Thomas W. Raasch

Repeatability of visual acuity measurement.

Purpose. This study investigates features of visual acuity chart design and acuity testing scoring methods which affect the validity and repeatability of visual acuity measurements. Methods. Visual acuity was measured using the Sloan and British Standard letter series, and Landolt rings. Identifiability of the different letters as a function of size was estimated, and expressed in the form of frequency-of-seeing curves. These functions were then used to simulate acuity measurements with a variety of chart designs and scoring criteria. Results. Systematic relationships exist between chart design parameters and acuity score, and acuity score repeatability. In particular, an important feature of a chart, that largely determines the repeatability of visual acuity measurement, is the amount of size change attributed to each letter. The methods used to score visual acuity performance also affect repeatability. Conclusions. It is possible to evaluate acuity score validity and repeatability using the statistical principles discussed here.

Between-Eye Asymmetry in Keratoconus

Purpose. To report baseline differences between eyes on key variables in the Collaborative Longitudinal Evaluation of Keratoconus (CLEK) Study cohort compared with a retrospectively assembled group of myopic contact lens wearers without ocular disease. Methods. A total of 1,079 keratoconus patients who had not undergone a penetrating keratoplasty in either eye before their baseline visit were enrolled and examined at baseline. Records from 330 contact lens-wearing myopes were reviewed. Corneal curvature (keratometry), visual acuity, refractive error (manifest refraction), and corneal scarring were measured. Results. The mean differences between keratoconic eyes are as follows (better eye–worse eye for each variable, separately). Flat keratometry: −3.59 ±4.46 D and steep keratometry: −4.35 ±4.41 D; high-contrast best-corrected visual acuity: 7.30 ±6.83 letters; low-contrast best-corrected visual acuity: 8.53 ±7.51 letters; high-contrast entrance visual acuity: 9.03 ±8.40 letters; low-contrast entrance visual acuity: 9.43 ±7.88 letters; spherical equivalent refractive error: 3.15 ±3.84 D; and refractive cylinder power 1.55 ±1.42 D. Twenty-one percent of the keratoconus patients had corneal scarring in only one eye. There is an association between patient-reported unilateral eye rubbing and greater asymmetry in corneal curvature, and between a history of unilateral eye trauma and greater asymmetry in corneal curvature and refractive error, with the rubbed/traumatized eye being the steeper eye most of the time. Conclusions. Keratoconus is asymmetric in the CLEK Study sample.

Human electroretinogram responses to video displays, fluorescent lighting, and other high frequency sources.

Time-averaged human electroretinogram (ERG) responses were determined for several workplace visual stimuli which are temporally modulated at rates exceeding the perceptual critical fusion frequency (CFF). A clearly identifiable synchronous response was in evidence for a video display terminal (VDT) stimulus operating with a refresh rate as high as 76 Hz. A directly viewed fluorescent luminaire with controllable driving frequency elicited a synchronous response at rates as high as 145 Hz. In addition, an intense stimulus created by modulating the light from a slide projector produced responses at least as high as 162 Hz. The implications of these high-frequency responses are representing a potential basis for visual symptoms are discussed.

Visual acuity and chart luminance

ABSTRACT It is desirable to standardize the conditions under which visual acuity is measured because of its importance in determining whether subjects meet occupational vision standards and as an indicator of the extent or stability of pathological conditions. The chart luminance is one parameter which needs to be standardized, and the effect of the luminance level upon acuity measurement is a critical factor in this determination. These data are measured for a subject population using Landolt rings and British letters. Over a “normal” photopic range of 40 to 600 cd/m2 the relation between the logarithm of the minimum angle of resolution (log MAR)) and log L (luminance) can be approximated by a straight line. A doubling of the luminance level within this range improves the acuity measurement by approximately one letter on a five‐letter row. Landolt ring acuities are less affected by luminance than letter acuities. The application of these results to establishing a standardized luminance level and tolerance range is discussed.

Spherocylindrical refractive errors and visual acuity

Background. Understanding the relation between refractive error and visual acuity is complicated if astigmatic blur is present. No models are in widespread use that allow the combination of spherical and astigmatic errors for the purpose of predicting visual performance. Methods. Models for combining spherical and astigmatic errors are discussed, and predictions of these models using data from the literature are presented. Results. Three models for combining astigmatic with spherical errors are shown to predict visual acuity performance in uncorrected myopic refractive errors. A dioptric vector addition model is shown to have advantages over other candidate models. Conclusions. It is possible to combine spherocylindrical refractive errors into a single value when the objective is to correlate these values with visual acuity performance.

Automated decision tree classification of corneal shape

Purpose. The volume and complexity of data produced during videokeratography examinations present a challenge of interpretation. As a consequence, results are often analyzed qualitatively by subjective pattern recognition or reduced to comparisons of summary indices. We describe the application of decision tree induction, an automated machine learning classification method, to discriminate between normal and keratoconic corneal shapes in an objective and quantitative way. We then compared this method with other known classification methods. Methods. The corneal surface was modeled with a seventh-order Zernike polynomial for 132 normal eyes of 92 subjects and 112 eyes of 71 subjects diagnosed with keratoconus. A decision tree classifier was induced using the C4.5 algorithm, and its classification performance was compared with the modified Rabinowitz–McDonnell index, Schwiegerling’s Z3 index (Z3), Keratoconus Prediction Index (KPI), KISA%, and Cone Location and Magnitude Index using recommended classification thresholds for each method. We also evaluated the area under the receiver operator characteristic (ROC) curve for each classification method. Results. Our decision tree classifier performed equal to or better than the other classifiers tested: accuracy was 92% and the area under the ROC curve was 0.97. Our decision tree classifier reduced the information needed to distinguish between normal and keratoconus eyes using four of 36 Zernike polynomial coefficients. The four surface features selected as classification attributes by the decision tree method were inferior elevation, greater sagittal depth, oblique toricity, and trefoil. Conclusion. Automated decision tree classification of corneal shape through Zernike polynomials is an accurate quantitative method of classification that is interpretable and can be generated from any instrument platform capable of raw elevation data output. This method of pattern classification is extendable to other classification problems.

Repeatability of subjective refraction in myopic and keratoconic subjects: results of vector analysis

This paper evaluates the repeatability of refraction in keratoconus patients and normal myopes, using representations of spherocylindrical power that are theoretically valid. Data consist of test–retest refraction data from the Collaborative Longitudinal Evaluation of Keratoconus (CLEK) Study and similar data from normal myopes. Dioptric powers are transformed to an orthogonal vector representation of dioptric power. The metric of change is the dioptric difference between test and retest. The median difference between test and retest in keratoconus patients is four to six times larger than in normal myopes. Refraction over a rigid contact lens on a keratoconic cornea improves repeatability but remains approximately twice as large as in normal myopes. The methods demonstrated here possess advantages over previous methods and provide a more valid comparison between test and retest and between different subject groups. The repeatability of refraction in keratoconus patients is substantially worse than in normal myopes.

Corneal Topography and Irregular Astigmatism

BACKGROUNDnThe term irregular astigmatism has been used to refer to a variety of types of optical irregularity, although there are no widely recognized quantitative definitions of irregular astigmatism. This paper proposes a particular approach to defining and quantifying irregular astigmatism, and relates this model to blur disc formation.nnnMETHODSnA model of irregular astigmatism is developed and illustrated using corneal topography data. This method quantifies the variation in dioptric power with meridian by expressing that profile as a series of sinusoidal components. The relation between these components of irregular astigmatism and defocus blur discs is described, as well as the relation between irregular astigmatism and other models used to quantify aberrations.nnnRESULTSnIrregular astigmatism is expressed in diopters, and may predict blur of the retinal image in the same way that spherocylindrical defocus causes blur.nnnCONCLUSIONSnThis model of irregular astigmatism is an efficient, quantitative means of describing irregular astigmatism.

Clinical refraction in three-dimensional dioptric space revisited.

The traditional clinical designation of spherocylindrical power unambiguously specifies the refractive properties of a thin lens or refractive surface. This representation of dioptric power is not, however, optimum in mathematical terms, as is apparent when, for example, two spherocylindrical lens powers are added. Alternative systems have been described which are not subject to this same type of difficulty, and the essential feature of these other systems is that spherocylindrical power is defined in terms of a three-dimensional dioptric space in which the axes are usually orthogonal. The advantages of this orthogonality can be exploited in the practice of clinical refraction, provided lens powers in these three dimensions can be physically implemented. Systems using these characteristics have been introduced in the past, but the clinical community has not adopted them on a widespread basis. However, systems which take advantages of these features do have unique advantages relative to traditional clinical refraction procedures. These characteristics, and refractive procedures which exploit their advantages, are described.

Design and fabrication of a freeform phase plate for high-order ocular aberration correction

In recent years it has become possible to measure and in some instances to correct the high-order aberrations of human eyes. We have investigated the correction of wavefront error of human eyes by using phase plates designed to compensate for that error. The wavefront aberrations of the four eyes of two subjects were experimentally determined, and compensating phase plates were machined with an ultraprecision diamond-turning machine equipped with four independent axes. A slow-tool servo freeform trajectory was developed for the machine tool path. The machined phase-correction plates were measured and compared with the original design values to validate the process. The position of the phase-plate relative to the pupil is discussed. The practical utility of this mode of aberration correction was investigated with visual acuity testing. The results are consistent with the potential benefit of aberration correction but also underscore the critical positioning requirements of this mode of aberration correction. This process is described in detail from optical measurements, through machining process design and development, to final results.