Ophthalmometric prediction of correcting cylinder axis.
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Astigmatism↗
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An easier method to obtain the sphere, cylinder, and axis from an off-axis dioptric power matrix.
Dr. W. F. Long pointed out that calculations of decentration in spherocylindrical lenses, as well as calculations of combinations of obliquely crossed spherocylindrical lenses, are considerably simplified by the use of matrix methods. In the obliquely crossed lens problem, Long used eigenvalue techniques to obtain the sphere, cylinder, and axis of the equivalent lens. This paper presents an alternative to the eigenvalue method. This alternative method uses the invariance of the trace and determinant of the dioptric power matrix. This alternative is conceptually easier to understand than the eigenvalue method and perhaps will encourage more people to use the matrix methods.
Eyeglasses↗
Working distance comparison of plus lenses and reading telescopes.
Low vision aids used in the spectacle plane may be either plus lenses or telescopes focused for near. The plus lens has a shorter working distance than a near point telescope of the same equivalent power. A relationship between the anterior focal length (fv) of the near point telescope and the equivalent focal length (fe) of a thin lens of equal power can be derived from the formula fv = (mag) (fe). This formula provides a basis for determining what equivalent powers are equal and interchangeable between the two types of aids. Furthermore, the advantages of the increased working distance afforded by the near point telescope can be defined.
Eyeglasses↗
Changes in angle lambda during growth: theory and clinical applications.
The eye undergoes rapid growth during the first years of life. Using a mathematical model, we analyzed angle lambda from birth through adult life to determine what change in its magnitude occurs with growth of the eye. The effect of changes in angle lambda on measurement and correction of astigmatic errors and on the analysis of fixation patterns are discussed.
Adult↗
Loss of power with flexure of hydrogel plus lenses.
Both clinical impressions and theoretical analysis suggest a slight loss of power with flexure of low-plus-power hydrogel contact lenses. Low-minus-power hydrogel lenses do not appear to change power. This study confirms this effect.
Contact Lenses, Hydrophilic↗
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.
Aniseikonia↗
Peripheral power errors and astigmatism of eyes corrected with intraocular lenses.
We compared the theoretical peripheral power errors and oblique astigmatism of eyes corrected with commercially available intraocular lenses (IOL's) with experimental data of normal phakic eyes. The peripheral power errors and the oblique astigmatism of the pseudophakic eye are larger than those of phakic eyes. The most sensitive component of the optical system of the pseudophakic eye to the peripheral power errors is the shape of the IOL, but only if the lens is away from the iris. The corneal and the retinal surfaces do not affect the peripheral power errors and oblique astigmatism significantly. A plano-convex lens with the flat surface facing the cornea gives the least peripheral power errors and oblique astigmatism and thus the value closest to the experimental data of phakic eyes. However, this design does not give the minimum spherical aberration. Therefore, eyes corrected with IOL's are expected to have poorer peripheral retinal image quality than normal phakic eyes.
Astigmatism↗
Effect of ocular chromatic aberration on monocular visual performance.
This brief review outlines the theory of ocular chromatic aberration and describes the three primary forms in which the aberration appears: chromatic difference of focus, chromatic difference of magnification, and chromatic difference of position. Our central theme is that all three aspects of chromatic aberration have as their common basis the chromatic dispersion of light. The magnitude of each form of the aberration is related to the others by simple linear formulas in which a key parameter is the location of the pupil relative to the nodal point of the eye. The way in which retinal image quality is affected by chromatic aberration is described and we assess the impact of the aberration on visual performance.
Color Perception↗
Subjective and objective assessment of soft bifocal contact lens performance.
Subjective and objective techniques were used to assess the on-eye performance of soft bifocal contact lenses. In the subjective technique a young observer whose accommodation had been paralyzed with a cycloplegic agent was fitted with the contact lens type under investigation and aligned with a Maxwellian view Badal optometer using a bite-bar. Visual acuity was measured as a function of both target vergence (0.00 to -4.00 D) and pupil size (1 to 5 mm). Aspheric, concentric, and diffractive soft bifocal contact lens designs were investigated. Diffractive and concentric bifocal designs with +2.00 D near additions showed "twin peaks" of visual acuity with one peak at 0.00 D target vergence (equivalent to distance viewing) and the second at -2.00 D target vergence (equivalent to a target at 50 cm). Some aspheric designs produced a relatively constant visual acuity across this vergence range, whereas others gave poor acuity at near. Visual acuity with the Echelon diffractive lens was relatively unaffected by pupil size, confirming theoretical predictions. Visual acuity with concentric designs was also relatively free of pupil size effects. In the objective technique, the variation in surface power across the lens was assessed using video-keratography. This technique provided an elegant means of visualizing the power profile of the lens. The location of the zones of increased power and the magnitude of power variations allowed an accurate prediction of the visual performance measured subjectively. Temporal displacement of lenses may explain the occasions where visual performance did not vary with pupil size.
Accommodation, Ocular↗
Keating's asymmetric dioptric power matrices expressed in terms of sphere, cylinder, axis, and asymmetry.
Twelve years ago Keating pointed out that dioptric powers existed which could not be represented by the familiar three parameters sphere, cylinder, and axis. They are the equivalent powers of optical systems (including many eyes) with separated obliquely crossing astigmatic elements. Four parameters are required to represent such powers, and all four are unfamiliar to most clinicians and researchers. This note shows that it is, in fact, possible to transform the four parameters so that the three familiar parameters are retained and only one (called asymmetry) remains unfamiliar. The consequence is that it is always possible to represent a power by means of sphere, cylinder, axis, and asymmetry. Powers commonly used in practice all have asymmetry equal to zero which is why only the first three are usually necessary. Powers, however, do exist, and are of potential interest in optometry, for which asymmetry is not zero and cannot be omitted from the representation. Two numerical examples are given, including Keating's model eye.
Humans↗
Reducing effective vertical prism in bifocals.
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Eyeglasses↗
Measuring resolution in the contrast domain: the small letter contrast test.
BACKGROUND: Recent evidence suggests that small letter contrast sensitivity (CS) is more sensitive than visual acuity (VA) to defocus, luminance, binocular enhancement, and visual differences among pilot trainees. It would be valuable to make this test available for general use. We developed a hard copy (letter chart) version called the Small Letter Contrast Test (SLCT) and evaluated its sensitivity and reliability in comparison to standard vision tests. METHODS: The SLCT has 14 lines of letters with 10 letters per line. The letters are of constant size (20/25 or 4/5 at 4 m), but vary in contrast by line in 0.1 log steps (0.01 log units per letter). Normal room illumination is used. The SLCT was evaluated in 16 subjects under various conditions (spherical and astigmatic blur, low luminance, 2 eyes vs. 1 eye) to determine test sensitivity and reliability, and in patients with clinical conditions. Scores were compared to those obtained with standard tests of VA (Bailey-Lovie) and CS (Pelli-Robson). RESULTS: SLCT scores were similar to previous measures, and retest reliability was one line. The SLCT was more sensitive than VA to spherical and astigmatic blur, low luminance, and vision with two eyes vs. one eye. Greater sensitivity of the SLCT endured despite correction for variability. The SLCT was more sensitive than standard tests to visual loss from early cataract, keratoconus, corneal infiltrates, edema, and amblyopia. CONCLUSIONS: The SLCT is a sensitive, adjunctive test, which complements existing measures of VA. It can reveal subtle visual deficits that may be undetected by standard clinical techniques. The SLCT should prove useful for monitoring vision in refractive surgery, corneal and macular edema, optic neuritis, and for selection and evaluation of candidates for occupations requiring unique visual abilities like aviation.
Contrast Sensitivity↗
Equivalent dioptric power asymmetry relations for thick astigmatic systems.
For optical systems consisting of separated obliquely crossed toric interfaces, the equivalent dioptric power has principal meridians that are not necessarily orthogonal to each other. In this case it takes four parameters to specify the equivalent power. A set of parameters convenient for ophthalmic optics consists of three traditional spherocylindrical parameters SC x theta together with a dioptric asymmetry parameter g. The parameter g has been described as "so far" being entirely mathematical in nature. The purpose of this paper is to develop further optical knowledge about the equivalent power asymmetry g. The method was a theoretical and numerical study involving optics and the dioptric power matrix theory. Among the results of this study are a number of new equations involving g that clarify the relationships between the nonorthogonal principal meridians and the power and axis meridians of SC x theta, as well as explicitly illustrating the parameters that can increase or decrease g. It is also pointed out that the asymmetry g is formally identical to the circular astigmatism that has previously been presented in discussions of ray vector deflection fields (and is used in the Humphrey Lens Analyzer measurements). In conclusions, the theoretical relations presented here provide optical insight into the equivalent dioptric power asymmetry and the parameter g. The relations and insight can assist further developments.
Astigmatism↗
Modeling human eye aberrations and their compensation for high-resolution retinal imaging.
We introduced a mathematical eye model using Gullstrand's six-surface eye model modified by clinically measured aspherical data to study human eye aberrations and their compensation for high-resolution retinal imaging. Ray tracing was used to characterize aberrations and point spread functions (PSFs) of the eye model. By using the Zernike polynomial decomposition of the calculated pupil function, we quantified the wavefront aberrations. Based on calculated PSFs, we designed optical inverse filters to reduce the aberrations for a large pupil size and improve the resolution. Spherical aberration and oblique astigmatism were found to be in good agreement with published experimental measurements. Spherical aberration and defocus were the most significant aberrations for on-axis imaging, whereas oblique astigmatism and coma combined with spherical aberration and defocus were most significant for off-axis imaging. The best retinal image resolution occurred at 2- to 3-mm pupil diameter. After aberration correction for an 8-mm diameter pupil, the resolutions for on-axis or 9 degrees off-axis imaging points were very close to diffraction-limited resolutions. Over a limited field of view (FOV), retinal image resolution of the eye model can be greatly improved by aberration correction using aspheric and astigmatic lenses. For imaging large FOVs, space-variant compensation techniques will be required for aberration correction.
Astigmatism↗
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.
Aniseikonia↗
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.
Anisometropia↗
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.
Eyeglasses↗
Comparing laser ray tracing, the spatially resolved refractometer, and the Hartmann-Shack sensor to measure the ocular wave aberration.
PURPOSE: To compare quantitatively three techniques to measure the optical aberrations of the human eye: laser ray tracing (LRT), the Hartmann-Shack wavefront sensor (H-S), and the spatially resolved refractometer (SRR). LRT and H-S are objective imaging techniques, whereas SRR is psychophysical. METHODS: Wave aberrations were measured in two normal subjects with all three techniques implemented in two different laboratories. RESULTS: We compared the experimental variability of the results obtained with each technique with the overall variability across the three methods. For the two subjects measured (RMS wavefront error 0.5 microm and 0.9 microm, respectively), we found a close agreement; the average standard deviation of the Zernike coefficients within a given method was 0.07 microm, whereas the average global standard deviation across techniques was 0.09 microm, which is only slightly higher. CONCLUSIONS: There is a close match between the Zernike coefficients obtained by LRT, H-S, and SRR. Thus, all three techniques provide similar information concerning wave aberration when applied to normal human eyes. However, the methods are operationally different, and each has advantages and disadvantages depending on the particular application.
Adult↗