Douglas G. Horner

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° and the other at axis 45°. 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.

Sensory, Cognitive, and Linguistic Factors in the Early Academic Performance of Elementary School Children The Benton-IU Project

Standardized sensory, perceptual, linguistic, intellectual, and cognitive tests were administered to 470 children, approximately 96% of the students entering the first grade in the four elementary schools of Benton County, Indiana, over a 3-year period (1995-1997). The results of 36 tests and subtests administered to entering first graders were well described by a 4-factor solution. These factors and the tests that loaded most heavily on them were reading-related skills (phonological awareness, letter and word identification); visual cognition (visual perceptual abilities, spatial perception, visual memory); verbal cognition (language development, vocabulary, verbal concepts); and speech processing (the ability to understand speech under difficult listening conditions). A cluster analysis identified 9 groups of children, each with a different profile of scores on the 4 factors. Within these groups, the proportion of students with unsatisfactory reading achievement in the first 2 years of elementary school (as reflected in teacher-assigned grades) varied from 3% to 40%. The profiles of factor scores demonstrated the primary influence of the reading-related skills factor on reading achievement and also on other areas of academic performance. The second strongest predictor of reading and mathematics grades was the visual cognition factor, followed by the verbal cognition factor. The speech processing factor was the weakest predictor of academic achievement, accounting for less than 1% of the variance in reading achievement. This project was a collaborative effort of the Benton Community School Corporation and a multidisciplinary group of investigators from Indiana University.

Comparison of Elevation, Curvature, and Power Descriptors for Corneal Topographic Mapping

Corneal topography systems sample thousands of surface points and from these data different descriptors are derived to create maps of the cornea. Without visualizing and comparing the maps, it is difficult to appreciate the implications of each descriptor for mapping. We created and compared several maps of an ellipsotoric cornea based on the following surface descriptors: relative elevation, dioptric curvature, and refractive power. Each map presented a different picture of the same cornea. Only elevation maps show true topography but must be calculated relative to an appropriate reference surface to reveal important features. Axial and to a greater degree instantaneous curvature maps bring out optically significant shape asymmetries but misrepresent refractive power away from the apex. Ray tracing maps display optical properties that are not apparent from the elevation or curvature maps, including spherical aberration. Oblique astigmatism can be described using a pair of maps for the sagittal and tangential powers at each surface point. A knowledge of these principles is necessary to interpret color maps of the corneal surface correctly.

Contrast Sensitivity Perimetry and Clinical Measures of Glaucomatous Damage

Purpose To compare conventional structural and functional measures of glaucomatous damage with a new functional measure—contrast sensitivity perimetry (CSP-2). Methods One eye each was tested for 51 patients with glaucoma and 62 age-similar control subjects using CSP-2, size III 24-2 conventional automated perimetry (CAP), 24-2 frequency-doubling perimetry (FDP), and retinal nerve fiber layer (RNFL) thickness. For superior temporal (ST) and inferior temporal (IT) optic disc sectors, defect depth was computed as amount below mean normal, in log units. Bland-Altman analysis was used to assess agreement on defect depth, using limits of agreement and three indices: intercept, slope, and mean difference. A criterion of p < 0.0014 for significance used Bonferroni correction. Results Contrast sensitivity perimetry-2 and FDP were in agreement for both sectors. Normal variability was lower for CSP-2 than for CAP and FDP (F > 1.69, p < 0.02), and Bland-Altman limits of agreement for patient data were consistent with variability of control subjects (mean difference, −0.01 log units; SD, 0.11 log units). Intercepts for IT indicated that CSP-2 and FDP were below mean normal when CAP was at mean normal (t > 4, p < 0.0005). Slopes indicated that, as sector damage became more severe, CAP defects for IT and ST deepened more rapidly than CSP-2 defects (t > 4.3, p < 0.0005) and RNFL defects for ST deepened more slowly than for CSP, FDP, and CAP. Mean differences indicated that FDP defects for ST and IT were on average deeper than RNFL defects, as were CSP-2 defects for ST (t > 4.9, p < 0.0001). Conclusions Contrast sensitivity perimetry-2 and FDP defects were deeper than CAP defects in optic disc sectors with mild damage and revealed greater residual function in sectors with severe damage. The discordance between different measures of glaucomatous damage can be accounted for by variability in people free of disease.

Blur-resistant perimetric stimuli.

Purpose To develop perimetric stimuli that are resistant to the effects of peripheral defocus. Methods One eye each was tested on subjects free of eye disease. Experiment 1 assessed spatial frequency, testing 12 subjects at eccentricities from 2 to 7 degrees using blur levels from 0 to 3 diopters (D) for two (Gabor) stimuli (spatial SD, 0.5 degrees; spatial frequencies, 0.5 and 1.0 cycles per degree [cpd]). Experiment 2 assessed stimulus size, testing 12 subjects at eccentricities from 4 to 7 degrees using blur levels 0 to 6 D for two Gaussians with SD of 0.5 and 0.25 degrees and a 0.5-cpd Gabor with SD of 0.5 degrees. Experiment 3 tested 13 subjects at eccentricities from fixation to 27 degrees using blur levels 0 to 6 D for Gabor stimuli at 56 locations; the spatial frequency ranged from 0.14 to 0.50 cpd with location, and SD was scaled accordingly. Results In experiment 1, blur by 3 D caused a small decline in log contrast sensitivity for the 0.5-cpd stimulus (mean ± SE, 0.09 ± 0.08 log units) and a larger (t = 7.7, p < 0.0001) decline for the 1.0-cpd stimulus (0.37 ± 0.13 log units). In experiment 2, blur by 6 D caused minimal decline for the larger Gaussian, by 0.17 ± 0.16 log units, and larger (t > 4.5, p < 0.001) declines for the smaller Gaussian (0.33 ± 0.16 log units) and the Gabor (0.36 ± 0.18 log units). In experiment 3, blur by 6 D caused declines by 0.27 ± 0.05 log units for eccentricities from 0 to 10 degrees, by 0.20 ± 0.04 log units for eccentricities from 10 to 20 degrees, and 0.13 ± 0.03 log units for eccentricities from 20 to 27 degrees. Conclusions Experiments 1 and 2 allowed us to design stimuli for experiment 3 that were resistant to effects of peripheral defocus.

Assessing assumptions of a combined structure-function index.

Medeiros et al. developed a combined structure‐function index for glaucoma by combining two ganglion cell models developed by Harwerth et al. The current study assessed assumptions of the Medeiros combined structure‐function index by evaluating whether the two Harwerth models gave similar distributions of ganglion cells in an independent dataset.

Assessing spatial and temporal properties of perimetric stimuli for resistance to clinical variations in retinal illumination.

PURPOSE To develop perimetric stimuli for which sensitivities are more resistant to reduced retinal illumination than current clinical perimeters. METHODS Fifty-four people free of eye disease were dilated and tested monocularly. For each test, retinal illumination was attenuated with neutral density (ND) filters, and a standard adaptation model was fit to derive mean and SEM for the adaptation parameter (NDhalf). For different stimuli, t-tests on NDhalf were used to assess significance of differences in consistency with Webers law. Three experiments used custom Gaussian-windowed contrast sensitivity perimetry (CSP). Experiment 1 used CSP-1, with a Gaussian temporal pulse, a spatial frequency of 0.375 cyc/deg (cpd), and SD of 1.5°. Experiment 1 also used the Humphrey Matrix perimeter, with the N-30 test using 0.25 cpd and 25 Hz flicker. Experiment 2 used a rectangular temporal pulse, SDs of 0.25° and 0.5°, and spatial frequencies of 0.0 and 1.0 cpd. Experiment 3 used CSP-2, with 5-Hz flicker, SDs from 0.5° to 1.8°, and spatial frequencies from 0.14 to 0.50 cpd. RESULTS In Experiment 1, CSP-1 was more consistent with Webers law (NDhalf ± SEM = 1.86 ± 0.08 log unit) than N-30 (NDhalf = 1.03 ± 0.03 log unit; t > 9, P < 0.0001). All stimuli used in Experiments 2 and 3 had comparable consistency with Webers law (NDhalf = 1.49-1.69 log unit; t < 2). CONCLUSIONS Perimetric sensitivities were consistent with Webers law when higher temporal frequencies were avoided.

Individual differences in the shape of the nasal visual field.

Graphical abstract Figure. No Caption available. HighlightsThe stimulus was resistant to peripheral defocus and reduced illumination.Between‐subject differences in the shape of the nasal visual field were substantial.In some people there was no peripheral depression of sensitivity, in most the depression was mild.A few had more severe peripheral depression that persisted in longitudinal testing. ABSTRACT Between‐subject differences in the shape of the nasal visual field were assessed for 103 volunteers 21–85 years of age and free of visual disorder. Perimetry was conducted with a stimulus for which contrast sensitivity is minimally affected by peripheral defocus and decreased retinal illumination. One eye each was tested for 103 volunteers free of eye disease in a multi‐center prospective longitudinal study. A peripheral deviation index was computed as the difference in log contrast sensitivity at outer (25–29° nasal) and inner (8° from fixation) locations. Values for this index ranged from 0.01 (outer sensitivity slightly greater than inner sensitivity) to −0.7 log unit (outer sensitivity much lower than inner sensitivity). Mean sensitivity for the inner locations was independent of the deviation index (R2 < 1%), while mean sensitivity for the outer locations was not (R2 = 38%, p < 0.0005). Age was only modestly related to the index, with a decline by 0.017 log unit per decade (R2 = 10%). Test‐retest data for 21 volunteers who completed 7–10 visits yielded standard deviations for the index from 0.04 to 0.17 log unit, with a mean of 0.09 log unit. Between‐subject differences in peripheral deviation persisted over two years of longitudinal testing. Peripheral deviation indices were correlated with indices for three other perimetric stimuli used in a subset of 24 volunteers (R2 from 20% to 49%). Between‐subject variability in shape of the visual field raises concerns about current clinical visual field indices, and further studies are needed to develop improved indices.

Accuracy of the EyeSys 2000 in measuring surface elevation of calibrated aspheres

Abstract This article examines the accuracy of the EyeSys 2000 videokeratoscope in measuring aspheric surfaces for calculation of the wavefront aberrations of the anterior cornea. Six rotationally symmetric aspheric surfaces were measured. The surface elevation was computed from the normal measurement files. Both elevation error and relative error were computed from the average of the three maps. The root-mean-square errors for the various surfaces ranged from 1.48 to 6.55 microns, with less error on the oblate and spherical surfaces. The error found was very systematic, increasing monotonically toward the periphery. The article includes a strategy to compensate for the systematic error to meet the required 0.5-micron accuracy needed. An equation was developed that used only the apical radius and shape factor, which improved the accuracy to the required 0.5-micron level.

Using perimetric data to estimate ganglion cell loss for detecting progression of glaucoma: a comparison of models

Models relating perimetric sensitivities to ganglion cell numbers have been proposed for combining structural and functional measures from patients with glaucoma. Here we compared seven models for ability to differentiate progressing and stable patients, testing the hypothesis that the model incorporating local spatial scale would have the best performance.