Howard C. Howland

Accommodation, refractive error and eye growth in chickens.

We raised chickens with defocusing lenses of differing powers in front of their eyes. For this purpose, small hoods made from soft, thin leather were carefully fitted to their heads. Lenses were attached to the hoods by velcro fasteners and could be easily removed for cleaning. The powers of the lenses were such that their optical effects could be compensated for by accommodation. It was verified by infrared (IR) photoretinoscopy that the chickens could keep their retinal images in focus. Wearing a lens resulted in a consistent shift of the non cycloplegic refractive state (measured without the lens) which was in the direction to compensate for the lens. We used a sensitive technique (precision = +/- 50 micron as estimated from the variability of repeated measurements) to measure the posterior nodal distance (PND) in excised eyes of birds grown with lenses. The PND, in turn, was used to compare eyes treated with different lenses. It was found that the PND was increased in eyes which were treated with negative lenses compared to those treated with positive lenses. This effect occurs independently in both eyes and it is not due to changes in corneal curvature. We discuss our result in terms of a closed-loop feedback system for the regulation of eye growth.

A subjective method for the measurement of monochromatic aberrations of the eye.

We have designed an aberroscope that differs from Tscherning’s classical instrument in that it makes use of an artificial astigmatism rather than an artificial myopia to defocus the image of a point source of light. A subject views the source through a ±5 D crossed cylinder lens with axes at 45° to the principal axes of an intercalated grid and sees a shadow image of the grid. The distortions of this grid image are quantitatively related to the wave aberration of the eye. Using this device we have obtained drawings for more than 50 subjects. These drawings of the grid pattern have been analyzed by means of a two-dimensional polynomial curve Fitting technique that computes Taylor polynomial terms to the fourth order. From the Taylor coefficients it is possible to reconstruct the wave aberration surface. Examination of the Taylor terms so obtained shows that the monochromatic aberrations of the eye are dominated by third-order Taylor terms within the range of physiological pupil sizes, and that spherical aberration frequently appears predominantly about one axis only, a condition that we have termed “cylindrical” aberration. We have computed the optical MTF of our subjects’ eyes and find that the role of aberrations in degrading the MTF may be greater than generally believed.

Comparison of corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis.

PURPOSE To compare changes in the corneal wavefront aberrations after photorefractive keratectomy and laser in situ keratomileusis. METHODS In a prospective randomized study, 22 patients with bilateral myopia received photorefractive keratectomy on one eye and laser in situ keratomileusis on the other eye. The procedure assigned to each eye and the sequence of surgery for each patient were randomized. Corneal topography measurements were performed preoperatively, 2 and 6 weeks, 3, 6, and 12 months after surgery. The data were used to calculate the wavefront aberrations of the cornea for both small (3-mm) and large (7-mm) pupils. RESULTS Both photorefractive keratectomy and laser in situ keratomileusis significantly increased the total wavefront aberrations for 3- and 7-mm pupils, and values did not return to the preoperative level throughout the 12-month follow-up period. For a 3-mm pupil, there was no statistically significant difference between photorefractive keratectomy and laser in situ keratomileusis at any postoperative point. For a 7-mm pupil, the post-laser in situ keratomileusis eyes exhibited significantly larger total aberrations than the post-photorefractive keratectomy eyes, where a significant intergroup difference was observed for spherical-like aberration, but not for coma-like aberration. This discrepancy seemed to be attributable to the smaller transition zone of the laser ablation in the laser in situ keratomileusis procedure. Before surgery, simulated pupillary dilation from 3 to 7 mm caused a five- to six-fold increase in the total aberrations. After surgery, the same dilation resulted in a 25- to 32-fold increase in the photorefractive keratectomy group and a 28- to 46-fold increase in the laser in situ keratomileusis group. For a 3-mm pupil, the proportion of coma-like aberration increased after both photorefractive keratectomy and laser in situ keratomileusis. For a 7-mm pupil, coma-like aberration was dominant before surgery, but spherical-like aberration became dominant postoperatively. CONCLUSIONS Both photorefractive keratectomy and laser in situ keratomileusis increase the wavefront aberrations of the cornea and change the relative contribution of coma- and spherical-like aberrations. For a large pupil, laser in situ keratomileusis induces more spherical aberrations than photorefractive keratectomy. This finding could be attributable to the smaller transition zone of the laser ablation in the laser in situ keratomileusis procedure.

Optimal strategies for predator avoidance: The relative importance of speed and manoeuvrability

Abstract The relative importance of speed and manoeuvrability in predator-prey chases was assessed by investigating whether or not a pursuing predator could catch its prey in a simple turning gambit initiated by the prey animal. The turning radius and velocity of the prey were normalized by dividing them by those of the predator. With the use of numerical methods to solve implicit equations it was determined for what values of relative radii and velocity the prey could escape. When escape was possible the optimal time of initiation of the preys turn and the minimum closure distance of the predator were computed. It was found initially by numerical and subsequently by analytic techniques that, in order for the prey to escape the predator in the turning gambit, its normalized velocity must be related to its normalized radius by the inequality: v>r 1 2 over the interval 0 ⩽ r ⩽ 1. Situations in which the results of the turning gambit may be expected to give realistic predictions of capture or escape are discussed together with physical factors governing the relationship between turning radius and velocity, and the conditions under which the prey might profitably trade higher velocity for a smaller turning radius. Lastly, a number of specific predator-prey combinations are treated with a view towards illustrating the application of the theory and promoting the collection of simultaneous turning radii and velocity data.

Corneal Aberrations and Visual Performance After Radial Keratotomy

BACKGROUND Refractive surgery and videokeratography have allowed us to study the effects on visual performance of relatively large changes in corneal aberration structure induced by surgical changes in corneal shape. METHODS We quantified in one eye of nine normal and 23 radial keratotomy patients, the area under the log contrast sensitivity function (AULCSF) and corneal first surface wavefront variance for two artificial pupil sizes (3 and 7 mm). Contrast sensitivity was measured with sine-wave gratings at six spacial frequencies. Wavefront variance was derived from videokeratographs using Zernike polynomials. RESULTS For normals eyes there were no significant changes over time. For eyes that had radial keratotomy, there were significant pupil size-dependent changes. For the 3 mm pupil, there were significant surgery-induced changes in the corneal wavefront variance which became large (approximately 30 times preoperative values) at 7 mm. Significant correlated changes in AULCSF for the 7 mm pupil but not for the 3 mm pupil occurred immediately following surgery and remained. CONCLUSIONS Radial keratotomy, like photorefractive keratectomy, shifts the distribution of aberrations from third order dominance (coma-like aberrations) to fourth order dominance (spherical-like aberrations). Radial keratotomy-induced aberrations and loss in contrast sensitivity are reduced with increasing clear zone diameter. Radial keratotomy induces an increase in the optical aberrations of the eye and the increase for large pupils (7 mm) but not small (3 mm) is correlated to a decrease in contrast sensitivity.

Developing eyes that lack accommodation grow to compensate for imposed defocus.

The eyes of growing chicks adjust to correct for myopia (eye relatively long for the focal length of its optics) or hyperopia (eye relatively short for the focal length of its optics). Eyes made functionally hyperopic with negative spectacle lenses become myopic and long, whereas eyes made functionally myopic with positive spectacle lenses become hyperopic and short. We report here that these compensatory growth adjustments occur not only in normal eyes but also in eyes unable to accommodate (focus) because of lesions to the Edinger-Westphal nuclei. Thus, at least in chicks, accommodation is not necessary for growth that reduces refractive errors during development, and may not be necessary for the normal control of eye growth.

Compensation of corneal horizontal/vertical astigmatism, lateral coma, and spherical aberration by internal optics of the eye.

Both the anterior surface of the cornea and the internal optics (the posterior cornea, crystalline lens) contribute to the aberration of a wavefront passing through the eye. Artal, Guirao, Berrio, and Williams (2001) reported that the wavefront aberrations produced by the internal optics offset, or compensate for, the aberrations produced by the cornea to reduce ocular wavefront aberrations. We have investigated the wavefront aberrations of the cornea, internal optics, and complete eye on both the population and individual level to determine which aberrations are compensated and probable paths leading to that compensation. The corneal and ocular aberrations of 30 young subjects at relaxed accommodation were measured with the Topcon Wavefront Analyzer, which simultaneously measures refraction, corneal topography (videokeratoscope), and wavefront aberrations (Hartmann-Shack sensor). We found strong evidence for compensation of horizontal/vertical (H/V) astigmatism (Zernike term Z5) lateral coma (Z8) and spherical aberration (Z12). H/V astigmatism compensation is scaled for each individual, suggesting that it is actively determined by a fine-tuning process. Spherical aberration shows no individual compensation, suggesting that is a passive result of genetically determined physiology. Lateral coma shows individually scaled compensation, some of which may be attributable to eccentricity of the fovea.

Laboratory, clinical, and kindergarten test of a new eccentric infrared photorefractor (PowerRefractor).

Purpose Photorefraction is a convenient way to determine refractive state from a distance. It is, therefore, useful for measuring infants and noncooperative subjects. However, its reliability (or precision) and accuracy (or validity) has been questioned. In a study in subjects without cycloplegia, we have tested whether, after complete automatization, eccentric photorefraction at a 1-m distance can be as reliable as a common autorefractor. Methods In a laboratory study of 15 student subjects without the use of cycloplegia (30 eyes, refractive errors ranging from −6 D to +6 D), age 25 to 31 years, the photorefractive measurements were compared with spectacle prescriptions. In a clinical study, photorefraction, autorefraction, and subjective refraction were performed in 40 patients without cycloplegia (refractive errors ranging from −4 D to +4 D), most of them with various ocular pathologies. Subjective refractions were obtained by an experienced clinical ophthalmologist but were not accessible to the examiner who used the two refractors. Visual acuity was 20/20 or better except for five subjects. Ages ranged from 6 to 75 years. In the kindergarten screening study, 108 children aged 3 to 6 years were screened for refractive errors. Results In the laboratory study, it was found that the mean difference between spectacle prescription and PowerRefractor measurements was <0.6 D for spheres and below 0.4 D for cylinders. In the clinical study, data were obtained by all three procedures in 78 eyes. The photorefractor and the autorefractor performed similarly for spheres (mean absolute dioptric difference between refractor and subjective measure: 0.593 D and 0.696 D) and cylinders (mean absolute dioptric differences: 0.399 D and 0.389 D). However, the photorefractor was superior with regard to the measurement of the magnitude and axis of astigmatism (mean weighted difference between objective and subjective axis 0.644 D and 0.769 D, respectively). In the kindergarten study, it was found that the PowerRefractor was very convenient to handle. The autorefractor measured more myopic refractions than the PowerRefractor (mean of the left eyes 0.11 ± 1.1 D vs. 0.62 ± 0.53 D, p < 0.001). There was no indication that the PowerRefractor failed to detect hyperopia, because all but one child with more than 2 D of hyperopia measured with autorefractor (n = 7) was also hyperopic with the PowerRefractor. Furthermore, presenting an interesting fixation target at a 3-m distance did not cause more hyperopic refractions, indicating that the camera of the PowerRefractor at a 1-m distance was not a significant stimulus to accommodation. Conclusions The PowerRefractor was shown to have comparable or slightly better reliability and accuracy than a modern autorefractor; however, it has major advantages over current autorefractors in that it is faster, measures both eyes at once, and gives interpupillary distance, pupil size, and information on the alignment of the eyes at the same time.

Photorefraction: a technique for study of refractive state at a distance.

Photography of the fundus reflections of a point source of light from a human subject facilitates estimation of the refractive disparity about any desired axis, between the plane of focus of the subject’s eyes and that of the camera. The method employs a special attachment to a 35-mm reflex camera, consisting of a fiber-optic light guide mounted in the center of an array of pie-shaped cylinder lens sectors and placed in front of the camera’s wide-aperture lens. The light guide supplies a 1/4 second flash of filtered tungsten light of irradiance less than 1 μW/cm2 at the corneas of the subject, who is seated 1–2 m distant. The reflected light emanating from the subject’s pupils is transformed by the array of cylinder lenses into a star-shaped pattern at the film plane; the lengths of the arms are proportional to the dioptric disparities about the corresponding axes. Theoretical intensity distributions of star patterns for spherical and astigmatic errors have been computed upon the assumption that the retina is a diffuse reflector. They are shown to agree well with experiments. The technique provides an objective method for estimating the refractive states of both eyes of a subject simultaneously, under more-or-less-natural circumstances, and may find practical application in the visual screening of very young children.

The allometry and scaling of the size of vertebrate eyes

We compiled data from the literature and colleagues to examine the relationship between eye axial length and body weight for vertebrates as well as birds, mammals, reptiles, and fishes independently. After fitting the data to logarithmic and semi-logarithmic models, we found that axial length of vertebrate eyes does obey a conventional logarithmic relationship with body weight rather than a semi-logarithmic relationship as suggested by the results of previous studies. The regression slopes and intercepts appear to be characteristic of various animal groups. The axial length of the eye is largest in birds and primates, smaller in other mammals (especially rodents) and reptiles, and widely varying in fishes.