Bradford Howland

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.

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.

High-pass spatial frequency letters as clinical optotypes

It is generally accepted that there are two visual thresholds for any given target. Consider that we are approaching a target of finite size from an infinite distance. A distance will be reached where the target is first detected; its form and shape will ordinarily not be identifiable unless it is a long thin line. Say it is an r-numeric character. Then at a much closer distance it will be recognized and identified. However, objects such as z-numeric characters can be constructed where the detection and recognition thresholds are almost identical. An example is shown in Fig. 1. The characters are displayed on a grey background. The width of the black line outlining the character is adjusted so that from a great distance the addition of the white and black segments add linearly to equal the grey background. The visual acuity for the letters is the same as for a letter of identicai size composed entirely of black. Such a test pattern may be of clinical value, for the patient need only report which lines are seen. Thus the tedium of listening to the patient calling out every letter is avoided, resulting in a considerable saving of clinical time. Its use will simplify the testing of illiterate patients, e.g. children. Normally, a black object like an a-numeric character, on a white background, is detected when it subtends 1 arc min (under good lighting conditions), It is recognized and identified when it subtends 5 arc min. That is the definition of 20/20 visual acuity. Thus, in the case illustrated the letters will not be detected until the observer is five times closer to the target. If this principle was used to camouflage other objects there would be a gain in camouflage distance of a factor of five. The irnp~~~on of this observation is that the very low spatial frejuencies do not contribute significantly to the identification and recognition of the letters. However, they do contribute dramatically to the detection threshold. Figure 2 shows the Fourier magnitude spectrum of a normal letter E composed entirely of black and white, and a letter E made like those of Fig. 1. Note that the very low frequencies are effectively absent in the latter, while the high spatial frequency components are still present. To illustrate this phenomenon we have used black and white contrast. There is every reason to believe that it should be equPlly effective for color contrast.

Use of crossed cylinder lens in photographic lens evaluation.

Two methods are described for testing cameras and camera lenses by utilizing the properties of the crossed cylinder lens, an ophthalmic test device. In the first, the cylinder lens is used in conjunction with a rectangular grid to defocus the star image formed by a collimator. This test permits quantitative determination of axial chromatic aberration, spherical aberration and its variations with wavelength, and coma of the lens. In the second, a segment of the cylinder lens is used as a supplementary lens attachment to the camera, which photographs a polar coordinate chart. Analysis of the photograph permits determination of the sagittal and tangential field curvatures, and also indicates errors in focal adjustment and misalignment of film plane with respect to the lens axis. Since these tests require cylinder lenses of smaller dioptric power and quality superior to that available from the ophthalmic lens industry, methods for the construction and synthesis of large-aperture, weak, cross cylinder lenses and segments thereof are given. Experimental details of the lens testing procedures, together with examples of photographic determination of the various camera and lens defects, are presented. A sensitive test for lateral chromatic aberration is included in an appendix.

Bridge for Measuring the Impedance of Metal Microelectrodes

This note describes an ac bridge for measuring the series components of high‐impedance metal‐liquid interfaces. The real and imaginary components of the impedance may vary over a wide range. All frequency‐independent residual error‐introducing elements in the measuring circuit may be balanced out through a single square‐wave initial balance step. This allows accurate, direct‐reading measurement of the unknown. The bridge design is based upon superposition of frequency‐independent bridge circuits.

A Theorem about Zig-Zags Between Two Circles

(1974). A Theorem about Zig-Zags Between Two Circles. The American Mathematical Monthly: Vol. 81, No. 7, pp. 754-757.

Improved Square Wave Inductance Bridge

This paper describes an ac bridge useful for comparing an inductance coil with its dual equivalent circuit so as to determine, with one square wave null measurement, the values of the inductance, the equivalent series and shunt resistances, and the distributed capacitance. This circuit, which features a wide band transformer of novel but simple construction, has the important advantage that one terminal of both the inductor and its dual circuit are at ground potential. Shielding problems are thereby minimized, and laboratory‐type decade boxes and precision variable condensers may be used to synthesize the dual equivalent circuit or to adjust the distributed capacitance of the inductor. A prototype bridge circuit, operating in the frequency range 0.1 to 350 kc, and incorporating compensation for errors due to residual elements is given, together with a simple alignment procedure and the results of a sample measurement of a standard inductor. It is shown that the frequency limitations of the present bridge ...