JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Temporal Summation during Dark Adaptation*

BARBARA R. STEWART

Columbia University, New York, New York 10027(Received 19 March 1971)

The change of critical duration and of the form of the function relating threshold energy to stimulusduration was determined during the first 22 s of dark adaptation following light adaptation to several lumi-nances. For all adapting luminances tested, the critical duration increased during dark adaptation from thevalue obtained for the increment threshold. As adapting luminance decreased or time in the dark increased,the form of the summation function changed, so that the transition from complete temporal summation tono summation became less abrupt. The data show departures from the equivalent-background analysis ofdark adaptation. A filter model relating threshold energy and time constant under varying adaptationconditions provides a general, but not precise, description of the data. The change of temporal summationduring dark adaptation is similar to that found for decreased size of test field, decreased wavelength of testfield, and decreased background luminance.INDEX HEADING: Vision.

Psychophysical studies have demonstrated that thevisual system processes brief flashes of light on thebasis of integrated energy. This is expressed by Bloch'slaw,' Lt= k, i.e., increased flash duration t allows acorresponding decrease of luminance L for a constantresponse. Beyond a critical duration l,, this relationbreaks down, and there may be only a partial reductionof threshold luminance with increased test-flash dura-tion, or independence of test-flash duration L= k'.

The state of adaptation of the eye is a principaldeterminant of temporal integrating ability. Studies2-5

of increment and decrement luminance thresholds haveshown a decrease of temporal summation with increasedsteady-state background luminance. Studies of thesensitivity changes during the process of dark adap-tation, using test flashes of various durations, havebeen reported by Wolf and Zigler5 and by Crawford,'"and although these authors do not discuss temporalsummation, these studies bear on the problem ofchanging critical duration. Wolf and Zigler's thresholdsfor an acuity grating" indicate increases of temporalsummation throughout the 30-min period of darkadaptation. From Crawford's data we can infer that,for his stimulus conditions, critical duration is less thanor equal to 0.05 s at about 2 s in the dark, increases toapproximately 0.25 s after 3 min in the dark, andremains constant thereafter.

The present experiment verifies the change of criticalduration during dark adaptation that is implied inCrawford's data and investigates the change of theform of the temporal-summation function during darkadaptation in order to relate these to changes of sum-mation observed under other stimulus manipulations.

METHOD

Apparatus

A two-channel maxwellian-view optical system wasused. Details of the optical unit were presented byMatin.'2 In the present study, which used monocular

vision, only the left half of the binocular system wasused. Sylvania glow-modulator tubes R1131C were thelight sources. Luminance was varied by crossed polar-izers and Kodak Wratten neutral density filters. Abeam splitter superimposed the beams for the adaptingand test stimuli and deflected a portion of each beamthrough a lens that focused the light at a photomulti-plier (RCA 931A). In a third beam, light from a 6-Vpilot bulb was diffused, selectively filtered, and re-stricted by a field stop to form a small red fixation spot.The subject, whose head was held steady by means ofa dental impression, viewed images of field stops formedat optical infinity. The visual field is sketched in theupper right corner of Fig. 1.

The durations of light flashes and dark times werecontrolled by Tektronix waveform generators (type162), a Tektronix pulse generator (type 161), andRoush phantastron timers. Output pulses from theseunits generated a series of clicks as warning signals and

LIGHTADAPTED

- 5. -

0-4'-

L

DARKADAPTED

1n i

-26 -6 0 1SECONDS

8 15 22

FIG. 1. Visual field and temporal sequence of stimuli for a singletrial. At -26 s the subject initiated the trial by triggering an ad-apting flash (which appeared as a 40 -diam circular field 5° fromthe fixation spot), as in the upper sequence, or a dark time, as inthe lower sequence. The vertical line 0.3 s before onset of each testflash indicates the warning click. All test flashes (which appeared as

°-diam fields centered on the adapting field) on a single trial wereof the same duration, as shown, but two test-flash durations werevaried among trials within a session.

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VOLUME 62, NUMBER 3 MARCH 1972

BARBARA R. STEWART

operated two current generators (Roush lightflashgenerators) to drive the glow-modulator tubes.

Neutral density filters and polarizer settings werecalibrated with an SEI densitometer. Light sourceswere calibrated by making a split-field photometricmatch with light from a diffuse source reflected from amirror placed just in front of the focusing lens and thendetermining the luminance of the reflected image of thediffuse source with the SEI photometer.

Durations controlled by the various electronic unitswere calibrated with a Beckman 6144 electroniccounter. Durations of the adapting flash and theinterval between test flashes (see Fig. 1) were within3% of stated values; test-flash durations were main-tained within 1% of stated values.

Output of the photomultiplier was displayed on aTektronix type 532 oscilloscope for calibrations of thestimulus waveform. Rise time was approximately 30 us;decay time was approximately 15 ,s. During the first3 s of the 26-s adapting flash the luminance rose to110% of the initial value; it was steady thereafter.During the longest test flash (1 s) luminance rose about3% (0.01 log increment); proportionately smallerchanges occurred for flashes of shorter duration. Nochange of luminance could be detected over the seriesof test flashes in a single trial. Luminance calibrationsover several days were within 10% (0.04 log increment).

Procedure

Data were collected from two subjects; each servedalternately as subject and experimenter.

TABLE I. Values of stimulus variables presented in the experi-ment. Luminance thresholds were determined for each of the test-flash durations at each of the times in the dark following each ofthe adapting luminances.

Adapting Times in Test-flashluminances the dark durations

Part (mL) (s) (s)

2.4X 10'7.6X 10 -6a2.4X 10 1

I 7.6 8 0.0052.4 15 0.2

(7.6X 101)b (22)bDark adapted

0.0050.01

2.4X 102 -6" 0.02IIA (2.4X lQ)b 1 0.05

7.6X 10-' 8 0.1(Dark adapted)b 15 0.2

22 0.51.0

-6a

IIBo 2.4X 102 8 0.0057.6X 10-1 15 0.2

22

-The -6-s time "in the dark" denotes the increment threshold of thetest flash superimposed on the adapting field.

b Values in parentheses were presented to subject B only.e Part IIB was presented to subject A only.

Luminance thresholds were determined as functionsof test-flash duration, adapting-flash luminance, andelapsed duration of dark adaptation. During a session,only one adapting luminance and two test-flashdurations were employed. A 26-s adapting flash (or20-s dark time, for the dark-adapted condition) plus anumber of test flashes, one at each of the selectedelapsed times in the dark, were presented on everytrial, as indicated in the stimulus sequence shown inFig. 1. Each test flash was preceded by a click 0.3 sbefore flash onset. After each flash, the subject re-sponded "seen" or "not seen." Trials were triggeredby the subject with minimal intertrial interval (1-2 s).Before each session, the subject was dark adapted10-40 min, depending on the adapting luminance. Atthe beginning of each session, five trials were allowedfor adaptation and warmup before data were collected.

Luminance of the test flash at each elapsed time inthe dark was varied independently, according to theup-and-down (staircase) method." This design simul-taneously generates several staircases (and severalthresholds) during a single session. The starting pointfor each staircase was randomly set at twice, at half,or at the expected threshold value. Seventeen trials ateach of the two test-flash durations were presented ineach session. The test-flash durations were randomizedamong trials, with the restriction that the same dura-tion could not occur five times consecutively. Twoblank trials were randomly inserted in each of thestaircases. Subject A's reports contained no false alarms.Subject B reported a light seen on approximately 2%of the blank trials.

The stimulus conditions presented in the experimentare listed in Table I. In Part I, only two test-flashdurations were presented. In each session, one thresholdfor each of these durations was determined at eachelapsed time in the dark for a single adapting luminance.The adaptation conditions were randomized within ablock of sessions. Each adaptation condition was pre-sented five times. In Part IIA, which was conductedapproximately 2 months after Part I, eight test-flashdurations were presented. These were randomly paired,making up four sessions at each adapting luminance.A second determination of each threshold was madewith a different random pairing of durations in a secondgroup of four sessions for each adapting luminance.Adaptation conditions were randomized within eachblock of sessions. In Part IIB, the two test-flashdurations of Part I were presented in five sessions ateach of two adapting luminances. Sessions for PartsIIA and IIB were randomized within the same block.

RESULTS

The luminance threshold was calculated from eachstaircase by averaging the logarithms of the luminancesat which changes of response occurred (peaks andvalleys)." The first such change of response was not

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included, in order to lessen the influence of the startingpoint on the threshold value. The median number ofpeaks and valleys entering into a threshold was seven.For repeated adaptation conditions, the logarithms ofthe luminance thresholds calculated from each staircasewere averaged.

The luminance thresholds for Part I for subject Bare presented as dark-adaptation functions in Fig. 2.Similar data were obtained for subject A.'4 Increasedtemporal summation is indicated by increased sepa-ration of the two curves at times later in dark adap-tation. In this and following figures, data points havebeen connected in a manner that indicates the con-stancy of threshold from -6 s to a time shortly beforeadapting-flash offset and that allows for the rapidfluctuations in threshold that occur", 6 during thehalf-second that brackets adapting-flash offset.

The critical duration for Part I was calculated byassuming that the 0.005-s duration falls in a periodduring which Lt=k and that the 0.2-s duration falls ina period during which L = k'. If we assume a sharp breakat the critical duration, at which both equations hold,t1=k/k'.' 7 Critical durations for Part I for subject Bare presented in Fig. 3. Similar data were obtained forsubject A. There is a steep increase of critical durationfrom the value for the increment threshold to that at1 s in the dark, followed by more gradual increases or aleveling off of critical duration. Values shorter thanabout 0.1 s-occurring principally in the -6- and 1-sconditions-are, with only one exception, inverselyrelated to adapting luminance at each time in the dark.Longer critical durations are not regularly related tothe adapting luminance.

The luminance thresholds for Part IIA for subject Bare presented as dark-adaptation functions in Fig. 4.Similar data were obtained for subject A. Superpositionof the curves for longer test-flash durations indicatesthe range of L constancy; increased divergence indi-cates increased temporal summation; durations thatare within the critical duration at all times in the dark

(R) 2.4 102 ,rL 7.6 x10 (C) 2.4 102.5 0 - 1.5--

1.0 0. 5-

-c - - 1.0 , ,0.0,

-0 5 -0 02 S0

0.2,-I --20 -2.5

(d) 7.6 (e) 2.4 MII 7.6 10'1.5 1.0 0.5

1 OR 0 -0.5 - L 0

0.2-;5-2.0 0 5 -

-6 1 a 15 22 -6 1 8 15 22 -6 I 8 15 22 DARKTIME IN THE DARK () ADAPTED

FIG. 2. Dark-adaptation functions for two test-flash durationsfollowing six levels of adapting luminance.

-0.7

-0.8

-0.9

-1.0

z° -I.1 -o

~0- -1.2

F-

-1.3(900-J

1.4

x

-1.51-

-1.6I I I I I i/ I

-6 1 8 15

TIME IN THE DARK (sW

22 // DARKADAPTED

FIG. 3. Change of critical duration with time in the dark fol-lowing light adaptation at 2.4X102 (-), 7.6X10 (v), 2.4X10(iN), 7.6 (+), 2.4 (*), and 7.6X10-' () mL.

produce parallel curves like the higher three curves ineach portion of the figure.

In Part IIA, the critical duration was calculated byassuming that the three shortest durations fall in theLt= k period and that the two longest fall in the periodduring which L= k'. These points were averaged toevaluate the constants. Figure 5 shows the fit of theLt=k and L=k' equations to the data for subject B.

2.5

2.0

1.5

- 1.0

0.5

7

-I

40

-0.5

0-1.0

.C

0.5

0

-0.5

- 1.0

-I 5

-2.0

-25

i -0.5

S -30

-0.5

- -2.5

* -3 0

- -3.5

I

-6 1 8 15 22 -6 1 8 15 22 -6 I 8 15 22 DARKADAPTED

TIME IN THE DARK (I)

FIG. 4. Dark-adaptation functions for test-flash durations of0.005 (e), 0.01 (A), 0.02 (m), 0.05 (v), 0.1 (o), 0.2 (A), 0.5 (0),and 1.0 (v) s, following light adaptation at 2.4X 10' (left), 2.4X10 (center), and 7.6X10-' (right) mL.

DURING DARK ADAPTATION

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BARBARA R. STEWART

Despite these differences, Part IIA replicates thegeneral finding of Part I. For higher adapting lhmi-nances, critical duration continues to increase beyond1 s of dark adaptation. As shown in Fig. 5, the limitof the complete-summation period tends to change withtime in the dark in the same manner as the calculatedcritical durations, although the change is probably notas great because the lengthening effect of the partial-summation period on the calculated critical durationis not equal in all cases.

Part IIB provided a check on the reliability of thecritical durations estimated in Part I. Of the four con-ditions repeated, all critical durations were replicatedwithin 0.01 s. The differences between the criticaldurations estimated from Parts IIB and 11A, whichwere run concurrently, are very much like the differ-ences between those estimated from Parts I and IIA,indicating that the latter were not unduly influencedby variability introduced by the time separation ofthose two parts of the experiment.

In summary, during dark adaptation the criticalduration increases, with greater increases for higher

-3.0

-3 5

--AK-4��� .4-

-. , -

t�ct�-�- ,

- / _

-- ZI I I

-2.5 -2.0 -1,5 -1.0 -0.5 0LOG t (S)

FIG. 5. Log Lt as a function of log t for test flashes that occurred6 s before (+, and I (A), 8 (N), 13 (e), and 22 (v) s, after thetermination of an adapting light of 2.4X 102 (top), 2.4X 10~center), and 7.6X 10-' (bottom) mL, and in the dark-adaptedstate (x). The - 6-s functions are displaced - 1.5 (top), -1.0(center), and -0.5 (bottom) on the ordinate. Straight lines werefitted by using only the extreme points, as explained in the text.

Similar fits were obtained for subject A. Intermediatepoints generally fall less well on the lines for loweradapting luminances and times further into darkadaptation. The theoretical functions intersect at thecalculated critical durations.

The change of critical duration with time in the darkfor Part IIA for subject B is presented as filled pointsand solid lines in Fig. 6. Half-filled points and brokenlines show the Part I data for the corresponding adap-tation conditions. Longer critical durations weregenerally obtained by the method employed in PartIIA. The differences of critical durations estimated bythe two methods are generally explained by deviationof the 0.2-s thresholds from the L=k' lines in the LIfunctions (Fig. 5). The difference is particularly evidentin the values obtained in the dark-adapted condition.In the corresponding Li curve (bottom of Fig. 5) thethreshold at 0.2 s more nearly fits the Li=k limb thanthe L= le' limb of the function. When the second limbis based on the longer durations, therefore, the estimateof critical duration is very much greater.

-0.5

-0.6

-0.7

-0.8

-0.9 ~z0

-1.0

a:I

0J -wC-,

-1 .2CD

-1.3

-I.4f

-1.5

S

--&- - --

H4

a = ie I- - - __ I

-6 I 8 15

TIME IN THE DARK {s)

22 "' DARKADAPTED

FIG. 6. Change of critical duration with time in the dark fol-lowing light adaptation at 2.4X102 (circles), 2.4X10 (squares),and 7.6X 10-1 (triangles) mL. Filled points (solid lines) are fromPart IA; half-filled points (broken lines) are from Part I.

04J

- X - # H - --

#E- - -ye

Vol. 62452

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March 1972 TEMPORAL SUMMATION DURING DARK ADAPTATION

adapting luminances. Following the highest adaptingluminance tested (2.4X102 mL), where the change ofcritical duration is greatest, the critical duration, basedon combined estimates from all of the data, increasesfrom approximately 0.04 s for the increment thresholdto 0.09 s after 8 s of dark adaptation, with an additionalincrease to 0.10 s by 22 s in the dark; dark-adaptedcritical duration is approximately 0.18 s. As adaptingluminance decreases or time in the dark increases, theform of the summation function changes, so that thetransition from complete temporal summation to nosummation becomes less abrupt.

DISCUSSION

The results of this experiment support the thesis thattemporal summation increases during dark adaptation.They indicate that test flashes of very brief durationshould be used to study dark adaptation wheneverchanging energy requirements due to changing temporalsummation are to be excluded from the analysis. Theimportance of considering changes of critical durationwhen interpreting increment-threshold data has beenemphasized by Keller3 and by Cornsweet and Pinsker.'8The latter authors, however, also determined thresholdsafter 5 s in the dark as a function of adapting luminance.Apparently assuming that the critical duration isaffected only by current illumination, Cornsweet andPinsker (p. 308) state that "integration time could notchange as a function of the base luminance" for thatadaptation condition. Data of the present experimentindicate, on the contrary, that critical duration after5 s in the dark is dependent on the adapting luminanceand that interpretation of the data obtained under thoseconditions would require consideration of change ofintegration time if a long stimulus duration had beenused.

Equivalent-Background Analysis

Crawford'0' 15 related the threshold changes that occurduring dark adaptation to the changes of steady-stateincrement thresholds that are observed when back-ground luminance is varied. He defined the equivalentbackground at a particular point in dark adaptation asthe background luminance whose increment thresholdis equal to the absolute threshold at that time in thedark. This analysis eliminates differences in the dark-adaptation function that are introduced by varyingcertain characteristics of a test flash, because thedifferences that appear in the dark-adaptation func-tions are exactly equal to the differences that appearin the increment-threshold functions when the stimuluscharacteristics are changed. He found that the declineof equivalent background with time in the dark is thesame, despite variations of test-stimulus size'5" 9 or ofretinal location.'0 When the duration of the test flashwas varied,' 0 however, he found small differences in theequivalent backgrounds during the first minute or twoof dark adaptation.

o01

\0005s -70.2

-10

1 8 15 22 -0.62 -0.12 0.38 0.2 8 1.38TIME IN THE DARK (s LOG BACKGROUND LUMINANCE (.L)

FIG. 7. Equivalent-background analysis. The dark-adaptationthresholds for subject A (open points) are the means of the Part Iand Part IIB determinations for the 2.4X 101-mL adapting lumi-nance; the increment thresholds for background luminances of log-arithms 1.385 0.88, and-0.12 were determined only in Part I, thatfor -0.62 was determined only in Part IIB. All thresholds forsubject B (filled points) are from Part I. Straight lines for the in-ce;nthreehold relations were fitted by the method of leastsquares.

The results of the present experiment do not allowan extensive equivalent-background analysis becausenearly all dark-adaptation thresholds are lower thanthe increment thresholds (- 6-s condition). However,a few interesting comparisons can be made. Figure 7presents dark-adaptation thresholds following thehighest adapting luminance for the 0.005- and 0.2-sflashes for each subject and the increment thresholdsfor each of these test-flash durations at the four lowestadapting luminances. (A discussion of the influence ofthe adapting conditions under which these incrementthresholds were determined is presented in the Ap-pendix.) Following the horizontal lines from thethresholds for subject B at 1 s in the dark to theirintersections with the increment-threshold functionsgives the values of the equivalent backgrounds. Thesevalues are not equal. The logarithm of the equivalent-background luminance for the 0.005-s flash is approxi-mately 0.3 less than that for the 0.2-s flash. The sameanalysis for subject A gives a difference of approxi-mately 0.2. At 8 s in the dark the difference is still 0.2for subject A and about 0.1 for subject B. At 1 s in thedark following 7.6X 10-mL adaptation, the differenceis 0.2 for both subjects.2 0 For the six points at which theanalysis can be made, therefore, the equivalent back-ground for the shorter test flash is always lower thanthat for the longer test flash, in agreement with Craw-ford's'0 data. For the level of sensitivity indicated bythe short test flash, the thresholds for the long testflash show less temporal summation for the equivalentbackground of dark adaptation than for a real back-ground.

The equivalent-background transformation is afoundation of the dark-adaptation theories presentedby Barlow2" 22 and by Rushton."9 Neither, however,considers duration of summation as a fundamental

453

BARBARA R. STEWART

TABLE II. Values of constants for best-fitting solutions of equations predicting the relation between criticalduration (t4) and integrated threshold energy (Li, K•4).

Equation (l) Equation (11),(k,/t4 ) +k2 =log L AlVmaX/ A 4= '[rt ~"(n- 1) -2(n-2) !]

DataPart Subject points k, k2 SDb n Vmax/A SDb

A 21 0.160 -2.74 0.425 6 1.5 X 10-7 0.489B 31 0.104 -2.28 0.394 4 1.91 X105 0.446

IIA A 10 0.117 -2.11 0.514 5 4.20X 10-6 0.467B 16 0.101 -2.03 0.527 4 3.85X10-5 0.454

IIB A 10 0.138 -2.66 0.264 6 1.1 X 107- 0.355

LL=threshold luminance; .=test-flash duration; 1¢=critical duration; gxmax'=increment of neural response; it=number of stages in model filter.The constants include a scaling factor converting to the logarithm of integrated energy in units of td a, consistent with the treatment by Martin(Ref. 23). Ordinal values determined from these constants are displaced -1.2 in Fig. 8 to convert back to the logarithm of integrated energy in units ofmL s.

b Standard deviations (SDs) are in units of log LD.

variable in adaptation. Matin's2" development of theFuortes and Hodgkin2 4 model and treatment of in-crement-threshold data includes the relation betweentemporal summation and signals measured by theequivalent background; it specifies a relation betweencritical duration and integrated threshold energy thatis independent of time in the dark and of adaptingluminance (i.e., although critical duration and thresholdenergy are assumed to be influenced by time in the darkand adapting luminance, the relation between the twois not). Matin presents three such functions, based onslightly different theoretical developments. Two of theseequations, each containing only two constants, werefitted to the data of the present experiment by mini-mizing the standard deviation of observed integratedthreshold energy from the predicted value. (The thirdequation contains four constants and cannot be evalu-ated without additional restrictions.) In Table Ir the

o.5

E

2

0:

I

0

-0.5k

-1.0

-'.5

-2.0C-

-2.5k #I

3.01-

-3.5k

5 10 15 20 25 30 35RECIPROCAL CRITICAL

AI

. , * ,J * J_5 10 15 20 25 30 35

DURATION Is-el

Fir. 8. The relation between integrated threshold energy(determined from luminance thresholds for 0.005-s flashes) andthe reciprocal of the critical duration. The right portion is datafor subject A; the left portion is data for subiect B. Included arevalues at -6, 1, 8, 15, and 22 s from Omiet of an adapting light ofluminance 2.4X102 (el, 7.6X10 (v), 2.4X10 (n), 7.6 (+), 2.4(*), and 7.5X10- (A) nL, and in the dark-adapted state (x).The solid line is the theoretical function specified by Eq. (1) inTable II; the broken line is that specified by Eq. (11).

equations are given, with constants evaluated from thedata of the present experiment. Figure 8 shows thetransformed data of Part I and the theoretical functions.Results for Part II data were similar. Although theequations appear to describe the general trend of thedata, standard deviations of the order of 0.4-too largefor a satisfactory fit-were obtained. This analysis,like the equivalent-background analysis, therefore,suggests that a single mechanism is inadequate toexplain the changes of threshold and of temporal sum-mation that occur during dark adaptation. Residualeffects dependent on adapting luminance may enter asadditional factors, especially during the early part ofdark adaptation.

Interrelation of Variables in Terms ofTemporal-Summation Effects

The changes of the form of the Li function duringdark adaptation are similar to some changes that havebeen observed with decrease of stimulus area 7' 25

-29

and decrease of stimulus wavelength, 2 8 as well as de-crease of background luminance.2 -8 Sperling andJolliffe2 8 relate the effects of stimulus size and ofstimulus wavelength on the form of the Li function byanalyzing the stimulus manipulations in terms of theresultant relation between the size of the stimulus fieldand that of the retinal summation field. They note thatas the stimulus field decreases relative to the summationfield in the area studies (or conversely the summationfield increases relative to the stimulus field in the wave-length study), the complete temporal-summationperiod increases and the amount of partial-temporalsummation beyond this period increases. This analysismay also be applied to the effects of background lumi-nance and of dark adaptation. Increased backgroundluminance decreases summation area30 and the ex-pected changes of the LI functions for a constant test-stimulus size have been reported.2 -8 The temporal-sum-mation changes found in the present experiment aregenerally consistent with an explanation in terms ofincreased retinal-summation area during dark adap-tation,3 ' i.e., the data show increased critical duration(or period of complete summation) and increased partial

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March 1972 TEMPORAL SUMMATION DURING DARK ADAPTATION

summation with increased time in the dark. If thechanges of temporal summation during dark adaptationwere wholly attributable to changes of the spatialrelations, however, it would be expected that theequivalent backgrounds for stimuli of different dura-tions would be equal throughout dark adaptation if itis true that the equivalent backgrounds for stimuli ofdifferent sizes are equal throughout dark adaptation.'9The discrepancies evident in the equivalent-backgroundanalyses by Crawford'" and of the present study sug-gest that the changes of temporal summation duringdark adaptation may not be completely subsumed undera theory of the spatial effects that occur during darkadaptation.

ACKNOWLEDGMENTS

I thank Professor L. Matin for substantial assistancein all phases of this research, Dr. J. Kerr for helpfulsuggestions regarding the manuscript, and my husband,Dr. R. W. Stewart, for his gracious and forbearingparticipation in the experimental studies.

APPENDIX

The procedure under which the increment thresholdswere obtained in this experiment-the test flashesoccurring 20 s from the onset of an adapting light in acontinuous series of trials each consisting of a 26-s lighttime and approximately 23-s dark time-may raisequestions regarding the validity of the use of thesethresholds in an equivalent-background analysis, forwhich fully adapted thresholds have previously beenused. Two arguments against such an objection areconsidered.

First, the increment thresholds are not changing inany regular manner across the session (i.e., the stair-cases are essentially flat); therefore, the state of adap-tation at 20 s from adapting-light onset must be un-changed in successive trials. Since light adaptation ismuch more rapid than dark adaptation, 26 s is a rela-tively long light time but 23 s is a relatively short darktime, and it might be expected that light adaptationwould increase during the course of a 30-min session ifthe adaptation state were very far from the fullyadapted condition.

Second, even if the increment thresholds are notcharacteristic of the fully adapted condition, the argu-ment below indicates that the "mislabeling" of thisparticular state of adaptation by identifying it with thethe adapting luminance does not invalidate the equiva-lent-background analysis.

Assume the simplified case, outlined in Fig. 9, ofincrement thresholds (for two test-flash durations) T.and T3 at background luminance B, and T 4 and T6 atbackground luminance B4, and the dark-adaptationthresholds T2 and T5 at a given time in the dark.Projecting T2 and T5 to their respective increment-threshold functions, one obtains equivalent back-

T6 -

T5 L

T4

1T,

T

B,

TIME IN THE DARK

S.

B2 B3 B4

BACKGROUND LUMINANCE

FIG. 9. Hypothetical equivalent-background analysis. Uppercurves are for short-duration test flashes; lower curves are for long-duration test flashes.

grounds B2 and B3, with difference 60. Assume now thatincrement-threshold values T 4 and T6 are not deter-mined as the fully adapted increment thresholds foradapting luminance B4 but are descriptive of the fullyadapted condition for some other adapting luminanceB.. The question arises: given a nonzero value of bofor T 4 and T 6 located at B4 , is there a value B.,, (atdistance a from B2) at which 3=0?

The problem can be treated by considering that theincrement thresholds T 4 and T6 are moved away frombackground luminance B4 at a constant velocity v0.The velocities v, and v2 of the intersection points (notedas open circles) of the dark-adaptation thresholds T2and T5 with the increment-threshold functions thenwill move with velocities

vj=a/t (1)and

V2= (a+6o)/t, (2)

where t is the time required for the intersection pointsto reach B,.

Using similar right triangles, it can be shown that

v,/vo= (T2- T,)/(T 4 - T,) (3)and

v2/vo= (T6- T,)/(T,- T,). (4)Because all of the threshold values are held constant

V1/V2 = C

and from Eqs. (1) and (2)

V1/V2,= a/(a+3o).

Therefore,a=c3o/(I-c).

(5)

(6)

(7)

An obvious solution is a=B2-B,, i.e., the case wherethe increment-threshold functions are collapsed to asingle vertical line, which is meaningless in the experi-

455

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BARBARA R. STEWART

mental situation. Because, however, the equation for ais linear, this must be the only solution. Misplacing theincrement thresholds on the background-luminanceaxis, therefore, cannot account for the obtained nonzerovalues of 6o. On the other hand, if ao= 0, i.e., theequivalent backgrounds are equal, V1 = V2, and a cantake on any value. Relocating the increment thresholdson the background-luminance axis, therefore, cannotintroduce inequalities into a situation in which theequivalent-background analysis does hold.

The above treatment is unchanged by adding move-ment (in either direction) of the increment thresholdslocated at B1, since velocity vo can be defined as thevelocity of the points initially at B 4 relative to thatof those initially at Bi, and the vertical distancesremain unchanged. If the increment-threshold func-tions are determined by more than two sets of points,all of which are allowed to move along the background-luminance axis, the analysis would still hold as longas the movement of points were such as to maintainlinear relationships. This would be true, for example,if the magnitude and direction of displacement of a setof points were regularly related to initial placement, aswould be expected in this experimental situation. Non-linear increment-threshold functions present a morecomplicated problem, but, again, for similar monotonicfunctions for long and short test-flash durations, in-equalities in equivalent backgrounds would probablybe maintained as long as the general form of the func-tions is maintained.

Because the value of Bo obtained will depend on thelocation of increment thresholds on the background-luminance axis, its magnitude is not a good measureof the adequacy of the equivalent-background analysisof dark adaptation in any situation where such locationmight be questioned. A more meaningful measure inthese circumstances is the amount by which one of thedark-adaptation thresholds would have to be changedin order to eliminate a nonzero value of 6o, because therequired change in threshold is invariant with changein B.. In the present experiment the observed 6o valuescould be eliminated by a 0.17 log decrement in thedark-adaptation threshold of the 0.2-s flash or a 0.12log increment in the threshold of the 0.005-s flash.These values are only slightly larger than the typicalvariability, but the fact that the six observed 8&os are inthe same direction and consistent with the earlier studynoted in the text suggests that these represent a realeffect.

The assumption involved in the analysis above-that increment thresholds for different test-flash dura-tions determined at some point during light adaptationto a particular luminance are equal to the thresholdsthat would be obtained for the fully adapted conditionat some other background luminance-is an "equiva-lent-background" theory of light adaptation and re-quires experimental verification. It may be that the

relation between sensitivity and temporal summationis not the same for the transient adaptation changesthat occur during light adaptation (or dark adaptation)and for changes effected in going from one steady stateto another.

REFERENCES

* This study is part of a thesis submitted in partial fulfillment ofthe requirements for the degree of Doctor of Philosophy at Colum-bia University. It was supported by a National Science Founda-tion Graduate Fellowship to the author, by NSF grant No.GB5947 and PHS Research Grant No. EY-00375 from theNational Eye Institute, National Institutes of Health to ProfessorLeonard Martin, and by funds from the Columbia UniversityInstitutional Scientific Research Pool.

1 A. M. Bloch, C. R. Soc. Biol. 2, 493 (1885).2 C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635

(1938).3 M. Keller, J. Exptl. Psychol. 28, 407 (1941).4 G. van den Brink and M. A. Bouman, J. Opt. Soc. Am. 44,

616 (1954).5 W. R. Biersdorf, J. Opt. Soc. Am. 45, 920 (1955).6R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).7 H. B. Barlow, J. Physiol. (London) 141, 337 (1958)."M. Ikeda, J. Opt. Soc. Am. 55, 1527 (1965).9 E. Wolf and M. J. Zigler, J. Opt. Soc. Am. 41, 130 (1951)." B. H. Crawford, Proc. Roy. Soc. (London) B123, 69 (1937).11 Because critical-duration studies with acuity targets have in

general not conformed well with studies based on the thresholddetection of light [see D. Kahneman, Vision Res. 4, 557 (1964),Vision Res. 6, 207 (1966), and C. H. Graham and C. Cook, Am. J.Psychol. 49, 654 (1937)], these data need not be expected tocompare ivell with the effects of adaptation on the critical durationfor the increment threshold. Wolf and Zigler's study does, how-ever, provide some evidence of increased temporal summationduring dark adaptation.

12L. Matin, J. Opt. Soc. Am. 52, 1276 (1962).la G. B. Wetherill and H. Levit, Brit. J. Math. Stat. Psychol. 18,

1 (1965).14 Complete tabular data are given in B. R. Stewart, disserta-

tion, Columbia University, 1969. University Microfilms OrderNo. 70-7074.

" B. H. Crawford, Proc. Roy. Soc. (London) B134, 283 (1947).16 H. D. Baker, J. Opt. Soc. Am. 43, 798 (1953).17 This calculation could yield a value of critical duration greater

than 0.2 s only if the measured value of LI for the 0.2-s flash wereless than the value of Li for the 0.005-s flash. In fact, this relationof Li values was never found, and all critical durations calculatedby this method are less than 0.2 s.

18 T. Cornsweet and H. M. Pinsker, J. Physiol. (London) 176,294 (1965).

1" W. A. H. Rushton [Proc. Roy. Soc. (London) B162, 20(1965)] confirmed this finding, but E. J. Rinalducci, K. E. Higgins,and J. A. Cramer [E. Opt. Soc. Am. 60, 1578 (1970)] found thatthe equivalent-background analysis did not hold during photopicdark adaptation.

2 The thresholds at 8 s in the dark following 2.4X 10'-mL adap-tation and at 1 s in the dark following 7.6X10-mL adaptationintersect the increment-threshold functions in the region of theextension below the lowest background luminance tested. Becauseall thresholds at that luminance are still about 100 times the dark-adapted thresholds, the extension of this line through another dec-ade of background luminance is probably a valid approximationof the function in that range.

21 H. B. Barlow, Vision Res. 4, 47 (1964)."2H. B. Barlow, in Photophysiology, edited by A. C. Giese

(Academic, New York, 1964), pp. 163-202.2 3 L. Matin, J. Opt. Soc. Am. 58, 404 (1968).24 M. G. F. Fuortes and A. L. Hodgkin, 3. Physiol. (London)

172, 239 (1964).21 C. H. Graham and R. Margaria, Am. J. Physiol. 113, 299

(1935).26 H. W. Karn, J. Genm Psychol. 14, 360 (1936).27 E. Baumgardt and B. Hillmann, J. Opt. Soc. Am. 51, 340

(1961)."H. G. Sperling and C. L. Jolliffe, J. Opt. Soc. Am. 55, 191

(1965).

456Vol. 62

March1972 TEMPORAL SUMMATION DURING DARK ADAPTATION

29 Data obtained by C. H. Graham, M. Akita, and E. H. Gra-ham, cited by N. R. Bartlett, in Vision and Visual Perception,edited by C. H. Graham (Wiley, New York, 1965), pp. 154-184.

30 Psychophysical data [H. R. Blackwell, J. Opt. Soc. Am. 36,624 (1946), Ref. 6] show decreased spatial summation with in-creased background luminance, and physiological studies [S. W.Kuffler, J. Neurophysiol. 16, 37 (1953)] show a decreased recep-tive field with increased background luminance when the field ismapped with a small test stimulus of constant luminance. Thedifferent discharge patterns of different parts of the receptive fieldand the interactions that are observed with multiple small teststimuli within the field indicate, however, that the spatial-sum-

mation changes observed psychophysically should not be simplyattributed to the change of receptive field size.

31 Psychophysical studies [K. J. W. Craik and M. D. Vernon,Brit. J. Psychol. 32, 62 (1941), Ref. 16; G. B. Arden and R. A.Weale, J. Physiol. (London) 125, 417 (1954)] indicate increasedsummation area during dark adaptation. Physiological studies[H. B. Barlow, R. FitzHugh, and S. W. Kuffler, J. Physiol.(London) 137, 338 (1957)] indicate, however, that dark adapta-tion causes a change of the organization of the receptive field, sothat inhibitory influences from the peripheral zone of the light-adapted receptive field are eliminated, leaving a smaller butwholly excitatory dark-adapted field.

457