JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Contrast Thresholds of the Human Eye

H. RICHARD BLACKWELL*Louis Conifort Tiffany Foundation, Oyster Bay, New York

(Received July 12, 1946)

THE L. C. Tiffany Foundation is an artT school in peacetime, but its facilities werecompletely engaged during the war years under acontract with the Office of Scientific Researchand Development. The part of the war programupon which this paper is based pertains to thedetermination of the contrast threshold of thenormal human observer under a wide variety ofexperimental conditions. The typical experi-mental procedure consisted in projecting a spotof light on a white screen some sixty feet from agroup of observers who individually reportedwhether the stimulus had been seen. A largenumber of such presentations, made with varyingbrightness of the stimulus, provided data fromwhich, by statistical analysis, the contrastthreshold could be determined. Experiments ofthis sort were repeated with stimuli of varyingsizes and with values of screen brightness coveringa range from full daylight to slightly less than the

darkest night. In all, more than two millionresponses to the test stimulus were recorded,some four hundred and fifty thousand of whichhave been statistically analyzed and reportedherein.

I. EXPERIMENTAL PROCEDURE

LaboratoryThe laboratory in which experiments were

conducted is shown in Figs. 1 and 2. The entireinner surface of the observation room was coveredwith flat white paint, whose reflectance was ap-proximately 0.89. A ventilation system, details ofwhich are shown in Fig. 2, maintained a moderatetemperature and kept the air relatively free fromdust particles.

Illumination of the observation room was pro-vided chiefly by a number of special lightingunits. The lighting units (troffers) were stra-tegically situated in order to provide maximum

FIG. 1. Sketch of laboratory. A plywood structure was installed within an existing framework. The large plywood roomserved as a field of standardized brightness (the observation room). To the right was located the main control room.To the left was a supplementary control room.

* Now Technical Aide, Army-Navy-NRC Vision Committee, University of Michigan.

624

VOLUME 36, NUMBER 11 NOVEMBER, 1946

CONTRAST THRESHOLDS

IPSE PACRN PROJECT0O I ON N LAMP TRAPPERS CIRTIN SCREEN EXIT

FIG. 2. Floor plan of laboratory. Dimensions of the plywood room (observation room) were:length, 63 feet; height, 10 feet, and width at the narrowest points, 10 feet.

uniformity of illumination. As can be seen inFig. 2, five troffers were located on each of theleft and right walls of the observation room. Thebrightness of the surfaces of the room could bevaried from zero to 1000 footlamberts by ad-justing the components of the troffers.

The front wall of the observation room,subtending 10° at the eyes of the observers,served as a screen upon which test stimuli wereproduced. The use of multiple sources of illumi-nation and walls of high reflectance insured thatthe brightness of the portion of the screen uponwhich the stimuli were produced was uniformwithin the precision of visual photometry. Overthe entire surface of the screen, variations inbrightness did not exceed ht3 percent.

It was not possible for all surfaces of theobservation room to be made equally bright. Be-cause the troffers were directed forward, theobservation screen was always somewhat brighterthan other portions of the room. By carefulmanipulation of the output of the several troffers,surface brightnesses were made to decreasegradually from greatest brightness at the obser-vation screen to least brightness near the rear ofthe room.

Figure 3 is a view of the observation screenfrom the rear of the room under typical illumi-nation conditions. 'It is evident that no portion ofthe room had a greater brightness than the obser-vation screen and that, in general, the brightnessof the room decreased gradually from a maximumat the screen. The irregularities which existed-were not distracting.

Preliminary experiments indicated the neces-sity for control not only of the brightness of thescreen, but also of the pattern of brightness of thevarious surfaces of the observation room. It wasshown that the threshold contrast of a stimulusprojected onto the observation screen was afunction of the pattern of brightness in the visualfield surrounding the stimulus. As a consequence,the relative brightnesses of various surfaces of theobservation room were rigidly controlled. Thepattern of surface brightnesses illustrated byFig. 3 was standardized. In the few instances inwhich deviations from this pattern were necessary,it was proved that no significant change inthreshold contrast resulted.

The over-all brightness of the observation roomwas subject to precise control. Whenever possi-ble, the sources of illumination were supplied bystorage batteries. When the requisite power couldnot be produced in this way, a stabilized a.c.supply was employed.

To illuminate the observation screen to abrightness greater than 0.2 footlambert, eachtroffer was supplied with 120-volt, general servicelamps, ranging in wattage from 20 to 300 and innumber from 2 to 20. Each troffer extended theentire height of the room, but light emanatedonly from a flashed opal window 4 inches in widthaidd 40 inches in height.

The output of the troffer units was varied notonly by the number and wattage of lamps butalso by means of a metal baffle which served toreduce the width of the diffusing window. Awooden reflector extended the full length of the

625

H. RICHARD BLACKWELL

FIG. 3. Observation room wvith standard illumination, viewed from observers' stations.

troffer which was used to distribute -output fromthe troffer in order to achieve maximum uni-formity of illumination.

The lamps were supplied by a three-phase a.c.line, standardized by the Long Island LightingCompany. In order to insure even greater sta-bility, the phase supplying the lamps in the twotroffers nearest the observation screen on eachside of the room was manually controlled bymeans of a variable transformer and compen-sator.

To illuminate the observation screen to abrightness less than 0.2 footlambert, each trofferwas provided with from two to four speciallydesigned fixtures. Each fixture was a light-tightbrass tube containing an automobile head lampand ground glass plates, which served as asecondary source. The head lamps were suppliedby storage batteries. Reduction in output wasobtained by varying the separation between thehead lamp and the ground glass plates and by theaddition of supplementary ground glass platesand opaque diaphragms. Sufficient ground glass

plates were fixed in place to serve as the second-ary source so that the addition of supplementaryplates did not alter the optical properties of thefixtures. The flashed opal windows of the trofferswere removed so that the secondary sources ofthe fixtures illuminated the observation roomdirectly. Precise control over the spectral qualityof the illumination was possible in this way sinceinternal reflection within the troffers was notpermitted.

Auxiliary illumination of specific portions ofthe observation screen was provided by pro-jection equipment located in the control room atthe rear of the observation room. Three standardBausch and Lomb Balopticons were employed,modified somewhat for special purposes. It wassometimes necessary to illuminate extremelysmall areas of the observation screen. Imagedefinition with the projection apparatus located65 feet away was unsatisfactory. Accordingly,special techniques were devised by which theobservation screen was transilluminated from thesmall control room shown in Fig. 2.

626

CONTRAST THRESHOLDS

FIG. 4. View of ob

Psychophysical Procedure

Observers were seated at the rear of the ob-servation room in upholstered chairs mounted onthe floor and on a balcony (Fig. 4). The observersentered the observation room from the largecontrol room through light traps.

A standard experimental session consisted of320 presentations of a test stimulus. An electricalbuzzer served as the signal for a stimulus presen-tation, remaining activated continuously duringthe presentation. Breaking the buzzer circuitserved as a signal for the observers to indicatewhether they had detected the presence of thestimulus.

The duration of the stimulus varied among ex-periments. In each case, a 6-second rest periodfollowed each stimulus presentation. Additionalrests were scheduled so that the observers did notbecome excessively fatigued.

In preparation for an experimental session, thetroffers were adjusted for the desired level ofillumination, and projection or transilluminationequipment was prepared with a stimulus ofselected.size. The observers were allowed to adaptto the observation room brightness sufficiently

servers' stations.

long to insure stable visual performance. At lowbrightnesses, the period of adaptation was short-ened by preliminary adaptation outside the labo-ratory with standard Polaroid dark adaptationgoggles.

Five appropriate stimulus contrasts were se-lected on the basis of preliminary observations.Both during preliminary observations and duringthe regular session, each of the stimuli waspresented in random sequence an equal numberof times. The five stimuli were detectable by theobservers with varying probability. The largeststimulus contrast was usually detected with aprobability of 95 percent and the smalleststimulus contrast, with a probability of 10percent. Three additional stimuli were selected sothat an adequate function relating probability ofdetection and stimulus contrast was obtained.Threshold contrast was defined as the contrastwhich was detected with a probability of 50percent, due allowance having been made forchance success.

The functions relating probability of detectionand stimulus contrast were considered to benormal probability integrals. Graphical analysis

627

H. RICHARD BLACKWELL

00

0

. 5 -4 -3 o. 1 0

LOG ADAPTATION BRIGHTNESSIPooILAM3ERTS)

FIG. 5. The arithmetical mean of It valufrom individual probability curves, plotted agtion brightness.

*1

0 .

0

0 *1 *2

LOG VISUAL ANGLEIINoJIS O ..C

FIG. 6. The arithmetical mean of valufrom individual probability curves, plotted agaarea.

of large numbers of such functiongratifying conformity to the predictiGaussian formula.

Accordingly, solution for the contsponding to 50 percent probability plished by what has been called Urbanprocess.1 This solution yields M1/, thivalue corresponding to a probability of.'due allowance having been made fsuccess, and h, a constant which ismeasure of the steepness of the probabThe constant h can be converted iistandard deviation of the normal integral.

The adequacy of the Urban soluti(vestigated for a substantial number of functions in the following way: A nor]bility curve was generated from valuera- and plotted together with the aexperimental points. An attempt wa

1 J. P. Guilford, Psychomnetric Methods (lBook Company, Inc., New York, 1935), p. 17

improve the fit of the normal curve to the experi-mental points by varying the values of M and a-from those obtained by the Urban process. In nocase was an M found which resulted in a better fitof the date, and in only a few cases was a slightlybetter value of o- found. Since only M valuesfigure in the reported results, this analysis wasconsidered to be an adequate demonstration ofthe adequacy of the Urban solution. All experi-mental data reported herein are based uponthreshold contrasts computed in this way.

Les computed At the outset of experimentation, it was sup-ainst adapta- posed that the five stimulus contrasts would have

to vary not only absolutely, but also relatively,among the various experimental sessions. If thesteepness of the probability curves varied sig-nificantly among the various experimental ses-sions, in order to include an adequate range ofprobability values, five stimuli of different rela-tive contrast would have to be selected. Elaborateprovisions were made for the production ofstimuli with different relative and absolutecontrasts.

-3 It soon became evident that an appropriatefour to one variation in stimulus contrast corre-

es computed sponded very nearly to a variation in probabilityLinst stimulus from 10 to 95 percent for all experimental ses-

sions. In other words, the shapes of probabilitys revealed curves were very nearly identical in all experi-ons of the mental sessions. Accordingly, five contrasts

bearing the same relationship to each other were

rast corre- employed in all experimental sessions.ras accom- The five contrast stimuli used in every experi-Is constant mental session were related approximately as thea stimulus numbers: 1.0, 0.75, 0.55, 0.37, and 0.24. In order50 percent, to produce contrasts related in this constantfor chance fashion, four gelatine filters were obtained whose

an inverseility curve.ito a-, theprobability

mon was in-)robabilitynal proba-; of M andppropriate

3 made to

vlcGraw-HillOff.

i

400IX

- .. .- .- 1.0

RELATIVE CONTRAST

FIG. 7. Average probability curve.

I I

" " w - w " S s

628

I I I I I

CONTRAST THRESHOLDS

FIG. 8. Permanent record-ing of experimental data.

transmittances were identical with the last fournumbers in the above series. A mechanism wasconstructed by which either an empty bracket ora bracket containing one of the four filters couldbe rotated into the projector beam.

A qualitative estimate of the extent to whichthe shapes of probability curves were inde-pendent of experimental variables such as adap-tation brightness and stimulus area can be ob-tained by comparing h values computed bythe Urban method. Data are presented inFigs. 5 and 6, representing a total of 200,000observations. Values of h were computed by theUrban method from individual probability curves,derived from the body of data reported below in"Results, Part I."

It is apparent that substantial differences in has a function of either adaptation brightness orstimulus size do not exist.2

The definition of "threshold" probability asprobability 50 percent greater than chance suc-cess was selected primarily because the steepnessof the probability curve is greatest at this point,

2 Although only random differences are present in Fig. 5,the data of Fig. 6 exhibit a consistent trend of smaller h forlarger stimuli. The differences in h between the largeststimulus and each of the other stimuli were tested forsignificance. Value of CR, and of P (probability of adifference existing in the direction obtained) are presented:

Stimulus size (rankedwith respect tolargest stimulus) CRa P

2 1.83 0.9663 4 33 0.9999924 3.90 0.999955 5.13 0.999997

resulting in maximum precision in the determi-nation of thresholds. If the "threshold" beredefined in terms of any probability other than50 percent, the original threshold data can beconverted by means of a simple constant. Thisprocedure is valid because it has been shown thatthe steepness of probability curves is constant toa first approximation for all experimentalconditions.

The average probability curve for all the ex-perimental data reported in this paper wasconstructed in the following manner: The proba-bility curve for each observer, for each experi-mental session, was solved by the Urban methodfor M and a. The constants M and a- for 1500individual probability curves were averaged.From the average values of the constants, anormal probability integral was constructed fromstandard tables. The average probability func-tion can be used in determining the constantwhich will convert the contrast thresholds pres-ented in this paper to "thresholds" correspondingto other levels of probability.

The average probability curve for 450,000 ob-servations is plotted in Fig. 7. The use of thiscurve can be illustrated by the following example:If "threshold" contrasts are desired which corre-spond to a probability of detection, P = 0.90,thresholds presented in this paper should bemultiplied by the constant 1.62.

Interpretation of probability data must bemade with care. Trained observers can respond

629

H. RICHARD. BLACKWELL

TABLE I. Ophthalmological records.

Visual acuity (20 ft.) Near point (mm) Muscle balance

Ouserver U.LJ. U.S. O.U.

B.B. 20/20- 20/20 20/20+

20/25+ 20/25+ 20/20-

(a) 20/15- 20/15- 20/15-

(b)* 20/15- 20/15- 20/15-

20/15- 20/15- 20/15

(a) 20/20- 20/25- 20/20+

(b)* 20/20+ 20/20+ 20/15-

20/15- 20/15- 20/15-

20/20+ 20/20+ 20/20+

20/20

20/25+

20/20+

20/20

20/20

20/25

20/15 -

20/20

20/15- 20/15

20/20+

20/20 -

20/15 -

20/20

20/15

20/15- 20/15- 20/15

20/15- 20/15- 20/15-

20/15- 20/15- 20/15-

20/20+ 20/15- 20/15-

20/20+ 20/20 20/15-

20/20 20/20 20/20+

20/15 20/15- 20/15

O.D. O.S. O.U. 20 ft.

100 110 110 0.25 Eso.

100 110 90 0.5 Eso.0.25 RH.

140 140 130 0.5 Eso.0.25 Hyper.

140 140 130 0.5 Eso.

130 110 105 1.0 Exo.0.5 Hyper.

120 108 95 0.5 Exo.0.25 Hyper.

120 110 110 0.25 Exo.1 Hyper.

70 80 70 2 Eso.0.5 RH.

120 130 120 0.75 Eso.

90 90 90 0.5 Eso.0.25 RH.

110 110 100 0.5 Eso.

140 140 140 0.5 Eso.

120 130 110 0.5 LH.

120 120 100 0.5 Exo.0.5 RH.

105 100 100 3 Eso.

100 120 100 1.5 Exo.

105 115 95 2 Eso.2 Hyper.

130 120 120 Normal

100 110 90 0.37 RH.

110 110 110 0.5 Eso.

90 10 90 2 Eso.0.5 RH.

Abbreviations: Eso. EsophoriaExo. Exophoria

Hyper. Hyperphoria* Repeat examinations made after three months of intensive observatic

very successfully on the basis of hunches. It wasfound by interrogation that the observers did notfeel confident of having "seen" a stimulus unlessthe level of probability of detection were greaterthan 0.90.

Recording of Data

The method used in recording experimentaldata was rapid and free from error. A large

RH. Right HeterophoriaLH. Left Heterophoria

ins.

number of electrical circuits were used, each in-cluding a neon signal lamp. Master control panelswere constructed, at which complete informationwas at all times available in the form of a constel-lation of excited neon lamps. Each observerrecorded her responses by means of an 8-pointselector svitch, connected in circuit with eightneon lamps. In this way, each observer had arepertoire of eight possible responses. Projection

I.T.B.

M.J.B.

E.L.C.

C.C.C.

M.C.

L.H.

E.L.H.

33 cm

5 Exo.

1.5 Exo.

Normal

Normal

* Normal

Normal

Normal

1.75 Eso.

0.5 Eso.

Normal

2 Exo.

Normal

0.5 Eso.

2 Exo.

3 Exo.

9 Exo.

Normal

7 Exo.

2.5 Exo.

3 Exo.

2 Exo.

D.H.

L.T.H.

N.L.H.

J.J-

E.S.K.

V.R.M.

M.R.R.

S.R.

M.S.

J.T.

G.H.W.

630

CONTRAST THRESHOLDS

or transillumination equipment was equippedwith similar switches so that information con-cerning stimulus presence, stimulus location, andstimulus contrast was represented by appropriateneon signal lamps at the master control panel.

Permanent records were made for each stimuluspresentation, which included characteristics ofthe stimulus and the response of each of the ob-servers. This was accomplished by placing atissue paper over the master panel and circlingwith pencil the locations of the excited neonlamps. A record assistant is shown in Fig. 8recording a typical stimulus presentation. Thetissue record sheets were sorted, responses werescored, and probability of detection values wereobtained for each observer for each of the fivestimulus contrasts. Threshold contrast was thencomputed for each observer by the Urban method.

Observers

The observers were young women, aged 19-26years, whose visual acuity in each eye and in botheyes was approximately 20/20 without refractivecorrection. Table I presents. ophthalmologicalrecords for the young women whose observationsconstitute the experimental data of this paper.These and other ophthalmological examinationswere made by Dr. Gertrude Rand, ColumbiaUniversity, and represent a generous personalcontribution to the experimental program. Theobservers were employed full-time for periodsvarying from six months to two and one-halfyears. Observing occupied approximately halftheir time, the remainder being devoted to thestatistical analysis of their data. A priori ob-jections to this procedure were soon overcome bythe obvious stability of individual experimentalresults.

Observers were never considered "trained"until they had made approximately 6400 obser-vations under varied experimental conditions. Ingeneral, the experimental data of this report wereobtained with observers who had been occupiedfrom six months to a year in preliminary experi-ments. Consequently, they were veterans of from35,000-75,000 observations when the experimentsreported here were begun. The exceptional ex-perience of the young women in the task ofobserving resulted in unusual sensitivity andgratifying stability of response.

Photometric Procedure

Preliminary investigations revealed that underthe conditions of these experiments, the precisionof ordinary photometric measurements was lessthan the precision of responses to visual stimulus.As a consequence elaborate photometric determi-nations were made throughout the experimentsreported in this paper. The resulting photometricprecision was always at least as good as that ofresponses to visual stimulus. Measurements weremade of brightnesses varying from 100 to 1 X 10-6footlambert. At least two independent photo-metric measurements were made of each surfacebrightness. The two measurements ordinarilyagreed within 5 percent, so that brightness valuesbased on two measurements were accuratewithin less than 5 percent.

All photometric quantities were expressed infootlamberts, defined in terms of the photopicvisibility function. Surface brightnes'ses wereevaluated in terms of standard brightnesses bymeans of null visual photometers. The visualphotometers were modifications of the Macbethilluminometer, chosen for its stability and pre-cision. Standard brightnesses of a special testsurface were provided by means of standardlamps, varying in candlepower from 20 to 1000.

FIG. 9. Apparatus for producing standardb.rightnesses of a test surface.

631

H. RICHARD BLACKWELL

Three sets of standard lamps were available.Their reliability was assured by cross-checks andby frequent calibrations at the Electrical TestingLaboratories, New York.

The test surface was always mounted near theobservation screen. The standard lamps, inhousings mounted on a carriage, could be posi-tioned at distances from the test surface varyingfrom 10 to 50 feet. The carriage moved on thetracks shown in Fig. 2. A black felt calibrationscreen was mounted before the observation screenwhen the test surface was illuminated by stand-ard lamps. By preventing re-illumination of thetest surface, the calibration screen made it possi-ble for the inverse square law to be used incomputing standard brightnesses. A view of thetest surface, standard lamp housing, and calibra-tion screen is shown in Fig. 9. The calibrationscreen was swung into place from its normalposition against the right wall as indicated inFig. 2. Standard brightnesses of the test surfacecould be varied from 0.006 to 10 footlamberts.When larger or smaller values were needed,gelatine filters were used in the visual photome-ters, the transmittance of which had been de-termined for the photopic eye by means of theinverse square law.

In order to fulfill the specification of thephotometric unit, it was necessary either to main-tain spectral equivalence between surface bright-nesses and standard brightnesses, or else to makeall brightness evaluations with the photopic eye.It was sometimes possible to obtain spectralequivalence with low intensities by the physicalreduction of high intensity sources of knownspectral quality. In these instances, evaluationswere made at fairly low adaptation brightnesses.More customarily, it was impossible to maintainthe spectral quality of surface brightnesses ex-actly because of the slight selectivity of availablematerials. In these instances, photometric meas-urements were made indirectly so that thephotopic eye could always be used. Since theselectivity of materials was only slight, direct lowlevel photometry was used occasionally as acheck on the indirect photometry. Although thelow level photometry exhibited less precisionthan the indirect photometry, no systematicdiscrepancy was ever discovered between the two.

The photometric policy adopted insured that

surface brightnesses were evaluated correctlyin footlamberts. Apparent brightnesses alwaysdiffered somewhat from actual brightnesses be-cause of the slight selectivity of materials, andthe variations in luminosity factors of the ob-servers. The question arose whether brightnesscontrasts were equivalent to apparent brightnesscontrasts. In order to compare actual and ap-parent brightness contrasts, spectrophotometricdata for each surface brightness, and luminosityfactors for each observer at each brightness level,would be required. Adequate spectrophotometricdata were available; no information was availableconcerning the luminosity factors of the observers.As an approximation, interpolations from averageluminosity factors offered by Jones3 were used.Analysis indicated that significant differences be-tween actual and apparent brightness contrastsdid not exist.

II. RESULTS AND DISCUSSION

Part I

A comprehensive investigation was made todetermine the mutual relationships betweenadaptation brightness, stimulus area, and thresh-old contrast. Stimuli, circular in form andbrighter than the observation screen, were pres-ented in any of eight possible positions on thescreen for an exposure of six seconds. As a conse-quence, the observers scanned the screen at a ratecomparable to that employed by lookouts in themilitary service in determining the position theythought the stimulus occupied.

General Procedure

Adaptation brightnesses were investigatedvarying from zero to 100 footlamberts. Circularstimuli varied in diameter from 121.0 to 3.60minutes of arc. Threshold contrasts were ob-tained for each of a group of nine observers foreach of seventy-seven experimental sessions, con-sisting of 320 stimulus presentations each. A totalof approximately 220,000 observations was made,therefore, under experimental conditions differingonly in adaptation brightness, stimulus area, andstimulus contrast.

L. A. Jones, "Summary of American opinion, BS/ARP18, British standard specification for fluorescent andphosphorescent paint," Great Britain Ministry of HomeSecurity. RC(C) 85 (July, 1942).

632

CONTRAST THRESHOLDS

Let us set the brightness of the observationscreen equal to Bo. When a stimulus was pre-sented, a brightness increment, AB, was eitheradded to or subtracted from the prevailing Bo.The stimulus brightness, B8, equaled Bo+AB orB o -AB. Following standard practice,

C (contrast) = (B-Bo)/Bo

= (B o-B.,)1B o

for stimuli brighterthan the observa-tion screen,

for stimuli darkerthan the observa-tion screen.

Values of C range from 0 to + o for stimulibrighter than the screen and from 0 to +1 forstimuli darker than the screen. In the experi-ments of this section, only stimuli brighter thanthe observation screen were investigated.

Near threshold, the difference between B, andBo is often less than 1 percent. In order to insuresufficient precision, AB was produced inde-pendently of Bo by a projection system located inthe control room behind the observers. The beamof the projector passed between the observers, asshown in Fig. 4, and struck the observationscreen at the opposite end of the observationroom.

A small red orientation point was located in thecenter of the observation screen. The stimuluswas projected in one of eight positions on thecircumference of a circle generated about theorientation point on a three degree radius. Theeight positions used corresponded to the eightmajor points of a compass. A thin prism, rotatedbefore a standard lantern-slide projector, pro-vided reliable stimulus positioning. At the soundof a signal buzzer, the observers looked towardthe screen and instigated a systematic searchroutine to attempt to locate the stimulus. Thesix-second exposure permitted only a rapidscanning of the stimulus orbit.

The observers were not given specific scanninginstructions. They were told to fixate and tosearch in the manner they found most efficient.They were instructed that they might find itprofitable to use parafoveal vision at low bright-nesses. The scanning routine was not identical forall observers, but long experience tended tostabilize the scanning procedures so that repro-ducible data could be obtained.

At the conclusion of the six-second stimulusexposure, the observers selected the positionwhich they believed the stimulus had occupied.Response consisted of rotating their recordingswitch until its handle assumed a position analo-gous to the position of the stimulus. The observerswere required to respond to each presentation.They were shown their own data at the conclusionof each experimental session, and soon learnedthat their hunches were quite often correct. Afterrepeated performance, their responses becamesemi-automatic.

Response data were recorded from the mastercontrol panels as shown in Fig. 8. Each responsewas scored and the probability of successful de-tection was computed for each observer for eachof the five stimulus contrasts. Threshold con-trasts were computed by the Urban method(corresponding to 50 percent probability, dueallowance having been made for chance success).Under the experimental conditions, chance successcould be expected in one of eight presentations.

Analysis of the response data revealed thatthere were no systematically favored positions.Further, if an error were made, there was equalprobability that the incorrect response would fallin each of the seven positions not occupied by thestimulus. The analysis from which these con-clusions were drawn was made with stimulidetected successfully only a few percent betterthan chance.

Photometric Procedure

Values of Bo and AB were always photometeredindependently in order to obtain maximum pre-cision in the determination of contrast. When Boor AB was as great as 0.1 footlambert, a directmeasurement was made from the rear of theobservation room. A Macbeth illuminometer,fitted with a telescopic attachment, was used as anull instrument in evaluating the unknown sur-face brightness in terms of the standard bright-ness of a test surface. For brightnesses less than0.1 footlambert, special techniques were devisedso that brightnesses could legitimately be ex-pressed in footlamberts.

Reduction in the output of the projectionsystem used to provide AB was accomplished bythe use of gelatine filters, chosen for their lack ofselectivity. In addition, when AB values less than

633

H. RICHARD BLACKWELL

In1:

I-z0U

-J

z

-J

30-J

r o ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. 1

-2

LOG ADAPTATION BRIGHTNESS (FOOTLAMBERTS)

FIG. 10. The arithmetical mean of threshold contrasts, computed from individual prob-ability curves, plotted as a function of adaptation brightness for five stimulus areas.

0.1 footlambert were required, a ground glassplate was inserted in the lantern-slide projectornear the aperture. The ground glass became thesecondary source of the projection system. Sincethe absorbing filters were inserted between theground glass and the projection lamp, reductionin output did not alter the optical properties ofthe system.

Two independent measurements were made forsmall values of AB:

(1) The gelatine filters were removed and theunattenuated AB was measured directly with theMacbeth illuminometer and telescopic attach-

ment. The transmittance of the gelatine filterswas then measured in the projection system.Ground glass plates were inserted near the pro-jection lens, on the side away from the projectionlamp. The brightness of the foremost ground glassplate was measured with a visual photometerwith the gelatine filters in place and with thefilters removed. The ratio of the brightnesses wastaken as a measure of the visual transmittance ofthe filters.

*(2) A photometric technique was devised inwhich the gelatine filters were positioned as theyhad been during experimentation. It was recog-

TABLE II. Arithmetical mean threshold contrast. Stimuli brighter than surround (Part I).Angular subtense of stimulus (minutes of arc).

121.0 55.2 18.2 9.68 3.60

Log Bo Log C Log Bo Log C Log Bo Log C Log Bo Log C - Log Bo Log C

2.080 -2.124 2.084 -2.041 2.081 -1.894 2.053 -1.739 1.072 -1.1272.061 -2.127 1.083 -2.061 2.078 -1.895 1.077 -1.671 0.523 -0.9801.074 -2.082 0.605 -2.085 1.086 -1.861 0.533 -1.568 0.075 -0.8680.076 -2.102 0.531 -2.049 0.542 -1.863 0.076 -1.460 -0.996 -0.401

-0.471 -2.081 0.078 -1.997 0.070 -1.736 -0.994 -1.083 -2.053 0.175-0.497 -2.065 -0.504 -2.021 -0.975 -1.415 -2.031 -0.505 -2.768 0.703-0.994 -1.937 -0.504 -1.971 -2.034 -0.918 -2.757 -0.044 -2.951 0.905-2.029 -1.579 -0.99t -1.858 -2.755 -0.460 -2.979 0.090 -2.978 0.896-2.756 -1.274 -2.020 -1.438 -2.952 -0.344 -2.984 0.116 -3.341 1.144-2.907 -1.280 -2.769 - 1.150 -2.989 -0.313 -3.346 0.298 -3.964 1.397-2.987 -1.228 -2.981 -1.012 -3.323 -0.219 -3.982 0.618 -5.016 2.026-3.065 -1.178 -3.331 -0.831 -4.002 0.151 -4.986 1.179 -6.032 2.868-3.296 -1.148 -3.995 -0.595 -4.982 0.705 -5.999 1.944-3.979 -0.891 -4.989 -0.079 -6,012 1.479-4.995 -0.474 -5.948 0.622-5.969 0.212

634

CONTRAST THRESHOLDS

10 I to- lo. 1 oo

LOG LIMIMAL CONTRAST

FIG. 11. Interpolations from Fig. 10. Each curve represents the relation betweenthreshold contrast and stimulus area for a given adaptation brightness.

nized that the illumination striking the observa-tion screen bore a constant relation to thebrightness of the secondary source of the pro-jection system. The constant factor relating ABto the brightness of the secondary source of theprojector was established at maximum output.Subsequently, the secondary source brightnesswas measured and AB was computed.

Agreement between the two measurements ofAB was ordinarily obtained within -43 percent.

At low brightnesses, Bo was provided by thespecial fixtures described under "ExperimentalProcedures." Since reduction did not affect theareas of the secondary sources, or in any wayalter their optical properties, there was a constantrelationship between the brightness of the ob-servation screen and the brightnesses of thesecondary sources of the fixtures.

At a screen brightness level of 0.1 footlambert,the constant factor relating Bo to the brightnessesof the secondary sources of the fixtures wasmeasured. For low brightnesses, Bo was com-puted from measurements of the appropriatebrightnesses.

The validity of the indirect photometric meas-

urement was established by the following photo-metric technique: A disk, three feet in diameter,was mounted at the center of the observationscreen. Since its surface reflectance was lowerthan that of the screen, the disk appeared as alarge dark circular patch in the center of theobservation screen. An increment of illuminationcould be added to the disk from the projectionapparatus located in the control room behind theobservers. When the appropriate increment ofillumination was added, the disk became indis-tinguishable from the observation screen.

The group of nine observers used the disk andscreen as a huge visual photometer. Increments ofillumination were selected, some of which wereinsufficient to increase the disk brightness to thatof the screen, while others made the disk brighterthan the screen. The increments were presentedrandomly to the observers, who judged whetherthe disk was brighter or darker than the sur-rounding screen. The increment just sufficient tomake the disk indistinguishable from the screenwas interpolated from the psychophysical data.The spectral quality of the disk and the observa-tion screen were carefully equated so that

TABLE III. Interpolations from Fig. 10. Log (arithmetical mean threshold contrast).

Angular subtense Boof stimulus

(minutes of arc) 100 10 1 1 X10' 1 X10- 1 X1053 1 X10-4 1 X10-6 1 X10-6

121.0 -2.132 -2.130 -2.114 -1.959 -1.640 -1.198 -0.910 -0.461 0.23855.2 -2.062 -2.060 -2.020 -1.857 -1.500 -0.996 -0.590 -0.069 0.66618.2 -1.889 -1.857 -1.738 -1.421 -0.928 -0.325 0.137 0.716 1.4679.68 -1.730 -1.658 -1.437 -1.070 -0.526 0.124 0.615 1.196 1.9503.60 - -1.111 -0.812 -0.385 0.182 0.911 1.410 2.017 2.821

635

Z;II

I-I:1X

II11.4I

H. RICHARD BLACKWELL

'4

.3

_ a

X .2

x I

_ .1

N

6. -...Ih.

-2

.3

0 *1 .2 .3 +4

LOG STIMULUS AREA(SOUARI MINUTES)

45

FIG. 12. Interpolations from Fig. 10. The product ofAB and stimulus area is plotted as a function of stimulusarea for various adaptation brightnesses.

evaluation errors were not introduced at lowbrightnesses.

The value of illumination increments from theprojection system was computed in the followingmanner: A ground glass plate was inserted in theprojection system which served as a secondarysource. Reduction in the output of the opticalsystem was accomplished by the insertion ofgelatine filters between the secondary source andthe projection lamp; consequently, the opticalproperties of the system were not altered. Aconstant factor related the brightness of thesecondary source to the illumination striking thedisk.

With Bo set for 0.1 footlambert, the relationbetween secondary source brightness and-illumi-nation at the disk was measured. The relationbetween illumination required to render the diskindistinguishable from its surrounds and Bo wasestablished. Subsequently, critical values of illu-mination were determined from observer judg-ments, and Bo was computed. The direct meas-urement of Bo did not vary systematically fromthe value computed from the indirect photometricmeasurement. Random differences between the

two measurements usually did not exceed h4percent.

The circular stimuli used in the various experi-mental sessions varied in size from 0.7 to 26inches in diameter. Measurements were made todetermine the exact distribution of energy in eachof the stimuli. For each stimulus the diameterwas considered to be that of a stimulus of equiva-lent flux, uniformly distributed. For large stimuli,the diameter thus computed did not differsignificantly from the diameter measured withrule and calipers. For the smallest stimulus, therewas a 15 percent difference between the computeddiameter and the measured diameter. The diame-ter based upon energy considerations was con-sidered the most adequate measure of size becausein the case of a stimulus as small as 3.60 minutesof arc, the eye usually responds on the basis oftotal physical energy.

The experimental data are presented in Table IIand are plotted in Fig. 10, fitted by empiricalcurves. The data represent approximately 220,000observations obtained during a period of fourmonths by a group of nine observers. (The opencircles represent experimental data obtainedunder different experimental conditions. Subse-quent reference will be made to these points inPart II.)

Two interesting aspects of the contrast sensi-tivity functions are apparent. At high bright-nesses, especially for large stimuli, contrastbecomes constant with respect to adaptationbrightness. For a 121-minute stimulus, for ex-ample, there is no appreciable change in thresholdcontrast as adaptation brightness is reduced from100 to 1 footlambert. This relation has beencalled the Weber-Fechner law.

Each of the curves shows a discontinuity atapproximately 7 X 10- footlambert. From inter-rogation, it was clear that this discontinuity

TABLE IV. Arithmetical mean threshold AB (Bo=O).

Angular subtenseof stimulus

(minutes of are) Log AB

121.0 -5.836-5.951

55.2 -5.44418.2 -4.5949.68 -4.184

-4.0563.60 -3.268

, 100 FOOT-,. LAMERTS

10

._/Eo /,^""/ I X 10'

,, ' / ,,. I X 10

X, -*606 ,0" ,#..........I X lo-3

I X 104

. .............

............... ........ IX I -O'I X 10o6

636

CONTRAST THRESHOLDS

TABIE V. Arithmetical mean threshold contrast. Stimuli brighter than surround (Part II).Angular subtense of stimulus (minutes of arc).

121.0 55.2 18.2 9.68 3.60

Log Bo Log C Log Bo Log C Log Bo Log C Log Bo Log C Log Bo Log C

-2.831 -1.208 -4.505 -0.372 -2.994 -0.308 -2.117 -0.434 -1.823 0.078-3.551 -1.031-5.134 -0.297

corresponded to a change in the nature ofscanning. Since the observers were allowed tofixate where they chose, they used foveal visionat high brightnesses and parafoveal vision at lowbrightnesses.

Interpolations from Fig. 10 are presented inTable III and in Fig. 11.

Figure 12 is presented in order to compare thedata of Fig. 10 with data obtained at zeroadaptation brightness. The basic data for zeroadaptation brightness are presented in Table IV.It is apparent that the performance of the eye isvery similar for adaptation brightnesses smallerthan 1 X 10-5 footlambert.

Precision

Analysis of photometric measurements re-vealed that each surface brightness was accu-rately measured within 4t4 percent. Estimates of-the repeatibility of the observer's response datawere obtained by computing the probable errorsof group probability functions constructed fromall the observer data in each of the experimentalsessions. The average P.E. obtained indicatedthat in 99 percent of repeat experiments the sameresponse data would be obtained within -tL8percent; in 50 percent of repeat experiments,within -L2 percent.

Inspection of Fig. 10 indicates that the experi-mental points fall on the smoothed curve within]5 percent on the average, with an occasionalpoint deviating as much as 16 percent. Theprecision of experimental data measured in thisway is in agreement, therefore, with the precisionpredicted from standard statistical measures.The over-all precision of the experimental pro-cedure was approximately h5 percent. Theprecision of the smoothed curve is approximately4A0.6 percent.

Examination of the data for individual ob-servers revealed that the average deviation from

a smoothed curve was 12 percent, with anoccasional deviation of 40 percent.

Part II

An experimental program was conducted todetermine whether stimuli darker than the ob-servation screen are equivalent to stimuli brighterthan the screen of equivalent contrast. For con-venience, stimuli brighter than the screen will beconsidered positive and stimuli darker than thescreen will be considered negative. (It must beemphasized that the definition of contrast resultsin positive values of contrast for both negativeand positive stimuli.)

In almost all particulars, the experimentalprocedure duplicated that of Part I. Specialprojection apparatus was devised to permit thepresentation of negative stimuli. A transparentslide containing an opaque spot was placed in anordinary lantern-slide projector. When the entireobservation screen was illuminated, a negativestimulus could be produced in any of eightlocations. The negative stimulus was positionedby means of a special mechanism designed tochange the position of the opaque spot in theprojector beam. In order to reduce the contrastof the negative stimulus, additional illuminationof the screen was provided by a second projector,adjusted to illuminate exactly the same area asthe first. Additional reduction of contrast wasaccomplished by illuminating the screen and theremainder of the observation room with thetroffer units.

It was necessary to produce five values of con-trast related in a constant fashion, to be used ifnobtaining probability curves in each experimentalsession. This was accomplished by inserting oneof a pair of filters of complementary transmit-tances in the beam of each of a pair of projectors.The initial output of the projectors was equated;as a consequence, their combined output was

637

H. RICHARD BLACKWELL

LOG ADAPTATION BRIGHTNESS ( FOOTLAMBERTS)

FIG. 13. The arithmetical mean of threshold contrasts computed from individualprobability curves, plotted as a function of adaptation brightness for five stimulus areas.The solid curves represent interpolations from Fig. 11.

maintained constant as the relative contributionfrom each was varied. The transparent slide andopaque spot were included in only one of theprojectors. Consequently, as the different combi-nations of filters were used, stimulus contrastvaried in a systematic fashion. For a given ex-perimental session, the proportions of screenbrightness provided by the troffer units and thepair of projectors were adjusted so that the con-trasts approximated those used in the corre-sponding experiment of Part J.

In order to change the position of the stimulus,

it was necessary to remove the stimulus from theobservation screen. Accordingly, a shutter inter-rupted the beams of the pair of projectors at theend of each six-second stimulus presentation.Removal of the stimulus reduced the brightnessof the observation screen and affected the bright-ness adaptation of the observers. Accordingly, athird projector was used to compensate for thereduction in screen brightness resulting fromstimulus removal. The output of the third pro-jector equaled the combined output of the pair ofprojectors. A single shutter arm uncovered the

TABLE VI. Arithmetical mean threshold contrast. Stimuli darker than surround (Part II).Angular subtense of stimulus (minutes of arc).

114.0 55.5 18.9 9.55 5.01

Log Bo Log C Log Bo Log C Log Bo Log C Log Bo Log C Log Bo Log C

2.022 -2.119 2.012 -2.033 2.022 -1.821 2.024 -1.699 1.073 -1.3441.914 -2.103 1.894 -2.018 1.911 -1.881 1.901 -1.712 1.066 -1.2781.035 -2.122 1.039 -2.037 1.041 -1.835 1.047 -1.667 0.115 -1.0961.027 -2.143 1.029 -2.046 1.029 -1.869 1.024 -1.641 -1.152 -0.5900.040 -2.096 0.027 -1.950 0.019 -1.740 0.070 -1.490 -1.826 -0.173

-1.029 -2.033 -1.012 -1.867 -0.949 -1.494 -1.200 -1.033-2.068 -1.611 -2.024 -1.452 -0.999 -1.520 -2.004 -0.554-2.807 -1.382 -2.798 -1.140 -1.952 -1.012-2.970 -1.325 -2.900 -1.072 -2.603 -0.636-3.190 -1.256 -3.457 -0.842 -3.042 -0.403-3.287 -1.250 -3.920 -0.696-3.546 -1.112 -4.532 -0.402-4.055 -0.932- 5.073 -0.520-5.156 -0.366-5.224 -0.375

638

I-

01

z

0

-J

-e

.,6 -__4 - -2__ I _

CONTRAST THRESHOLDS

projection lens of the compensating projector asit covered the projection lenses of the pair ofprojectors. In this way, the brightness of theobservation screen was unchanged during theremoval and production of the stimulus.

The production of contrasts approaching theupper limit of negative stimuli (+1.0) necessi-tated that only the pair of projectors illuminatethe observation screen. Illumination from thetroffer units always served to reduce the stimuluscontrast. It is apparent, therefore, that produc-tion of large stimulus contrasts was possible onlyby reduction in the relative amount of illumi-nation of the screen produced by the troffers. Thepattern of surface brightnesses in the observationroom was somewhat different for illumination bytroffers and illumination by projectors. Whentroffer illumination was used, the standardizeddistribution of brightness shown in Fig. 3 re-sulted. The use of projectors illuminating theobservation screen alone resulted in greaterbrightness of the screen relative to the otherbrightnesses of the room. With troffer illumi-nation, the brightness of the areas immediatelyadjoining the screen were 95 percent as bright asthe screen. With projected illumination, thecorresponding value was 44 percent.

Experiments were conducted to determinewhether this variation in the pattern of bright-nesses in the visual field influenced thresholdcontrast. The observation screen was illuminatedsolely by a projector. A positive stimulus incre-ment was added by a second projector. Condi-tions duplicated corresponding 'experiments inPart I except for the difference in the pattern ofbrightness in the visual field. Seven experimentalsessions were conducted, corresponding to theinstances in which the maximum variations in thepattern of brightness were required with negativestimuli. The results are presented in Table V, andare plotted as open circles in Fig. 10. It is ap-parent that the maximum variation from thestandardized brightness pattern encountered inthe experiments of this section did not influencethe threshold contrasts of positive stimuli. As afirst approximation, it can be assumed that thesame variation- in the pattern of brightnesses didnot influence the threshold contrasts of negative

presented in Table VI and in Fig. 13, representinga total of approximately 125,000 observations bya group of eight observers. It is apparent that inmost instances there is evidence that negativestimuli are equivalent to positive stimuli ofequivalent area and contrast. In the case of largestimuli and low adaptation brightnesses, how-ever, a consistent discrepancy exists. Comparisonof the threshold contrasts of the same observersin corresponding experiments of Parts I and IIindicates 20 percent lower thresholds for negativestimuli.

Part III

Preliminary experiments indicated that thesix-second exposure used in the experiments ofPart I and Part II did not represent sufficienttime for minimal thresholds. A supplementaryprogram was conducted to determine thresholdcontrasts when an indefinitely long exposure wasused. In general, the experimental procedures ofParts I and II were followed very closely.

It was found that if the stimuli were presentedin any of eight positions as in Parts I and I I,extremely long exposures were necessary forminimal thresholds. An exposure as long as 60seconds was not clearly sufficient for minimalthresholds under all circumstances. Accordingly,the method of experimentation was modified sothat substantially shorter exposures could beused. The stimulus was always presented in thesame position, in the center of the observationscreen. Orientation points were provided at thefour edges of the target at a distance of approxi-mately 2 degrees from each edge. The customaryfive stimulus contrasts were used, interspersed.with trials in which no stimulus was presented.The observers were required to respond whetherthey believed a stimulus had been shown. Theirresponse consisted of rotating the handle of theirrecording switch to one position for "yes,"another for "no." The number of positive re-sponses obtained when no stimulus was presentedwas used as the "chance" score in interpretingthe resulting probability curves.

In each experimental session, it was provedthat doubling the exposure did not increase thefrequency of correct judgments. In general, ex-

stimuli. Al posures of 15 seconds were adequate for minimumThe experimental data of this section areithresholds.

639

I. RICHARD BLACI(WELL

AROUND CLA$S \~~~~TRACO 'GRUO

/ GLASS

FIG. 14. Stimulus illuminating system.

Analysis of the data of Part I indicated thatcertain profitable changes in emphasis could bemade in a supplementary program. It was ap-parent from the data of Fig. 10 that targets bothlarger and smaller than those of Part I should beinvestigated. The data of Fig. 12 indicated thatexperimentation at screen brightnesses less than1 X 10-5 footlambert was not very necessary. InPart I, large numbers of observations were madeto determine the exact nature of the discon-tinuities in the visual functions. Sufficient infor-mation was obtained so that less emphasis wasnecessary in the supplementary experimentalprogram.

In order to produce an extremely small stimu-lus, it was necessary to develop a new apparatus.Since it was impossible to obtain satisfactoryimage definition by projection, a small stimuluswas produced by transilluminating the observa-tion screen. A section of glass rod, opticallypolished on each end, was inserted in the exactcenter of the observation screen. The front faceof the rod was mounted flush with the frontsurface of the screen. An acid-etched opal platewas mounted 0.01 inch from the rear face of therod. The opal plate served as the stimulus,baffled by means of the glass rod to a knowndiameter.

The optical system used to illuminate the opalplate is shown in Fig. 14. A balanced pair ofautomobile head lamps served to illuminate theopal so that its brightness equaled that of theobservation screen. Additional illumination, pro-ducing a brightness increment, was provided bya lamphouse mounted on an optical bench.Preceding stimulus presentations, one of fivegelatine filters was inserted (corresponding to one

of five fixed stimulus contrasts) and a shutterwas removed from the beam. The absolute levelof the five contrasts was varied by means of theinverse square law and the addition of groundglass plates and opaque diaphragms to the face ofthe lamphouse.

The brightness of the opal plate through theglass rod was always measured with a Macbethilluminometer, fitted with a lens to focus the opalplate in the cube of the photometer. It wasrecognized that a more adequate photometricprocedure would involve the computation ofstimulus brightness from a measurement of itscandlepower. A test was made which indicatedexcellent agreement between measurements madewith the alternative photometric techniques.

Investigation was made to ascertain whether ashadow around the glass rod existed, which wouldserve to reduce the effective candlepower of the

TABLE VII. Arithmetical mean threshold contrast.Stimuli brighter than surround (Part III). Angular sub-tense of stimuli (minutes of arc).

360.0 121.0 55.2

Log Bo Log C Log B Log C Log Bo Log C

1.857 -2.519 1.850 -2.596 -0.053 -2.4361.024 -2.455 1.044 -2.510 -0.994 -2.174

-0.051 -2.603 -0.052 -2.441 -1.859 -1.688-1.041 -2.296 -1.005 -2.209 -2.924 -1.149-1.883 -2.033 -1.878 -1.799-2.948 -1.558 -2.939 -1.361-3.997 -1.221 -3.969 -1.029-5.052 -0.847 -4.974 -0.569

18.2 9.68 3.60 0.595

Log Bo Log C Log Bo Log C Log Bo Log C Log Bo Log C

1.853 -2.462 1.874 -2.063 1.044 -1 .559 1.854 -0.3230.070 -2.294 -1 .023 -1.672 0.039 -1.324 1.034 -0.051

-0.984 -1.971 -1.900 -1.075 -1.887 -0.384 0.039 0.264-1 .871 -1.322 -2953 -0.157 -2.965 0.593 -1.019 0.643-2 .923 -0.655 -3.932 0.425 -1.894 1.136-4.982 0.584 -2.941 2.104

-3.957 2.756-4.999 3.397

REA3

ROD

.. K.-

640

CONTRAST THRESHOLDS

-H

z0V

-S -4 -C- I 0

LOG ADAPTATION BRIGHTNESS (FOOTLAMBERTS)

FIG. 15. The arithmetical mean of threshold contrasts computed from individualprobability curves, plotted as a function of adaptation brightness for sevenstimulus areas.

opal source. Measurements made with an inte-grating sphere and visual photometer revealedthat there was no such effect.

The experimental data of this section arepresented in Table VII and in Fig. 15, summa-rizing approximately 90,000 observations by agroup of seven observers. It is evident that theprecision of results is significantly less than inPart I and Part I I. The lower precision isattributed to the fact that the observers wererequired to search for the stimulus repeatedlyover a very small area. Under these conditions,the motivation and fatigue of the observersbecame extremely important. The curves fittedto the experimental data of Fig. 15 were em-pirically determined as the best-fitting curvesconsistent with characteristics of the contrastsensitivity functions established in Part I.

Interpolations from the smoothed curves arepresented in Table VIII and in Fig. 16.

Each curve in Fig. 16 consists partially of alinear portion representing the fact that theproduct of area and stimulus brightness, AB, is aconstant. Stimuli whose areas place them on thelinear position of these curves are effectively"point sources." The point at which each curvedeparts from linearity corresponds to a funda-

mental property of the human eye. "Criticalvisual angle" is defined as the angle at which therelationship: area X brightness = a constantceases to exist. "Critical visual angle" is plottedas a function of adaptation brightness in Fig. 17.The shape of this function is similar to that of thefunction relating threshold contrast and adapta-tion brightness.

Interpolations from Fig. 16 are presented inFig. 18. The curves for most contrasts showdiscontinuities, indicating the change from fovealto parafoveal vision. For high contrasts, thecurves are parallel, indicating that area X bright-ness = a constant.

ACKNOWLEDGMENTS

The dependence of the success of the experi-mental program upon Professor Arthur C. Hardycan scarcely be overemphasized. As Chief, Section16.3, NDRC, he was responsible for appreciatingthe need for the research, for initiating bothadministrative and technical aspects of the pro-gram, and for maintainingclose contact withexperimental results and with laboratory prob-lems encountered in obtaining them. Because hewas willing to concern himself with the bother-some details of the research more completely than

641

H. RICHARD BLACKWELL

v0

I.0

(n

-

z

-

zU)0-J

LOG LIMINAL CONTRAST

FIG. 16. Interpolations from Fig. 15. Each curve represents the relation betweenthreshold contrast and stimulus area for a given adaptation brightness.

TABLE III. Log (arithmetical mean threshold contrast). Interpolations from Fig. 15.

Angular subtense Boof stimuli

(minutes of arc) 1000 100 10 1 1 X100< 1 X1- X0-3 I X10- 4XO-

360.0 -2.566 -2.566 -2.558 -2.478 -2.272 -1.959 -1.519 -1.205 -0.866121.0 -2.561 -2.561 - 2.553 -2.464 -2.212 -1.818 -1.324 -0.967 -0.56255.2 -2.547 -2.547 -2.538 -2.428 -2.131 -1.666 -1.096 -0.686 -0.23918.2 -2.460 -2.460 -2.428 -2.276 -1.914 -1.341 -0.614 -0.094 0.4449.68 -2.339 -2.328 -2.241 -2.051 -1.672 -1.041 -0.208 0.396 0.9783.60 -1.812 -1.721 -1.569 -1.322 -0.924 -0.300 0.622 1.253 1.8370.595 -0.383 -0.248 -0.060 0.196 0.607 1.246 2.179 2.813 3.397

could have been reasonably expected, many ofthe unusual features of the research techniquecan be attributed to him.

Dr. S. Q. Duntley, Section Technical Aide, andthe members of the Section, especially ProfessorEdwin G. Boring, contributed invaluable pro-fessional advice to the general conduct of theresearch.

The professional staff employed temporarily bythe Tiffany Foundation to conduct the researchprogram varied considerably during the period ofexperimentation. Without exception, members ofthe staff devoted themselves diligently to theprogress of the program. Special acknowledgmentmust be made to Dr. Helen M. Richardson for herearnest and often inspired work with the psycho-physical aspects of the program, and to Mr.William F. Little of the Electrical Testing Labo-ratories, New York, with whose aid the photo-metric procedures were developed.

Of the many assistants, without whom theprogram would have been impossible, specialmention should be made of Mr. B. S. Pritchard,

FIG. 17. "Critical visual angle" as a function of adapta-tion brightness. The area under the curve represents"point sources."

642

CONTRAST THRESHOLDS

m.010 L o I 03

_t3 >. \ \_

LOG ADAPTATION BRIGHTNESS (FOOTLAMBERTS)

FIG. 18. Interpolations from Figs. 15 and 16. The relation between stimulus areaand adaptation brightness for stimuli of various contrasts.

Mrs. S. C. Taplin, Miss M. J. Bernstein, Miss I.T. Bell, and Miss Jane Tapley.

Although not present during the conduct of theexperiments reported herein, Dr. Helen Peak,Mr. Carl Foss, and Dr. Parry Moon wereinstrumental in designing the experimental appa-ratus and procedures for the earliest experiments.Some of the original apparatus and procedureswere utilized in the reported experiments, whereas

-others were adapted.

SUMMARY

Experimental data are presented representingapproximately 450,000 responses made by trainedobservers under laboratory conditions. Contrastthresholds are presented for stimuli brighter anddarker than their background, and for two valuesof stimulus exposure. In each case, wide varia-tions were studied in the parameters: stimu-lus contrast, stimulus area, and adaptationbrightness.

W

0

AdI-

Z

Ad9

AD

0-J

643