Milton Katz

Aspherical surfaces used to minimize oblique astigmatic error, power error, and distortion of some high positive and negative power ophthalmic lenses.

Ophthalmic lenses are generally corrected for oblique astigmatic error or optimized to balance astigmatic and power errors. Distortion is not corrected in these lenses. The nature of the aspheric surface needed to minimize astigmatic error, power error, and distortion in -20-, -14-, and +14-diopter lenses was investigated using the ACCOS V lens design programs. The best correction for the -20- and -14-diopter lenses was obtained by allowing their front and rear surfaces to become deformed ellipsoids of revolution about the minor axis. The +14-diopter front and rear lens surfaces became deformed ellipsoids of revolution about the major and minor axes, respectively. Performance data over the full field of view, corresponding to +/-30 degrees of eye rotation, are given.

Visual acuity through fresnel, refractive, and hybrid diffractive/refractive prisms.

BACKGROUND This article compares the effect on visual acuity of the Fresnel and wedge-shaped refractive prisms with newly developed hybrid diffractive/refractive prisms (ComPrisms), which combine a wedge-shaped refractive prism with a diffractive component. The diffractive component of hybrid elements can be designed to correct the chromatic aberration of the refractive component. METHODS The monocular visual acuity of 21 subjects and binocular acuity of 20 subjects were measured with computer-generated logMAR charts. Visual acuity was measured without prisms (NP) and through ComPrisms, 3M Press-on Fresnel, and acrylic refractive prisms of 20delta, 30delta, and 40delta powers. RESULTS A repeated measures analysis of variance indicates a significant main effect of treatment (without prisms and through the three types of prisms) at each prism power, both monocularly and binocularly. Results of the Scheffé test for all possible comparisons between pairs of means of the treatments are provided. CONCLUSIONS Although all the prisms reduced visual acuity, the ComPrisms provide significantly better visual acuity than acrylic refractive or 3M Press-on Fresnel prisms of equivalent power

Contrast sensitivity through hybrid diffractive, Fresnel, and refractive prisms

BACKGROUND Fresnel and wedge-shaped refractive prisms are used diagnostically and therapeutically in clinical practice. This article extends the study on the effect of prisms on visual acuity to the effect on contrast sensitivity by membrane Fresnel (F), refractive (R), and newly designed hybrid diffractive (C) prisms (ComPrisms), which combine a wedge-shaped refractive prism with a diffractive element. METHODS Vistech contrast sensitivity function (CSF) Charts A, B, and C were used to measure the monocular and binocular contrast sensitivity of 21 and 20 subjects, respectively. CSF was measured without prisms (U), through the hybrid diffractive prisms, membrane Fresnel prisms, and acrylic refractive prisms in powers of 20delta, 30delta, and 40delta. RESULTS Repeated measures analysis of variance calculations resulted in significant main effects in contrast sensitivity across prism types, prism powers, and between monocular and binocular measurements. Results of the Scheffé test for all possible contrast sensitivity comparisons between spatial frequencies are provided. It was found that as prism power increased from 20delta to 40delta, the rate of reduction in area under the CSF curve of ComPrisms became half that of the refractive and Fresnel prisms. CONCLUSIONS Although all three prism types reduced contrast sensitivity with respect to the unaided condition, the ComPrisms at all powers provided significantly better contrast sensitivity than the refractive or Fresnel prisms of equivalent power. Significant binocular summations in contrast sensitivity were found without prisms and across all prism types and powers.

Angular and linear fields of view of Galilean telescopes and telemicroscopes.

Purpose. The calculation of the angular fields of view (FOVs) of Galilean telescopes generally necessitates the calculation of the pupils and ports. This, in turn, requires knowledge of the optical design of the telescope, in particular, the focal lengths or powers of the objective and ocular lenses. Equations for finding the FOV that obviate the need to calculate pupils and ports, or even to know the lens powers of the telescope, are presented in this article. The equations can be used to find the FOVs in image space of real Galilean telescopes of known magnification, merely by measuring the distance between the objective and ocular lenses and the diameter of the objective lens. The equations include the effects of eye pupil diameter and eye relief. Linear FOVs (LFOVs) of Galilean telemicroscopes are similarly determined. Methods. Two image space angular FOV equations were derived: (1) an equation to determine the angular FOVs of a telescope with various amounts of vignetting and eye relief; and (2) an equivalent equation for the LFOVs of telescopes fitted with lens caps for near vision. Results. The FOV increases linearly with increasing vignetting. Increasing the eye relief results in a nonlinear decrease in the FOV, shown as a fraction of the normalized value for zero eye relief. Decrements in the FOVs with increasing eye relief as a fraction of the normalized field angle when the eye relief = 0 are shown to be constant regardless of the vignetting level. A transition of the objective lens from field stop to aperture stop occurs when the eye pupil diameter exceeds the diameter of the objective lens divided by the magnification. Conclusions. Equations have been derived for Galilean telescopes and telemicroscopes that make it unnecessary to find pupils and ports, or to know the powers of the lenses. They provide a direct and simple evaluation of angular and LFOVs as functions of magnification, objective lens diameter, eye pupil diameter, eye relief, and vignetting, and enable comparisons of actual telescopes.

Apparent image quality of magnifiers depends on amplitude of accommodation.

We investigated the importance of the role of amplitude of accommodation in assessing the usefulness of magnifiers. Accommodation must be exerted to scan across the image produced by a magnifier that exhibits astigmatism and curvature of field. In general, increasing amounts of negative accommodation are required to scan from the center to the edge of the image field of view (FOV) when a simple magnifier is set for nominal magnification. It is necessary to refocus the magnifier (move it closer to the object plane) to convert the demand to positive accomodation. We used the OSLO program to design and evaluate the oblique astigmatism of four common types of magnifiers: Equiconvex, Best-form, Aspheric, and the Steinheil triplet, in powers of 10, 20, 40, 60, and 80 D. We found that the circle of least confusion (CLC), produced by the Equiconvex and Best-form lenses set at nominal magnification, lie on a surface that demands as much as 2.75 D of negative accommodation to view the CLC at the edge of a 30 degrees FOV. By refocusing the magnifier, the CLC at the edge of the field can be imaged at infinity, i.e., have zero vergence, and the demand for negative accommodation may be eliminated, but then about 2.4 D of positive accommodation is required to scan to the center of the field. The Aspheric and Steinheil magnifiers largely corrected the astigmatic errors and flattened the field. Less than 0.75 D of accommodation was sufficient to scan from the edge to the center of the object. Depending on the degree of uncorrected astigmatism and field curvature, presbyopic patients, lacking accommodative ability, will perceive constricted in-focus zones in the image field. They will continuously have to refocus the magnifier to bring adjacent zones into best-focus. This condition may cause a presbyope to reject a magnifier thought to be of good quality by a young clinician who can accommodate for best-focus across the entire FOV.

Modulation transfer functions and contrast sensitivity through low vision telescopes

Telescopes are coherently coupled to the eye. Because their wavefront aberrations may be altered by the optics of the eye, especially by accommodation, some researchers question the ability of their modulation transfer functions (MTF) to predict changes in contrast sensitivity functions (CSF) through them. We measured the CSFs of visually normal and aphakic subjects through telescopes. We found that MTF appears to be useful for ranking the telescopes, and accommodation appears to improve focus and partly balance wavefront errors. Our results suggest that cascading (multiplying the contrast of the instrumental MTF with the unaided CSF at each spatial frequency) is useful for predicting visually aided CSFs to within 4 dB.

Modulation transfer functions of low power telescopes

The modulation transfer functions (MTFs) of 131 low power Galilean and Pechan roof prism Keplerian telescopes comprising 20 models from 7 vendors were measured. MTF results are compared according to model, by type (Galilean or Keplerian), and magnification. Measurements were made on-axis and at the +/- 0.7 field angles. In addition to measuring tangential and radial MTFs some devices were tested with target grating azimuths of 45 degrees and 135 degrees. We also measured the effect of 3 and 6.4 mm exit pupil diameters on the MTF, and compared a color-corrected with a non-color-corrected design in monochromatic and white light. Galilean telescopes exhibited superior MTFs compared to Keplerian designs. The MTFs of Galilean telescopes tested on-axis with vertical and horizontal gratings were equivalent, as expected of rotationally symmetrical devices. However, similarly tested Keplerian telescopes exhibited significantly higher MTFs with vertical gratings. Tests at +/- 0.7 field angles showed that the tangential MTFs of Galilean telescopes were consistently poorer than radial MTFs, but the opposite was true for Keplerian telescopes. The comparatively poorer results obtained with the Keplerian telescopes are due to image doubling and deviation errors of the roof prisms that are dependent on the azimuthal orientation of the prism roof edge. Failure to adopt and maintain the same orientation of hand-held prism monoculars may result in experiencing a variable sharpness of image each time that they are used. Prism deviations of binocular devices must be controlled to avoid vertical disparities.

An instrument for measuring the modulation transfer functions of low power telescopes and telemicroscopes.

An instrument using an electro-optical Fourier method for measuring the modulation transfer function (MTF) of low power telescopes and telemicroscopes is described. Because these devices are afocal, or nearly so, relay optics are needed to form real images at the detection section of the apparatus. The system is capable of measuring the MTF in monochromatic and white light, at any target azimuth, across the field of view, and through focus. The target system contains 14 square-wave gratings with spatial frequencies that range from 2.5 to 156 cpd. Images of these gratings are scanned across a slit. The output data are fed to a first-order recursive digital Butterworth bandpass filter for MTF analysis. The apparatus is diffraction limited at f/31.4. Therefore, it negligibly affects the measurement of the MTF of telescopes and telemicroscopes tested with exit pupils of up to 6.4 mm.

Deformed Aspheric Ophthalmic Lenses

A previous study [1] indicated the feasibility of minimizing astigmatic error, power error, and oblique astigmatic error in −14 and −20 diopter ophthalmic lenses. Attempts to minimize these errors in a +14 diopter lens were unsuccessful. The aims of the present study are to determine whether any positive lenses between +6 and +14 diopters can be aspherized to minimize astigmatic error, power error and distortion, and the general form of negative lenses that are satisfactorily aspherized. Lenses of the following dioptric power are included in this study: −20, −14, −10, −8, +6, +8, +10, and +14 D.

A method for using relay lenses with display monitors for vision testing at far and near.

Resolution limitations preclude the use of display monitors for near testing of acuity and contrast sensitivity. Relay lenses can form minified aerial images of the display at any given near viewing distance, but the image will differ in spatial frequency from the display. Equations are presented that can be used to specify the far- and near-viewing distances and the necessary focal length of a lens so that the display and its near aerial image have identical spatial frequencies when viewed by a subject at a fixed location. Modulation transfer function (MTF) calculations show that achromatic doublets will not degrade the resolution across a 300-mm wide display, thereby providing the versatility of display monitors for near vision testing.