shack-Hartmann technique for measuring the optical aberrations of the eye was evaluated for four classes of clinical conditions associated with optically abnormal eyes. These categories (with specific examples) are: anomalies of the tear film (dry eye), corneal disease (keratoconus), corneal refractive surgery [laser-assisted in situ keratomileusis (LASIK)], and lenticular cataract. We show that in each of these cases, it is possible to obtain at least a partial topographic map of the refractive aberrations of the patient's eyes, but severe losses of data integrity can occur. We further show that the Shack-Hartmann aberrometer provides additional information about the eye's imperfections on a very fine spatial scale (< 0.4 mm) which scatter light and further degrade the quality of the retinal image. Taken together, spatial maps of the variation of optical aberrations and scatter across the eye's entrance pupil represents an improved description of the optical imperfections of the abnormal eye.

Analysis of orientation bias in cat retina

1. Responses of cat retinal ganglion cells to a drifting sinusoidal grating stimulus were measured as a function of the grating orientation and spatial frequency.2. The response at fixed frequency and contrast varied with orientation in the manner of a cosine function. A new measure was introduced to quantify this orientation bias in the response domain on an absolute scale of 0-100%. Under experimental conditions designed to maximize the effect, the mean bias for 250 cells was 16% and the range was 0-46%. In 70% of cells there was significant bias.3. Orientation bias varied with spatial frequency and was maximal near the high-frequency limit. The majority of biassed cells preferred the same orientation at high and low frequencies but in some cells a reversal occurred: the orientation which gave maximum response at high frequencies gave minimum response at low frequencies. The greatest variation of cut-off frequency with orientation was (2/3) octave.4. Orientation bias was due to neural, not optical, factors. Nevertheless, the phenomenon could often be imitated by deliberately introduced optical astigmatism of up to 4 dioptres for brisk-sustained units and over 10 dioptres for brisk-transient units.5. The grating orientation preferred by cells varied systematically with position in the visual field. The central tendency was for the grating which yielded maximum response to lie parallel to the line joining the cell to the area centralis. This generalization failed for units within 2 degrees of the centre of the area centralis.6. Analysis of orientation bias indicates a functional asymmetry of receptive fields such that the centre mechanism, and sometimes also the surround mechanism, is elongated along the line joining cell to area centralis.

Theory and measurement of ocular chromatic aberration

We have determined the transverse chromatic aberration of the human eye by measuring the apparent offset of a two-color vernier viewed foveally through a displaced, pinhole aperture. For the same subjects, we also determined the longitudinal chromatic aberration for foveal viewing by the method of best focus. In both cases, the results were closely predicted by a simple, reduced-eye optical-model for which transverse and longitudinal chromatic aberration are directly proportional, with the constant of proportionally being the amount of displacement of the pinhole from the visual axis. Further measurements revealed that the natural pupil was closely centered on the visual axis for two subjects and slightly displaced in the temporal direction for three other subjects. One implication of these results is that, although the eye has substantial chromatic aberration, the pupil is positioned so as to minimize the transverse component of the aberration for central vision, thereby optimizing foveal image quality for polychromatic objects.

Relationship between refractive error and monochromatic aberrations of the eye

PURPOSE

To examine the relationship between ametropia and optical aberrations in a population of 200 normal human eyes with refractive errors spanning the range from +5.00 to -10.00 D.

METHODS

Using a reduced-eye model of ametropia, we tested the hypothesis that the optical system of the eye is uncorrelated with the degree of ametropia. These predictions were evaluated experimentally with a Shack-Hartmann aberrometer that measured the monochromatic aberrations across the central 6 mm of the dilated pupil in well-corrected, cyclopleged eyes.

RESULTS

Optical theory predicted, and control experiments on a model eye verified, that Shack-Hartmann measurements of spherical aberration will vary with axial elongation of the eye even if the dioptric components of the eye are fixed. Contrary to these predictions, spherical aberration was not significantly different from emmetropic eyes. Root mean square of third-order aberrations, fourth-order aberrations, and total higher aberrations (third to 10th) in myopic and hyperopic eyes were also uncorrelated with refractive error. Astigmatic eyes tended to have larger total higher-order aberrations than nonastigmatic eyes.

CONCLUSIONS

We conclude that a reduced-eye model of myopia assuming fixed optical parameters and variable axial length is not tenable.

Predicting subjective judgment of best focus with objective image quality metrics

PURPOSE

To determine the impact of higher-order monochromatic aberrations on lower-order subjective sphero-cylindrical refractions.

METHODS

Computationally-aberrated, monochromatic Sloan letters were presented on a high luminance display that was viewed by an observer through a 2.5mm pupil. Through-focus visual acuity (VA) was determined in the presence of spherical aberration (Z40) at three levels (0.10, 0.21 and 0.50D). Analogous through-astigmatism experiments measured visual acuity in the presence of secondary astigmatism (Z4+/-2) or coma (Z3-1). Measured visual acuity was correlated with 31 different metrics of image quality to determine which metric best predicts performance for degraded retinal images. The defocus and astigmatism levels that optimized each metric were compared with those that produced best visual acuity to determine which metric best predicts subjective refraction.

RESULTS

Spherical aberration, coma and secondary astigmatism all reduced VA and increased depth of focus. The levels of defocus and primary astigmatism that produced the best performance varied with levels of spherical aberration and secondary astigmatism, respectively. The presence of coma, however, did not affect cylindrical refraction. Image plane metrics, especially those that take into account the neural contrast sensitivity threshold (e.g. the visual Strehl ratio, VSOTF), are good predictors of visual acuity in both the through-focus and through-astigmatism experiments (R = -0.822 for VSOTF). Subjective sphero-cylindrical refractions were accurately predicted by some image-quality metrics (e.g., pupil fraction, VSOTF and standard deviation of PSF light distribution).

CONCLUSION

Subjective judgment of best focus does not minimize RMS wavefront error (Zernike defocus = 0), nor create paraxial focus (Seidel defocus = 0), but makes the retina conjugate to a plane between these two. It is possible to precisely predict subjective sphero-cylindrical refraction for monochromatic light using objective metrics.

Retinal limits to the detection and resolution of gratings

The maximum spatial frequency for the detection and resolution of sinusoidal gratings was determined as a function of stimulus location across the visual field. Stimuli were produced directly on the retina as interference fringes, thus avoiding possible loss of image quality, which may occur when the optical system of the eye is used to form the retinal image. Contrary to earlier reports, we found that subjects could detect gratings with spatial frequencies much higher than the resolution limit. At 5 degrees of eccentricity from the fovea, the detection limit was about three times the resolution limit, and this factor increased to about 10 as the test stimulus was moved 35 degrees into the periphery. Quantitative comparison of the data with retinal anatomy and physiology suggests that pattern resolution is limited by the spacing of primate beta (midget) retinal ganglion cells, whereas pattern detection is limited by the size of individual cones.

A statistical model of the aberration structure of normal, well-corrected eyes

A statistical model of the wavefront aberration function of the normal, well-corrected eye was constructed based on normative data from 200 eyes which show that, apart from spherical aberration, the higher-order aberrations of the human eye tend to be randomly distributed about a mean value of zero. The vector of Zernike aberration coefficients describing the aberration function for any individual eye was modelled as a multivariate, Gaussian, random variable with known mean, variance and covariance. The model was verified by analysing the statistical properties of 1000 virtual eyes generated by the model. Potential applications of the model include computer simulation of individual variation in aberration structure, retinal image quality, visual performance, benefit of novel designs of ophthalmic lenses, or outcome of refractive surgery.

Orientation bias of cat retinal ganglion cells

Kuffler described the receptive fields of cat retinal ganglion cells as having a concentric arrangement. This has usually been taken to mean that they are approximately circular in form (see, for example, ref. 2). Hammond tested the circularity of the centre component of receptive fields by plotting a contour of isosensitivity to a small flashed spot. He concluded that centres were often ellipitical (average ratio of major to minor axis 1.23) and that more than 50% of the recorded cells had the major axis oriented within /+- 20 degrees of the horizontal. Such data are important for discussions of the neurophysiological basis of the 'oblique effect' (reduced visibility for periodic grating patterns when oriented away from the vertical or horizontal) observed in psychophysical experiments on humans because subcortical units are often assumed to be orientationally unbiased. Orientation selectivity is a prominent attribute of visual cortical neurones so analysis has usually emphasized the distribution of orientation selectivity at that level. The results presented here redirect attention to the retinal level since they reveal a previously unsuspected systematic relation between orientation bias of ganglion cells and their location relative to the area centralis.

Validation of a clinical Shack-Hartmann aberrometer

PURPOSE

To validate the accuracy, tolerance, and repeatability of the complete ophthalmic analysis system aberrometer (COAS, Wavefront Sciences Inc.) with model eyes and normal human eyes.

METHOD

Model eyes were constructed from six polymethyl methacrylate, single-surface lenses with known characteristics. Accuracy of second-order aberrations was verified by measuring defocus and astigmatism induced by series of spherical and cylindrical trial lenses. Accuracy of higher-order aberrations was evaluated by comparing ray-tracing predictions with measured spherical aberration and coma of the aspheric model eyes. Tolerance to axial and lateral misalignment was measured by controlled displacements of the model eye relative to the aberrometer. Repeatability was tested on the same model eyes with repeated measurements taken within 1 s or within half an hour with realignment between each trial. Analyses were based on a 5-mm pupil diameter.

RESULTS

Defocus and astigmatism were accurately measured within the working range of the instrument automatic focus adjustment (e.g., measured defocus was within +/-0.25 diopters over a -6.50 to +3.00 D range of refractive error). Accuracy of spherical aberration and coma agreed closely with theoretical predictions (e.g., for all six aspheric models, the mean absolute difference between predicted and measured Z(4)0 was 0.007 microm). Axial displacements over the range +/-2.5 mm had little effect on measurements for myopic and emmetropic model eyes. Also, lateral displacements over the range +/-1.5 mm did not produce significant coma. The standard deviations of repeated measurements of higher-order root mean square on model eyes were <1% of the mean with repeated measures within 1 s and 10% of the mean for five individual measurements with realignment in between each. Tolerance to small lateral displacements was also observed for human eyes.

CONCLUSION

The complete ophthalmic analysis system aberrometer can measure second-, third-, and fourth-order aberrations accurately and repeatedly on model eyes.

Vision beyond the resolution limit: aliasing in the periphery

Pattern resolution is generally considered a prerequisite for spatial vision because details too fine to be resolved cannot be distinguished from a uniform field. However, our experiments using peripheral vision demonstrate that reliable pattern detection is possible for images far beyond the resolution limit. The visual percept which arises in this case is an illusion called aliasing in which the apparent spatial structure of the stimulus is quite different from that actually present. Aliasing begins at spatial frequencies just above the classical resolution limit, which is taken as evidence that peripheral resolution is limited by the coarse spacing of visual neurons rather than by increased size of their receptive fields. At a given eccentricity, the very finest pattern which produces aliasing has a spatial period which approaches the smallest anatomical dimension: the diameter of a single cone photoreceptor.

Characterization of spatial aliasing and contrast sensitivity in peripheral vision

Psychometric performance was measured for contrast detection and spatial resolution tasks in foveal and peripheral vision. Objective evidence was obtained for a quantitative difference between resolution acuity and detection acuity in the peripheral field. These two types of spatial acuity differed by up to an order of magnitude (3 vs 30 c/deg at 30 deg eccentricity) and they varied with stimulus contrast in distinctly different ways. Contrast sensitivity at the resolution limit was an order of magnitude above the absolute threshold of unity and the shape of the contrast sensitivity function was significantly different from that measured for foveal vision. The results suggest that current models of eccentricity scaling of contrast sensitivity be re-evaluated to take account of the extensive aliasing zone of spatial frequencies which becomes functional in peripheral vision when the retinal image is well focused.

Test-retest reliability of clinical Shack-Hartmann measurements

PURPOSE

To evaluate the stability of clinical monochromatic aberrometry measurements over a wide range of time scales.

METHODS

Monochromatic aberrations in four normal eyes were measured with a clinical Shack-Hartmann aberrometer. A chin rest or a supplemental bite bar attachment was used to stabilize head and eye position. Five repeated measurements were taken within one test (5 frames, t < 1 second) without realignment. With realignment between each measurement, aberration measurements were repeated five times (t < 1 hour) on each day, at the same time of day on five consecutive days, and again on 5 days at monthly intervals. A control experiment studied the effect of systematically misaligning the eye to determine whether fixation errors can account for the variation in the repeated measurements.

RESULTS

Variability of wavefront root mean square (RMS) error (excluding defocus and astigmatism) was tracked across repeated measurements. Variances for different time scales were: 8.10 x 10(-5) microm2 (t < 1 second), 3.24 x 10(-4) microm2 (t < 1 hour), 4.41 x 10(-4) microm2 (t < 1 week), 9.73 x 10(-4) microm2 (t < 1 year). Bite bar and chin rest data were almost identical. Rotational fixation error up to 3 degrees accounts for only part of the variability.

CONCLUSIONS

Increased variability in aberration maps between days and months indicates biological fluctuations that are large enough to prevent achievement of "perfect vision," even in the unlikely event that spherical and astigmatic refractive errors are corrected perfectly. However, lack of stability does not justify withholding treatment. A lasting benefit of aberration correction is expected despite temporal variability.

Retinal stretching limits peripheral visual acuity in myopia

Axial elongation of the myopic eye has the potential to stretch the retina, thereby reducing the sampling density of retinal neurons. Resolution acuity in the peripheral field of normal eyes is known to be sampling-limited, which suggests that retinal stretching in the myopic eye should have a direct effect on resolution acuity everywhere in the visual field except perhaps the fovea, which is usually optically limited. We tested this prediction that neural sampling density is reduced in myopic eyes by measuring resolution acuity for sinusoidal gratings in the fovea plus five peripheral locations in 60 myopic subjects exhibiting a wide range of refractive errors. Control experiments using a detection paradigm to provoke spatial aliasing verified that peripheral resolution was sampling limited. Retinal spatial frequencies of the grating stimulus were computed assuming Knapps' Law of visual optics, which ensures that retinal image size (in mm) is independent of refractive error when axial myopia is corrected by a spectacle lens located in the anterior focal plane of the eye. Results obtained at every retinal locus showed that resolution acuity declined linearly with magnitude of refractive error. Regression of the population data indicated that approximately 15 D of refractive error doubles the spacing between retinal neurons, thereby halving peripheral resolution acuity relative to the emmetropic eye. Several subjects also demonstrated sampling-limited performance in the fovea, which indicated that optical filtering by the eye's optical system failed to protect the fovea from aliasing artifacts of neural undersampling in these eyes. We conclude that stretching of the retina is a primary cause of reduced spatial resolution of the peripheral field, and occasionally of the fovea, in myopic eyes. Stretching appears to be locally uniform over the central +/-15 degrees of visual field but is globally non-uniform since the foveal region appears to stretch more than the globe itself.

The response properties of the steady antagonistic surround in the mudpuppy retina

1. The graded response of bipolar and ganglion cells to test flashes at the receptive field centre, spans only a limited portion of the test intensity domain: more than 90% of the graded response range can be elicited by test flashes differing by less than 100 to 1. 2. In the presence of steady illumination of the receptive field surround, the absolute levels of log test intensities required to elicit 90% of the graded response are increased (reset), but the relation in (1) still applies. 3. Each point in the receptive field surround, when illuminated, contributes to the resetting of the required centre test flash intensities by a weighing that decreases exponentially with distance from the centre. The space constant is 0.25 mm. 4. When the receptive field surround is fully covered with illumination, the centre test flash intensities required to elicit 90% of the response range must be increased by about tenfold for each tenfold increase in surround intensity over a surround intensity domain of about 1000 to 1. 5. The absolute levels of surround and required centre test intensities are inter-related: when the receptive field surround is fully covered, a test flash with intensity equal to that of the surround elicits a half-maximal response. Thus, in the presence of a full field background, the bipolar potential is held near its half-maximum response potential. 6. The graded resetting of the required centre test flash intensities is well correlated with the graded increase in horizontal cell response as the surround intensity and area are varied. It is inferred that units with response and receptive field properties like those of the horizontal cells, when driven by surround illumination, act as interneurones to reset the relationship between required test flash intensity and response in bipolar and ganglion cells.

Nonveridical visual perception in human amblyopia

PURPOSE

Amblyopia is a developmental disorder of spatial vision. There is evidence to suggest that some amblyopes misperceive spatial structure when viewing with the affected eye. However, there are few examples of these perceptual errors in the literature. This study was an investigation of the prevalence and nature of misperceptions in human amblyopia.

METHODS

Thirty amblyopes with strabismus and/or anisometropia participated in the study. Subjects viewed sinusoidal gratings of various spatial frequencies, orientations, and contrasts. After interocular comparison, subjects sketched the subjective appearance of those stimuli that had nonveridical appearances.

RESULTS

Nonveridical visual perception was revealed in 20 amblyopes ( approximately 67%). In some subjects, misperceptions were present despite the absence of a deficit in contrast sensitivity. The presence of distortions was not simply linked to the depth of amblyopia, and anisometropes were affected as well as those with strabismus. In most cases, these spatial distortions arose at spatial frequencies far below the contrast detection acuity cutoff. Errors in perception became more severe at higher spatial frequencies, with low spatial frequencies being mostly perceived veridically. The prevalence and severity of misperceptions were frequently found to depend on the orientation of the grating used in the test, with horizontal orientations typically less affected than other orientations. Contrast had a much smaller effect on misperceptions, although there were cases in which severity was greater at higher contrasts.

CONCLUSIONS

Many types of misperceptions documented in the present study have appeared in previous investigations. This suggests that the wide range of distortions previously reported reflect genuine intersubject differences. It is proposed that nonveridical perception in human amblyopia has its origins in errors in the neural coding of orientation in primary visual cortex.

Effect of ocular chromatic aberration on monocular visual performance

This brief review outlines the theory of ocular chromatic aberration and describes the three primary forms in which the aberration appears: chromatic difference of focus, chromatic difference of magnification, and chromatic difference of position. Our central theme is that all three aspects of chromatic aberration have as their common basis the chromatic dispersion of light. The magnitude of each form of the aberration is related to the others by simple linear formulas in which a key parameter is the location of the pupil relative to the nodal point of the eye. The way in which retinal image quality is affected by chromatic aberration is described and we assess the impact of the aberration on visual performance.

On-eye evaluation of optical performance of rigid and soft contact lenses

A Shack-Hartmann aberrometer was used to assess the optical performances of eyes corrected with rigid or soft contact lenses compared with spectacles. Metrics of optical quality derived from the measured wave aberrations were consistent with the subjective rating of visual clarity by subjects. Optical aberration analysis illustrated the differences in aberration structures of eyes wearing different optical corrections. For our subjects, correction with a rigid gas-permeable lens yielded significantly better optical quality than did the soft contact lens or spectacle lens. This was due to a reduction in the eye's asymmetric (odd-order) aberrations and a reduction in the amount of the eye's positive spherical aberration. These observations can be explained by theoretical calculations of the aberrations of the eye plus lens optical system. We conclude that aberrometry provides a better understanding of the optical effects of contact lenses in situ and could be useful for optimizing future designs of contact lenses.

Contrast sensitivity in humans with abnormal visual experience

1. Grating contrast sensitivities have been determined over a range of spatial frequencies for a normal subject and for subjects who are visually biased in that they have a lower resolution capacity for targets of specific orientations. The bias si only found in astigmatic subjects and the grating orientation yielding poorest acuity coincides with the most defocused astigmatic meridian. However this resolution anisotropy remains when optical factors are accounted for. 2. For the normal subject, high and low frequency attenuation is found and a typical reduction in contrast sensitivity is exhibited for oblique target orientations. 3. The biased subjects, called meridional amblyopes because they have reduced acuity for a given grating orientation, show markedly abnormal contrast sensitivity functions. Their cut-off spatial frequencies are different for various target orientations and this difference applies also to contrast sensitivity over nearly the entire spatial frequency range tested (0-5-16 cycles/deg). The differences are of about the same magnitude for most frequencies and they are found in all types of meridional amblyopes. 4. Optical explanations of these differences are ruled out by laser-interference fringe tests and by varying effective pupil size. 5. Theoretical effects of defocus have been calculated to compare predicted visual deprivation with performance. Results indicate that reduced contrast sensitivity functions can be equivalent to a small defocus effect. 6. To examine the results in the spatial domain, inverse Fourier transforms of representative contrast sensitivity functions have been computed. The optical portion of the resulting spatial weighting functions has been parcelled out to obtain neural spatial weighting functions.