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SESSION 111: DISPLAY REQUIREMENTS IMPOSED BY VISUAL FACTORS CHAIRMAN Professor Clarence H. Graham THE INTERPRETATION OF SIMULATED, ACHROMATIC, RADAR-SCOPE TARGETS Harold P. Bishop, Institute for Applied Experimental Psychology, Tufts University THE DISCRIMINATION OF SIMULATED, CHROMATIC, RADAR TARGETS Mason N. Crook, Institute for A pplied Experimental Psychology, Tufts University SOME EFFECTS OF GRID BIAS AND VIDEO INPUT LEVELS ON DETECTION WITH AN INTENSITY-MODULATED CATHODE-RAY TUBE Paul M. Hamilton, U. S. Navy Electronics Laboratory THE EFFECT OF NUMBER OF SIGNAL PUI,SES UPON SIGNAL DETECTABILITY WITH PPI SCOPES Robert L. Erdmann and Robert D. Myers, Rome Air Development Center TARGET DETECTION AS A FUNCTION OF SIGNAL-TO-NOISE RATIO, PULSE REPETITION FREQUENCY, AND SCAN RATE J. L. Piazza and I. B. Goodman, Air Arm Division, Westinghouse Electric Corporation EFFECTS OF RATE AND PROLONGED VIEWING OF RADAR SIGNAL FLICKER Anthony Debons and Charles Fried, Rome Air Development Center TARGET DETECTABILITY AS A FUNCTION OF THE AREA OF SEARCH WITH VARIOUS DEGREES OF NOISE PRESENT M. Harold Weasner, Rome Air Development Center THE PERCEPTION OF SPACE IN A THREE-DIMENSIONAL DISPLAY Walter C. Gogel, U. S. Army Medical Research Laboratory, Fort Knox 77

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The Interpretation of SimulatecI, Achromatic, Raclar-Scope Targets* HAROLD P. BISHOP, Tufts University Summary-The interpretation of radar displays involves, in part, the visual separation of two adjacent targets. Two experiments were designed to measure separation thresholds as a function of target size, luminance, and amount and direction of contrast be- tween target and background, for sharply defined rectangular targets, In three other experiments, the curvature and luminance gradient of the target's edges were varied as well. Discrimination improved with luminance, contrast, and definition of target's edge. Curvature of the target's opposed edges made separation judgments unreliable. The interpretation of radar displays involves a complex of many visual functions. While discrimination of two adjacent targets is among the simpler of such functions, it is none-the-less affected by a large number of variables. Historically, work on the visual separation of two targets has been directed toward understanding the resolving mechanism of the eye. This has dictated the use of relatively simple test objects, bounded by sharp contours, usually with rectilinear and parallel edges. With this type of test object, the effects of such variables as target size, luminance, and contrast have been investigated in some detail. Radar targets not only vary in these respects, but also may have irregular outlines, contour gradients which impair the sharpness of definition, a luminance cycle related to the scanning rate, and perhaps eventually color. . ~. The purpose of this project was to investigate the discriminability of simu- iatea radar targets as affected by both classes of variables. Optical simulation of targets was employed in the interest of flexibility and precision of control. As a first step, it was considered advisable to determine separation thresholds as a function of certain classical variables. This would insure coverage of all types of variables within the same experimental context, facilitate examination of inter- actions, and perhaps help clarify the facts where the literature was in conflict. Accordingly, the first two experiments reported here were designed to obtain separation thresholds as a function of target size, luminance, and amount and direction of contrast between target and background for sharply defined, rectag- ular targets. The remaining experiments were designed to obtain comparable data on targets with edges having varying degrees of curvature and varying luminance gradients. Apparatus Basically, the apparatus is a system for the projection of two targets, one movable relative to the other, upon the back surface of a transilluminated screen, *This research was supported by the United States Air Force, under Contract OF #33(616)- 5087, monitored by the Aero Medical Laboratory, WADC. 78

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with a second projector to flood the front of the screen and so provide variable contrast between background and targets. Details of the system are presented in Fig. I. In Fig. 1A, the system is shown set for the projection of dark targets. Light from the source at H illuminated the slides at S by way of the condensing lenses CL. Lateral movement of one slide was controlled from the subject's position by knob ~ via a line and pulley system to micrometer screw MS on which was mounted a calibrated dial D. Intensity of light from the target slides was controlled by filters FL and projected by the lens PL onto the back of the viewing screen VS by way of the front-surface mirrors M1 and M2. Figure 1B shows the system set for the projection of light targets. The slides at S are re- placed by a metal diaphragm with a single aperture. Light from this aperture was split by a semireflector R1. One half passed on to the viewing screen by way of the front-surface mirror M and the semireflector R2; the other half, by way of the front-surface mirror M1 and through R2. . H CL Fl Ml K ~ r k NISI | N~ n0 0 - --N ~ B Ma_-= ~ ~ Fig. 1. Apparatus: A, darl`-target protection system; B. light-target system. H. lamp housing; CL, condensing lenses; S. slides; Fl, F2, filters; PL, projection lens; Ml, M2, M3, mirrors; Rl, R2, semireflectors; MSl, MS2, micrometer screws; D, dial; VS, viewing screen; K, long; P. projector; CP, crossed Polaroids. Lateral movement of the image produced by this second beam was also con- trolled from the subject's position by way of the micrometer screw MS~' which controlled the angle of mirror M2. A calibrated dial D was mounted on this micrometer screw. Change-over from one system to another facilitated by means of a vertically sliding metal panel (not shown) on which the mirrors M1, R1 and R2 were mounted. A supplementary diffusing screen, used when targets with 79

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blurred edges were desired, is not shown. This was mounted behind the viewing screen and positioned by means of third micrometer screw. Front-surface lighting was provided by the second projector P with screen illuminance controllable by means of filters F2 and the crossed Polaroids CP. Subject's head position was con- trolled by means of a chin rest and lateral guides (not shown). Procedu re In the interest of comparability with previously existing data and to expedite the testing of a large number of combinations of variables on the same individuals, a more-or-less traditional psychophysical study was indicated. Therefore, two to four subjects were used in the main experiments, and one or two in minor ex- periments. Subjects were male and female graduate students and laboratory staff between the ages of 22 and 31 with visual acuities within the range of 20/20 to 20/15. A modified method of limits was used, with the subject controlling the sepa- ration between the targets. Separation thresholds were taken as the mean of ascending and descending judgments. Such a mean is closer to the classical 50 per cent recognition threshold than judgments based on separation alone, and errors arising from sources such as anticipation, perseveration, and mechanical lag in the system would tend to cancel out. The subject was required to make two kinds of judgments: (1) starting with the targets separated, he moved them together until he could just no longer observe a separation (a "together" judgment), and (2) with the targets together, he moved them apart until he could just detect a separation (an "apart" judg ^ ~ _ ~ ^ ~ ~ ~ ~ r ~ meet). On a given trial, the subject was permitted to bracket the threshold point by moving back and forth past it but was restricted to the extent that his final adjustment had to be in the designated direction. The subjects were given un- limited time within which to make their judgments and were encouraged to make careful adjustments. In the experimental routine, subjects were dark adapted 20 min prior to commencement of an experimental period, with subsequent light adaptation to the luminance of the particular experimental conditions. Experiments 1 and 2 were concerned with the determination of separation thresholds for rectangular targets with sharp edges, ire a variety of sizes and height/width ratios and under a number of luminance and contrast conditions. . Experiment 1. In experiment 1, targets with heights of 1 1/2, and 1/8 in. and a helght/wldth ratio of A: 1 were used. Both light and dark targets were user with five contrast values varied from 0.95 to 0.10 at five luminance levels cover- ing the range from 20.5 to 0.0059 ft-l. In experiment 2 and subsequent experi- ments, a limited sampling of these luminance and contrast values was used. The values were chosen so as to effect a coverage of the range of these variables with a minimization of the total number of combinations of the experimental variables to be tested. 80

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Figure ~ is a sample of the results of this experiment. Salient features of the results as a whole may be summarized as follows: ( 1 ) With decreasing luminance or contrast, thresholds rose at an accelerated rate under all cor~ditior~s of the other variables, in accordance with most data reported by previous investigators. (2) A decrease in target height tended to raise thresholds but, within the limits of the experiment, the effect was somewhat variable and generally not large. (3) With mirror exceptions, (lark-target thresholds were higher than the corre- sponding light-target thresholds. (4) Mean thresholds under favorable condi- tions were among the lowest that have been reported for minimum separation. err 4 In _ z 3 J ah 2 . 11 1 . 11 1 : 11 1 1: 1 r o ~ 8 - : ;~.~81 . i 1 1 1 LIGHT . 1 1 1 1 1/2 IN . . . . . CON TRAST .10 ~ ~ .27 o o .50 ~ ~ .66 e e - .95 0 0 ,,, 1 - _ ~ ~ 1 1 1 111 - I: .006.01 .02 .()4 .06 .1 .2 .4.6 1 2 4 6 10 20 LUMINANCE ~ FOOT- LAMBERTS Fig. 2. in terms of visual angle as a function of luminance at five contrasts for l/2-in. light targets with a height/width ratio of 2:1. Experiment 1. Separation thresholds based on "together" and "apart" scores combined, Three independent checks supported the conclusion that the dark-target thresholds were higher. A further check on the effect of background size indicated that it had no significant effect within the limits of the present experiment. Another interesting feature of these results is that, for comparable con- ditions, our thresholds drop over the region of retinal illuminance where Wil- coxi found them to rise. Hecht and Wald2 ascribed the Wilcox effect to absence of light in the surrounds, but our light-target thresholds ire this comparison were also obtained in the absence of light surrounds. Experiment 2. This was similar to experiment 1, but with the targets used having heights of 1 in. and t/8 in. and height/width ratios of 2:1, 6:~1, and 10:1. The results were generally consistent with those of experiment 1, with the further indication that a decrease in target width at a given height had relatively little effect except at low luminances arid contrasts. - ~Wilcox, W. W. The basis of the dependence of `-isual acuity on illumination. Proc. Nat. Acad. Sci., Wash., 1932, 18, 47-56. 'Hecht, S., and Wald, G. The visual acuity and intensity discrimination of Drosophila. J. Gen. Physiol., 1934, 17, 517-547. 81

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Experiments 3 and 4. Thresholds were obtained using 1-, t/2-, and Run-in. targets with edges having a variety of curvatures (reciprocal of radius of curva- ture in inches). Figure 3, presenting the results obtained with the t/2-in. light target with curvatures of 0, 0.25, arid 4.0, shows a fair sample of the salient results of the experiment. Thresholds on curved edges do not fall into a systematic pattern with respect to target size, luminance, or contrast. A feature of some interest is the several negative threshold values. These, possibly, reflect both a problem of criterion of separation on the subject's part and on odd perceptual flattening of the opposed curved edges as they are brought together by the subject. Experiment 5. This was similar to experiment 1 except that the rectangular targets had blurred edges. Widths of the edge gradients, measured between the 10 and 90 per cent luminance levels, were 3.0, 4.4, and 7.1 min of visual angle. Figure 4 is a sample of the thresholds obtained under these conditions. The thresholds show the same systematic relation to the experimental variables, luminance, contrast, and target size, as noted in experiment 1. Furthermore, there was a systematic increase in magnitude with increased gradient width. 4 ,n 3 A 2 J Z 1 > o 1 I Fit- LIGHT _ C(JR\/ATlJRE _ _ CONTRoST _ .25 4.0 .9S 0-0 o--oo~ o _ _ . . ... . . ... ~)_ _~, I 1 1 1 1 1 ; L1 1 1 1111 1 ~ i, -1 .006.01 .02 04.06 .1 .2 .4 fi 1 2 4 6 10 20 L UMINANCE ~ FOOT- LAMBERTS Fig. 3. Separation thresholds based on "together" and "apart" scores combined, in terms of visual angle as a function of luminance at two contrasts for l/2-in. light targets with three edge curvatures. Experiment 4. Operational implications Salient features of the results on light targets can be summarized for in- strumental applications: Discrimination improves continuously with increasing luminance from near cone threshold to at least the region of ordinary room illumination. With rectangular targets, the higher the contrast and the sharper 82-

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the edge definition the better is the discrimination, especially if the targets are small. Ever1 a small curvature of the opposed edges tends to make the separa- non judgments unreliable. In the operational situation viewing time cart be influenced by many factors, including instrumental variables such as sweep rate and rate of phosphor decay, and others, such as urgency and distracting stimuli' which are more dif- ficult to evaluate. Viewing time can be expected to influence thresholds, probably ire a more significant degree when the task is more difficult. Therefore, these data, obtained as they were with unlimited exposure time, should be regarded as limiting values in relation to operational tasks generally. 4 In 3 A 1 J > o -1 CONTRAST GRADIENT W IDTH 44' 7.1' ; _ .10 .-- ~ ~ ~ ~.96 0 0 0--0 0 ~0 LIGHT | . . 1/2 IN . . . . . ~ I I 1 Ill I ~, , ~, ~, .006.01 .02.04.06.1 .2 .4.6 1 2 L UMINANCE - FOOT- LAMBERTS 4 6 10 20 Fig. 4. Separation thresholds based on "together" and "apart" scores combined, in terms of visual angle as a function of luminance at two contrasts for '/2-in. light targets with three edge gradients. Experiment 5. ,... _ SS __

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The Discrimination of Simulatect, Chromatic, Raclar Targets. MASON N. CROOK, Tufts University. Summary Separation thresholds were measured for two sim- ulated radar targets. The targets were varied in size, curvature- of-edge, blurring-of-edge, luminance, hue, and saturation. The background was varied in luminance, hue, and saturation. Results obtained with two subjects indicate small separation thresholds under most conditions. Two blue or violet targets on a white or desaturated green background of low luminance required the greatest separation to be seen apart. Consideration of the data, in conjunction with the literature on color acuity, suggests the operation of complex interactions. This is a progress report on colored targets which were studied in a later phase of the project on which the preceding paper, concerned with achromatic targets, was based. It will minimize mental strain all around if we think of this as an exploratory study, because it was done with a large number of variables and a small number of experimental subjects in a limited time, and it raised more questions than it answered. It was terminated under pressure of other activities some time ago, but the data analysis is still going on. The general por- cedure was the same as in the achromatic phase of the program. Movable targets, controlled by the subject, were used, and "apart" and "together" judgments were called for. Apparatus An optical system was developed for completely independent control of illumination on target and background. The plan of the system is shown in Fig. 1. The subject, on the rights viewed a transilluminated viewing screen VS. An image of the targets at T was projected onto the rear of the screen by the pro- jection lens PL. In the diagram, the targets are drawn oversize; everything else is about to scale. The targets had mirror surfaces and were illuminated by light from the lamp L2. All light from L2 not reflected by the targets was absorbed by black screening. There was no glass surface in the plane of the targets, so secondary reflections were avoided. The targets were attached by transparent plastic handles to narrow rods extending from the sides of the field. Background light was supplied from the lamp L1, which uniformly illuminated an area on the screen about 5 in. in diameter except where the light was blocked by the targets. With this arrangement, the subject could view targets of any desired size or shape in a circular field, and the target and background lights did not contaminate each other. The rods supporting the targets were usually quite visible, the plastic handles faintly ~risible. The angle that the targets themselves made with the optical axis produced a slight distortion of the images and loss of focus in the outer edges, but we were concerned only with the definition of This research units supported by the United States Air Force, under Contract OF 33(616)- 3091~ I'l(~?il(~Cd by the Hero Medical Laboratory, WADC. 84

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LO it, 1 ~ CLAM ; We al CL: CC \H L2 CL ~ Lb .: VS, Fig. 1. Apparatus: Ll, _ cells; F - filters; W - wedges; R - reflectors; T - targets; PL - projection lens; VS viewing scren; K - loot; S - subject; MS - micrometer screw. Target and micrometer screw oversize; other components to scale. Light dot screen indicates target-illumina tion path. ~ AS ~-1 L2 La Lb - lamps; CL - condensing lenses; CC - cooling S the juxtaposed edges, so that the qualitative imperfections of the rest of the field were not a source of disturbance. For control of hues narrow-band filters were interposed in light paths 1 and 2. The accessory paths, from lamps La and Lb, were provided with Illuminant C filters, and light from them was mixed with the monochromatic light at the semireflectors R to reduce the saturation when desired. Other components in the system were optical wedges, holders for addi- tional filters, and water cells for cooling. Filters of the Corning narrow-band-pass series used for wavelength con- trol. Luminance control was by means of photographic filters and wedges, which were slightly selective for wavelength and were, therefore, calibrated in the optical system at several points in the spectrum with a Macbeth Illuminometer. Gelatin filters were interposed on the photometer side to give an approximate wavelength match to the Corning filters on the sample side It was necessary to equate light through the several Corning filters for luminance, by flicker photometry. A sectored disc with a mirror surface was rotated in the plane of the targets and the matching field projected onto the screen being viewed from the subject's position. Triangular matches (e.g., red against white, white against blue, blue against red) showed some discrepancies, but it was possible to choose settings such that even the most deviant values were within 15 per cent of the mean for a given subject. It was necessary to change targets from time to time in the experimental routine. This sometimes resulted in slight shifts in the path of the reflected beam through the projection tense which in turn affected the luminance on the screen. For this reason, the background path was used for primary calibration, and the target path was adjusted to it by means of a homochromatic match at the begin- ning of each experimental period. 85

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One target was fixed, and the other was movable by means of microme- ter screw MS' the movement being controlled by the subject through the knob K. Procedure Two experimental subjects were used. Flicker matches were made by the two separately, and luminance settings were based on matches by the subject being tested. Observation was binocular, with natural pupils, at a viewing dis- tance of 20 in. Targets were varied in size, curvature-of-edge, blurring-of-edge, luminance, hue, and saturation; background was varied in luminance, hue, and saturation. This amounted to piling several new variables on top of several variables in the achromatic phase of the program, and no attempt was made to test all com- binations. The coverage of experimental conditions was both thin and selective. For example, the higher of the two main luminances tested, 20 ft-l, was used primarily for one subject, and the lower, 0.1 ft-l for the other, with cross check- ing at selected points for the second subject at each level. Some spot testing was done, also, at 1 ft-l. The two subjects differed noticeably in their spectral sensitivity functions, but, with the procedure used, they showed a surprising degree of agreement on separation thresholds when tested under the same conditions. The primary data were obtained on targets t/8-in. high, with straight, un- blurred edges. Colors were red, green, and blue, with respective dominant wave- lengths of approximately 631, 521, and 467 ma. Three levels of saturation were used as represented by calorimetric purities of 90 to 100 per cent, 55 to 60 per cents and 0 per cent (white). Luminance contrasts were 0, 0.50, and 1.00, the target always being lighter than the ground. Secondary data were obtained on 1-in. targets, curved edges, blurred edges, and two other colors, yellow and violet. Results Results cannot be concisely summarized, either in verbal or graphic form, but a few selected curves will illustrate the general nature of the data. In Figs. 2 and 3, separation thresholds in minutes are plotted as a function of luminance as with the achromatic data in the preceding report, but, in the present instances the luminance range from 0-1 to 20 ft-1 is spread over the entire scale. Individual curves in these figures are comprised, in some cases, of data obtained from two different subjects. This method of plotting made possible the construction of more complete curves. Figure 2 shows results obtained with rectangular Run-in. targets with sharp edges. The target colors were red, green, and blue at 55 to 60 per cent purity, and the background was green throughout. The top row represents a background of 91 per cent purity' the bottom row one of 55 per cent purity. The left-hand column is for a condition of no luminance contrast, the middle column for a ~

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A) 4 Lo , 3 He ~ 2 1 1 J ~ 4 > 3 2 1 O , L UM INANC E o 4~ 3t .50 x-FRED -~ GREEN -o BLUE 9 1~% C O N T R. A S T 4 3 at. .00 . . ... .1 1. 20. 4 1 1. 20. 2- . I 1.1 20. - .t 1. 20. o ^_ L U M I N A N C E BAC K OR O U N D PUi ITY 4 o 1. 20. .1 1. 20. Fig. 2. Separation thresholds in terms of visual angle as a function of luminance, based on "together" and "apart" judgments combined, for colored targets on a green bacl~ground, at three different luminance contrasts. Upper and lower rows represent two levels of bacl~around saturation specified in calorimetric purity. Three curves in each graph represent target colors as per key, each at a purity of 55-60 per cent. Rectangular targets lapin. high with sharp edges. luminance contrast of 0.50, and the right hand column for a luminance contrast of 1.00 (dark background). The upper and lower graphs for the dark back- ground condition are duplicates. The three curves in each graph represent the target colors as indicated by the key. Perhaps the most notable feature of these data is that quite low separation thresholds were obtained under most of the experimental conditions. This appa- ratus and the apparatus described in the preceding report gave very similar, small, separation thresholds for comparable achromatic targets. One inference from the generally low thresholds is that, at these luminance levels, discrimina- tion is nearly as good on the basis of wavelength differences alone (left-hand column) as on the basis of luminance differences alone (right-hand column). ~ second feature is that a combination of the two (middle column) may in some cases be worse than either alone, as indicated especially by the point on the blue curve at 0.1 ft-1 in the lower graph. Whatever the interpretation of this particular point, we can be confident that it is no fluke. Several sets of data tend to con- firm the fact that something different was happening under these particular conditions, e.g., this is a combination on which both subjects were tested, and their two scores, plotted as the open and closed circles, almost coincide. Let us proceed to another sampling of data. Figure 3 compares different types of target edge. In this figure, we have targets of maximum saturation (in contrast to the reduced saturation of Fig. 2) viewed again against a green back- ground. The top row is 91 per cent background purity and the bottom row 55 per cent purity as before. The left-hand column is for straight, sharp edges, the middle column for curved edges, and the right-hand column for straight, blurred edges. The targets are Run-in., as before. The curved edges were semicircular, with -87-

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Comments following Weasner's paper: Graham: Thank you, Mr. Weasner, for a very interesting and very clear result. I know that a number of people here are interested in the general problem of detection and search. Anonymous: During a study performed at Ohio State University several years ago, when the number of presentations per min were increased, the sub- ject seemed to develop a greater drive and incentive to look harder for his targets and thus performed considerably better. Weasner: As I mentioned, we thought about limiting the stimulus time but in this initial investigation, we wanted to see how long people would take if they were not pressed. Of course, we realize that if you would compress the time in which subjects have to respond, they would probably increase accuracy and cut down on their detection times as contrasted with the free situation. - 130

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The Perception of Space in a Three-Dimensional Display WALTER C. GOGEL, U. S. Army Meclical Research Laboratory Summary-Perceptions ire three-dimensional space are examined with particular reference to the perceptions of frontal size, depth between objects, arid three-dimensional shape. Major attention is paid to the relations between the visual and physical world. After derivation of equations for the perceived depth between objects, predictions are made. Similarly, there is a detailed mathematical analysis of the perception of three-dimensional shape. It is reasonable to expect that the use of the depth dimension ir1 addition to the two frontal dimensions will result in an increase in the efficiency with which a display can convey certain kinds of information. For example, the suggestion has been considered that the depth dimension be introduced in the radar scope by using a stereoscopic presentation.~-4 This paper will discuss some of the scaling problems involved in different types of judgments in a three-dimensional display, where the perceived depth component is produced by stereoscopic cues. Perceptions in three-dimensional space v Several types of perceptual judgemeIlts which might be required can be considered with the aid of Fig. 1. Here the eyes of the observer are represented at the left' with A indicating the interpupillary distance. A frontal extent (S) and depth extent (X) are presented at distances De and Do from the observer. In the upper part of Fig. 1' the two frontal widths Se and Sg are shown as having angular frontal sizes be arid be while in the lower part of Fig. 1, the two depth intervals Xef and X 7h are shown as producing the binocular disparities orb- OLf and OLn OCh. Table l gives a notation relating extents in visual space to ~ . . . . . ~ . . . . ~ ~ 1 1 . 1 _ _ _ 1_ ~ _ _ ~ corresponding extents in physical space. This notation will be used througnout this paper. It is assumed that within the intervals Xef and X'h of Fig. 1 only the binocular disparity cue is present to produce the perceived extents t(`e rife), and (~7 ah) Table 1. A notation for Perceived and Physical Space and the Correspondence between Them. Perceived Ee ED (lye off), (log ah), Physical angular the 8g (lye off) (Cry ah) Physical linear se Sg Fief XDh iBaker, A. and Grether, W. F. Visual presentation of information. Wright Air Development Center, 1954, Technical Report 54-160. 2Fitts, P. M. Engineering psychology and equipment design. In Handbook of Experimental Psychology, Wiley, 1951, 1287-1340. 3Coher~, J. Binocular disparity as a coding dimension for pictorial instrument and radar dis plays. Wright Air Development Center, 1955, Technical Report 55-393. 4Gebhard, J. W. Visual Display of Complex Information. In Human Factors in Undersea Warfare, National Research Council, 1949, 39-66. - 131

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A - - 1~ Sg e ~Xef 9 ~Xgh it' f ~e: / thy ~ Fig. 1. Schematic diagram for considering several types of judgments in a three- dimensional stereoscopic display. A. Perceptions of frontal size Perceptions of frontal size might involve judgments of the perceived sizes Ee and E7 of Sc end S7. Or, perhaps more Ire quently, the perceptual ratio Ee/Eg would be involved. Often, in frontal size ex- periments, Se is adjusted until EC Eg. If the resulting value of Se is such that Se So, this is termed perfect frontal size constancy. If, however, the resulting value of Se is such that (e L,, this is termed zero frontal size constancy. Over frontal size constancy would be the case in which Ee < Ed when Se SD. B. Perceptions of the depth between objects Perceptions of the depth between objects would involve the perceived sizes (are Offs' and (cY7-Ah)' or more frequently their perceived ratio. A common type of problem would be to determine, given a particular value of Xef, the size of Xgh required in order for (ore atf), to equal (a(9 th)~- A special case of this type of judgment would be the perception of the midpoint of a depth interval. C. Perceptions of three-dimensional shape It will be seen in Fig. 1 that the frontal size Se' together with the depth interval Xef, defines an object having a frontal and a depth component and thus a particular three-dimensional shape. The perceived shape of this (the nearer) object is designated (ore cYf)~/Ee and the perceived shape of the more distant object is designated (ag ah)'/Eg. A particular problem would involves for example, predicting the physical extents required in order for (cYe CYf)~iEe to be equal to (fig a},/Eg. -132

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Relations between the visual and physical world A. Perceptions of frontal size-[frontal size judgments have been investi- gated under conditions in which binocular factors apparently played a critical role. The results indicate that under these conditions considerable frontal con- stancy and sometimes over frontal constancy was present throughout an ap- preciable portion of the visual field.~~7 B. Perception of the depth between objects 1. Equations for perceived depth The experimental investigation of the relation between perceived and physical space when using binocular disparity cues has produced evidence for a simple relation between these two dimen- sions.~-~i This relation given in the notation of Fig. 1 and Table 1 is that: (I cte al )) (I (he ~ af) He Abe (1) Equation 1 states that the ratio of the perceived depth to the perceived frontal extent is proportional to the ratio of the binocular disparity to the angular size of the frontal extent. The constant of proportionality is 1/C where C is assumed to be an individual constant. The left side of equation 1 represents a perceived three-dimensional shape. A perceived depth extent can be defined by rearranging equation 1 as follows: (ache-CXf) `,e ~ ~ C f) (2~) The term Ee/6'e in equation 2 is the perceived size per unit of angular frontal size at the distance De and is therefore (within limits) independent of the size Se used in its determination. In general, the perceived frontal size per unit of angular frontal size at any distance Dv is EV/V. There are reasons for considering that the right side of equation 2 should be written in differential form. If this is done with do substituted for ore ctf' equation 2 becomes: e e idol' 1 r E1; do (3) ((he turf) C J (v r r Chalmers, E. L. Monocular and binocular cues in the perception of size and distance. Amer. J. Psychol., 1952,65,415 423. ~Hermans, T. G. The relationship J. Exp. PsychoZ., 1954,48,204-208. 7Holway, A. H. and Boring, E. G. Determinants of apparent visual size with distance variant. Amer. J. Psychol., 1941,54,21-37. Morel, W. C. Perceived frontal size as a determiner of perceived stereoscopic depth. U. S. Army Medical Research Laboratory, 1957, Report 296. 9Gogel, W. C. An observer constant in the perception of stereoscopic depth. U. S. Army Med- ical Research Laboratory, 1957, Report 316. ~Gogel, W. C. The perception of shape from binocular disparity cues. U. S. Army Medical Research Laboratory, 1958, Report 331. Vogel, W. C. Apparent depth duplication with binocular disparity cues. U. S. Army Med- icaZ Research Laboratory, (in press). of convergence and elevation changes to judgments of size. 133

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It is necessary only to specify Ev/~, as a function of ax to find a useable ex- pression for (ae-aft. For this purpose, consider the following relation: E7, _ {Dcit' Ee \, Do ) Where Ee is the perceived size of a frontal extent S at De and Ev is the perceived size of the same frontal extent at Dv. When n-0, from equation 4, Ev Ee Equation 5 states that when n 0, the perceived size of S is always the same independent of its distance from the observer. This is the case of perfect frontal size constancy mentioned above. When n 1, equation 4 becomes: (4) E7, De E,: Dv (6) Equation 6 states that when n = 1, the perceived size of the constant physical size S varies inversely with distance, i.e., directly with jV7 the angular retinal size of S. This is the case of zero frontal constancy noted above. When n 1, equation 4 becomes: E7, D7, Ee De Equation 7 states that a constant size S of frontal extent increases linearly in its apparent size with an increase in distance. This is a particular case of over frontal size constancy. Therefore, n is a measure of the amount of frontal size constancy in a situation. For simplicity, it will be assumed that, for a particular set of conditions, n remains constant throughout the portion of the visual field being considered. The perceived size Ee of S at distance De can be written as follows: Ee-Kne S and, En' the perceived size of S at Do, can be expressed as: Ey _ Kn9 S or, in general, EV the perceived size of S at Dv is: Ev Knv S (7) (8) (10) Equation 10 states that the perceived size of S at a particular distance can be expressed as the physical size (S) multiplied by a constant (K), where K' as indicated by the subscripts n and v, may vary as a function of the distance Dv and the amount of frontal constancy n. It is easily demonstrated by combining equations 4, 8, and 9 that: Kne Den Kng Den Two additional relations are helpful. These are: A cat in radians D 134 (11) (12)

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and, S id in radians D where A is the interpupillary distance of the observer. Combining equations 3, 4' 8, 12, and 13 gives: e e (eve Hi)' red CAD ~-J~v7l-ly ~(14) ( 13) t ~ From equation 14, specific equations are derived readily for any value of n. Also, by means of equations 12 and 13, the resulting equations can be expressed either in angular or linear terms. For the present purposes only certain of these derived equations will be considered. 2. Predictions from equations for perceived depth Referring to Fig. 1, the problem is to determine the size of X97t which will be perceptually equal to (or in the more general case be some perceived multiple of) the perceived size of Xef. Consider the case in which Xef and Xgh are perceived as equal. Equa- tion 14 specifies the perceived size of Xe:, i.e.7 (are Orf)~. The perceived size of Xgh' i.e., (~9 Ah)', iS similarly written. ~ Knq Don ( ~ ) and if h (~e `f)~- (~D eh)~, then 9 ~ Jan n- 1 do (15) e ~ Knot Do 5~ c~vn-l d OCR for page 77
It seems, therefore, that the amount of physical depth required to reproduce the same apparent depth interval using binocular disparity cues is the same at all distances when n -1, increases directly with distance when n 0, and increases approximately as the square of the distance when n 1. From the frontal size constancy studies noted previously, it appears that not all of these different amounts of frontal constancy are equally likely to occur. However, ob- servers will differ in the amount of frontal constancy they evidence in a ar- ticular binocular situation and the above equations indicate the direction of the consequences of these differences. 3. Perception of a midpoint Suppose that a depth interval Xe~ is presented and the observer is asked to adjust an object f to the apparent mid- point of this interval. In this case, (cue orf), _ (af ag)' It is readily demon- strated in a manner similar to that used in deriving equations 18, 19, and 20 that, when n 1, and, when n-O. or, when n +1, Do-De Df 2 Df :/ De TV D 2 De D' f De + Do (21 ) (22) (23) Thus we find that, depending upon the amount of frontal constancy present, the perceived midpoint can be at the arithmetic mean, at the geometric mean, or at some more incorrect position. C. Perception of three-dimensional shape 1. Equations for perceived shape The equation for the perception of the shape of a three-dimensional object, or a comparison between the perceived shape of several of these objects, is derived readily from equation 14. For this purpose, let the perceived shape be called m such that me ~ ore-O`f :) From equations 8, 14, and 24, Den c me = S. CAT-1 J an do (24) (25) Equation 25 not only defines the perceived shape me but it is also useful in de- termining C. For example' if me 1, i.e., the frontal and depth extents are per- ceived as being equal, then, c S An-1 136 (26) ,.

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From equation 25, and when m_ 1~ m - Den ~ or n Se CA- \ n ,' C _ De ~ `~ n ale ~ S. An-1 ~nJ (27) (28) As before, specific equations for m and C for particular values of n are readily derived from equations 25 through 28. 2. Predictions from equations for perceived shape-From equations 12 and 27: me e r_ r_ _~1 CSe l n \Den Die)] (29) Consider the case in which a physically constant size of frontal extent S is located at two distances De and D`, from the observer. At distance De a depth interval Xef is adjusted to appear me times as large as Ee' the perceived size of S at De. A1SO7 at Dg a depth interval X9h is adjusted to appear m`; times as large as E7, the perceived size of S at Dg. Suppose that the value of m in the two cases is identical, i.e., me-me. What will be the physical shapes required to produce these two perceptually equal shapes? This question can be answered from equa- tion 29 when C has been experimentally determined previously by using equation 28. How will the physical depth components of the perceptually equal shapes vary as a function of frontal size constancy? This question can also be answered by considering equation 29. Since the ms in the two cases are identical, Den A ~ 1 ~ NIL ~ ill Don A ~ 1 ~ ~ ~ )1 (302) CS ~ n ~ Den Din JO C S ~ n ~Dgn Dhn/] which, when simplified, gives: or. De D9 Df Dh (31 ) Xef De ( 32) X9h Dg Since the term n does not appear in equations 31 and 32, this means that these relations are not changed by the amount of frontal size constancy present. From equation 32, the change in the depth X required to maintain a constant perceived shape of a three-dimensional object of constant frontal size S increases linearly with distance, independent of the amount of frontal constancy present. But, from equation 29, the amount of binocular disparity or linear depth required to produce a particular value of m for a particular value of S is not independent of n. Also, if a constant value of ~ is used instead of a constant value of S. the change in X as a function of D required in order to keep m constant is not independent of n. -137 r

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Equation 32 as derived from equation 30 applies only when S is the same value at all distances. Conclusions ~. . It is obvious from the previous discussion that the amount of frontal con- stancy present is considered to be important in determining the perception of cteptn resulting from a binocular disparity. The role of the observer constant C was less discussed. It will be seen that C is important in the determination of a perceived shape and a perceived depth extent (equations 25 and 14~. There is considerable evidence that observers often show large reliable differences in the perception of a three-dimensional shape. This is attributed largely to differences in individual values of C.9-~t It is clear, therefore, that if we are to understand the judgments which an observer will make in a three-dimensional binocular display, we must know something about his values of n and C. This does not mean that both n and C are important or are equally important in all types of stereoscopic spatial judgments. As discussed previously' C was not considered to be significant in the perceived ratio of two depth intervals or the perceived ratio of two shapes. In the latter perceived ratio, a circumstance was considered in which the value of n was also not significant. The previous equations specify some factors which should be measured if perceived events are to be predicted. In addition, these equations specify the particular judgments in which these factors are important. This type of information is of value if it is desired, for example, to produce perceptually equal intervals in the stereoscopic display' or more generally, to predict what the observer will see. All this assumes, of course, that the only cue to the perceived distance be- tween the pair of objects is the binocular disparity cue from these objects. When the binocular disparity cues between one of the pairs of objects and additional objects is considered, or when other cue systems are introduced to influence the perception of the depth interval, the situation may become more comple.~ Cer- tainly, additional experimental data are needed, not only to test further the va- lidity of the point of view presented in the above equations, but to extend our information concerning the psychophysical scaling of three-dimensional space to increasingly complex situations. Comments following Dr. Gogel's paper: Graham: Thank you' Dr. Gogel' for this valuable and interesting discussion. In my opinion, this is a very impressive presentation. Dr. Gogel starts with the fundamental concept that the important thing in depth perception is retinal disparity and then, in a systematic, clear-cut way' carries the development to other areas of the psychology of depth, i.e., depth constancy' shape discrimina- tion' and other topics. The consideration of the latter topics was one of the claims to value and importance of Luneburg's account; but I do think that Gogel's account, if it is validated in an appropriate way, will take into consideration more psychological effects than does the Luneburg account at present. - 138

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This account, I think, will have-again I say if it is validated a good influence on the psychology of depth perception. It is sometimes said that if you are paying most of your atteention to retinal disparity, geometrical optics, and topics of that sort, you are not really a psychologist; you are something else. A real psychologist (it is implied) deals only with the phenomena of space, and of course mathematics is of extremely secondary interest in this connection. This attitude has led in the past to what I call a schizophrenic cleavage in the study of depth. If you are a psychologist, you study the phenomenonology of space. I hope that Gogel's approach or something like it may be valuable in demonstrating that many of the important phenomena dealt with by phenomenologists will in fact be taken care of by a quantitative type of approach. Because of Dr. Ogle's background and interests, I have no doubt that he will have a number of com- ments about this type of approach. Ogle: It is very true that I am interested in this approach to binocular space perception. Unfortunately, I haven't seen this development prior to this morning and I think it will take a great deal of study really to digest it. I don't feel that I am in a position either to commend or to critize at all, but I am glad to see more work being done in this field. I feel that the Lundburg theory has many de- ficiences7 one of which is that it has not taken into account the psychological, and even physiological, factors. If we do not take them in, I don't believe we will haste ~ wall -ro,~nA'?d nict'~r'? That' the ran son I'm very interested in Dr. Gogel's . . ~ ~ ~ ~ ~ of_ ~ ~ ~ hi_ ~ ~ hi_ ~ ~ ~ ~ ~ ~ ILL ~ ~ ~ V ~ ~ ~ ~ A J ~ ~ ~ v ~ approach here, but I am going to have to study it. Graham Dr. Ogle's point of view is one that I certainly subscribe to. I didn't mean to imply when I talked about Dr. Gogel's account that I subscribe to it, at least not before validation. However, I do agree with Dr. Ogle that it is important that researches and theories be developed to encompass much more than what has been considered the classical area of depth perception. Dr. Gogel's discussion attempts to do this. 139

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