Compensating for vertical anisometropic imbalance by the positioning of segment centers.

Prismatic imbalance produced in the reading area by an anisometropic spectacle correction can be offset by various methods. If a reading addition is present, one method is to provide differently shaped segments and allowing their optical centers to be separated vertically while the segment tops remain in horizontal alignment. Traditionally, to apply this method, the relative prismatic difference at the reading point is first determined by a thin lens application of Prentice's rule. This rule is then applied a second time to determine the placement of the segments that will offset the prismatic difference produced by the major lenses. However, the conventional application of Prentice's rule for determining the fusional demand in a particular area of the spectacle field often produces very large errors, which will affect the calculation of the placement of the segments. This article develops and demonstrates more accurate methods for applying the principle of compensating segments.

Perceived segment misalignment in anisometropic spectacle corrections.

In anisometropic bifocals or trifocals, the magnification difference between left and right lenses will often distort the perceived alignment of the segments. The effect is most noticeable with the segment tops in bifocals or the dividing line between near and intermediate fields in trifocals. The perceived misalignment occurs because off-axis image points are displaced unequal amounts in right and left fields, which forces the lines of sight to diverge to achieve fusion. Hence, the left and right segments will appear at different levels even though they may be perfectly aligned in the spectacle lenses. This article explains why the perceived misalignment occurs, how it can be determined and quantified, and how it can be reduced or eliminated.

New equations for determining ocular deviations produced by spectacle corrections.

The relation between prismatic deviations at the spectacle plane and corresponding ocular deviations is demonstrated and expressed in the form of an equation. In addition, basic equations for the ocular prismatic deviations produced by spectacle lenses placed before the eyes are developed. These equations are a sequel to previous studies demonstrating that the current use of Prentice's rule for finding the prismatic effect produced by realistic spectacle lenses is not suitable for present day spectacle corrections. One set of equations is based on tangents of angles of ocular rotation, whereas another set of equations expresses ocular deviations in degrees. The former is appropriate for clinical purposes; the latter is suitable when greater accuracy is desired.

A new method for determining prismatic effects in cylindrical spectacle corrections.

This study presents a new method of finding differential prismatic effects in an anisometropic spectacle correction containing cylindrical lenses. The calculations are based on dynamic spectacle magnifications rather than Prentice's rule. If an imaginary circular object is considered, cylindrical lenses will produce elliptical far point images, which can be superimposed on the spectacle plane for comparison. The difference between left and right ellipses, in any meridian, then represents the distance the eyes have to diverge in order to fuse the object of regard. This distance can be translated into prism diopters of differential prismatic effect. Although the conventional methods for finding this effect often result in very large errors, the new method can be performed with great accuracy. In part, this is because it uses the actual eccentricities of the two eyes rather than an assumed average eccentricity. Moreover, the method includes considerations of base curves and center thickness. Contrary to the classical methods, it can thus be applied to clinically realistic lenses.

Determining exact prismatic deviations in spectacle corrections.

For nearly 100 years, Prentice's rule has been used to determine the prismatic effect and prismatic differences at peripheral points in the binocular spectacle field. However, calculations show that the current application Prentice's rule is valid only for a single lens and only if that lens is considered as a thin lens approximation. When center thickness and base curves are taken into account, Prentice's rule is no longer valid. In addition, when the prismatic difference in an off-axis region of the lenses is determined with the assumption that both eyes look through the lenses at identical distances from their optical centers, the errors are further compounded. If the eyes are to maintain fusion, this assumption is optically impossible and will produce incorrect results. It is also shown that Prentice's rule cannot be applied to iseikonic corrections to find differential prismatic effects. The article demonstrates how exact prismatic effects can be determined from the spectacle-generated images and the angles they subtend at the ocular rotation centers.

The multimeridional apparent frontoparallel plane: introduction of the induced effect.

The application of vertical rod stimuli to obtain apparent frontoparallel plane (AFPP) settings is well-known. A geometrical relation based on observation distance, interpupillary distance, and retinal disparity determines the deviation of the setting from the objective frontoparallel plane. Further developments of this procedure have established that a similar relation exists for oblique presentations of parallel rod stimuli, the orientation of the rods being an additional variable. This extension of the AFPP procedure is referred to as the multimeridional AFPP or MAFPP. It permits the determination of aniseikonia in oblique as well as horizontal meridians. Although oblique disparities contain a vertical component, an induced effect is absent as long as parallel rod stimuli are used alone. If an induced effect were present, the MAFPP geometrical relations would be expected to break down. To test this hypothesis, random dot arrays and a row of dots of the same frequency as a control stimulus of parallel lines were presented alone and in combination with the line stimuli. Binocular disparities were induced by a meridional afocal magnifier placed at various axes before one eye. It was found that the dot arrays caused a breakdown of the geometrical relation when presented alone or in combination with the parallel lines. The amount of deterioration varied only slightly with the number and arrangement of dot stimuli but increased as the vertical component of the oblique magnification increased. In addition to proving the main hypothesis, the data provide information pertaining to the MAFPP theory as well as offering some insight into the induced effect. The most important practical implication of the results is that the MAFPP theory can be used to measure unknown retinal disparities only if continuous parallel lines are presented in isolation.

Multimeridional apparent frontoparallel plane: relation between stimulus orientation angle and compensating tilt angle.

The classical apparent frontoparallel plane (AFPP) setting is typically obtained by having the subject move a series of parallel rods farther or closer until they line up in a plane perceived to be parallel to the face plane. If there is a size difference between the two ocular images, the AFPP setting defined by the rods will exhibit a tilt from the objective frontoparallel plane, about an axis parallel to the rods. The multimeridional apparent frontoparallel plane (MAFPP) is an extension of this procedure to rod orientations other than the vertical meridian. In previous studies, it was found that oblique tilt angle settings corresponding to rod orientations of 45 degrees and 135 degrees are equal to square root 2 times the tilt angle for the vertical rod orientation for the same interocular magnification difference along the meridian perpendicular to the rods. In this study, we measured the tilt angles produced by a series of oblique rod orientations between 15 degrees and 165 degrees, inclusive. Throughout the 150 degrees range tested, the tilt angles were found to be consistently proportional to the cosecant of the rod orientation angle, the factor square root 2 previously used being a specific example of this relation. Within this range, neither empirical cues nor the induced effect cause the cosecant relation to break down. It is suggested that the MAFPP procedure can be applied more extensively than previously anticipated.

New developments in the application of the multimeridional apparent frontoparallel plane.

This study is a sequel to a previous publication that introduced the multimeridional apparent frontoparallel plane (MAFPP) as a method of measuring aniseikonia. As the term implies, apparent frontoparallel plane (AFPP) responses are obtained not only in the horizontal meridian, but also in oblique meridians. Since the introductory publication, the method has been applied extensively for measuring aniseikonia and has been found to be reliable, accurate, and easily adapted to clinical purposes. This study presents a more detailed and comprehensive account of the underlying theory than did the introductory report. It clarifies some problems inherent in the method originally presented and describes a simplified and improved procedure for measuring aniseikonia. It describes the application of the theory to a number of specific clinical situations. Finally, it is suggested that the method has a much broader application than the clinical measurement of aniseikonia.

Effect of induced static aniseikonia on fixation performance during oblique gaze.

In a previous study, it was found that oblique gaze and the prismatic effect inherent in dynamic aniseikonia combine to affect the ability to fixate centrally. In the current study, retinal image differences were introduced, whereas prismatic effects were eliminated. This simulates static aniseikonia as opposed to dynamic aniseikonia. At the same time, oblique gaze was simulated by presenting the stimuli in directions other than straight ahead. The directions of presentation contained both horizontal and vertical components. Fixation eccentricity was monitored by using the border enhancement method, as described in previous experiments. It was found that fixation eccentricity increased as the eyes were directed toward stimuli oriented in directions other than straight ahead. When vertical and horizontal components of oblique gaze were combined, the fixation eccentricity was found to be greater than with either component alone. When differential magnification between left and right retinal images was introduced, the fixation eccentricity increased further, the increment being approximately constant for all directions of gaze.

Effect of induced dynamic aniseikonia on fixation performance during oblique gaze.

This is a sequel to other papers dealing with the effect of induced aniseikonia and optical anisophoria on fixation eccentricity during bifixation. To stimulate the effect of induced anisophoria, controlled amounts of differential prism were induced in the vertical meridian. At the same time, stimuli were presented at various angles from the subject's straight ahead orientation. As demonstrated in other studies, it was found that a vertical prismatic difference will cause the eyes to fixate slightly eccentrically in the horizontal meridian. The eccentricity was measured with the border enhancement method, described and tested in other studies. In addition, it was found that the fixation deviation is increased further by oblique gaze, the greatest obliquity having the greatest effect. It was also found that whereas short-term adaptation reduces the prism effect somewhat, it has less influence on the effect of oblique gaze. In general, the study demonstrates the potential oculomotor problems inherent in optical anisophoria.

Anisophoria and aniseikonia. Part II. The management of optical anisophoria.

Part I of this publication dealt with the simultaneous occurrence of aniseikonia and optical anisophoria when anisometropic spectacles are worn. Part II deals with the correction and management of spectacle-induced anisophoria. It presents simple formulas for calculating the constants of an iseikonic correction that circumvent much of the trial and error inherent in the older methods. It shows how such iseikonic lenses rather than prisms can be used to correct a large portion of optical anisophoria and how such corrections can improve binocular visual performance. It also discusses dynamic phorometry and some new methods for measuring induced anisophoria. The essential message of Parts I and II is that the two effects, aniseikonia and optical anisophoria, should be considered together and not as separate entities.

Anisophoria and aniseikonia. Part I. The relation between optical anisophoria and aniseikonia.

Part I of this publication demonstrates and explains the close relation between aniseikonia and anisophoria induced by spectacles. It discusses the clinical implications of this relation by discussing certain aspects of aniseikonia theory, prismatic effects during oblique gaze through spectacles as for reading, and a simple formula that presents a comprehensive description of all prismatic effects and prismatic differences produced by a pair of spectacles. It also describes an easy method of specifying iseikonic lenses, as well as some conventional methods of measuring aniseikonia and anisophoria. Part II will deal with the correction and management of anisophoria when induced together with aniseikonia. Parts I and II, together, will convey a new approach toward the management of anisophoric spectacle corrections.

Aniseikonia and fixation performance: effect of retinal stimulus location.

It has been shown previously that induced aniseikonia amplifies any latent fixation eccentricity associated with binocular fusion stress. This study determines if the retinal location of the stimulus plays a part in this effect. The stimulus consisted of a vertical border formed by the juxtaposition of two fields of unequal luminances and a line segment parallel to the border whose distance from the border can be varied. At the same time, the border allowed the application of a previously tested method of measuring fixation eccentricity, based on the border-enhancement response. It was found that the fixation eccentricity produced by aniseikonia is maximal for the smallest distance of the variable target from the border but unaffected by the larger distances tested. It was concluded that the retinal location of the stimulus has an important influence on the response to aniseikonia.

Variation of convergence limits with change in direction of gaze.

Until recently, convergence limits have been measured only in the primary position of gaze. A new instrument permits such measurements in all directions of gaze and at various angular distances from the primary straight-ahead position. Aberration and distortion-free stimuli based on Heine's principle were incorporated in the apparatus. For each of the nine subjects participating, convergence limits were obtained in the primary straight-ahead position, secondary, and tertiary positions and in varying degrees of obliquity of these directions of gaze. The convergence limits were measured in 10 degrees steps away from the straight-ahead position of gaze in 18 different meridians. It was found that convergence limits vary markedly with the direction of gaze, the maximal vergence range usually being found between 10 to 20 degrees below the primary horizontal plane in the lower right-half field, possibly because subjects spend most of their time looking in this direction.

Effect of induced aniseikonia on fixation performance.

The purpose of the study was to determine to what extent induced aniseikonia affects fixation performance. Aniseikonia was induced in the vertical meridian only, whereas fixation alignment was monitored in the horizontal meridian. A previously developed technique based on the dependency of border enhancement bandwidth on fixation eccentricity was used to monitor deviations from central fixation during fusion. Stress on the fusion mechanism was supplied by controlled increments of forced horizontal vergence. It was found that deviation from central fixation in the horizontal meridian generally increases with increasing amounts of vertical aniseikonia. The effect is particularly pronounced for small amounts of aniseikonia.

Effect of vertical prism imbalance on fixation performance.

It is well known that induced vertical imbalance will bring about deviation from central fixation in the vertical meridian. This study seeks to determine if vertical imbalance will affect the fixation performance in the horizontal meridian as well. For this purpose, a technique previously developed for monitoring fixation eccentricity was used. The technique, which is based on the effect of fixation eccentricity on border enhancement, is unaffected by adaptive changes in perceived visual direction. The results show a rapid increase in horizontal fixation misalignment with the first increments of vertical prism difference, followed by a slower increase for additional prism differences. When horizontal forced vergence was applied in addition, fixation misalignment increased throughout the range of vertical vergences. Similarly, vertical fusion misalignment was increased by horizontal fusion stress. It was concluded that forced vergence presented in one meridian will amplify any fusion misalignment that might exist in other meridians. This calls for a reevaluation of existing methods of assessing binocular fixation performance.

Objective measurement of binocular fixation misalignment.

The amount of deviation from central fixation during binocular fusion of a vertical border was compared with conventional fixation disparity measured at the same time, forced convergence serving as the independent variable. Fixation eccentricity was measured objectively by monitoring a scleral blood vessel with a video camera and by analyzing the movement, greatly magnified, on a video screen. Fixation disparity was measured conventionally by interocular nonius alignment of vertically dissociated line segments. The results agree well with previous comparisons of these responses, in which the fixation eccentricity was measured by using a technique based on the effect of retinal stimulus location on border enhancement. As in the previous experiment, the fixation misalignment was found to be many times larger than the corresponding disparity for most forced convergence values. The large discrepancy between actual fixation misalignment and fixation disparity has thus been documented objectively as well as subjectively.

Field of vergence limits.

The binocular visual field is the combined visual field obtained when the eyes are fixating a given point without head movements. The binocular field of fixation is the area within which central bifixation is possible by moving the eyes but not the head. This study introduces a new concept of the binocular field, namely, the vergence limit field, defined as the binocular field of fixation that allows for a specified amount of vergence eye movements at its limits. A newly developed instrument and technique were used to measure this field for a number of normal subjects.