Transfer Function of an Annular Aperture in the Presence of Spherical Aberration

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Transfer Function of an Annular Aperture in the Presence of Spherical AberrationRICHARD BARAKAT AND AGNES HOUSTON

Itek Corporation, Lexington, Massachtsetts 02173(Received 11 December 1964)

The transfer function of an annular aperture in the presence of spherical aberration and defocusing isevaluated. The technique employed is the sampling method developed in a previous paper. The Mar6chalaberration-balancing theory is extended to annular apertures. Representative numerical results are discussed.

1. INTRODUCTION

THE transfer function of an annular aperture inTincoherent light was obtained independently bySteel' and O'Neill.2 The analysis of O'Neill was confinedto that of an aberration-free system in the Fraunhoferplane and was achieved by actually taking the Fouriertransform of the point spread function. Steel, in a moredetailed treatment, determined the effect of smallaberrations (0.9 (thin-ring aperture)in the sense that a large number of sampling points(over 50) are required to achieve moderate accuracy.In fact, Rayleigh7 showed that an aperture consisting

4 Z. Kopal, Numerical Analysis (John Wiley & Sons, Inc., NewYork, 1955).

6 C. G. Steward, Tle Symmnetrical Optical Systemi (CambridgeUniversity Press, Cambridge, England, 1928).

6T. Asakura and R. Barakat, Oyo Butsuri 30, 728 (1961).7 Lord Rayleigh, Collected Papers (Cambridge University

Press, Cambridge, England, 1902), Vol. 3, Article 148.538

17OLUME 55, NUMBER 5 MAY 1965

TRANSFER FUNCTION OF ANNULAR APERTURE

of a narrow rim has a point spread function given by

t (v) = Jo2 (v) (4)for the aberration-free case. Since Jo(v) has the asymp-totic behavior

Jo(v)- (2/7rv)' cos~v- (7r/4)], (5)

then 1(v), for this case, varies as O(v-'). Contrast thisto the behavior of t(v) for a clear aperture which yields 8

A .4 .8 12 16(6) NORMALIZED SPATIAL FREQUENCY

This leads to the conjecture that t(v) behaves ast (v) o 0 (V+ e) r (7)

for an annular aperture. In any case it is now obviousthat the asymptotic behavior of the point spread func-tion plays a critical and limiting role.

The gross effect of an obscuration on the transferfunction of an aberration-free system is to decrease thelow-frequency response and provide an almost constantresponse in the medium-frequency region. This isillustrated in Figs. 1 and 2. Note how the effect ofdefocusing is merely to lower the level of the responsein the medium-frequency range. The high-frequencyresponse increases as e is made larger; O'Neill madedetailed calculations for the aberration-free case in theFraunhofer plane (W2= 0) and showed the remarkableincrease. However, this phenomena is less pronouncedwhen defocusing is present as witness Fig. 2. Thissituation is entirely changed when spherical aberrationis included.

3. OPTIMUM-BALANCED WAVEFRONTS

One of the most important problems in the diffractiontheory of aberrations is that of balancing the individualaberration coefficients in such a manner as to achieveoptimum image quality. One approach derived byMar6chal9 is to minimize the mean square deviation ofthe wavefront and hence maximize the Strehl criterion.The mean square deviation of the wavefront Eo for an

1.0

z0 .8

-)z

LU_

C,)LIJ

0.2

04 .8 1.2 1.6 2.0

NORMALIZED SPATIAL FREQUENCY

FIG. 1. Transfer function for aberration-free annular aperturewith obscuration e=0.4 for amounts of defocusing correspondingto: (A) W 2 =0, (B) W2=0.25, (C) W2=0.50, (D) W2=0.75.

8 R. Barakat and A. Houston, J. Opt. Soc. Am. 53, 1244 (1963).9 A. Mar6chal, Rev. Opt. 26, 257 (1947).

FIG. 2. Transfer function for aberration-free annular aperturewith obscuration re=0.6 for amounts of defocusing correspondingto: (A) W2 =0, (B) W2 =0.25, (C) W2 =0.50, (D) W2 =0.75.

annular aperture with a rotationally symmetric aberra-tion function is:

2 r'Eo r2I [W(p)]2pdp(1 e2) Je

4 1 2

In order to illustrate the main features of such ananalysis, let W(p) be a polynomial of the simple form

W= W2p2+W4p4+ WVp6. (9)Substitution of (9) into (8) yields the following ex-pression for Eo:

(1 -2) -(6) (4)21 [(10) (6)2 1Eo-F= --- w2

2+ - 1W422 L6 8(2)1 L 10 18(2)1

(14) (8) (12) (6) (8)114 32 (2) 6 12(2)

r(8) (4) (6) r(10) (4) (8)5+L- W2W4+ - ,_ jW2W6, (10)

4 6(2) 5 8(2)where

(n)= 1-"n. (11)We now seek to minimize F with respect to the un-

controllable aberration coefficient (i.e., the highest

TABLE I. Wavefront coefficient ratios for optimum-balancedfifth-order spherical aberration as a function of e.

e W2/V 6 W4/w60 0.6000 -1.50000.1 0.6181 -1.51500.2 0.6728 -1.55980.3 0.7669 - 1.63500.4 0.9032 -1.73990.5 1.0875 -1.87500.6 1.326 -2.0400.7 1.627 -2.2360.8 1.98 -2.45

z0H

D.LS

LU

zMH,

2.0

539May 1965

R. BARAKAT AND A. HOUSTON

z0.8

U-

NORMALIZED SPATIAL FREQUENCYFIG. 3. Transfer function for optimum-balanced third-order

spherical aberration of amount W4 =1.0 for obscurations: (A)e=0.4, (B) e=0.5, (C) 6=0.6, (D) E=0.7, (E) e=0.8.

coefficient in the expansion of W)Following the usual procedure,derivatives of F with respectaberrations:

at a fixed value of e.we take the partialto the controllable

OF/OW2 1= 0, (j= 1, 2, *.., n- 1), (12)given that W2n is the uncontrollable aberration coef-ficient. The final result is:

OF F(6) (4)21 r(8) (4)(6)1-= -- 12+ --- I T 4OW2 3 4(2)i L 4 6(2)i

(10) (4)(8)1+ -~ W6= O.

- 8(2)-OF (+) (4)(6)] (to) (6)2;

= - W2+ - - W4aW4 -4 6(2) - -5 9(2)-

r(12) (6) (8)1+ -~ W6= 0. (13)

-6 12(2)-As the first case, let TV consist of only TV4 and TV2.

Solving the first equation for the ratio W2 /W4 ,

W2 [(8) (4)(6)1W4 L4 6(2) -

/[(6) (4(4)] (14)

TABLE III. Strehl criterion of an annular aperture possessingfifth-order spherical aberration for: (A) optimum-balancedwavefront with WI=3.0, (B) regular wavefront with W 6=3.0.

e A B

0 0.893 0.8930.1 0.869 0.8680.2 0.834 0.8260.3 0.770 0.7440.4 0.674 0.6280.5 0.550 0.5000.6 0.406 0.3680.7 0.260 0.233

the usual balancing relation

W2=-TV4.In the second case, let W consist of W2, W4, TV6.

This requires the solution of both equations in (14).Although an explicit solution can be achieved, theactual values were obtained by numerical techniques.Wavefront-coefficient ratios are listed in Table I forrepresentative values of e. If intermediate values arerequired then interpolation can be employed. Note thatfor values of e up to 0.2, the ratios vary only a fewpercent from their clear-aperture values. This is alsotrue for third-order balancing. Of course, e=0.2represents only 4% of the area of the aperture!

Higher-order spherical aberration can be included inexactly the same manner, although the complexity ofthe analysis increases very rapidly. Another point tobe considered is the usefulness of optimum balancing;do we really gain much by this procedure? The answeris in the affirmative as is demonstrated in the nextsection.

4. NUMERICAL RESULTS

In view of the almost unlimited combinations ofindependent parameters, we restrict ourselves toillustrating the main results of the previous section.

The Strehl criterion t(0) as computed from (2) islisted in Tables II and III in order to demonstrate theadvantages of optimum balancing. Incidentally, thecolumns marked B refer to wavefronts optimum

(15)

When 6=0 (clear aperture), then (14) degenerates to

TABLE II. Strehl criterion of an annular aperture possessingthird-order spherical aberration for: (A) optimum-balancedwavefront with W4 =1.0, (B) regular wavefront with W4=1.0.

e A B

0 0.800 0.8000.1 0.799 0.7910.2 0.795 0.7900.3 0.782 0.6960.4 0.753 0.5970.5 0.700 0.4680.6 0.618 0.3310.7 0.503 0.2080.8 0.387 0.108

2CU

zU-

U,2n'I

XaI-_

4 .8 12iNORMALIZED SPATIAL FREQUENCY

FIG. 4. Transfer function for optimum-balanced fifth-orderspherical aberration of amount W6=3.0 for obscurations: (A)fE=0, (B) e'=0.3, (C) E=0.5, (D) t=0.7.

540 Vol. 55

TRANSFER FUNCTION OF ANNULAR APERTURE

balanced only for the clear aperture. The B in Table II 2.5. This is easily explained and is due to the obscura-refers to the wavefront

W(p) =W4 (p4 -p2), (16)and B in Table III implies

W(p) = W6(p6-2P4+ p2). (17)In both cases, there is very little difference in t(O) forsmall obscurations. As e increases, the difference alsoincreases. It is interesting to note how rapidly theColumn B in Table II decreases as e increases whencompared to Column A. At e=7, the difference inStrehl criterion amounts to a factor of approximately

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

tion cutting out the wavefront where it has its smallestvalues. Since there is only one degree of freedom, thereis almost no possibility for corrective action. The situa-tion is less pronounced in Table III. In fact, optimumbalancing does very little. Here there are two degreesof freedom and this is sufficient to cover correctiveaction.

ACKNOWLEDGMENT

We wish to thank Elgie Levin for her help duringvarious stages of this work.

VOLUME 55, NUMBER 5 MAY 1965

Temporal and Spatial Visual Masking. I. Masking by Impulse FlashesGEORGE SPERLING

Bell Telephone Laboratories, Incorporated, Murray Hill, New Jersey 07971(Received 26 October 1964)

Masking is defined as the change in threshold energy eT*(r) of a test stimulus T induced by a maskingstimulus M of energy eM as a function of the relative time T of occurrence. Masking is maximum when T andM occur simultaneously. A slight decrease in threshold for tests preceding the masking impulse by about0.1 sec was explained as an alteration in appearance of the subsequent masking flash by a "subthreshold"test flash. Impulse-contrast threshold eT*/eM was investigated for masking impulses M of seven differentenergies superimposed on five backgrounds B. The increases in test threshold caused by M and by B werefound to be independent and a modified Weber's law (adjusted contrast threshold Ca*0.1) held approxi-mately. This conclusion was supported in a supplementary investigation of Ca* using a category-rating-scalemethod.

Impulse masking results were applied to predicting the masking peak at the onset of a long flash by treat-ing the first 60 msec as an impulse. The lowering of thresholds of tests delayed in a long masking flash impliedother detection mechanisms (e.g., temporal resolution). Theoretical predictions accounted for 94% and 97%of the variance in two relevant experiments, correctly predicting the effect of masking-flash duration and ofbackground intensity.

In both steady and intermittent light, masking is attributed primarily to fast processes (time constant

GEORGE SPERLING

general introductory remarks and by a complete methodsection intended also to serve subsequent reports.

DefinitionsIt is well known that the minimum energy an ob-

server needs to detect a visual stimulus depends uponwhat else has been, is, and will be present in his visualfield. The stimulus he is trying to detect may be calledthe test T (or test field, test patch, etc.). We may denotea visual stimulus other than the test either as a maskingfield M (if it varies in time), or as a background B(if it is steady). The word masking is used because lightother than the test in the visual field usually causes anincrease in threshold for the test; that is, it masks it.Thus visual masking refers to a phenomenon observedin experiments involving two visual stimuli. The visualmasking experiment is designed to determine justwhat changes in test visibility are induced by a par-ticular masking stimulus.

Masking StimulutsA monocular masking stimulus M is described by

giving its luminance IM as a function of four variables:time I, wavelength X, and spatial location (xy) or(r,O). To emphasize the dependence of IM on thesevariables we may write 1M(Xy,t,).

Test

The test T similarly may be denoted lT(X,Y,t-7,X).Here r is the time delay of the test with respect tothe masking stimulus.

BackgroundA background B usually is an unvarying field of

steady luminance tB(x,y,X). It is useful to designate Bseparately from M because it enters into computationsdifferently.

Pre-adaptation "backgrounds" are time-varyingbackgrounds. In all of the work to be reported, pre-adaptation "backgrounds" are turned off 1 sec orlonger before the onset of M but are assumed to beequivalent to continuous backgrounds'4 210 2 during theinterval of interest, thus the appellation "background."

Test Energy

In masking experiments, interest usually is directedat how the areal density of luminous energy of thetest

eT= f f lTdtdXvaries as a function of other variables. With very brief

20 L. L. Holladay, J. Opt. Soc. Am. 14, 1 (1927).21 B. H. Crawford, Proc. Roy. Soc. (London) B123, 69 (1937).22 W. A. H. Rushton, J. Opt. Soc. Am. 53, 104 (1963).

stimuli whose energy is spread uniformly over aspatial area, it is more convenient to consider theareal density of luminous energy e at each point thanit is to consider total energy. The units of areal densityof luminous energy used here are ft-LXmsec and thequantity is abbreviated to "energy" when no confusionarises.

Test ThresholdAn asterisk superscript is used to denote a threshold

quantity. Experimentally determined values of testthreshold energy are designated as eT*. The value ofeT* depends mainly on the masking stimulus M (allx, y, t, and X), on T, on who the observer 0 is, and onthe criterion k (i.e., "just barely visible," "equal indetectability to a reference standard," etc.). Otherfactors (e.g., motivation, sequential-response depend-encies, etc.) will not be specifically denoted. Thus wemay write eT(M; T; 0; k).

Threskold Masking ResponseIn the usual temporal-masking experiment, only

test energy eT and the time delay T between occurrenceof the test and masking stimulus are varied. The varia-tion of threshold eT with T [abbreviated eT*(r)] isdetermined. In the temporal- and spatial-maskingexperiment the spatial location of T relative to M alsois varied and eT*(r,x,y) is determined. The entirefunction eT* may be called a threshold masking response(to the masking stimulus M).

Designation of Inmpulse Masking FlashesThe present article deals with a variety of impulse

masking flashes superimposed on various backgrounds.These have luminances representable by 'M(x,y)3(t)and IB(x,y), where 5(t) is the unit impulse. An impulseM is most conveniently described by its areal densityof luminous energy ("energy")

em (xy) f lM(Xjy)b (t)dt.In all the experiments to follow, the masking and

test stimuli are periodic in time. In each case, theperiod (usually 1 sec) is explicitly stated in the text butis omitted from the notation in order to keep it simple.

Three Principles of the Masking ProcedureThe first complete temporal-masking experiment was

conducted by Crawford.' He presented a circular patternof light (masking stimulus M) to foveal view for 524msec. The threshold luminance for a smaller, spatiallysuperimposed 10-msec flash of light (test T) wasdetermined for each of various times of occurrencebefore, during, or after M. In this way, thresholdluminance-thereby energy-of the test was obtained

542 Vol. 55

VISUAL MASKING BY IMPULSE FLASHES

as a function of time [threshold masking responseeT*(r)].

Crawford found that the peak of the thresholdmasking response occurred when the onsets of the testand masking stimuli coincided approximately. He alsonoticed that the masking stimulus masked tests whichpreceded it by as much as 100 msec. Subsequent toCrawford, a number of investigators have used moreor less similar procedures to determine complete-"or partial8 -'9 masking responses. Three methodologicalimplications of these procedures are discussed below.

SamplingThe method of threshold determination is a sampling

method. This is not obvious in Crawford's experiment,because one test flash occurs with each masking flash. Aslong as masking flashes are widely separated in time,this one-to-one relation is not a drawback. However,when masking flashes occur at a rapid rate (e.g., 20flashes/sec) it may no longer be desirable to have onetest flash paired with each masking flash. In this case,the time between successive test flashes could bechosen to meet a different criterion, namely that suc-cessive test flashes do not appreciably interact witheach other. Each test flash occurs at the same phase Trelative to the masking flash with which it is paired (forexample, exactly at the onset), but this pairing needoccur only once in every n masking flashes.'2, Asampling procedure permits us to determine theresponse to any kind of masking stimulus that can berepeatedly presented to the eye. In particular, it isdesirable to use "infrequent" sampling in order tomeasure responses to rapidly flickering masking stimuli.

Impulse in TimeThe test flash should be "instantaneous." In visual

masking, "instantaneous" may mean several msec orshorter in duration. A very brief flash is called animpulse. The purpose of using an impulse test flash isprimarily for simplicity. If T is of long duration, thenthe threshold energy eT* for this flash is closely relatedto an averaged sensitivity for impulse tests during thewhole time spanned by the longer test flash.2 4 It iseasier to interpret thresholds obtained with impulses,particularly when the relation between long and shorttest flashes is not known exactly.

The masking stimulus of course also may be animpulse. In masking experiments to be reported here,the response to impulse masking stimuli is determinedwith impulse tests.

Point in SpaceThe third consideration is the effect of area of the

test stimulus. Just as temporal effects are sampled by

23 G. Sperling, J. Opt. Soc. Am. 53, 520 (1963).24 G. Sperling, presented at the Psychonomic Society, Washing-

ton University, St. Louis, September 1962.

an impulse in time, spatial effects may be determinedby an "impulse" in space; i.e., a point. The thresholdfor a spatially extended source should be predictablefrom the threshold at each point of the extended area.

By using a test stimulus of very small area to approxi-mate a point source, it is possible to find the responseto any spatial pattern of masking stimulus at eachretinal location. For example, T may be located inside,at a boundary, or outside the area stimulated by M.At each spatial location, the response to the maskingstimulus eT*(x,y,t) is determined as a function of time,using infrequent sampling if necessary. Formally,there is a close analogy between the spatial- and thetemporal-masking experiment.

These three considerations show that it is possibleto measure a threshold masking response to any spatialor temporal distribution of light on the retina (maskingstimulus). In general, this requires the use of a samplingmethod with an impulse point source. In the experi-ments to be reported, the three principles are used tomeasure responses to a variety of impulse maskingstimuli. All the experiments are limited to short-termeffects, less than about 1 sec in duration.

So far, we have assumed that the observer's task wasto detect a patch of light, masked by flashes of light.For every such experiment there is a complimentaryexperiment in which the observer's task is to detect apatch of "darkness."25 This variation will be explicitlyconsidered. Certain other relevant variables, such as theeffect of peripheral stimulation and variations inwavelength are not considered in great detail, althoughthe procedure easily can be generalized to cover thesecases.

METHOD

ApparatusTachistoscopes

The experiments were conducted over a period of5 years. Three different sets of apparatus, each havingcertain advantages over its predecessor, were used topresent stimuli to subjects. These devices (tachisto-scopes)26 all used a similar principle to permit normalmonocular or binocular viewing of the visual stimuli.By means of partially reflecting mirrors, two or threeseparate stimulus fields were optically made to appearsuperimposed2 7: a masking stimulus, a test, and, whenpresent, a background field which was intended pri-marily to regulate the average light flux reaching theeye. Except in one instance, viewing was monocular.Viewing distance was varied from 16 to 42 in. Fieldsizes are given in terms of visual angle.

Two different kinds of light sources were used:argon flash lamps and fluorescent bulbs. The argon gas

25 G. Sperling, J. Opt. Soc. Am. 52, 603 (1962)."6 A. W. Volkmann, Sitzber. Kg1. Sachs. Ges. Wiss. (Leipzig),

Math.-Phys. 11, 90 (1859).27 R. Dodge, Psychol. Bull. 4, 10 (1907).

May 1965 543

GEORGE SPERLING

ment for transmitted light. Any light source may beused with any field. When only two fields are used, thepartially reflecting mirror PM1 is removed. Intensity ofthe test field usually is under continuous control of theobserver by means of a hand switch, which operatesthe optical wedge.

Fluorescent LampsA large number of fluorescent lamps were tested for

their ability to produce rectangular pulses of whitelight. The Sylvania Super Deluxe Cool White (SDCW)lamp was selected. Figure 2 shows the circuit used toobtain simultaneous square waves from two of theselamps. The circuit supplies regulated dc to the lampswhile the timing relay is closed. The current is con-trolled by the 300-V source and by the variable resist-ance R. The duration is controlled by a timing circuitwhich opens and closes the relay. With WE 291 mercury-wetted relays, operating times of one msec and longerare possible.

Figure 3 shows oscilloscope traces of the light outputof these lamps as measured by an RCA type 934vacuum photocell through a Corning #3486 yellowfilter, which combination has maximum sensitivity atabout 545 nm. Figure 3 shows that the SDCW lampsproduce constant pulses of light with a duration of 5msec as well as pulses of 50 msec. Comparable results

+550 V

+100 TO 300V DCREG, 250 -A

TIMER

>I M

FIG. 1. Schematic diagram of a three-field tachistoscope. Sub-scripts refer to the individual stimulus fields. ALS, adjustablelight shield; FL, fluorescent lamp (end view); FM, front-surfacemirror; L, gas-discharge flash lamp; LS, light shield; NDF,neutral density filter; R, reflecting surface; S, stimulus field; W,adjustable neutral density logarithmic wedge; W', balancingwedge.

discharge lamps generated flashes of light less thanT-0 msec in duration. Fluorescent lamps generatedsquare waves of light of 1-msec duration and longer,as well as steady light.

Figure 1 illustrates schematically the location of thevarious elements in a three-field tachistoscope. Thepartially reflecting mirrors (PM 1, PM 3 ) opticallysuperimpose the three fields. The reflections are verticalrather than horizontal so that the optical path foreach eye will be more nearly equivalent.

Fields may be viewed either by transmitted or byreflected light. The test field Si normally is viewed bytransmitted light from a gas discharge lamp. Field S2illustrates the arrangement of fluorescent lamps forviewing stimuli by reflected light; field S3, the arrange-

RELAY WE-291A

I WE-426A I

0.021 F1 117ACJX

L----------------- - ------- I-9 V DC (FLOATING)FILAMENT SUPPLIES

L--------------FIG. 2. Electrieal circuit for operating fluorescent lamps

to produce rectangular pulses of light.

S2EYE I

FL3QQ_~R

LS

14 WFLUORESCENr

544 Vol. 55

L',


are obtained for shorter and longer times and at allother regions of the visible spectrum.

Over a range exceeding 10 to 1, the light output isnearly proportional to the current with little colorchange. The linear range of variable intensity wassupplemented with neutral density filters.

Gas-Discharge LampsTwo similar flash lamps are used, GR Strobulux

648A and GR Strobolume 1532C. Each of these lamps,when set to give flashes of maximum intensity, pro-duces bluish-white light of which 90% is confined to aduration less than about 0.04 msec. Less intense flashesare even shorter. Usually, Kodak color-balancing filterswere used to minimize color differences due to differentlight sources or light paths.

Photometric Calibration of Impulse FlashesImpulse energy is determined by a split-field match

of a surface illuminated by the gas-discharge lamp(impulse) and a surface illuminated to a known lumi-nance by a fluorescent-lamp flash of 5.00 msec duration.The impulse flash is adjusted to occur during the middleof the 5-msec flash (see Fig. 4). In this way, the areailluminated by a brief flash of unspecified waveform ismatched to a known luminance and duration, theequivalent energy e being computed in ft-LXmsec.

The calibration match does not depend upon theparticular duration of the fluorescent lamp. Longer andshorter flashes give the same e if the impulse is centeredin the longer flash. The calibration match is independentof background luminance, the level at which the matchis made (at moderate energies), and slight color differ-ences between fields that sometimes prevent the dis-appearance of the boundary. However, a constant errorwhich depends on geometry may occur if the split-field match is used with small test fields. The day-to-dayrepeatability of the match is about 5%. The split-fieldmethod of calibrating stimuli illuminated by gas dis-charges was not used* during some of the earlierexperiments.

TimerElectronic, phantostron-type2 8 timers are used to

control all time intervals, e.g., the duration of lightflashes and the times between various flashes. Forexample, the duration of a 5-msec light flash can beset to an accuracy on the order of microseconds.Generally, short time intervals are set to an accuracy of0.05 msec; it is not considered necessary to set longintervals more accurately than 0.1%.

Monitoring and CalibrationBy means of photocells, every stimulus presentation

is displayed on a calibrated cathode-ray oscilloscope.28 D. Sayre, M. I. T. Radiation Laboratory Series, 19 (McGraw.

Hill Book Co., Inc., New York, 1949), p. 195.

5 msec 50 msec

FIG. 3. Oscilloscope traces of light pulses produced by SylvaniaSDCW, 14W fluorescent lamps. Ordinate is the same for eachtrace; the time base has been reduced by 1OX for right figure.The slight 60-cps ripple in right figure is an artifact.

Critical time intervals are continuously monitored withan electric counter.

Neutral density filters and the wedge unit arecalibrated for density with the fluorescent light beingused. Transmittance of the neutral filters as a functionof wavelength is obtained with a Beckmann spectro-photometer. Mathematical and experimental checksshow that the filters are sufficiently neutral so that forpractical purposes they have the same density for allof the white light sources used.

Because of the construction of the tachistoscopes,absolute luminance levels for the various stimulus fieldsare measured with a Spectra brightness meter.29 Themeter was originally calibrated against a Macbethstandard and a Spectra standard, subsequently againsta standard lamp obtained from the National Bureau ofStandards. Absolute light levels are to be regarded asapproximate, but probably within 25%.

ObserversSix employees of the laboratories served regularly as

observers for periods ranging from several months tothree years. Data obtained in the first ten sessions or sousually were not used. Occasionally, inexperiencedobservers were recruited from among laboratorypersonnel to check specific points.

Psychophysical MethodMethod of Adjustment

Preliminary experiments indicated that data obtainedby the method of limits were considerably more variablebut not otherwise different from data obtained by themethod of adjustment. The method of constant stimuli

FLUORESCENT LAMP 5MSEC

STROBOLUME

FIG. 4. Photometric calibration of gas-discharge lamps. Thegas-discharge lamp illuminates the disk (illustrated at right)while the fluorescent lamp illuminates the concentric annulus.The time relation between the two flashes is illustrated at left.

29 Photo Research Corporation, 837 North Cahuenga Blvd.,Hollywood, California.

May 1965 545

mM% .M i; Fa

GEORGE SPERLING

is too time-consuming for gathering the necessaryamount of data. The method used in most experiments,therefore, is the method of adjustment. In this method,the observer is given continuous control of one parame-ter in the stimulus presentation (usually the energyof the test) and asked to set this parameter so that thetest spot is "just barely visible." With experience,observers develop a stable criterion of "just barelyvisible" and learn to make consistent settings within areasonable time. Bracketing (varying the parameterboth above and below its final setting) makes theprocess of adjustment very similar in practice to anefficient method of limits.

Sequential ProceduresTwo procedures are used to determine the amount of

data to be obtained. (a) In any given condition, theobserver makes two consecutive settings. If thesediffer by less than a prescribed amount (usually 23%,i.e., 0.1 log units), he progresses to the next condition.If not, he is required to make a third setting. If thethird does not fall between the first two, he is requiredto make two more settings. (b) The condition is thenrepeated in subsequent sessions until the experimenteris satisfied that a reliable mean (for all sessions) hasbeen reached.

In determining the mean, only the average thresholdobtained in each session is used, whether it is the meanof two, three, or five settings.

For practiced observers, two sessions (four or fivesettings) usually are sufficient. However, when thedifference method is used to obtain small differencesbetween large quantities, as many as ten sessionsoccasionally are necessary. The sequential methodscreate an incentive for careful settings because theexpected number of repetitions increases rapidly as afunction of the average error.

Pupil SizeNo direct attempt is made to compensate for varia-

tions in pupil diameter. There are a number of reasonsfor believing that pupillary variations do not influencethe main results. (1) Most experiments are conductedwith only slight variations in the average amount oflight reaching the eye during successive seconds. Thisis accomplished by means of large continuous (orfrequently repeated) background fields. (2) The ob-server is required to look at the stimulus until a "steady-state" level of light adaptation has been reached beforehe makes a setting. The average pupil aperture com-pensates for only a fraction of a change in averageluminance. (3) Within a particular experiment, thetime intervals between flashes are short (severaltenths of a second) compared to the response time forthe pupil. (4) In masking experiments, pupil fluctuationis a second-order effect because changes in steady-statepupil size affect both the masking and test stimulus.

Thresholds are reproducible from day to day and frommonth to month. The disadvantages of uncontrolledpupil size are offset by the naturalness and convenienceof ordinary viewing and by the reproducibility of theresults.

MASKING BY IMPULSE FLASHES

In physical systems the impulse response of thesystem is defined as the output of the system when theinput is an impulse. The impulse response has specialsignificance for the analysis of the system, particularlyif the system is a linear one. In a linear system it ispossible, from measurement of the response to a singleimpulse, to calculate the response of the system to anyother input whatsoever.

By analogy, in these experiments, the fovea isstimulated by a very brief masking flash. The maskingflash may be considered as an impulse "input" to theeye. The threshold for a brief test flash is then measuredwhen it occurs at various times before and after theimpulse masking flash. The data which describe thechange in test threshold as a function of the time ofoccurrence of the test (threshold masking response)may be considered the "output" of the eye in responseto a stimulating impulse; i.e., an impulse response.

If the relation between masking stimulus (input, IM)and threshold masking response (output, eT*) werelinear, then the one experiment described above wouldsuffice to predict all other temporal-masking experi-ments using an identical spatial arrangement of thestimuli. But, the original data of Crawford5 are suf-ficient to reject the linear hypothesis. They show alarge relative peak in threshold at the onset of a maskinglight but not the required symmetrical dip in thresholdat light termination (see, for example, Fig. 5).

To analyze a nonlinear system, it is necessary toknow the impulse response. Knowledge of impulseresponse is particularly useful when parameters of thesystem vary with time (e.g., adaptation) because thesevariations are minimal during impulse stimuli. Maskingby impulses also provides a link between temporal-masking experiments and measurements of contrastthresholds. The zero point of the impulse response(simultaneity of masking and test impulses) correspondsto the contrast threshold in a brief flash. Its relation-ship to contrast will be considered in Exp. 5.

1. Response to the Pre-Adaptation FieldA 250-msec flash was used in some experiments as a

pre-adaptation background. Repeated at 1 cps, thisflash supplies more light to the eye than the otherstimuli and thereby it-and not the masking stimuli-determines the average light flux. Since the response tothe 250-msec flash itself is of only secondary interest,it is desirable to determine in advance what changes inthreshold may be expected because of exposure to thepre-adaptation background.

546 Vol. 55


ProcedureA circular masking field of 1.380 alternately was

illuminated to 50 ft-L for 250 msec and extinguishedfor 750 msec. The exposure was repeated once per sec.

The test field was a disk, 0.360, concentric with themasking field.30 It was illuminated for about 0.04msec-at a time fixed relative to the masking flash-once per sec. By the method of adjustment, the subjectdetermined the intensity of the test flash for which itwas just visible, for each fixed time r relative to themasking field. The physical arrangement of the stimuliis indicated at the bottom of Fig. 5. Viewing wasbinocular.

ResultsTypical results obtained by a practiced observer are

shown in Fig. 5. Each point eT*(r) is the average offour (or more) settings made by the sequential methodin two sessions. The data show four phases: (1) in thedark period of the cycle the threshold is low and nearlyconstant, (2) in the first few msec after onset of themasking flash, the test threshold is at a peak, (3) duringthe remainder of the light period it drops to a lowervalue, (4) in a few hundred msec after the light isturned off, test threshold falls to the dark value. Theshape of the curve is similar to that which Crawford5obtained with a 524-msec masking flash and a 10-sectest.

Rapid changes in threshold are confined to an intervalfrom about 50 msec prior to onset of the masking fieldto about 200 msec after its termination. For theremaining 500 msec of the cycle, the threshold changesonly slowly. In subsequent experiments, the impulsemasking flash is delivered to the eye during the 500-msec "quiescent" period.

2. Masking by Impulse Flashes ofThree Different Energies

ProcedureA pre-adaptation background B subtending 9.31,

luminance of 41 ft-L was exposed for 250 msec, onceper sec.3" This field stabilized the total amount oflight reaching the eye per second. B provided 10 250ft-LXmsec, much more than any other stimulus usedin the experiment except the most intense maskingflash. The pre-adaptation background therefore isresponsible for most of the long-term light adaptationin this experiment.

31 The test stimulus in this and subsequent experiments, thoughsmall, definitely is not a point source. As spatial position is notvaried and as there are no boundaries near the test, it is probablethat the observed test-threshold changes are quite similar (thoughnot exactly equivalent) to those that would have been observedwith a point test. Preliminary observations support thisassumption.

31 The pre-adaptation field used in Exp. 2 is larger than the oneused in Exp. 1, but as both are substantially larger than the test,their masking effect is similar (see for example, Battersby et al.t).

-a-WLI

CL-'L2I -u 20

0-J

( - TEST (0.360) a .

I III0 - 250 o500 t750(-250) 0

TIME OF ONSET OF TEST IN MILLISECONDS

FIG. 5. Masking response eT*(r) to a 250-msec flash. Lowerfigure illustrates procedure. First traces indicate time sequence ofmasking stimulus IM (t), lowest trace indicates test IT (t- T). Thearrow and broken baseline indicate a variable time r of occurrenceof test. Spatial arrangement of stimuli is illustrated at far left;dashed outline of test indicates it is superimposed on maskingdisk. Upper figure illustrates results. Ordinate gives test thresholdenergy eT* in log units of attenuation relative to arbitrary refer-ence. Abscissa gives time base r relative to masking-stimulus onset(refer to lower figure). Positive times indicate test occurrencesafter masking-stimulus onset. The last seven data points at farright are the same as those at far left.

Three hundred msec after the termination of B, themasking impulse M occurred. It subtended 1.800 and90%O of the light was emitted within 0.04 msec. Threedifferent eM were used (56, 567, and 15 700 ft-LXmsec).More intense flashes were not used because of subjects'complaints of headaches after the experimental sessions.

"Experimental" thresholds [masking impulse present,designated as eT*(M+B,r)] were determined for an0.04-msec test by the sequential method. "Control"thresholds Emasking impulse omitted, eT*(B,r)] were al-ternated with experimental thresholds in an ABABA ...order (BABAB... order in alternate sessions). Thetest T subtended 0.240. Viewing was monocular.

ResultsThe abscissa of Fig. 6 represents the delay r be-

tween M and T. The ordinate indicates the inducedchange in test threshold. Each point is the differencebetween the logarithms of the experimental- and control-test thresholds. The experimental-test threshold wasobtained with a masking flash, and the control-testthreshold was obtained without a masking flash.

In Fig. 6, data are shown for two observers and forthe three different eM. Each point is the average of four(or more) judgments obtained by the sequentialmethod in two sessions. Points between -50 and -200

547Mtay 1965

GEORGE SPERLING

3.0

- 200 -100 0.0 +100 +200 +300 +400

o 3 SUBJECT MWH

- 1 ' 700r FT-L XmSEC

V -- 567 MASKING

2 FLASHeM

200 -0

.0Z

2

200 100 0.0 100 200 300PRE- ADAPTATION,9.31-

300 mSEC 41 FT-L, 250 mSEC

MASKING 18)IMPULSE (1a) I

TEST (0.24')

-200 . 10 0.0 +100 +200 +300 +400TIME OF TEST IN MILLISECONDS

FIG. 6. Masking responses eT*(T) to three impulse flashes ofdifferent energies. Lowest figure illustrates procedure (see Fig. 5).Pre-adaptation field B terminated at -300 msec; masking impulseM occurs at time 0.0; time of test T is variable. Spatial arrange-ment of stimuli illustrated at far right, not to scale. Upper figuresillustrate results. The dashed vertical line at time 0.0 indicatesthe masking flash. An increase in test threshold [eT* (M+B)>eT* (B)] is indicated by ordinate values greater than zero, adecrease [sensitization, eT*(M+B)


M occurs. To indicate the results more fully, in Fig. 6the limits of the data have been represented by twoshort lines rather than by average points. All threecurves fit between the short horizontal lines indicatedin Fig. 6. The figure shows that the maximum sensitiza-tion (equivalent to a 6% decrease in eT*) occurs 75to 100 msec before M.

Sensitization occurs repeatedly in spite of precautions,such as counterbalancing of trials and an increased num-ber of judgments. A similar kind of sensitization wasobserved in the first experiment (Fig. 5, subjectMWH) 125 msec prior to a 250 msec M. SubjectMWH also shows a similar effect prior to a 500 msec M.It is curious, but typical of these small effects, thatsubject MWH did not show sensitization prior to animpulse M.

"Backward sensitization" has not been previouslyreported. Therefore, a survey experiment was con-ducted in order to see how frequently it occurred in apopulation of five observers.

3.0

2.5

2.0 /It-

O 1.5

z

0>

0.5k

Procedure

EA

JK

JL,

ASC

I I l I

The masking stimulus M was a 1.38 field illuminatedto a luminance of 44 ft-L for 10 msec. A 250-msec(1.38, 42-ft-L) field served as a pre-adaptation back-ground B. Termination of B was followed by M after300 msec. The test field T subtended 0.1380 and wasilluminated for 2.3 msec. The subjects adjusted theintensity of T to be "just visible." Two or more dif-ferent settings were made at each point. The sequence

SUBJECT SUBJECTSMS UNIT { MWH

UNI

0L M-T G:0:

0-J R-Gj R-

-20 -10 0 10 20 -20 -10 0 10 20-j-3OO mSEcH PRE-ADAPTATION (9.31)

| MASKING STIMULUS (180)- | TEST (0.240)TIME OF TEST IN MILLISECONDS

FIG. 7. Masking by red and green impulse flashes. Lowest-figureillustrates procedure and spatial geometry. (Pre-adaptation fieldB is not indicated.) Upper figures indicate thresholds. Barmarkers indicate the scale. Each curve has been moved up ordown an arbitrary amount. Spectral composition of the variousmasking-test-field combinations is indicated at right by colornames (R = red, G = green).

MASKING STIMULUS (1.38) L

Ad TEST (0.138')

I I I I I I-250 -200 -150 -100 -50

TIME OF ONSET OF TEST IN MILLISECONDS0

FIG. 8. Masking prior to a 10-msec flash. Lower figure illustratesprocedure and spatial arrangement of stimuli. Pre-adaptationstimulus terminated at -300 msec is not indicated. Upper figureillustrates absolute thresholds eT* (T) of five observers. Eachcurve has been displaced up or down an arbitrary amount forease of comparison.

of settings was conducted in a pseudo-random, balancedorder.

There are several differences in procedure betweenExp. 4 and Exp. 2. These differences in part are attribut-able to the fact that Exp. 4 was conducted about ayear earlier. (1) Viewing is binocular, not monocularas in Exp. 2. (2) The test illumination is produced bya fluorescent lamp rather than by a gas-discharge lamp.One significance of this is that the discharge lampproduced an audible click simultaneously with the lightflash; the operation of the fluorescent lamps was silent.(3) The spatial geometry of the stimuli is slightlydifferent.

ResultsThe threshold masking response eT*(r) for each

observer is shown in Fig. 8. Each observer's data hasbeen moved up or down in the figure to permit easycomparison of the curves. Data are presented for the200 msec preceding onset of M. These data are notthreshold differences (as in Fig. 6) but simply thresh-olds. The termination of B at r= -300 msec thereforecauses a slow change in base line.

549May 1965

11

GEORGE SPERLING

INTENSITY t T~~1e

TEST

Ie(r=O)MASKING FLASH I

MASKING RESPONSE

FIG. 9. Comparison of four masking proceduretry of the stimulus is illustrated schematicstemporal sequence is illustrated on the right.dimension represents time, the depth dimensionposition along a diameter of the stimulus, and thsion represents luminance. The height of theenergy eT at threshold. (a) Defining conditionstrast, Ca. (b) Defining conditions for threshold:to an impulse M ("impulse response"). FourIpositions are indicated for the test flash, but on]on a particular trial. Heights of the test increproportional to their thresholds. Below, a graheights plotted against their time of occurrthreshold-masking response CT* (r) (see Fig.Conditions for measuring contrast threshold a~background (see Fig. 10). (d) Conditions investiland Kandel. The effect of varying backgrourCT* was determined (see Table I).

Four, perhaps all five observers shov(a dip in the curve) at about 75 to 100 nonset of M. In fact, there is a sugge.detailed shape of the curve may be evplicated for some observers.

Discussion

Backward sensitization does not reprEin eT* of more than 25% for any observer.it is an ubiquitous effect which may be ca variety of conditions of visual stimulaseen again in several of the following exI

The nature of backward sensitizatiowas suggested in an experiment on briging. In this experiment observer SMS N

CONTRAST- LeL temporal sequences of T and M flashes as above. SMSwas asked to adjust the test flash energy eT so thatbrightness observed at the center of the masking disk

(a) M was just barely unchanged by T. When T and M-- M (E coincided, this brightness judgment was identical to a

threshold determination for eT*. When T and M werewidely separated in time, T had little influence on the

( ) appearance of M. However, when T preceded M by 100msec, T apparently caused the subsequent M to appear

- =- different in its center (the area corresponding to T).-- In order to maintain a uniform appearance of M disk,

the eT had to be 25% less than its previously determined"threshold" value.

This result demonstrates that a T-even one belowits own threshold-can alter the appearance of asubsequent M occurring about 100 msec later. Thechange in the nature of what is being detected accounts

(C) for the puzzling aspects of backward sensitization.First, there is the haphazard presence or absence of thephenomenon in the same observer under very similar

MASKING viewing conditions. Presumably, the observer some-FLASH times examines M and sometimes not. When an audible

click occurs simultaneously with T (as with the gas-3~ (d) discharge lamps), the time interval within which Toccurs is clearly defined for the observer. An inducedchange occurring within a subsequent interval may be

ACKGROUND overlooked. When the audible time marker is removedes. Spatial geom- (as in Exp. 4 by using fluorescent lamps) an observerllYhe aleft.t oTghet must search the whole stimulus presentation for any

represents spatial kind of change in appearance. Under these conditionsLe vertical dimen- four or five observers clearly showed backwardtest indicates its ization.for imulse con- sniiain

nasking response In summary, backward sensitization can occur whenossible temporal a test flash of an energy slightly below its own thresh-

.y one test occuraments are drawn old alters the appearance of a subsequent maskingph of these test flash, and when the subject by instruction or by chanceence defines the observes this change.6 for data).- (c)gainst a variablerated by Boynton 5. Contrast Thresholds in Impulse Flashes3 3id luminance on

Consider two adjacent surfaces, one of luminanceIM, the other of luminance IM+IT. Stimulus contrast

. .nt C, may be defined as the ratio IT/IM. The subscripti sensitization indicates the duration of the stimuli. For stimuli briefntion that the enough to be considered impulses, contrast may bee more aoe Ca= eT/eM. Impulse contrast so defined does not dependen more com- on the particular time waveforms IT (t) and IM (I).

Impulse-contrast threshold may be defined aseT*/eM. However, in order to analyze the separateeffects of B and M upon eT* it will be more useful to

esent a change define an adjusted impulse-contrast threshold.Nevertheless, Ca*= [eT* (M+ B) - eT* (B)]/eM.observed undertion. It will be Here M is an impulse flash of energy eM, T is a flash ofteriments. energy eT added to a portion of M, eT*(M+B) is then surprisingly threshold value of eT when T is added to M plus alhtness match- 33 For a preliminary account of this experiment see G. Sperling,riewed various Am. Psychol. 17, 354 (1962).

550 Vol. 55


background B, and eT*(B) is the threshold value of thetest on B alone. When B induces small threshold changesas compared to M, Ca* reduces to eT*/eM.

The definition of stimulus impulse-contrast Cs isillustrated in Fig. 9(a). An incremental disk of energyeT is superimposed upon a background of energy CM.Figure 9(b) illustrates the similarity of the presentationwhich defines Ca to that which defines an impulsemasking response. C3 is defined for the particular casein which M and T occur simultaneously. In the maskingexperiment, M and T occur in all time relations.

In Exp. 2 it was noted (see, for example, Fig. 5) thatmax eT*(r) occurs when T and M coincide (r= 0). Thusto a good approximation the impulse-contrast thresholdtimes the energy of the masking flash equals the peak ofthe impulse-response curve,

Ca* eM=max eT*(r).Since the shape of the various impulse responses wasqualitatively similar, knowledge of the peak of thecurve would be sufficient to describe an impulseresponse in considerable detail.

Brindlev34 studied eT*/eM as a function of flashintensity. He found it to vary from about 0.1 to 0.2from dim to very intense flashes. In extremely intenseflashes, however, the threshold increased sharply,presumably because of exhaustion of all the availablephotochemical pigment.

Brindley also noted that in flashes with energy greaterthan about 100 cd-sec/m 2 (3 X 104 ft-LXmsec), contrastthreshold is higher because contrast must be dis-criminated in the after-image rather than in the primaryimage. This suggests that the background upon whichthe flashes appear is important for the discrimination ofcontrast. A flash which looks blindingly bright indarkness can seem quite innocuous when added to asteady bright background. For this reason impulsecontrast threshold Ca* was studied both as a functionof masking-impulse energy cM and of backgroundluminance 1B

ProcedureThree concentric, circular-disk fields were optically

superimposed: background B (9.310), masking stimulusM (2.330), and test T (0.23). M and T were illuminatedsimultaneously for about 0.04 msec, at 1-sec intervals.Masking-flash energy eM was varied from 0.139 to159 000 ft-LXmsec. B was illuminated to one of foursteady luminances (0, 0.37, 3.7, 41 ft-L) or it wasilluminated for 250 msec to 41 ft-L and dark for 750msec. In the latter case (41-ft-L pre-adaptation), Mand T occurred 300 msec after termination of the250-msec B. This presentation is comparable to the oneused in the preceding experiments.

By the method of adjustment, test threshold eT*was determined. In each session, only B was varied, M

34 G. S. Brindley, J. Physiol. 147, 194 (1959).

0

E0 I PRE-A PTATION 3X =DARK

JaLL eT 2

MWH0 401 PRE -ADAPTATiON -

- - /5S 567 15,700 -1

I I1 1 1 lo I1 I-l 0 I 2 3 4 5

LOG FT-L x mSEC OF MASKING FLASH

FIG. 10. Test threshold as a function of masking-impulse energyand background luminance, data for two observers. Points withsame background luminance are connected. The 41 pre-adaptationrefers to a 0.25-sec field of 41 ft-L terminated 0.3 sec before mask-ing flash. When points fall too close together to be graphed in-dividually, the range is indicated by parallel horizontal dashes.Control-threshold levels (masking flash omitted) are indicated bythe horizontal lines. The energies eM of the three masking impulsesof Exp. 2 are indicated on the abscissa and the obtained testthresholds at simultaneity eT(r =0) are indicated by crosses (seeFig. 6). The values of CT/eM corresponding to the average adjustedcontrast threshold Ca* of the data are indicated (for method ofcalculation see text and Fig. 11.)

being held constant. The order in which various B'swere presented within a session was the same in ses-sions 1-7 and reversed in sessions 8-14. The observeradapted for 5 min to each B. For each condition, theobserver made two adjustments. Before each thresholddetermination (sessions 8-14) or after each determina-tion (sessions 1-7) the observer's threshold was deter-mined with the background alone (no masking flash).These two test thresholds are designated respectively aseT*(M+B), eT*(B).

Viewing was with the right eye only. As in previousexperiments, fixation was central. The visual presenta-tion (steady B) is illustrated schematically inFig. 9 (c).

Results and DiscussionTest energy eT(M+B) is graphed against CM in

Fig. 10. Each point is the average threshold, based onfour or more judgments in two sessions. The resultsare similar at each level of B. Increasing the intensity ofeither B or M increases eT* (M+B). For the M of lowestenergy, eT*(M+ B) is determined almost entirely by the

551May 1965

GEORGE SPERLING

SMSC - 2

- MWH

-2 I 3

LOG FT-L x FUEC OF MAKING FL-S

FIG. 1 1. Threshold changes induced by impulse maskingflashes added to five different backgrounds. The ordinate is thelogarithm of the increase in test thresholds in ft-LXmsec(Iog~eT*(M+B)-CT*(B)]}, top scale refers to observer SMS;bottom to MWJI. Points with same backgrounds are connected.Points for which the difference in thresholds is less than 40%(0.15 log units) are connected by dotted lines. Best-fitting line ofunity slope is indicated.

B; at high masking energies, log eT*(M+B) increaseslinearly with log eM. The slope is slightly less thanunity, indicating that CT/eM decreases at high energies.At the highest energy, eT*/eM is about 0.06 for observerMWH and about 0.08 for SMS. The interspersedthresholds with the background alone, eT*(B), do notvary with masking-stimulus energy; their levels areindicated by the horizontal dashed lines.

Thresholds in a 250-msec pre-adaptation backgroundobtained earlier from complete impulse responseseT*(M+B,T=O) (Fig. 5) are indicated by crosses inFig. 10. The agreement between experiments is good;the maximum discrepancy is about 40% (0.15 logunits) for one point. Observer SMS's threshold inbackground alone diminished by 25% to 50% be-tween experiments. While this change affects the ratioof thresholds, it does not appreciably affect the dif-ference between thresholds (see below).

Does the same M cause the same increase in thresh-old, independent of the B upon which it is super-imposed? To answer this question it is necessary toconsider the change in threshold energy produced bya masking flash of eM ft-LXmsec, that is, eT(M+B)- CT(B). Figure 11 displays log[eT*r(M+B)-eT*(B)]vs log eM. The coordinates are logarithmic because ofthe great range of the data.

When the expected value of a difference is small thelogarithm of the difference fluctuates wildly, owing tothe statistics of differences. For example, when eT*(B)slightly exceeds eT*(M+B) (as should happen halfthe time with infinitesimal eM) the logarithm of thedifference is not defined.

All points for which the logarithm is defined aregraphed in Fig. 11. Data points based on thresholdchanges of less than 40% (0.15 log units) are connectedby broken lines. These points are statistically unreliable,

biased overestimates of the true threshold difference.Although they indicate trends in the data, littleimportance should be attached to them, or to variationamong them, and they are omitted from subsequentstatistical analyses.

The most striking fact about Fig. 11 is that the fiveseparate curves of Fig. 10 are collapsed almost to one,and that the slope over four or five decades is nearlyunity. To a good first approximation, the data implythat B has no effect on the threshold increase inft-LXmsec produced by M and that a modified Weber'slaw is valid when the effects of B and M are consideredseparately.

The observed relation betweenlog eM and log[eT*(M+B)-eT*(B)]

may be examined statistically. For the SMS data, theslope of the regression line is 0.861 and the correspond-ing product-moment correlation is 0.989. For MWHthe slope is 0.891 and the correlation is 0.988. A regres-sion line with slope less than unity indicates that C6 *is greater in dim flashes than in intense ones. Theproportions of variance accounted for by the best-fitlines of slope 1.0 (Ca*=constant, a modified Weber'slaw) are 0.962 and 0.952, numbers whose square rootscorrespond to "correlations" only slightly lower thanthose of the regression lines.

Inspection of Fig. 11 shows that masking flasheswhich produce small percentage changes in threshold(i.e., small changes in log threshold) are somewhat moreeffective than flashes which produce large percentagechanges. Thus a dim masking flash added to a brightbackground barely alters the log threshold, but thissmall perturbation may correspond to an increase ineT * several times greater than the same masking flashproduces in darkness. Logarithmic (ratio) plots suchas Fig. 10 produce the false impression that flashesviewed in darkness produce the biggest thresholdchanges.

In summary, Fig. 10 shows that masking flasheswhich produce substantial threshold changes do soindependently of the background. Consideration oflinear threshold differences (Fig. 11) suggests thateven masking flashes which produce only small pre-centage changes in threshold do so almost independentlyof background. Statistical analysis indicates that amodified Weber's law (slope of regression line as-sumed= 1) accounts for over 0.95 of the variance inthe data. As there is no discontinuity in the curvesof Fig. 11, these conclusions appear to apply evento masking flashes which themselves are below"threshold."

6. A Methodological CheckIntroduction

The presentation rate of one flash per sec in theprevious experiment means that at high flash energies

552 Vol. 55

M 1 VISUAL MASKING BY IMPULSE FLASHES

much light adaptation is due to the masking flashitself, especially when the background is dim. Thefailure to observe any influence of B on eT*(M+B)with large eM might be due to a cumulative adaptationcaused by the repeated M, an adaptation which over-whelms the effect of the B. An obvious way to testthis hypothesis is to change the M flash presentationrate. The following experiment uses a presentation rateof one M flash per minute.

The change in presentation rate necessitates certainchanges in procedure. The method of adjustment nolonger is feasible. The 1-min time between presentationsis too long for the memory or patience of an observerusing the method of adjustment. A "yes-no" procedurealso is quite slow. Moreover, it yields thresholdsreadily influenced by factors extraneous to the visualpresentation, such as changes in the observer's cri-terion.35 As the experiment seeks to measure smalldifferences between conditions, it would be desirableto minimize the possibility of criterion changes or to beable to detect them when they occur.

The usual alternative to "yes-no" detection requiresa multiple-stimulus presentation followed by a single"forced choice" judgment. Its application would requireeither two or more simultaneous masking flashes (bothcould not be central) or two or more successive flashes,separated by an interval of 1 min. The simultaneous,noncentral presentation would be a great change fromthe presentation used so far. In the successive judg-ment, the subject estimates the probability of T ineach M flash, then chooses the highest. The problem isthat successive flashes must be separated by 1 min.Since the subject presumably recodes his informationabout the flash into one dimension (subjective proba-bility), he could be asked for this recoded responsedirectly. Therefore, by analogy to the temporal forced-choice experiment, subjects were asked to estimate theprobability of T having occurred in each M presenta-tion. This procedure is an elaboration of a rating scalemethod which has been used successfully in thresholddeterminations .36-39

ProcedureThe stimuli were of the same geometry and duration

as in the previous experiment; viewing was monocularas before. Onlv three of the five background conditions(IB= 41 ft-L, 0.37 ft-L, dark) and one intense maskingflash (eM=72 600 ft-LXmsec) were used. Fixationmarks adjacent to M were continuously present:

35 J. A. Swets, editor, Signal Detection and Recognition by HumanObservers: Contemtporary Readings (John Wiley & Sons, Inc.,New York, 1964).

36 J. P. Egan, A. I. Schulman, and G. Z. Greenberg, J. Acoust.Soc. Am. 31, 768 (1959).

37J. A. Swets, W. P. Tanner, and T. G. Birdsall, Psychol. Rev.68, 301 (1961).

38 D. J. Weintraub and H. W. Hake, J. Opt. Soc. Am. 52,1179 (1962).

39J. Nachmias and R. Steinman, J. Opt. Soc. Am. 53, 1206(1963).

tL0

..I-(J

I.2z

CE

zCw

# -1.6 -t.4 -1.2 -1.0 -0.8 -0.8LOG [CONTRAST = eT/eMI

- - 10

- 7

- a

5.4

-9

/ - a- 7

654

- a

7 7

- 5-4-3

2

-0.4 -0.2

FIG. 12. Confidence of detection in three different backgroundsas a function of test energy eT. Masking flash energy eM was 72 600ft-LXmsec. Vertical bars (observers SMS,MWH) representthresholds measured in Exp. 5 (see Fig. 10 and text for details.)The results of "catch" trials are plotted above 4 which has beendisplaced slightly to the left on the abscissa. Its true contrast isthe same as for the adjacent set of connected data points. Theordinate values above sF are based on 50 trials each, other points10 trials each.

dark marks in the light backgrounds, 4 dim light spotsin the dark background. Ten different test stimuli wereproduced, varying from eT=0.0 22eM to eT=O.5SeM inapproximately equal ratio steps. The simultaneousoccurrence of T and M constituted a stimulus presenta-tion [refer to Fig. 9(c)].

Sessions began with 5 min adaptation to darknessIB= 0 (or IB=4 1 ft-L on alternate days), followed at1-min intervals by a warning buzzer. As soon after thewarning as he was sure of his fixation and accommoda-tion, the observer pressed a button which initiated avisual presentation 0.5 sec later. Two sample trials(eT=0.0 2 2eM and eT=0.55eM) were followed by 10different tests and five "catch" trials in random order.This viewing condition was followed by an analogousadaptation and presentation sequence in the nextbackground until all three backgrounds had beenviewed.

After each stimulus presentation, the observer wasasked to rate on a 10-point scale his confidence that Thad occurred. The scale was defined as follows: (1)certain-no, (2) very sure-no, (3) pretty sure-no,(4) probably-no, (5) unsure-probably no, (6) un-

553May 1965

GEORGE SPERLING

10

'-9ia:0 8

06z5UM.4

03

2a

I 2 3 4 5 6 7 8 9 10

MWH0.37 FT-L BKGD

DETECTION* A. *a he NONDETECTION

1 2 3 4 5 8 7 a 9 10ENERGY OF TEST (RANK ORDERED)

to9876.5

432

FIG. 13. A sample of data obtained by category rating of near"threshold" stimuli. Background luminance is 0.37 ft-L. On theaverage, the energy difference between adjacent test ranks is38%. Each point represents one judgment by observer MIWH.The horizontal line separates "yes" (detection) from "no"(nondetection) judgments. The connected vertical lines representthe median test energy which elicited each judgment category ofresponse.

sure-probably yes, (7) probably-yes, (8) prettysure-yes, (9) very sure-yes, (10) certain-yes. Onthe five catch trials in each condition, immediatelyafter his response, the observer was told that T hadbeen omitted on that trial.4 0 No other informationabout the stimuli or sequence was given the observer.

The two observers of the previous experiment andthe author served as observers. After several practicesessions, the experiment continued for 10 sessions, for atotal of 10 judgments for each eT in each of the threebackgrounds.

Results

Figure 12 illustrates the median-judgment categoryas a function of test-stimulus energy. Data for eachobserver and each background are shown. The greaterthe test-stimulus energy, the more certain the observeris that he sees it, as indicated by judgment category.Observers are absolutely certain they see the brightertests. The same degree of certainty is never reached fordim tests. No matter how dim the test is, observersusually are unsure of its nonoccurrence.

In Fig. 12, test-stimulus energy is plotted on alogarithmic scale [logC5= log(eT/em)] to facilitate com-parison of the various curves. Visibility differencesbetween conditions would manifest themselves aslateral displacements of the curves. The data indicatethat the various backgrounds do not affect visiblity bymore than about 25% (A logCa-0.1) and furthermore,that the direction of these slight shifts varies fromobserver to observer. The conclusion of the previousexperiment is confirmed: background does not appreci-ably affect eT*/eM in an intense flash.

40 Actually, eT = 0.0 2 2 eM wvas presented onl catch trials as it wasinconvenient to produce eT=0 without informing the subject.This test stimulus contained about -1 the energy of the previouslydetermined threshold. The identity of the observers' distributionof responses to the "blank" and to the next-more-intense stimulusultimately justified its use.

The logarithmic plot of the data in Fig. 12 fails toindicate one aspect of the data. On a linear plot, thepoints on the left of Fig. 12 are compressed and theogival shape of the curve is lost. On such a linear graph,the left part of the curve becomes nearly a straight line.The slope indicates that over a range of from five toseven categories, confidence increases at a rate of aboutone category unit per increase in eT of 0.05eM forobserver MWH and at a smaller but constant ratefor observers GS and SMS.

Results: Methodological Issues

The apparent continuity of detection categories andnondetection categories is one of the most interestingaspects of the data; subjects provide significant informa-tion about the test stimulus even when they say theycannot detect it. The best way to illustrate this is toconsider the conditional distribution of test stimulito which a particular response was made.

Figure 13 indicates all the responses made by ob-server MWHI with a background of 0.37 ft-L. For eachresponse category (1, . . ., n), Fig 13 also represents therank of the median stimulus eT to which this responseoccurred. The fairly regular progression of the medianindicates that observer MWH is able to maintaindifferentiated criteria, not only for levels of detectionbut also for levels of nondetection. For example, Fig 13illustrates that of the 23 occurrences of judgments of 1or 2 (certain no, very sure no) in only 7 cases were thetest stimuli of rank 3 or higher (eT0.046eM), whereasof the 17 occurrences of judgments of 4 or 5 (probablyno, unsure probably no) in 15 cases the tests ranked 3or higher.

Figure 14 illustrates the extent to which each of theobservers is able to maintain differentiated criteria forlevels of detection and nondetection. The abscissarepresents judgment category; the ordinate, the rankof the median stimulus eliciting that judgment. Foreach observer, the data have been averaged acrossbackgrounds.

Figure 14 shows that observers differ in the extent towhich they are able to maintain clearly differentiated,monotonically related criteria; MXVH's criteria wereperfectly monotonic; GS and SMS each showed twoinversions. Observers MWH and GS maintain severaldifferent criteria of nondetection; SMS discriminatesonly slightly among nondetected tests.

Discussion: Methodological IssuesOne third of the presentations were catch trials, to

repress "false positive" responses It is noteworthythat observers were unable to avoid reporting detectionoccasionally and high-category nondetection frequentlyfor the "catch" test stimuli. These uncertain categoriesof response probably result from the blotchy appearanceof a brief masking flash. The appearance varies from

554 Vol. 55


flash to flash and it is not surprising that occasionally asubjectively brighter area in the center of the objectivelyuniform masking stimulus should be mistaken for thetest spot. This illusory signal-in-noise appearance of Mis a characteristic of the visual system, not of thestimulus. That is, for constant signal-to-noise ratio atthreshold, eT* should increase as the square root ofeM41-44 whereas it actually increases almost in directproportion to eM.

No "threshold" theory of detection is adequate toaccount for the data. As has already been noted,particularly by Nachmias and Steinman,3" there is acontinuity of process above and below detection. Theability of observers to discriminate among stimuli below"threshold" may account in part for the ability ofexperienced observers to make such extremely precisejudgments by the method of adjustment.

GENERAL DISCUSSION

Relations of Masking by Impulsesto Masking by Steps

Several attractive approximations emerge from thedata obtained: (1) the height of an impulse response isproportional to the impulse energy (Weber's law forthe impulse-contrast threshold) and (2) it is independ-ent of the background upon which the impulse issuperimposed. Although neither of these approximationsis strictly true, the intent of this discussion is to relatethese results of masking by impulses to other maskingexperiments, particularly those in which maskingresponses were obtained for long pulses (steps).

The results of Crawford and others have shown thatmasking is a nonlinear process.4 5 Therefore, super-position cannot be assumed and convolution calcula-tions are not appropriate. The hypothesis is proposedthat nonlinearity results when one process of detectionsupersedes another, depending on the time between testand masking flashes. An attempt will be made to relatethe peak of the masking response of longer pulses to thepeak of the impulse response.

Hypothesis33

The luminance energy occurring during the first50 to 60 msec of a longer flash is considered as thoughit all occurred in an impulse. The peak threshold isCa* times this energy.46

60max eT* (r) 6 Im ()dt. (1)

41 A. Rose, J. Opt. Soc. Am. 38, 196 (1948).42 A. Rose, Proc. I.R.E. 30, 295 (1942).43 HI. de Vries, Physica 19, 553 (1943).44 M. H. Pirenne and F. H. C. Marriott, in Psychology: A Study

of a Science, edited by S. Koch (McGraw-Hill Book Co., Inc.,New York, 1959), Vol. I, pp. 288-361.

45 See above section, Masking by Impulse Flashes, p. 546.46 No assumption is made about the time r at which max eT* (T)

occurs.

U-L0

LL0,-..0

6U

2u s9

c

1 4 6 8 toI I I I I I I

MWH8 -

GS6 -SMS

z_ 1 H /\ /PI4 - i jc / d eY2

2 4 6 8 to 2 4 6 8 1OJUDGMENT CATEGORY

FIG. 14. Consistency of judgmental criteria. Data are shown forthree observers. Each point represents the median energy of thetests (average of the three background conditions) which elicitedeach judgment category. Vertical bars divide "yes" (detection)and "no" (nondetection) judgments.

Here Ca* represents an average value of Ca*, and IM(t)is assumed to be a step function at t= 0.

There is a good rationale for this hypothesis. Thefirst part of the long masking flash together with theimpulse test flash physically constitutes a contrasttarget. Subsequent light from the masking stimulus maybe regarded as a background which appears after thetarget. But as background has been shown to have littleeffect on impulse-contrast thresholds, it may beneglected.

At the core of the hypothesis is the assumption thatdetection of a test in an impulse flash is based purelyon a contrast judgment, i.e., a comparison of light inadjacent retinal areas. The peak of masking response toa step (so called on-response) is assumed to be causedby the observer's reliance on spatial contrast fordetection; the subsequent lowering of threshold afterthe peak is due to the observer's ability to discriminatethe temporal pattern of illumination at the test locationfrom the (steady) background.

Detection is defined as a function having two orseveral discrete values (e.g., 0= "no, I do not see it,"1= "yes, I see it"; etc.).

Contrast detection is defined as a function whoseargument is contrast [lM(x1,t)/lM(x2,t)j or somesimilar concatenation of 1M(xi,t) and IM(X2,t) in whichthe luminances of adjacent areas xi, x2, enter only incombination and never individually.

Pure temporal detection is a function whose argu-ment depends only on the time variation of luminancevalues at one location Ee.g., lM(x,1)-IM(xt-- 7)].

The definition of a detection function can be readilygeneralized to a function whose instantaneous valuedepends on all past luminances or to a function whoseargument is not simply luminance, but some transfor-mation of the visual stimulus, presumably carriedout by the visual system. For some reasons for choosinga particular definition of detection see SperlingA7

47 G. Sperling, Doc. Ophthalmol. 18, 3 (1964).

555May 1965

GEORGE SPERLING Vol. 550

-~ 0z 2 DURATION (mSEC)

LOG ENRG INFRT 05

tu 4, 50

OF 3AKN TMLS(~ SC

0 5000'uJ

U.Z

F ~IG 015 .Efeto akn-tmls uiac n uaino

IHW0 -J OBS.

0II- I

00 I 2 3 4

LOG ENERGY IN FIRST 60 MSECOF MASKING STIMULUS (mLx MSEC)

FIG. 15. Effect Of masking-stimulus luminance and duration onpeak test threshold, max CT"(7). Ordinate is logarithm of increasein test-threshold energy (mLX5 msec) induced by maskingstimulus: log[max eT* (7)-min eT* (r)]. Abscissa is logarithm ofmasking-flash duration in msecXflash-luminance in mL, usingeffective duration of 60 msec for flashes of 60 msec or longer, it isfo6 0 IM (t)dt. Upper scale refers to observer IHW, lower scale toobserver WSB. Equations of regression lines: IHW, logCs*=-0.551+0.152 log eM, (r=0.985); WSB, logCa*=-0.830+0.190Xlog eM, (1-=0.993). Best-fitting lines of slope one (not shown):Ca*=0.65(IHW); Ca*=0.43(WSB). Data from Battersby andWagman (see Ref. 10, Fig. 4, p. 756).

Duration of Masking FlashBattersby and Wagman' studied masking threshold

responses to rectangular pulses of 5, 50, and 500 msecduration. The stimuli were somewhat larger than thoseshown in Fig. 6 and viewing was peripheral.

In Battersby and Wagman's data, the shape of themasking response to a 5-msec masking flash (whichmay be considered an impulse response) is quitesimilar to the shape of the response to a 50-msec flashof -bth the intensity, and to the initial response to a500-msec flash. For quantitative comparison, however,only the peaks of the masking responses will beconsidered.

Figure 15 illustrates Battersby and Wagman's ob-served peak of the threshold response as a function ofthe luminous energy contained in the first 60 msec ofthese masking flashes. The points were estimated froman enlargement of their published graph' as moreprecise data were no longer available.49 The change inthreshold is estimated by max eT*(r) -min eT*(r).

The regression lines through the calculated pointshave slopes and correlation coefficients respectively of1.15 (r=0.985) and 1.21 (r=0.994). These slopes aresignificantly greater than one. The best-fitting linesof slope 1.00 (modified Weber's law) represent adjustedcontrast thresholds Ca* of 0.65 and 0.48 for IHW andWSB, and account for 0.96 and 0.92 of the thresholdvariance. The Cs*'s are substantially higher than thetypical values shown in Fig. 11. This is accountedfor mainly by the 70 peripheral viewing. Before ventur-

48 XV. S. Battersby (private communication).

ing an explanation of the large slopes and Ca* it isinstructive to examine certain aspects of the data.

For subject WSB a 50-msec flash of 10 mL producesmore masking than an equal energy flash of 100 mLfor 5 msec. The shapes of the two masking responsesare quire similar, however. Because the peak of themasking response is greater for the longer flash, itfollows that it is more efficient to distribute masking-stimulus energy in time after the instant of maximummasking rather than to cluster all the energy at thesingle, most effective instant of time. Obviously, thistype of masking implies a more complex process than asimple integration of masking energy.

The peak of the masking response for the mostintense 500-msec flash is about double the peak responseto a 50-msec flash, for subject IHW, and triple forsubject WSB. This means that masking light occurringmore than 50 msec after the test can still double ortriple the threshold energy requirement. The author hasnoted effects on test threshold occurring up to 150msec later. This effect occurs only at high maskingluminances. At low luminances, peak masking for 500-and 50-msec flashes is very similar. As thresholdintegration time is shorter at high intensities than atlow, 4 9-5 4 the great masking effectiveness of intense longflashes must arise not from longer integration but froma masking process which benefits from the spreading-outof light in time.

In intense masking flashes, the subject does notalways detect the test stimulus directly.6'3 4 Particularlywith test presentations corresponding to the peak ofthe masking response, the subject detects a negativeafter-image of the test. The apparent "superintegration"of masking energy for intense, long flashes seems to bethe result of detection of an after-image, which occurs50 msec or more after the test and which may thereforebe influenced by light occurring 50 msec or more afterthe test.

Equation (1) predicts thresholds well in presentationswhich minimize the observer's dependence on after-images for detection. When conditions favor after-image production, observed thresholds tend to behigher (e.g., double or more) than those predicted byEq. (1). The after-image process therefore wouldaccount for the slope being greater than one in Battersbyand Wagman's data, because after-images are moreimportant at high intensities. Admittedly, this is but apartial and imprecise account of the divergence of testthreshold measured in intense long flashes from thosemeasured in comparably energetic impulse flashes.Intense long flashes viewed after darkness pose problemsnot only for the observer but also for the theoretician.The final account will not be a simple one.

49 C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21,634 (1938).50 M. Keller, J. Exptl. Psychol. 28, 407 (1941).51 W. R. Biersdorf, J. Opt. Soc. Am. 45, 920 (1955).52 R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).53 H. B. Barlow, J. Physiol. 141, 337 (1958).54 H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963).

556

VISUAL MASKING BY IMPULSE FLASHESTABLE I. Comparison of test threshold luminances (mL) with the masking stimulus "on" IT*(M+B) and without the masking

stimulus IT*(B). B_=l0g11T*(M+B)/1T*{B)J-2.15 is Boynton and Kandel's estimate of neural masking response. Masking responseas calculated in text is given in the last column, log[jT*(MfB)-IT*(B)J. Masking stimulus=38 mL, duration=560 msec; pre-adaptation background B extinguished 280 msec before onset of M. Data from Boynton and Kandel (Ref. 14, p. 278), average of threesubjects.

1091B 10og* (M+B) 1og1T* (B) log[1T* (M+B)/lT* (B) ]-2.15 logE1T* (M+B)-IT* (B) ]-4.20 0.98 -2.11 0.95 0.98-1.50 0.98 -2.12 0.95 0.98-0.50 0.83 -1.85 0.54 0.83

0.50 0.68 -1.49 0.02 0.681.50 0.52 -1.10 -0.53 0.512.50 0.53 -0.36 -1.26 0.473.00 0.73 0.35 -1.77 0.503.50 1.25 1.23 -2.13 [-0.10Ja

S Insufficient data.

Eject of BackgroundA second prediction from impulse responses is that

the peak of the masking response to a long flash shouldbe independent of the background upon which it issuperimposed. In a thorough study, Boynton andKandel'4 measured the thresholds during the onset of along pulse of light as a function of the background illu-mination. Their procedure is illustrated schematicallyin Fig. 9(d), and may be compared with Fig. 9(c) whichillustrates the procedure used with impulses in Exp. 5.In their main experiment, however, the backgroundwas terminated 280 msec before the masking flash.

Boynton and Kandel used a 40-msec test flash, whichdefinitely is not an impulse test, being in fact near thelimit of integration. Their long test flash makes com-parison difficult because the long test tends to givelower values for the sharp peak than does an impulse.Furthermore, the threshold to a long flash is verysensitive to changes in the shape of a peak, and possiblyis subject to other less systematic differences. The bestcomparison with Boynton and Kandel's data is forsimultaneous onset of test and masking stimulus be-cause this presentation is most nearly comparable to theconditions for producing Ca. The procedure can beconsidered as a production of C40 followed by continua-tion of the background.

Table I gives average thresholds obtained withmasking stimulus, with the background alone, thedifference of the log thresholds minus 2.15, and the logof the difference of the two thresholds. As the pre-adapting background varies from dark to 3.2 mL, thelog of test threshold change varies from 0.98 to 0.68(log mL); for backgrounds between 32 and 1000 mLthe variation is only between 0.51 and 0.47 (log mL).This latter change (0.04) should be contrasted withBoynton and Kandel's estimate of the change ineffectiveness of the masking stimulus: 2.72 over thefull range being considered and 1.24 over the range ofbackgrounds from 32 to 1000 mL.

We can work backwards to estimate a contrastthreshold. From Table 1, the logarithm of the typicalobserved threshold change is 0.5 (3.2 mL). Test en-

ergy eT*=3.2 mLX4O msec= 128 mLXmsec. Maskingenergy eM=38 mLX60 msec=2280 mLXmsec. ThuseT*/eM= 128/2280= 0.06. This figure may be an under-estimate due to the long masking flash, but it lieswithin the range of observed foveal values.

In Boynton and Kandel's data, the logarithm of thethreshold is about 0.5 higher for flashes which may beexpected to induce after-images, i.e., intense flashesfollowing a dark background. The elimination ofsubsequent after-images by pre-adaptation to highluminances may account in part for the authors'apparently contradictory finding that increasing thebackground luminance can reduce test thresholds.

The most complete study of the effect of backgroundupon masking was made by Onley and Boynton.'"They studied masking of a 40 msec test by 300-msecflashes of different intensities following pre-adaptationto various backgrounds. The apparent brightness of the

0 1 2 3 4

3 -

u- 2 /a0o8 ~

a:'EA

a: COMPARISON0- C%=.106 LOGm L

0 o 3.5_.j LUJ 2.5

-1 0 -0.5

I / I . I0 1 2 3 4

LOG mL OF MASKING STIMULUS

FIG. 16. Effect of masking-stimulus luminance on test threshold(test occurs at nominal +12.5 msec after onset of masking stimu-lus, see text.) Masking stimuli of apparent brightness equal to acomparison standard are coded with points of same shape, asindicated. Background pre-adaptation was varied from 1 to 1000mL (Obs. JS) and from I to 8900 mnL (Obs. JO). Points of equalbrightness are arranged from left to right in order of increasingpre-adaptation luminance. Equations of regression lines (notindicated): JS, logCs*=-1.0.20+0.011 logeM (r=0.98 7 ); JO,logCa*=-1.207+0.033 logeM (r=0.985). Data from J. Onleyand R. M. Boynton (see Ref. 19, p. 938).

557May 1965

GEORGE SPERLING

masking stimuli also was determined. Complete datawere generously made available by Onley.

As with the data of Boynton and Kandel, the mostrelevant data for comparison with the present work isfrom the case in which the onsets of the test and maskingstimuli coincide. However, there is some internalevidence of a slight time shift in the data.5 5 Therefore,the data actually used here as an estimate of the0.0-coincidence values were obtained by extrapolatingbetween nominal 0.0 msec and +25 msec, and representa nominal time r= + 12.5 msec.

In Fig. 16 the induced threshold change [*(M+B)-ZT(B)] is graphed as a function of the masking-stimulus luminance. Points corresponding to maskingstimuli of equal apparent brightness are coded by thesame shape; the relative pre-adaptation intensity canbe deduced from their relative placement.

The slopes of the best-fitting lines and the product-moment correlation coefficients between maskingluminance and adjusted test threshold are, respectively,1.01 (r= 0.987) and 1.03 (r=0.985) for the two sets ofdata. These slopes are not significantly different from1.00. The best-fitting lines of slope 1.00 (modifiedWeber's law) correspond to an adjusted contrastthreshold C4io*=0.106 and 0.085, for JS and JO,respectively.

These values are based on an assumed integrationtime equal to the test duration of 40 msec. An assumedtime of 60 msec would reduce them by 33%. The best-fitting Weber's-law lines account for 0.966 and 0.976of the variance in the data.

Masking flashes of equal luminance may differenormously in apparent brightness, depending on theluminance of the pre-adaptation background. How-ever, masking flashes of equal luminance produce equalchanges in test threshold [IT*(M+B)-lT*(B)] re-gardless of their appearance. In this treatment of thesedata, pre-adaptation background and apparent bright-ness are ignored as determining factors in the maskingproduced at the onset of a long flash; threshold changeis directly proportional to masking luminance.

Fast Versus Slow Masking ProcessIn order to avoid physiological inference, the terms

fast and slow are used where previous authors haveused neural and photochemical. Fast and slow are usedrelative to 1 sec. The discussion will attempt to demon-strate that threshold phenomena seen in the above ex-periments are attributable primarily to fast processes.

(1) The threshold response to a masking impulse isfast. The data show that even after an intense impulse,

65 Onley and Boynton's" data show instances where increasingmasking luminance does not produce increases in thresholds oftests which nominally occurred at 0.0 msec (coincidence of on-sets). This result is more likely to have occurred at negativetimes (test flash preceding) than at 0.0.

threshold changes are negligible several tenths of asecond later.

(2) The data obtained with the 250-msec maskingflash here and for longer flashes elsewhere show thatinitial recovery from these flashes is equally fast.

(3) The question is whether in steady light thethreshold is high due to the cumulative action of lightfor several seconds (as would be required by a slowphotochemical process with a time constant of severalseconds), or whether the threshold is influencedprimarily by the light preceding the test by a fewtenths of a second.

The answer is implicit in (2) above but can bedemonstrated by direct comparison of the action oftwo backgrounds: the 0.25-sec pre-adapting flashrepeated at 1 sec intervals and an "equivalent" steadybackground. A pre-adapting field of 100 ft-L for 0.25sec produces about the same level of adaptation 0.3 secafter its termination as does a steady light of 0.37ft-L. All contrast thresholds measured in the twodiff erent backgrounds are comparable.

In viewing the steady background, only 1/28 asmuch light impinges on the cornea each second as inviewing the repeated 0.25-sec pre-adapting field, yetthe adaptation level is the same or slightly higher.From the great effectiveness of a steady light relativeto an intermittent one, it follows that the steady light'seffect is dependent on fast processes. Had it beenterminated 0.3 sec before the test, it would have hadto contain at least 28 times more flux in each second inorder to produce the same adaptation level.

Occasionally, during steady fixation, the 0.37 ft-Lbackground subjectively fades out completely. Thefading does not seem to perturb thresholds. That fadingdoes not influence thresholds is not surprising, sincethe boundaries which determine visibility of the pre-adaptation field are more than 40 away from the test.Thus, a steady light's main influence on thresholdsdepends not on a slow cumulative adaptation, nor onwhether it is visible or faded out, but simply on itsinstantaneous presence.

It is important not to misconstrue the above state-ments to mean that there are no slow masking processes,such as, for example, dark adaptation. What is assertedis that in masking by a steady light, the role of slowprocesses is dwarfed by that of fast masking processes.This point is worth emphasizing

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