Angular Subtense Research Articles

Variation of the visual threshold with retinal location: Part I. The central 20° of visual field Part II. The fovea

Threshold measurements have been carried out across the central 20δ of the visual field using white, red, green and blue stimuli of 2′ and 32′ angular subtense and of short and long duration under conditions of scotopic, mesopic and photopic adaptation. Whereas the degree of spatial summation increases in the periphery under all conditions of adaptation, the degree of temporal summation is uniform to a first approximation over the region investigated. Some of the results indicate that a group of retinal locations giving the same threshold under one set of observing conditions continue to have essentially equal thresholds under other quite different conditions of observation. A method is described whereby those regions of the retina where blood vessels may interfere with visual measurements may be avoided. Measurements with a small test field within 2° from the visual axis indicate that the central region of the fovea, about 30′ dia., may have very different properties from the rest and shows a reduced sensitivity at all wavelengths in the dark-adapted state.

Relative Effects of Raster Scan Lines and Image Subtense on Symbol Legibility on Television

This experiment examined the relative effects of (1) image size and (2) number of TV raster lines making up the image upon an observer's ability to identify 16 different geometric symbols on TV. Four raster-line values per symbol height were each tested at three image angular subtenses. Eight subjects were told to identify 25 symbols for each of the 12 conditions; all had 20/12 near and far visual acuity or better. The forced-choice method was used; no limits were placed on response times. The results showed that (1) at least eight raster lines per symbol height and (2) a symbol subtense of 10' of arc are necessary to obtain good symbol legibility on TV. An equation is developed from these and other data which quantifies the tradeoff between line number and angular subtense for different levels of performance.

Color discrimination under reduced angular subtense and luminance.

Under reduced visual conditions, small area and low luminance, color discrimination for normal eyes deteriorates in a manner similar to that observed for tritanopic vision. The purpose of this study was to investigate and quantify the reciprocal relation between area and luminance for conditions for which this loss of color discrimination occurs, for people with normal vision. Quadratic equations, ln s=a(lnF)2+b(lnF)+c, were obtained from the empirical data to describe the relationship between chromaticity discriminability, s, and luminous flux, F; where s=the standard deviation of color matches and F=ω34L (target solid-angle subtense, ω, and luminance L). The constants a, b, and c are different for the red–green and blue–yellow directions on the chromaticity diagram.

Adaptation, its effect on apparent brightness and contribution to the phenomenon of brightness constancy

The effect of a large surround field (to which the observer is preadapted) on the apparent brightness of a 2° test field has been investigated by interocular matching using a total of eleven observers. Supplementary tests suggest that the data may be applicable for observations of a few seconds on test fields of between 1° and 9° angular subtense, and for apparent brightnesses from near threshold to blinding white. The data have been used to explain the phenomenon of brightness constancy in terms of adaptation influences. A family of scales of apparent brightness is proposed. Evidence has been obtained of an ocular interaction when the two eyes are adapted to different conditions.

DIGITAL IMAGE FORMATION FROM ELECTRONICALLY DETECTED HOLOGRAMS

In high precision holographic imagery of weak objects of small angular subtense, electronic detection and digital image formation have distinct advantages. Experiments with a vidicon detector and a PDP-6 computer have yielded reconstructed images of good quality with computation times of five minutes.

An instrument for the interocular matching of apparent brightness.

An instrument has been built to study the influence of visual adaptation on the apparent brightness of simple fields of view, using an interocular (binocular or haploscopic) technique. Using this technique the observer adjusts the intensity of some attribute (e.g. the apparent brightness) of a luminous test field, viewed by only one eye, until it matches the same attribute of a second field, seen by the other eye. Among the more important adaptation variables are the levels of the preadaptation, contrast and glare luminances viewed by the observer, but the effects of other variables, including colour, field size and observation time, can also be studied by this method. Test fields of up to 14° angular subtense and adaptation fields of up to 60° are available. The instrument can be readily adapted to study the Helmholtz-Kohlrausch effect (where more saturated colours appear brighter than those less saturated but of the same luminance), while avoiding any effects of simultaneous colour contrast. Onley has suggested that the presence of contrast fields may cause interocular interaction when simultaneous interocular apparent brightness matches are made. Some experiments with the present instrument have shown that if this interaction exists, it is probably very small.

How Large is a Point Source?

A source of light having many times the angular subtense of the sun or moon can usually be treated as a point when making photometric calculations based on the inverse square law. When viewed by the eye, such sources are not perceived as points (like stars) but rather as extended surfaces. In this paper, some typical data on contrast thresholds for targets, both large and small, are converted into threshold stellar magnitudes. This is done for two important cases which, unless carefully distinguished, can lead to erroneous results.

Sensitivity of the Blind-Spot Region to Stimulation by Flicker*

Flicker functions were obtained with square test fields of 1°, 2°, 5°, and 10° angular subtense positioned at the center of the blind spot. When the test fields fell entirely on to the disk, duplex flicker curves were obtained, indicating excitation of adjacent elements by scatter of light. The disk area was explored with small test fields presented in various positions on a vertical and a horizontal line running through the center of the blind spot. A drop in critical flicker frequencies was obtained when the test field fell into the disk area. The possibility of using the decrease in frequency as a measure of retinal dysfunction in scotomata is discussed.

Size-Constancy and Critical Flicker-Frequency

Investigations of size-constancy have almost invariably employed direct judgments or estimates by Os of size or distance as dependent variables.' It was the purpose of the current experiment to determine whether sizeconstancy was demonstrable in a situation which required no such subjective estimation per se. The threshold of fusion, already shown to be a function of the visual angle subtended by the intermittent luminance,2 was employed. The primary question was whether the critical flicker-frequency (CFF) was also subject to the influence of apparent size under conditions productive of constancy. More specifically, would a size-constancy effect offset an expected decrement in the CFF which would normally follow a reduction of the retinal size of the stimulus ? METHOD Apparatus. The flickering luminance was produced by the electronic switchingunit manufactured by the Lafayette Instrument Company for its Model 1202A Fusion Apparatus. The square-wave output, variable from 0-100 v. Dc at 65 mills, was fed to an NE 40 lamp. The viewing assembly consisted simply of an aluminummount, 5 in. in length. An upright front-panel 43/8 in. by 5 in. contained a circular aperture of 2 in. The lamp was mounted to the rear panel. The front-panel was so flanged as to support a 4 x 5-in. sheet of ground glass and interchangeable aluminummasks of the same dimensions. Two such masks, painted black, were employed. One contained a circular aperture 1 in. in diameter, and the other an aperture 1/2 in. in diameter. The entire assembly could be moved to various distances from 0 along a black-top table. Observers. Eighteen women students in a general nursing program volunteered as Os. They were naive as to the purpose of the experiment. Procedure. The Os were assigned randomly to one of six groups, representing order of presentation of the flickering stimulus under the three conditions to be experienced by all the Os. In Condition A, the mask containing the 1-in. diameter aperture was employed at a distance of 40 in. from O, allowing the flickering stimulus to subtend a visual angle of 1'26P. In Condition B, the 1-in. diameter mask was also employed, but the viewing assembly positioned at a distance of 80 in. from 0, for an angular subtense of 43' at the eye. In Condition C, the mask

SENSITIVITY OF THE RETINAL AREA IN ONE EYE CORRESPONDING TO THE BLIND SPOT IN THE OTHER EYE.

Threshold sensitivity was studied in six observers on one vertical and three horizontal lines running through an area in the nasal visual field of one eye which corresponds to the blind-spot region of the other eye. The test fields were squares of 1° angular subtense on a side and were presented for 0.04 sec. Thresholds were found to be lower in this region than at retinal points immediately outside, yielding a mean increase in sensitivity of approximately 0.25 log unit. The findings are discussed in regard to density and innervation of retinal elements, cortical representation, and the possibility of compensation for lack of sensitivity in the blind spot in order to maintain uniform brightness in an integrated binocular field of vision.

UTILIZING THE VISUAL ENVIRONMENT IN SPACE.

Two procedures dealing with distance estimation in space are analyzed. In one, formulae relating angular subtense to target distance are derived for spherical and disk objects. A design for a simple reticle to be used in distance estimation is described. In the other procedure, the utilization of illuminance from spherical and disk-shaped satellites for the purpose of relating it to object distance is examined. Formulae describing the relationships for certain cases are developed. The appearance of spherical satellites when illuminated by sources of both small and large angular subtense is dealt with in some detail.

Effect of target size on critical flicker frequency in flicker perimetry

Am horizontalen Meridian des Gesichtsfeldes wurden zwischen 90° auf der nasalen und 90° auf der temporalen Seite mit Prüffeldern, die Sehwinkel von 4°, 2°, 1°,°,°,°,° und° ausmachten, kritische Flimmerfrequenzen bestimmt. Die Helligkeit war 32 Fusskerzen und das Licht: Dunkelverhältnis 1:1. Die kritische Flimmerfrequenz wächst bis zu Prüffeldgrössen von 1° bis 2° stark an und nur wenig mehr für Prüffeldgrössenüber 2°. Bei Flimmerperimetrie sind deshalb beste Resultate mit Prüffeldern von 1° bis 2° Sehwinkel zu erwarten.

Perceived movement in depth as a function of stimulus size.

The ability of subjects to perceive movement in depth of flat, circular luminous objects of various angular subtenses in an otherwise stimulus free field has been studied. The stimulus object bad a luminance of 1 ft-Lambert and varied in angular size from 1.5 to 60' of arc at the onset of movement. A method of constant stimuli was used to determine threshold values for the perception of movement. Accuracy in reporting direction of movement improved as the angular subtense of the stimulus increased. For stimuli with subtenses of 1.5 and 60' of arc the 75 per cent thresholds of perceived movement were 8 and 2 per cent change in angular size, respectively. A break in this function was found in the vicinity of stimulus sizes of 12' of are which indicates the possibility of two mechanisms involved in perceiving movement in depth.

Estimation of visually perceived closure rates.

The ability of subjects to estimate the relative distance travelled by a luminous object approaching on a collision course and viewed in an otherwise stimulus free field has been investigated. This research stems from an analysis of visual skills anticipated for certain manned space vehicle operations. The stimulus object at onset bad an angular subtense of 4, 12, or 36' of arc. It approached at two velocities from five starting distances, thus yielding a total of 30 experimental conditions. The subjects' task was to indicate when the stimulus object bad traversed one-half of the original distance. Large constant and variable errors were evident in the estimates of subjects with no training at the task. Subjects provided with training, through knowledge of results after each estimate, demonstrated a considerable reduction in both constant and variable errors. After training, subjects were able to estimate when the object had reached the half-way point with an accuracy such that 50 per cent of the half-way estimates fell within a range equal to 5 per cent of the initial observation distance.

Effect of hyperventilation on foveal critical flicker frequency

The effect of voluntary hyperventilation on the relation between foveal critical flicker frequency ( n) and retinal illumination ( I) was investigated with circular test fields ranging in angular diameter from 2.5′ to 2° 11′. Although the basic form of the n-log I relation was unaffected, the curves as a whole were displaced upwards along the critical frequency ( n) axis to higher frequencies. The amount of the displacement increased with increasing size of field from zero, for fields below about 7′ angular subtense, to 2–3 c/s for the largest field size. The results were interpreted in terms of increased foveal interaction and were discussed in relation to recent work on spatial integration in the retina.

Effect of striated fields on critical flicker frequency.

Critical flicker frequency measurements were obtained as a function of retinal illuminance for a square centrally regarded field (8.5 degrees on a side) containing various numbers of vertical stripes. The visual field contained under the different experimental conditions 0, 10, 30, 90, and 250 black lines per inch, corresponding to an angular subtense at the eye of 0.63, 0.21, 0.07, and 0.025 degree, respectively. Results indicate that CFF decreases with increases in the number of stripes reaching a minimum at approximately 30 stripes per inch, and then may increase with further increases in the number of stripes. Except at the highest illuminances where the curve for the field containing the largest number of stripes (250 per inch) overtakes that of an unpatterned field, all of the striped fields result in lowered CFF vs log retinal illuminance curves when compared with an unstriped field of the same size.

X-Ray Extinction in Type II Diamonds and Topaz

IN the course of experiments on divergent-beam X-ray photography, we applied extinction theory to find how the contrast σ of deficiency lines against the background depends on η, the standard deviation of mosaic-block disorientation in the crystal. We obtained a curve (reproduced herewith) with a maximum for a value of η comparable with the angular subtense of the X-ray source at the film. For smaller values of η, σ depends chiefly on the integrated intensity of reflexion from the lattice planes concerned rather than on the ideal line profile; in consequence, as η decreases, the contrast must eventually suffer secondary extinction in the same way as single-crystal spots on rotation photographs. Instead of reaching the ideal maximum of ½ (‘Laue’ case) or 1 (‘Bragg’ case), the curve near the origin, provided η is not too near the diffraction width, is given by the expressions: where Q′ is volume reflecting power and t′ is effective crystal thickness.

Photographic Granularity and Graininess VI Performance Characteristics of the Variable-Magnification Graininess Instrument*

Data obtained with the variable-magnification graininess instrument described in Part V of this series of communications are given showing the variation of graininess as a function of the luminance of the test field, the luminance of the various components of the observer’s field, the viewing distance, and the angular subtense of the test field. On the basis of these data, standard conditions for the various variables are established for the measurement of graininess. Graininess measurements in terms of blending magnification at a constant viewing distance are compared with graininess measurements in terms of blending distance at a constant magnification.

Note on the Brightness Profile and Photometric Contrast of a Test-object having small Angular Dimensions and Silhouetted against the Twilight Sky

Microphotometry of photographs of distant objects with small angular subtense has shown that inaccurate results are obtained if the apparent contrast is calculated on the assumption of uniform sky brightness. No evidence was found of any edge effect due to inward small angle scatter.

The Apparent Colors of Surfaces of Small Subtense—A Preliminary Report*

The early observations of Konig on the apparent tritanopia of the central fovea were confirmed by Willmer and Wright. Hartridge showed that the small size of the test field, rather than the location of its image on the retina, leads to the tritanopia. In the present work, twenty colors around the Munsell 5-plane were observed against a dark grey background at an angular subtense of 2 minutes and 1 minute of arc, under Macbeth (6800°K) daylight. They were matched with a complete chart of the 5-plane on a similar background and under the same illumination, a mask being provided for the isolation of one color. The phenomenon is somewhat personal but its main features are beyond question. The locus of the “reduced” colors approximates an ellipse with its long axis in the general direction red to blue-green but differing in eccentricity for different observers. The displacement of most of the colors is approximately towards or away from the blue end of the spectrum. There is evidence that the phenomenon cannot be explained by the effect of the macular pigment, but the “dominator-modulator” theory of Granit would seem to offer an explanation for it.