JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Detection of Separations between Adjacent Signals on a Simulated PPI Radar Scope*

ROBERT M. HERRIcK,t HELMUT E. ADLER,t JOHN E. COULSON,§ AND; GERALD L. HOWETTDepartment of Psychology, Columbia University, New York, New York

(Received February 7, 1956)

A simulated Plan Position Indicator (PPI) scope was used to evaluate the effects of a number of visualvariables upon the minimum signal luminance increment (I) required for the detection of a separationbetween two identical signals. The signal luminance increment is the difference between the signal lumi-nance and the scope face luminance. All of the variables, viz., background luminance, distance betweensignals, scan rate, and simulated phosphorescence decay were of importance in determining threshold logAlvalues. Moreover, most of the interactions among the variables were statistically significant.

As the background luminance increases, an increase in logAI is required for detection of a given separation.The background luminance is the most important determinant of the threshold logAI. In general, for a givenbackground luminance, the threshold logAI must increase as the separation between signals decreases. Theinfluence of simulated phosphorescence decay and scan rate upon logAI thresholds is relatively small.

INTRODUCTION

THE visual displays of a Plan Position Indicator(PPI) radar scope are exceedingly complex; dis-

plays used in basic laboratory studies of visual func-tions are ordinarily rigorously simplified. It is ques-tionable, therefore, whether analyses of data of basicexperiments would lead to a correct evaluation of therelative roles of the many variables in a PPI display.Because of this, it is desirable to use a real or a simu-lated PPI scope to uncover the effects of variableswhich are believed to be relevant.

The present experiment was undertaken to helpfulfill the need for visual acuity data applicable toPPI displays. The task of an observer was to detect,under a variety of display conditions, a separation be-tween two adjacent signals on a simulated PPI screen.Thus, the situation was similar to the task of a land-based radar observer who is required to report thenumber of aircraft overhead or to the task of an air-borne radar observer who must discriminate betweentwo land or sea targets.

An optically simulated PPI scope was designed andconstructed to carry out the present experiment. Thissimulator permitted control of each experimental vari-able over a considerable range of values-a rangegreater than that presently obtainable on real PPIscopes. To obtain a maximum degree of informationfrom the data, a factorial design was used.

APPARATUS

The PPI simulator of the present experiment per-mitted control of scope face luminance, signal lumi-nance, scan rate, phosphorescence decay characteristics,

* This report was prepared by Columbia University under AirForce Contract No. AF33(038)-22616. Dr. James M. Vanderplasof Wright Air Development Center acted as Project Engineer.Publication assisted by the Ernest Kempton Adams Fund forPhysical Research of Columbia University.

t Present address: U. S. Naval Air Development Center,Johnsville, Pennsylvania.

$ Present address: Yeshiva University, New York, New York.§ Present address: Rand Corporation, Santa Monica, California.

and distance between members of pairs of adjacentsignals.

A schematic diagram of the apparatus is presented inFig. 1. A Viewlex V-35 slide projector (BP) containeda slide holder which carried a slide consisting of anopaque disk with a centered circular aperture (B). Thisprojector provided the scope face (background) lumi-nance. Light rays from this projector were reflectedby a silvered mirror (M) upon a circular opal glassscreen (0). This opal glass was 0.059 inch thick. Thelight rays next passed through a circular rotatingphotographic negative (W) and a circular piece ofplain glass (G), 0.09 inch thick. The rays continuedthrough the 0.61-inch diameter circular viewing aper-ture (A) to the observer's eye (E). A stop (S,) helpedminimize stray light. Another stop (LS1 and LS2 )limited the view of the observer to a circular area of theopal screen, of 5.125 inches diameter. Since the viewingaperture (A) was located 14.34 inches from the opalscreen, the section of the opal screen seen by theobserver subtended a visual angle of 20°16'.

A Viewlex V-33 slide projector (SP) projected on theopal screen a display consisting of two adjacent signals.An extension attached to the tube of SP contained the

is P P F S S,

/M

S,

F,

B

BP

A

- E

0<

WG

FIG. 1. Schematic diagram of apparatus. See text formeaning of symbols.

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VOLUME 46, NUMBER o OCTOBER, 1956

HERRICK, ADLER, COULSON, AND HOWETT

projection lens unit. This unit was positioned to obtaina one-to-one relationship between object size andimage size. Two stops (S2 and S3) aided in reducingscattered light in this section of the apparatus. Fromthe opal screen the light from the image (two rectangu-lar signals) followed a path to the eye similar to thatdescribed above for the background light rays.

Phosphorescence Decay

Phosphorescence decay characteristics were simu-lated by means of three circular photographic negatives,hereafter called wedges (W). Each wedge was con-structed to give a constant density along any radiusand a particular gradient of density around the 360° ofthe wedge. Sectors of 20 of arc were cut out at thesections of minimum density of the wedges designatedX and Y. Thus, the minimum density of these twowedges was 0.00. The minimum density of the wedgedesignated as Z was 0.01; it was treated as having adensity of 0.00 in the analysis of the data. Figure 2indicates the logarithm of the relative luminance re-sulting from the density gradients of the wedges as afunction of angular degrees on the wedge, measuredfrom the radius of minimum density. The X-curverefers to the wedge which gives a gradient of luminancesimilar to that presented by the P7 phosphor of a PPIscope. The other two wedges, Y and Z, were constructedto yield widely different luminance decay characteristics.

Scan Rate

With a stationary wedge in place between the opalglass (0) and the plain glass (G) the observer vieweda display similar to a PPI display at a given moment intime. With the signal projector turned off, the lumi-nance at any given point in the display depended upontwo factors: (a) the amount of light provided by theopal screen which was uniformly illuminated by thebackground projector; and (b) the density of thewedge at the given point. In an actual PPI scope theluminance of any given point on the screen is continu-ously changing as a function of time since excitationof the phosphor. This change in luminance of a givenpoint was simulated in the apparatus by a clockwiserotation of the wedge which was sandwiched betweenthe opal glass and plain glass. A synchronous motor,with three sets of gears, was used to accomplish therotation. A friction drive in contact with the rim of anannular metal mount enclosing the opal-wedge-glasssandwich was used to obtain any of three rotationrates: 11, 22, or 64 rpm.

If the electrical variables of a real PPI scope are setat constant values, the luminance of a spot on thescope screen at the end of one rotation of the scan line(the terminal luminance) is determined by the char-acteristics of the phosphor. Phosphor characteristicslikewise determine the shape of the function whichdescribes the decrease in the luminance of the spot

during one rotation.' When the X-wedge rotated at 22rpm, a display similar to that of a PPI scope with a P7phosphor and an antenna rotation rate of 22 rpm waspresented. When the X-wedge rotated at 11 rpm and64 rpm, however, the decay characteristics werechanged. At 11 rpm the rate of decay was decreasedand at 64 rpm the decay rate was increased. Moreover,instead of a spot reaching a slightly different terminalluminance at each scan rate, as is the case with a realPPI scope, the terminal luminances remained constant.Analogous considerations apply to the use of the Y-and Z-wedges.

Size of Signals and of Separationsbetween Signals

Each acuity display was composed of two adjacentrectangular signals on the opal screen. The two signalswere separated by a different distance in each display.As viewed by the observer, the center of the separationwas 1.56 inches to the right of the center and 0.22 inchabove the center of the opal screen. To obtain fivedifferent separations between the two signals, fivemetal slides were constructed. A slide (S in Fig. 1)consisted of a metal plate with a rectangular aperturebisected, by a recessed metal rod or wire, into twosmaller rectangles. The width of the rod or wire deter-mined the separation between the rectangles. Eachsignal (small rectangle) of each acuity display was0.200 inch in the horizontal dimension and 0.080 inchin the vertical dimension, i.e., 48' visual angle hori-zontally and 19' visual angle vertically. The separationsbetween the two signals of the five displays were 0.32,0.51, 0.945, 4.73, and 25.20 minutes of visual angle,respectively.

Background (Scope Face) Luminanceand Signal (Pip) Luminance

The signal luminance and the background luminancewere varied in discrete steps by placing Wratten neutraldensity filters in filter boxes F and F, respectively.Finer control over the signal luminance was obtainedby means of the polarizer and its analyzer (P and P').The background and signal luminances were, of course,modified by the wedges. The lamps of the slide pro-jectors were operated on direct current and the currentdrawn by each was monitored.

Calibrations

An Eastman densitometer was used to measure thedensities of the wedges and the densities of the Wrattenneutral filters.

Measurements of the background luminance and ofthe luminance of the signals were made with a Macbethillumi nometer. These measurements were made on theopal screen with no wedge in place. To measure theluminance of the signal a rectangular slide without a

I National Research Council, Preparation and Claracteristics ojSolid Luminescent Materials (John Wiley and Sons, Inc., NewYork, 1948).

862 Vol. 46

October1956 DETECTION OF SEPARATIONS BETWEEN ADJACENT SIGNALS 863

bisecting bar was placed in the signal projector and amagnifying device2 was used in conjunction with aMacbeth illuminometer.

A delineascope, adjusted to a magnification of about15X, was used to measure the horizontal and verticaldimensions of the signals.

The separations between the two signals were meas-ured by several methods. Two of these methods will bedescribed and the results compared. With both methodsno wedge was in place, and a microscope of 100X mag-nification was used with a calibrated micrometer disk.In one set of measurements the acuity-object slideswere taped against the observer's side of the opal screenand illumination was provided by the signal projector.These measurements were made to determine the actualwidth of the bars or wires which bisected the largerrectangle into two smaller ones. These calibrations, interms of minutes of visual angle separation betweentargets, gave the following values for the four smallerseparations: 4.73, 0.945, 0.49, 0.24. The size of themicroscope field was too small to permit calibration ofthe largest separation under the conditions describedabove. However, with the aid of a mechanical micro-scope stage and with the microscope adjusted for 50Xmagnification, it was possible to determine the barwidth. This method indicated that the bar subtended avisual angle of 25.87 minutes.

In another set of calibrations each acuity object wasplaced, in turn, in the signal-projector slide carriage,and the separation between the projected images of thetwo rectangles was measured on the opal screen. Inthis case the separation between the two signals wasnot of equal luminance throughout its width. Thecentral portion of the separation was dark but theedges displayed a gradient of luminance. This gradientprobably resulted from the diffusing action of the opalglass and from diffraction effects. Two sets of measure-ments were made of the sizes of the image separations.One set was based on the maximum width of the sepa-ration, i.e., the width including the strips displayingthe luminance gradient. The other set of measurementsdid not include this area of uncertainty. The differencebetween any two corresponding measures was rela-tively small. The means of the maximum and mini-mum sets of measures of the separations between signalswere 4.73, 0.945, 0.51, and 0.32 minutes of arc for thefour smaller separations. The largest separation, meas-ured with a 1OX magnifier, was 25.20 minutes. The lastnamed set of figures gives the separations as they wereactually presented to an observer; these figures wereadopted for use throughout this report.

Check measurements were made of all wire and rodwidths with the acuity objects on the microscope stage.Moreover, measurements were made of these widthswith magnification obtained with a delineascope. Wherepossible, measurements were also made of the separa-tions of the signals projected on the opal with filters of

2H. B. Ranken, Wright Air Development Center TR 52-258(1952).

W2.0

W 1.5> ~~X

-0 0.5

0.0 0 60 120 180 240 300 360

DEGREES

FIG. 2. Angular luminance gradients produced by threecircular photographic negatives (wedges).

different densities in the light beam of the signal pro-jector. All of these measurements agreed well withthose reported above.

PROCEDURE

A modified descending method of limits was em-ployed to determine, under each of several sets ofconditions, the signal luminance required for the de-tection of a separation between two identical rectangularsignals of equal luminance. Five acuity displays wereused. Each display presented two signals separatedfrom each other by a different fixed distance. Thegeneral procedure consisted of obtaining, in one experi-mental session, the minimum signal luminance neces-sary for the detection of a separation, for each of thefive acuity displays. In each session only one wedgewas used and the scan rate and the background lumi-nance remained constant.

The observer first dark adapted for five minutes. Hethen monocularly viewed the illuminated revolvingwedge, fixating on the approximate place where thesignals would appear during testing. At the end of fiveminutes of such light adaptation, the experimenterpresented the acuity display with the greatest separa-tion between the two signals. The experimenter thenslowly decreased the signal luminance until the ob-server reported that the separation was barely detect-able. From that time onward the luminance of thesignals was decreased by about 0.03 log unit everyfifteen seconds. This procedure was followed until afifteen-second period was reached in which the observercound not detect any separation between the twosignals.

After obtaining a threshold measure, the experi-menter readjusted the polaroid setting to increase theluminance to a value well above threshold and repeatedthe procedure outlined above to obtain a second meas-ure of the threshold luminance.

In any experimental session two threshold measure-ments were obtained with each acuity display. The fiveacuity displays were presented in order of decreasingseparation between signals. For each wedge and scanrate combination, thresholds were determined with each

HERRICK, ADLER, COULSON, AND HOWETT

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-2.6 -2.1 -1.6 .1.1 -0.6 -0.1 0.4 0.9 1.4 1.9LOG(SIGNAL LUMINANCE - BACKGROUND LUMINANCE)

FIG. 3. Log visual acuity as a function of logAI, for X- andY-wedge conditions. The number adjacent to each group of 3curves is the logarithm of the background luminance. The experi-mental points are averages for 4 observers.

of five background luminances, presented in randomorder for each observer.

Four observers participated in the experiment. Onthe basis of clinical tests, two had normal acuity. Theother two observers employed corrective lenses duringthe experiment to achieve normal acuity.

Since three scan rates, three wedges, and five back-ground luminances were used, the total number ofscan-wedge-background combinations was 45. Eachobserver was tested with the five acuity displays undereach of the 45 sets of conditions. For comparison pur-poses data were also obtained for the five backgroundluminances with no wedge and no rotation.

RESULTS AND DISCUSSION

A log threshold luminance was taken as the mean ofthe logarithm of the lowest luminance at which thesignals were seen as separate and the logarithm of thehighest luminance at which they were not seen asseparate. Under each combination of experimental

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2.6 -2.1 .1.6 -LI -0.6 -0.1 0.4 .9 1.4 1.9LOG (SIGNAL LUMINANCE - BACKGROUND LUMINANCE)

FIG. 4. Log visual acuity as a function of logAI, for the Z-condition and the No Wedge condition. The number adjacent toeach group of 3 curves is the logarithm of the background lumi-Ilance. The experimental points are averages for 4 observers.

conditions, two log threshold values were obtained foreach observer.

The results of the experiment are given in Figs. 3,4, 5, 6, 7, and 8. 1 An elaboration of the meanings ofthe terms used in these figures may facilitate an under-standing of the figures and of the text of this section.First of all, visual acuity, in this experiment, is definedas the reciprocal of the visual angle in minutes sub-tended at the eye by the separation between the twosignals of a display. Secondly, with a rotating wedge inplace, the background luminance and the signals' lumi-nance at any point were continuously changing. Thebackground and the threshold signal luminance valuesthroughout this report refer to the maximum luminancevalues, i.e., the luminances obtained with the leastdense (scan line) portion of a wedge in place. Thirdly,some of the figures refer to the threshold differencebetween the signal luminance and the backgroundluminance. This difference is the luminance providedby the signal projector; it will be referred to as the Alluminance or simply as Al. The letter I will stand forthe background luminance.

-2.6 -2.1 -1.6 -1.1 -0.6 -0.1 0.4 0.9 1.4LOG (SIGNAL LUMINANCE - BACKGROUND LUMINANCE)

FIG. 5. Log visual acuity asafunction of logAI. The numberto the right of each curve is the logarithm of the backgroundluminance.

An analysis of variance of the logAI thresholds wasmade. The analysis did not include the no wedge con-dition. Five sources of variation were included in theanalysis, viz., (a) separation between signals, (b) back-ground luminance, (c) wedge, (d) rotation rate, and(e) observer. All the main effects, as well as all first-order and most higher-order interactions, were sig-nificant at the 0.01 level. The fact that the interactionswere significant indicates that, in addition to the in-dividual values of the variables, the particular combina-tions of conditions used in the experiment were ofimportance in determining the threshold luminances.

Figures 3 and 4 give the mean data for the four ob-servers. The following points should be noted withrespect to these figures.

1. All fifty curves indicate, in general, that a largerlogAl luminance is required for a higher visual acuity.Moreover, the increase in logAl becomes propor-tionally greater as the acuity requirements increase.

2. With each of the three wedges, and with no wedge,the log background luminance is the most important

¶ Tables of the results are presented in Wright Air Develop-ment Center TR 55-424 (1955).

I

864 Vol. 46

October1956 DETECTION OF SEPARATIONS BETWEEN ADJACENT SIGNALS 865

determinant of the abscissa position of the curves.For a given wedge and scan rate, the higher the logbackground luminance, the greater the required dif-ference between signal and background luminance. Theonly exception to this generalization is found at thetwo lowest log background luminances with the X-wedge at a rotation rate of 11 rpm. Earlier studies onthe detectability of pips have also indicated the im-portance of the background luminance.3

3. A comparison of the sets of curves for a givenbackground luminance and a given scan rate for thethree wedges shows that the position of a curve withrespect to the abscissa is affected by the wedge. Thegreatest logAI values were required when the X-wedgewas in place. The logAI luminances required for de-tection of the separations with the V-wedge wereapproximately equal to or slightly greater than thelogAI luminances obtained' with the Z-wedge. Thedifferences between the logAI luminances required with

1.8Z Z -WEGE

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0 4

° -.-20 -1.0 0.0 1.0 2.0

LOG BACKGROUND LUMINANCE

FIG. 6. Log AI as a function of logI (log background luminance).Experimental points are averages for 4 observers.

the three wedges were generally greater at the pointscorresponding to the lower background luminancesand lower acuity values. These findings with respectto the wedges indicate that a phosphorescence decaysimilar to the V or Z would be expected to be slightlymore advantageous than the X(P7) type of decay.

The signals of a display are visible for a longer timeduring each scan with a Z-type of decay than they arewith an X- or V-type decay. Because of this one wouldexpect, in addition to the advantage of low AlI values,other advantages to result from the use of a Z-type ofdecay. For example, when a PPJ display is viewed onlymomentarily, the chances of detecting the details of anear-threshold display would be greater with the Z-than with the X- or V-wedges. Moreover, if two near-threshold signals of a display were separated by a large

3 C. H. Baker and G. B. Thornton (editors), A Gnide to FactorsAffecting Radlar Operator Efficiency (Defence Research MedicalLaboratories Project No. 84-134-18, Report No. 84, Defence Re-search Board, Department of National Defence, Canada, 1953),p. 30 and p. 49.

0.0 0.49

W -0.6 X ; _

-2.0 -1.0 0.0 1.0 2.0LOG BACKGROUND LUMINANCE

FIG. 7. Log contrast [log(AlI/)] as a function of log back-ground luminance (logI). Experimental points are averages for 4observers.

distance on the PPI screen, both would be visiblesimultaneously with a Z-type decay but only succes-sively with an X- or V-decay.

4. The effect of the rotation rate on logAI is to someextent a function of the wedge used. With the X- andY-wedges, a lower logAI was usually obtained with aslower scan rate. The Z-wedge, however, yielded thelowest logAI values at the intermediate rotation rate of22 rpm. With the Z-wedge the differences due to scanrate were extremely small. The differences between themagnitudes of the logAI values for the different scanrates for a given wedge depend, to some extent, uponthe background luminance. At the lower log backgroundluminances the differences between logAI values aregreater.

Previous studies4 agree with the present one infinding that scan rate has a relatively small effect.

Comparisons of the lower graph of Fig. 4 with theupper graph, and with Fig. 3, indicate that the com-bined influence of the wedge and the scan rate upon theshapes and positions of the curves was relatively small.

5. The range of logAI values required for the rangeof acuities investigated decreases as the log backgroundluminance increases. With the X-wedge at 11 rpm, forexample, the logAI values ranged from -1.96 to-0.24 with a log background luminance equal to

t-04-J

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0.5

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-I.A-18 -13 -0.8 -03 0.2 0.7 1.2

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FIG. 8. Log visual acuity as a function of log contrast [log(AI/I)J3.Experimental points are averages for 4 observers.

4 See reference 3, pp. 7 and 33.

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2.62 / 2.76 2.

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I I

HERRICK, ADLER, COULSON, AND HOWETT

-2.13; at a log background luminance of 2.62, thelogAI range was much smaller, from 1.06 to 1.87. Thedecrease in the logAI range is reflected in the increasingslopes of the curves as the log background luminanceincreases. This increase in slope is most noticeablewhen a comparison is made of the sections of the curvescorresponding to the two lowest acuities. At someplaces, e.g., Y-wedge and log background of 2.62, theslope of this section of the curve passes through thevertical and takes on negative values. Under certaincombinations of conditions (e.g., at a logI of 2.62 withthe Y- or Z-wedge), all observers tended to havehigher Al thresholds for the widest separation than forthe second widest; and one of the observers displayedthe same tendency over a wide range of conditions.

Figure 5 gives a typical example of the variabilitydue to the four observers. The curves for the four logbackground luminances connect the mean values ofthe four observers, i.e., these curves are the same asthe curves of 22 rpm in the upper section of Fig. 4. Thehorizontal lines on each curve in Fig. 5 connect theexperimental points of the four observers. The lengthsof these horizontal lines indicate the range of experi-mental values obtained at each point and are thereforerough measures of variability. To increase ease of read-ing, the data for log background luminance of -0.76were omitted from this figure.

To point out the above and other relationshipsexisting among the variables, the data may be plottedprofitably in a variety of ways. The mean data obtainedwith the Z-wedge rotating at 22 rpm were selected toillustrate these relationships.

Figure 6 shows that for a given acuity requirementlogAI increases at an increasing rate as the log back-ground luminance increases. One interesting feature ofthis figure is the approximate coincidence, at the higherbackground luminances, of the curves corresponding tothe two lowest acuities. This finding indicates that, forrelatively wide separations between the two membersof a pair of signals, the logAI value remains approxi-mately constant for a constant background luminance.It should be mentioned in this connection that theobservers often noted that the greatest separation be-tween signals was seen, at threshold, at the same signalluminance required erely to detect the presence of asignal on the display. This observation implies that theAl luminances for the lowest acuity may be consideredroughly equivalent to the Al values which would befound if an observer were just required to detect thepresence of a signal.

Figures 7 and 8 present the data in terms of thecontrast between the signals and the background. InFig. 7 the data are shown in a type of plot ordinarilyused to present results of luminance discriminationexperiments; log contrast, i.e., log(AI/I), is plotted asa function of logI. Figures 7 and 8 show that as the logbackground luminance increases, the log threshold con-

trast decreases at a decreasing rate. Furthermore, ingeneral, at a given background luminance, higher acuityrequirements necessitate higher contrasts.

Changes in the values of the threshold signal lumi-nances would be expected to occur with changes in theconditions which were held constant throughout theexperiment. The influences of these conditions shouldtherefore be kept in mind when one applies the presentdata to the use of operational radar scopes or for recom-mendations to designers of radar equipment. Althoughno previous studies are directly comparable to thepresent one, the results of classical experiments as wellas those of studies on the detection of a single signalon a scope face may be used to estimate the qualitative,if not the quantitative, effects of different experimentalconditions upon threshold luminance values.

Almost all of the conditions of the present experi-ment would be expected to result in low thresholds.Adapting the eye to a background luminance equal tothat used in the testing situation, as was the case in thepresent experiment, has been found to result in lowerthreshold values.5 The fact that an observer knew thatany acuity display would always appear at a specificpart of the field of view doubtless aided in loweringthreshold luminance values.6 The long duration (15seconds) of exposure at each AI value with the descend-ing method of limits would also be expected to act inthe direction of lowering thresholds.7 The method-of-limits threshold corresponds to a probability of seeingof less than 100%; a higher probability of seeing wouldhave required higher Al values. Foveal fixation hasbeen found to result in maximum detectability.8 Theabsence of noise on the simulated screen' and the lackof ambient illuminations 0 are other conditions favoringlower thresholds. The absence of an artificial pupil,ordinarily used in laboratory studies of vision, wasanother factor which would result in the lowering ofthresholds."' Finally, it would be expected that thetrained observers taking part in the present experimentwould have luminance thresholds somewhat lower thanthose of untrained observers. Possibly the only condi-tion which might be expected to favor lower thresholdsand which was not used in the present experiment wasthat of binocular viewing.

6K. J. W. Craik, Brit. J. Psychol. 29, 252 (1939); R. M. anesand S. B. Williams, J. Opt. Soc. Am. 38, 363 (1948).

6 Buckley, Hanes, and Deese, Wright Air Development CenterTR 52-303 (1952); J. Deese and Elizabeth Ormond, Wright AirDevelopment Center TR 53-8 (1953); M. W. Harriman, J.Psychol. 29, 247 (1950).

7 Adler, Brown, and Herrick, Wright Air Development CenterTR 54-551 (1954); N. R. Bartlett and A. L. Sweet, J. Opt. Soc.Am. 39, 470 (1949); A. L. Sweet and N. R. Bartlett, J. Opt. Soc.Am. 38, 329 (1948).

8 S. B. Williams, J. Opt. Soc. Am. 39, 782 (1949).9 See reference 3, Sec. 2.10 Adler, Kuhns, and Brown, Wright Air Development Center

TR 53-266 (1953)." See reference 7, Adler, Brown, and Herrick.

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