Biomedical subjects
Publications and source records attributed to Larry N Thibos.
A new wavefront sensing and reconstruction technique is presented. It is possible to measure Laplacian and gradient information of a wavefront with a Hartmann-Shack setup. By simultaneously using the Laplacian and gradient data we reconstruct the wavefront by sequentially solving two partial differential equations.
PURPOSE: The purpose of this study is to determine the ability of single-value metrics of retinal image quality of the eye to predict visual performance as measured by high (HC) and low (LC) -contrast acuity at photopic (P) and mesopic (M) light levels in eyes with 20/17 and better visual acuity. METHODS: Forty-nine normal subjects in good health ranging in age from 21.8 to 62.6 with 20/17 or better monocular high-contrast logarithm of the minimum angle of resolution (logMAR) acuity served as subjects. Wavefront error through the 10th Zernike radial order over a 7-mm pupil was measured on each test eye using a custom-built Shack/Hartmann wavefront sensor. For each eye, 31 different single-value retinal image quality metrics were calculated. Visual acuity was measured using HC (95%) and LC (11%) logMAR at photopic (270 cd/m) and mesopic (0.75 cd/m) light levels. To determine the ability of each metric of retinal image quality to predict each type of logMAR acuity (P HC, P LC, M HC, and M LC), each acuity measure was regressed against each optical quality metric. RESULTS: The ability of the metrics of retinal image quality to predict logMAR acuity improved as luminance and/or contrast is lowered. The best retinal image quality metric (logPFSc) accounted for 2.6%, 15.1%, 27.6%, and 40.0% of the variance in P HC, P LC, M HC, and M LC logMAR acuity, respectively. CONCLUSIONS: In eyes with 20/17 and better P HC acuity, P HC logMAR acuity is insensitive to variations in retinal image quality compared with M LC logMAR acuity. Retinal image quality becomes increasingly predictive of logMAR acuity as contrast and/or luminance is decreased. Everyday life requires individuals to function over a large range of contrast and luminance levels. Clinically, the impact of retinal image quality as a function of luminance and contrast is readily measurable in a time-efficient manner with M LC logMAR acuity charts.
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.
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.
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.
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.
This article reviews the fundamental principles by which wavefront aberrometers measure ocular aberrations. Three different ways of interpreting aberration measurements are described in terms of wavefront phase, slope, and curvature. Although curvature is the more familiar concept from geometrical optics, the wave optics concept of wavefront phase is more useful for understanding the nature of aberrated retinal images and for prescribing treatments to correct high-order aberrations.
We wished to devise a measure of dissimilarity (D) which could predict psychophysical discrimination performance for Snellen letter pairs in peripheral vision. Threshold size for discriminating 33 pairs of Snellen letters was measured at 30 degrees eccentricity in the nasal retina for two subjects. D was computed for each pair by performing an overlap subtraction in the spatial domain, followed by a Fast Fourier Transform on this difference image, and dividing the total power in the resultant 'difference spectrum' by the sum of the powers of the individual letter spectra. A plot of D vs. psychophysical threshold letter size gave a mean correlation of R = -0.81. When D was calculated for letters that were low-pass filtered at different cut-off frequencies, the correlation with psychophysical performance was greatest when cut-off was between 1.25-1.9 cycles/letter (R = -0.85). Conversely, when the difference spectrum was high-pass filtered at different cut-off frequencies, the correlation decreased continuously as the cut-off increased. These results imply that the band of frequencies between zero and 1.25 cycles/letter are most important for letter discrimination in peripheral vision.
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.
A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R2 = 0.964 to 0.994). The sag error root mean square (RMS) was small, ranging from 0.1 to 0.17 microm for four of the five calibrated surfaces with the fifth at 0.36 microm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism (0.65-1.2 microm) and appreciable levels of trefoil (0.08-0.47 microm), coma (0.14-0.19 microm), and spherical aberration (0.18-0.25 microm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements.
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Repeated measures of wavefront aberrations were taken along the line-of-sight of seven eyes using two instruments: an objective, cross-cylinder aberroscope (OA) and a Shack-Hartmann (SH) aberrometer. Both instruments were implemented on the same optical table to facilitate interleaved measurements on the same eyes under similar experimental conditions. Variability of repeated measures of individual coefficients tended to be much greater for OA data than for SH data. Although Zernike coefficients obtained from a single measurement were generally larger when measured with the OA than with the SH, the averages across five trials were often smaller for the OA. The Zernike coefficients obtained from the two instruments were not significantly correlated. Radial modulation-transfer functions and point-spread functions derived from the two sets of measurements were similar for some subjects, but not all. When average Zernike coefficients were used to determine optical quality, the OA indicated superior optics in some eyes, but the reverse trend was true if Zernike coefficients from individual trials were used. Possible reasons for discrepancies between the OA and SH measurements include difference in sampling density, quality of data images, alignment errors, and temporal fluctuations. Multivariate statistical analysis indicated that the SH aberrometer discriminated between subjects much better than did the objective aberroscope.
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.
PURPOSE: The aim of the current study was to develop quantitative methods to assess optical aberrations caused by tear film disruption. METHODS: We used standard fluorescein imaging (FL) and a novel retroillumination (RI) method to image tear film disruption in 12 eyes. Using a clinical slit lamp biomicroscope, we alternated between widefield blue and narrow-beam white light to obtain an interleaved series of FL and RI images of the time course and pattern of tear film break-up. We developed an optical analysis that indicates that the RI image should be proportional to the spatial derivative of the FL image. Intensity fluctuations in the RI images are due to thickness changes in the tear film, whereas intensity fluctuations in FL images are directly determined by tear film thickness. RESULTS: As predicted by optical analysis of RI, the spatial distribution of gaps in the tear film seen with fluorescein appeared as pairs of light and dark contours in the RI images, and a precise correspondence between the spatial derivative of the FL image (slope) and the RI image was found. Both methods showed a gradual spreading of the tear disruption during blink suppression that varied tremendously among eyes in both time and spatial pattern. Resumption of normal blinking did not produce an immediate reconstitution of the normal tear film, and areas of tear break-up created during blink suppression remained abnormal for up to several minutes of normal blinking. CONCLUSIONS: Our analysis indicates that both FL and RI have the potential to quantify optical changes occurring during tear break-up. These results support an interpretation of RI as an intensity-based method for mapping the highly irregular optical aberrations of the eye produced by tear film disruption.
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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.
The concept of the wave-front guided design of contact lenses is presented from three vantage points: ray optics, wave front aberrations, and optical path-length errors. We argue that the goal of contact lenses is to make all of the optical paths from a distant object to the retina equal in length, regardless of where the path intersects the plane of the eye's pupil. The aberration map of an eye is a prescription for such a lens. Unfortunately, variability of measured aberration maps is a fundamental limit to our knowledge of the true aberration structure of an eye. Variability arises because the eye is a biologic system that changes over time for normal, physiologic reasons. Furthermore, uncertainty in our measurement of the aberration map because of such variable factors, such as alignment of the aberrometer to the eye by the clinician or small fixation errors committed by the patient, will make it difficult to achieve a full measure of success with aberration-correcting contact lenses. The clinical implication of these findings is that multiple measurements of the aberration map should be collected using a protocol that includes realignment of the instrument and then averaging the aberration maps to reduce the level of uncertainty associated with any single measurement.
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.