ANALYSIS OF VISUAL l4ODULATION SENSITIVITY: TWO COMPONENTS IN FLICKER PERCEPTION Department
of Ps)choiog>.
Cniversity
of Brisroi, Bristol, England’
.Abstract--An analysis of human psychophysical flicker thresholds is developed from thr incrsment threshold technique of Stiles (1939). TKO independent detection components are required to account for ail available modulation sensitivity data. These components are differentiated by properties corresponding to the d%erence between sustained and transient units in the cat retina.
Following de Lange’s (1952. 1957) attempts to model the visual response to flicker modulation, there has been a recent upsurge in analysis of the processes un-
derlying perception of small perturbations
in stimulus
iummance3.
Sperling and Sondhi (1965) and Kelly (1969a. 1969b. 1971a. 1971b) have proposed comprehensive theories of visual responses to flicker and tran-
sient flashes. including detailed review of past litrraturc. The purpose of this paper is to suggest a new approach to the analysis of visual sensitivity to luminance perturbations. to provide further understanding of the underlying visual processes. This approach will be called luminance function analysis. and has been previouslv described (Tyler, 1970). It is an extension of Stilss’ (1939) increment threshold analysis of color mechanisms. He measured the increment threshold of a smali test patch on a larger background. The amplitude of the increment as a function of luminance,_/‘(l), was described by an empirical function which had the limiting form, AL = liL + L,
(1)
where: AL is the luminance of the increment; Lo is the low luminance asymptote of AL; L is the adapting luminance: and k is a constant. VVhen plotted on double-logarithmic coordinates this increment threshold functionf(l) has a 45’ asymptote at high luminance corresponding to Weber’s lavv (Fechner. 1560) (2JA.f. = constant). and a horizontal asymptote corresponding to constant threshold at low intensities (see Figs. 2 and 3). If the retina were a unitary detection mechanism. onef‘(L) function would suffice to describe the visual response. aith appropriate adjustments of k and L, under different adapting conditions. Stiles (1939) demonstrated that the retina is not a unitary detection mechanism. The curve of increment threshold as fimc’ Supported by Science Research Council Grant So. B,’ SR4Y36. ’ Presenr address: &II Laboratories. ‘D-504, 600 Nounrain Ave.. Murray Hill. New Jersey 07974, U.S.;\. 3The term “luminance” wili be used throughout this paper although in man! experiments stimulus energy is expressed in terms of retinal illuminance. This shorthand seems reasonable since the two quantities are proportional for a fixed pupil aperture. With a standard artificial pupil of 1 mm the conversion hctor is 10 td = 1 mL.
tion of background luminance of the same spectral composition was fitted by two](L) functions. one COTresponding to the scotopic mechanism and the other to the photopic mechanism of the retinal system. He made the assumption that each mechanism acts independently in determining threshold, without interaction with other mechanisms. The observed increment threshold function is then determined by the threshold of the most sensitive mechanism for each stimulus condition. Kelly (1969b) has taken a different approach based on the assumption that only one mechanism determines visual sensitivity for a given field condition. He selected conditions which optimise the response to a single aspect of the stimulus, such as edge sensitivity. His analysis derives the sensitivities of serial processes within the retina and the conditions under vvhich they operate. This contrasts with Stiles’ assumption that there may be independent parallel processes contributing independently to sensitivity. The object of the analysis reported here is to determine. using Stiles’ method, vvhether separate mechanisms with different temporal characteristics contribute to individual flicker sensitivity functions. All sources of flicker data sufficiently extensive to allow analysis are used in this paper. I. THE FLNDA.MEZT.\L
LL-\IIS.AUCE
FL.SCTIOS
The luminance function of equation (,I) is oniy one of many that have been postulated as luminance functions for individual retinal mechanism. Weber (185-t) originally suggested a straight line function with no low lummance limitation. Stiles (1939) developed empirical functions which diverge slightly from the f’(L) form in the middle range. The quantum fluctuation theory (de Vries. 1933; iMueller, 1950) and the neural noise theory(Barlow, 1956) suggest that the luminance function is determined by statistical factors and should be proportional to the square root of adapting luminance. particularly in the low luminance range. However most data. both for luminance increments (Graham and Kemp. 1938: Stiles. 1939. 1949; Mueller, 1951) and for spatial and temporal modufation (see below). tend to converge to a constant at very low luminances and to Weber’s law at high luminances. It is possible that threshold is determined bv statistical factors in the middle range and neural limitations at
low and high luminances (by a neural threshold and neural adaptation respectively). but this combination results ina function very similar to the_/‘(L) function in many cases. It is therefore an empirical question whether the data can be accounted for using only_/(L) functions or whether a statisticai effect is indicated in addition. In this and companion papers it will be shown that no statistical effect need be introduced. At least two models have been suggested for the adaptation effect of the upper limb of the Weber Rtnction. Rushton (1965) and others have suggested that logarithmic encoding corresponds to the saturation of the intensity response of the receptor potential. The saturation is postulated to arise from the esistence of a limited pool of ions which can be transferred across the receptor membrane to create the receptor potential. Kelly (197 la. 1971b) suggests an alternative derivation for the adaptation comprising a complex feedback pathway with multiple integrators and feedback loops which varied in number and gain depending on adaptation level. This formulation is difficult to handle as the values of several parameters must be determined from the data being fitted at each luminance level.
De Lange’s (1957) data of flicker sensitivity for observer V with a 2” field and a 60’ steady surround are replotted in Fig. 1 by measurement of the points from his figure. since the actual data are no longer available. This type of stimuius is comparable with Stiles’ (1939) study on increment threshold utilizing a field on which was briefly superimposed a I’ test patch, the luminance of which was adjusted to threshold. These stimuli may be considered as spatially similar since the time-average luminance of the test area in both is almost the same as that of the surround. The differences are that decrements as well as increments were
Fig. I. Log relative modulation sensitivity as a function of log frequency. replotted from de Lange (19%). observer V. The fog retinal illuminances of the curves are as follows. FiIIed circfes--lowest curve: -05, next cur%-et:04. next curve: 0.5, dashed curve: 1.0 log cd. Open circles-dotted curve: 1.5. dashed curve: 2.0. full curve: 3.0 Iog td. Upper filled circle-cur\e: 44 log td.
Fig. 2. Data of Fig. 1. replotted in terms 21 log absolute modulation sensitivity as a function of adapting luminance, with frequencv as a garameter. Freciuencics of 40, 30. P.,. .to“. 5 and 1 Hz ar; shown successivelv hisplac4 to the right b) one log u&. involved in the flicker experiment and the principal parameter used was the frequency of the stimufus rather than the wavelength of test and background fields. Thus AL+in equation (I) now denotes the absolute amplitude of modulation at threshold. The data are replotted in Fig. 2 in terms of absolute modulation at threshold as a function of adapting luminance. Modulation frequency is the parameter. As an initial attempt the data at each frequency were fitted by inspection by two (or one) S(L) functions on the assumption discussed above that overall sensitivity is determined by the most sensitive mechanisms at a given adapting luminance and frequency. This may be stated mathematically in the form AL, = f;(L) :4fJL1.
iii
The values of k and L, used for the curves in Fig. 7 are given in Appendix I. As a guide to the exact position of each curve a vertical marker has been placed at the adapting luminance for which L= 1I 2k. Successive curves are displaced horizontally by one log unit for clarity. The points for each frequency were fitted with reference only to the data at that frequency. and it shouId be noted that this produced a marked regularity aeross curves, with the intersection of the two functions becoming deeper as frequency was increased. Stiles (1949) showed that for his data a function with a more gradual transition between the horizontal and 45’ asymptotes may be observed for each mechanism. If the luminance functions of physiological mechanisms had a shallower transition between the asvmptotes. a good fit might be obtained with fewer Stiles-type functions. It should therefore be noted that at several points they(l) function itself is hardly abrupt enough to fit the data (e.g. at 5, 20 and JOHz). This suggests that the use of the f(L) hmction is warranted by the data. An alternative possibility is that the data might conform to a square root relationship between dL and L. .A line with the slope of -0-j is shown in Fig. 3 (dashed line), as predicted from the square root law of fluctuation theory. Clearly when shifted it would not provide a good fit to the data at any luminance. De Lange’s data (and indeed Stiieii were obtained with a fovea1 increment which had a sharp boundary. Other flicker data have been measured with a large. homogeneous flickering field (Kell>, 1961). It is of in-
frequencies. the assumption 41 he made that the same two mechanisms are responsible for the NO branciiss ot the curves at all frsquencies. -This mukss it possible to consldsr the sensitivities of each mxhunism ssparately. The sensitivity of sach mechanism can be plotted over the bvhole range of frequencies and background luminances by extrapolation from the region where it determined overall sensitivity. For convenience the mechanism that dstsrminrd oLeraIl sensitivity predominantly at low adaptation luminances will be called the low luminance mechanism. and similarly for the 3c -A : / high luminance mechanism. (For frequencies at which , 4’ 4” 4. 4. 4 z liop ldl the data xvas fitted bv only ons_/‘(Lf function. this curve Fio=. 2. hlodulation sensitivity data from Ktliy { 1961) re- will be arbitrarily assigned to the 10% Iuminance plottsif ;1sin Fig 2. Frequtnctes of 40, 20. 10, 5 and 1.5 Hz mechanism.) ;irs displactd success~vtll; to the right by one toy unit. Before replotting ths derived srnsitivities oi the two mechanisms. the rationale for differsnt axis scales must tetest to compare the luminance function analysis for be considered. The most characteristic aspect of flicker fovea1 and large-lield flicker. Figure 3 presents the data is ths form of the high frequency asymptote. Kell! iuminance function anaiysis of Kelly’s data in a similar (1969a. l97la. 197lb) has established that the high frequency asymptote of absolute modulation of much manner to Fig. 2. It appears that a single component Ricker data conforms to a d#usion model in which is sr&icient to fit all the data. sensitivity is a linear function of the square root of freA numerical indication of the conformity of theory to data is desirable. since it was impractical to fit the quency. This contrasts with the earlier electrical analog curves by a standard formula. The log standard devi- of de Lange ( 1957)in which the high frequency asympation of the points from the curves in the vertical direc- tote ivas a linear function of log frequency determined by the number of cascaded integrators involved. The tion was computed both for the present analysis and sensitivities of the two mechanisms derived by b>-measurement from pubIish~d figures for the mod& described by Van Nes (1968) and Kelly (I971a). The luminance function analysis have therefore been plotf‘(L) functions tit de Lange’s data with G’ = IGO dB. tsd in accordance kvith the diffusion model (Fig. -la) De Lange did not attempt to model all his data. SO no and the cascaded integrator model (Fig. 4b). In Fig. 4~. ahsolute modulation sensitivities on a logarithmic fit can be calculated. The fit of the square root relationship to his data has G’ = 360 dB (from Van Nes. 1968). scale are plotted as a function of modulation frequency The i.(L) functions fit Keliy’s data with 0’ = 0.70 dB, on a square root scale with adaptation luminance as whereas Kellv’s (1971a) theoretical functions fit the a paramsttr. It is apparent that the sensitivity of the same points with 0’ = 2.75 dB. Clearly the f(L) func- low luminance mechanism (filled symbols) does not tions fit the data with smaller error variance than the show any tendsncy to asymptote for different theories of either of the other authors. A mathematical adaptation luminances, whereas the sensitivity of the curve-fitting procedure might improve the fit still high luminance mechanism (open symbols) clearly further. and certainly should not degrade it. Note that approaches a straight line asymptote with a slope of Van Nes and Kelly require two degrees of freedom (d,) -0.75. as fitted by inspection at all luminances. The for their theoretical curves. The use of two possiblef(l) plot of the same values in terms of logarithmic relative functions at each frequency requires four parameters. modulation versus frequency coordinates I Fig. 4b) sugbut they have the constraint that sensitivity is deter- gests an explanation for the non-asymptotic behavior mined by the most sensitive mechanism throughout of the low luminance component. While the sensitivi[squation (?)I. This gives three degrees of freedom at ties of the high luminance mechanism (open symbols) each frequency. now sprsad considerably, the sensitivitv of the low Each curve fit is determined to the same number of luminance mechanism (filled symbols) -is essentially degrees of freedom (J,) as it has points, since a11points constant for three adaptation luminances. while the are independent. The number of degrees of freedom fourth approaches them at high frequencies. The accounted for by each theoretical curve is therefore straight line asymptote fitted by inspection has a slope ti, - tl,. The sum of these E(d, - d,) over all de Lange’s of - 5 corresponding to five cascaded integrators. The frequencies is 33 for d, = 2 and 27 for d, = 3. In the data are not suficiently extensive to determine the case of Kelly’s data E(d, - d,) is I7 for d, = 2 and 12 slope with any great accuracy, but the number ford, = 3. The variance is redxed in proportion to the required seems to vary little tvith luminance level. It reduction in number of degrees of freedom. Thus tz should be noted that sensitivities of the low and high should be reduced by a factor of 080 for de Lange’s luminance mechanisms are each we11 determined at data and 0.70 for Kelly’s when the d, is increased fcom high frequencies of modulation. so that the difference 7 to 3. The l‘(L) functions reduce C? by factors of 0.28 in asymptotes cannot be due to inaccuracies of extraand 0.25 respectively. in comparison to the alternative polatlon. Description of the curves in terms of twoI‘ theory, so they still provide a better fit to the data functions. shifting relative to each other as frequency even when the extra degree of freedom is taken into of modulation is changed. corresponds to the irreguaccount. larity of the spacing of de Lange’s originai frequent! The principal result of the analysis is to show that response functions. This irregularity is particularly evit\s-of(L) functions are required to fit flicker sensitivity dent on the high frequency slopes of the functions of at many frequencies in the 2’ field data of de Lange. both‘subjects but was not commented upon by de In view of the regularity of the differences in fit across Lange himself. ,A
I
i?rminonce
I”
,1
,
i-
I I
I
2
5
-1
10 20 (IOQ 5cole)
Modulation
frequency
50
100
U4rI
Fig. It. Frequency characteristics of the two mechanisms identified in the dam of Fig. 2. FilIed symbols --low luminance com~nent, open symbols-high luminance component; circles--3.0, pyramids-20. squares-1.0, fuIcra-O~Olog td. (a) Sensitivities of both mechanisms are plotted in terms of iog absolute modulation threshold as a function of the square root of frequency. Asymptotes to a slope of -0.73 (solid line) are drawn by inspection for the high luminance mechanism (open symbols) onI>. as the sensitivities low luminance mechanism do not appear to asymptote. (b) Sensitivities of both mechanisms replotted in terms of log relative modulation as a function of log frequency. Asymptotes fdashed lines) to a slope of -5 (solid line) are now drawn by inspection for the low luminance mechanism (filled s,ymbols) only, as the high luminance mechanism fails to asymptote here. Since only onef(Q function was sufficient for Kelly’s (1961) data, the frequency response of that function is approximated by Kelly’s original smooth curve, and need not be redrawn. l-liehas shown (Kelly, 1969a) that the high frequency asymptotes of these data conform to the diffusion model. 111.DISCUSSION What mechanism might be producing the alternative sensitivities in Fig. 4? Since one predominates at low and the other at high luminance, the first hypothesis to be considered is that they result from rod and cone activity respectively. This hypothesis must be rejected for two reasons. Firstly, de Lange’s stimulus was specifically designed to eliminate rod activity. The 7” flickering area was fovea1 and the large equiluminant surround should have eliminated any effect of stray light in the periphery. Secondly, the analysis of Kelly’s (1961) data should have shown evidence of two mechanisms, since the 65’ field should adequately stimulate both rod and cones at appropriate luminance levels. Since only one mechanism contributed to 65” field sensitivity, it is most unlikely that rods in the periphery could contribute to the 2” field sensitivity. The other salient difiierences between the two stimulus configurations are that de Lange’s contained flickering edges, whereas Kelly’s was uniform and of greater area. Kelly (1969a, 1969b) has shown that the presence of flickering edges greatly alters the shape of flicker sensitivity. Flickering edge sensitivity is greater at low frequencies, whereas the uniform field shows a reduced low frequency sensitivity and a sharper peak. Comparing these results with Fig. 4b reveals a remarkable similarity in shape. The high luminance curves (open circles) appear to correspond with the uniform field sensitivity (Kelly. 1969b. Figs. 1 and 9) and the
low luminance curves (filled circles) with his flickering edge sensitivity. This identification is supported by the fact that both the high luminance curves and the uniform field sensitivity conform to a square root asktnptote (Fig. 4a). Note that the shape of the latter was essentially invariant with the number ofedgespresent. This correspondence suggests that the two components in Figs. 4a and b utilize uniform field and edge information, respectiveIy. Kelly (1969b) chose conditions which optimally select one or the other mechanism as the determinant of threshold. His results require only that the retina contains a single type of detection mechanism with area1 summation in which lateral inhibitory conncctions may or may not be stimulated, according to the stimulus configuration. On the other hand. the results of the analysis presented here conform to the assumption that the uniform field and edge sensitive mechanisms operate simul~neous1~ on the same stimulus input and that flicker threshold is determined by the response of the most sensitive mechanism. Iv.
RETINAL
MECH.C.3StlS
Having eliminated rods and cones as a possible explanation of the two mechanisms. it is of interest to
speculate on other physiotogical mechanisms which might explain the psychophysical data. The two main cell types projecting up the optic nerve may be referred to as “sustained and “transienr” ganglion cells (Cleland, Dubin and Levick. 197 1. 1973: Dowling, 1970; Enroth-Cugell and Robson. 1966: Ikeda and Wright, 1972). However, --sustained” cells also show an initial transient response. For the purpose of this paper the relevant distinction is between sustained and transient responses which may or may not occur in the same cell or fibrs but which must have different retinal substrates. It w-ill he assumed that the
517
Viji;al modularion jznsm\it! major eRects reported for the two cell-t!-pes derivs from their predominant response characteristic. Sustained responses may be identified with the edge sensitive mechanism and transient responses with the uniform field mechanism on the basis of five characteristics.
relatively faithful11 to the ganglion cell Ictsl. On the other hand. the edge-ssnsitive sustained response appears to be subject to a neural adaptation process which limits the response in the manner ofa series of cascaded integrators. REFERESCES
noise and absolute threshold. J. opt. Sot. Am. 36, 63-1-639. Cleland B. G.. Dubln bl. LV. and Levick W. R. I 1971) Sustained and transient cells in the cat’s retin,! xnd lateral gcniculate nucleus. J. Pi~Moi. Lord. 217. -L;T--196. Clcland B. G.. Levick LV. R. and Sanderson K. J. II9731 Properties ofsustainedJnd transient ganglion cells m the cat retina. J. Plryswi.. Lorul. 228, 649-680. de Lange H. I 1952) Euperim=znts on Hickcr and borne calculations on an electrical analogue of rhe fo\sal systems. Physicu 18. 935-950. de Lange H. (19571 Attenuation characterisrics ,Ind phaseshift charactsristlcs of the human fovea-cortex s!stcms in relation to Hicker-fusion phenomena. Doctoral dissertation, Tech. Hog.. Delft. dc Vries H. (1943) The quantum character of ljght and its bearing upon the threshold of vision. the differential sensitivity and the visual xuity of the elc. PI~ysw 10, 553-564. Dowling J. E. (1970) Oreanlzation of vertebrst? retinas. [)Iwsr. Ophtltai. 9, 65C6YO. Enroth-Cugell C. and Robson J. G. (19661 The contrast sensitivitv of retinal ganglion cells of the cat. J. Ph)~iol.. Lo&187. 5 I7-552. _ Fcchner G. T. ( 1860) Elrrw~rr drr Ps~honh~sk ITrans. bk ;\dler H. E.. 1966). Holt. Rinehart & W&on. New Yori. Fukada Y. (1971) Receptive field organization of cat optic nerve tibrcs with special reference to conduction velocity. 1’isiorz Rrs. 11, 209-226. Graham C. H. and Kemp E. H. (193s) Brightness discrimination as a function of the duration of rhc increment in intensity. J. yen. Ph~siol. 21. 63%650. Ikeda H. and Wright Xl. J. 11972) Differential effects of refractive errors and receptive field organization of the central and peripheral ganglion cells. I~isron Rrs. 12, 146%-1~36. Kelly D. H. (1961) Visual responses to time dependent stimuli--I: Amplitude sensiti\ity measurements. J. opr. sot. .4m. 51. -122-1’9. Kelly D. H. (1969a) DitTusion model of hnssr Bicker rssponses. J. opt. SOC..4rtz. 59, 16651670. Kelly D. H. (1969b) Flickering patterns and lateral inhibition. J. opt. Sot. .4m. 59, 1361-1370. Kelly D. H. (197la) Theory of Hicker and trsnsrsnt responses-1: Uniform fields. J. opr. Sot. .4m. 61. 53--546. Kelly D. H. (197lb) Theory of Hacker and tracsxnt responses-11: Counterphase gatings. J. opr. Sot. .4/n. 61. 633640. Mueller C. G. (1950) Quantum concepts in \isuA intensity discrimination. ,+n. J. Ps)chol. 63, 92-11X. Mueller C. G. (1951) Frequent) of seeing funstlons for intensit) discrimination at various levels of adapting intensity. J. ytm. Physiol. 31, -16N7-I. Rushton LV. A. H. (1965) The Ferrier Lecturs to the Royal Societ!. Visual Adaptation. Proc. R. Sot. B. 162, Z&-16. Sperling G. and Sondhi 51. bI. (1965) Model for visual luminance discrimination and flicker detection. /. opt. Sot. .4m. 58, I l33- I 145. Stiles W. S. (1939) The dirxtional sensitivity of the retina and the spectral sensitivities of the rods and cones. Proc. Barlou
(I) Rrcepticr-firld
orgmkatim
Sustained responses have a marked centre-surround organization. whereas transient responses do not. (Cleland. Levick and Sanderson, 1973). Sustained responses should therefore respond better to flickering edges. and transient responses better to a uniform field flicker. (1) Receptice-field
si:e
Sustained responses tend to have smaller receptive fields than transient responses (Cleland ef al.. 1973). Correspondingly, the edge-sensitive mechanism appeared with small field stimulation and the uniform field mechanism predominated with a large field.
The sustained response should by definition show little low frequency reduction, as was found for the edge-sensitive mechanism. The transient re>Tonse should be much reduced at low frequencies. as was found for the uniform field mechanism, since the high luminance sensitivity must fall below the low iuminante sensitivity in the region below 5 Hz (Fig. la).
Enroth-Cugell and Robson (1966) show that sustained responses change little with luminance level. reporting a variation of only threefold with a thousand-fold decrease in luminance in a typical sustained cell. Winters and Hamasaki (1972) show similarly that optic tract responses have different intensity rebszonse functions for the sustained and transient components of the response. With a two log unit variation in intensity. the sustained spike rate varies by a factor of 4 whereas the initial transient changes by a factor of IO. This difference is in accord with the insensitivity- of the edge-sensitive mechanism to luminance changes relative to the uniform field mechanism. (5) Rerir~al disrrihrriot~ Sustained cells predominate in the fovea and perifovea whereas transient cells are widely distributed across the retina (Fukada. 1971; Ikeda and Wright, 1972). Correspondingly. the edge-sensitive mechanism appeared only with a flickering edge close to the fovea, whereas the uniform field mechanism was present with stimulation both of the fovea and of the whole retina. Thus information gleaned from the psychophysics agrees at every point with an identification of the two mechanisms with the two major response types of ganglion cells of the retina. The different as>-mptotic behaviour of the two components is a final point for which there is no corresponding physiological information. If the identification with retinal cell tl;pes is correct, it suggests that the transient uniform field response has a limit determined by diffusion across the receptor membrane (Kelly, 1969a) which is transmitted
H. B. (1956) Retinal
R. Sot.
127B. 6-L-105.
Stiles W. S. (1919) The detxmination of rhe spectral sensirlvlties of the retinal mechanism bq sensor); metbdds. .Ved. Tijtischr. .Yatuwk. IS. l25- l-16. T>ler C. W. f 1970) A psychophysical study of the dynamics of color vision using wavelength-modulated light. Doctoral dissertation. University of Keele.
San .Nrs F. L. (t968) Experimental studies m spatiowmporal contrast transfer by the human eye. Doctoral dissertation. University of Utrecht. Weber E. H. (1833) De P&u. Resorptione. Auditu rr Tmt~c Annotatiunrs hxotnicar er Physioiogicae. C. F Koehler. Leipzig. Winters R. W. and Mamasaki D. I. 119i3) Comparison oi LGN and optic tract intensity-response functions. Cisiorr
APPEVD~S
1
Table I. Frsquenc]. I Hzr
i (log td) High Lou
i, cloy tdl tow High
Rzs. 12, W-608.
Values of k 2nd L,, [equation (I)] at ezch frequency for low and high luminance mechanisms, obtained as descrzbed in text for the data ofdr Lange (Fig 3!.
of Ps)choiog>.
Cniversity
of Brisroi, Bristol, England’
.Abstract--An analysis of human psychophysical flicker thresholds is developed from thr incrsment threshold technique of Stiles (1939). TKO independent detection components are required to account for ail available modulation sensitivity data. These components are differentiated by properties corresponding to the d%erence between sustained and transient units in the cat retina.
Following de Lange’s (1952. 1957) attempts to model the visual response to flicker modulation, there has been a recent upsurge in analysis of the processes un-
derlying perception of small perturbations
in stimulus
iummance3.
Sperling and Sondhi (1965) and Kelly (1969a. 1969b. 1971a. 1971b) have proposed comprehensive theories of visual responses to flicker and tran-
sient flashes. including detailed review of past litrraturc. The purpose of this paper is to suggest a new approach to the analysis of visual sensitivity to luminance perturbations. to provide further understanding of the underlying visual processes. This approach will be called luminance function analysis. and has been previouslv described (Tyler, 1970). It is an extension of Stilss’ (1939) increment threshold analysis of color mechanisms. He measured the increment threshold of a smali test patch on a larger background. The amplitude of the increment as a function of luminance,_/‘(l), was described by an empirical function which had the limiting form, AL = liL + L,
(1)
where: AL is the luminance of the increment; Lo is the low luminance asymptote of AL; L is the adapting luminance: and k is a constant. VVhen plotted on double-logarithmic coordinates this increment threshold functionf(l) has a 45’ asymptote at high luminance corresponding to Weber’s lavv (Fechner. 1560) (2JA.f. = constant). and a horizontal asymptote corresponding to constant threshold at low intensities (see Figs. 2 and 3). If the retina were a unitary detection mechanism. onef‘(L) function would suffice to describe the visual response. aith appropriate adjustments of k and L, under different adapting conditions. Stiles (1939) demonstrated that the retina is not a unitary detection mechanism. The curve of increment threshold as fimc’ Supported by Science Research Council Grant So. B,’ SR4Y36. ’ Presenr address: &II Laboratories. ‘D-504, 600 Nounrain Ave.. Murray Hill. New Jersey 07974, U.S.;\. 3The term “luminance” wili be used throughout this paper although in man! experiments stimulus energy is expressed in terms of retinal illuminance. This shorthand seems reasonable since the two quantities are proportional for a fixed pupil aperture. With a standard artificial pupil of 1 mm the conversion hctor is 10 td = 1 mL.
tion of background luminance of the same spectral composition was fitted by two](L) functions. one COTresponding to the scotopic mechanism and the other to the photopic mechanism of the retinal system. He made the assumption that each mechanism acts independently in determining threshold, without interaction with other mechanisms. The observed increment threshold function is then determined by the threshold of the most sensitive mechanism for each stimulus condition. Kelly (1969b) has taken a different approach based on the assumption that only one mechanism determines visual sensitivity for a given field condition. He selected conditions which optimise the response to a single aspect of the stimulus, such as edge sensitivity. His analysis derives the sensitivities of serial processes within the retina and the conditions under vvhich they operate. This contrasts with Stiles’ assumption that there may be independent parallel processes contributing independently to sensitivity. The object of the analysis reported here is to determine. using Stiles’ method, vvhether separate mechanisms with different temporal characteristics contribute to individual flicker sensitivity functions. All sources of flicker data sufficiently extensive to allow analysis are used in this paper. I. THE FLNDA.MEZT.\L
LL-\IIS.AUCE
FL.SCTIOS
The luminance function of equation (,I) is oniy one of many that have been postulated as luminance functions for individual retinal mechanism. Weber (185-t) originally suggested a straight line function with no low lummance limitation. Stiles (1939) developed empirical functions which diverge slightly from the f’(L) form in the middle range. The quantum fluctuation theory (de Vries. 1933; iMueller, 1950) and the neural noise theory(Barlow, 1956) suggest that the luminance function is determined by statistical factors and should be proportional to the square root of adapting luminance. particularly in the low luminance range. However most data. both for luminance increments (Graham and Kemp. 1938: Stiles. 1939. 1949; Mueller, 1951) and for spatial and temporal modufation (see below). tend to converge to a constant at very low luminances and to Weber’s law at high luminances. It is possible that threshold is determined bv statistical factors in the middle range and neural limitations at
low and high luminances (by a neural threshold and neural adaptation respectively). but this combination results ina function very similar to the_/‘(L) function in many cases. It is therefore an empirical question whether the data can be accounted for using only_/(L) functions or whether a statisticai effect is indicated in addition. In this and companion papers it will be shown that no statistical effect need be introduced. At least two models have been suggested for the adaptation effect of the upper limb of the Weber Rtnction. Rushton (1965) and others have suggested that logarithmic encoding corresponds to the saturation of the intensity response of the receptor potential. The saturation is postulated to arise from the esistence of a limited pool of ions which can be transferred across the receptor membrane to create the receptor potential. Kelly (197 la. 1971b) suggests an alternative derivation for the adaptation comprising a complex feedback pathway with multiple integrators and feedback loops which varied in number and gain depending on adaptation level. This formulation is difficult to handle as the values of several parameters must be determined from the data being fitted at each luminance level.
De Lange’s (1957) data of flicker sensitivity for observer V with a 2” field and a 60’ steady surround are replotted in Fig. 1 by measurement of the points from his figure. since the actual data are no longer available. This type of stimuius is comparable with Stiles’ (1939) study on increment threshold utilizing a field on which was briefly superimposed a I’ test patch, the luminance of which was adjusted to threshold. These stimuli may be considered as spatially similar since the time-average luminance of the test area in both is almost the same as that of the surround. The differences are that decrements as well as increments were
Fig. I. Log relative modulation sensitivity as a function of log frequency. replotted from de Lange (19%). observer V. The fog retinal illuminances of the curves are as follows. FiIIed circfes--lowest curve: -05, next cur%-et:04. next curve: 0.5, dashed curve: 1.0 log cd. Open circles-dotted curve: 1.5. dashed curve: 2.0. full curve: 3.0 Iog td. Upper filled circle-cur\e: 44 log td.
Fig. 2. Data of Fig. 1. replotted in terms 21 log absolute modulation sensitivity as a function of adapting luminance, with frequencv as a garameter. Freciuencics of 40, 30. P.,. .to“. 5 and 1 Hz ar; shown successivelv hisplac4 to the right b) one log u&. involved in the flicker experiment and the principal parameter used was the frequency of the stimufus rather than the wavelength of test and background fields. Thus AL+in equation (I) now denotes the absolute amplitude of modulation at threshold. The data are replotted in Fig. 2 in terms of absolute modulation at threshold as a function of adapting luminance. Modulation frequency is the parameter. As an initial attempt the data at each frequency were fitted by inspection by two (or one) S(L) functions on the assumption discussed above that overall sensitivity is determined by the most sensitive mechanisms at a given adapting luminance and frequency. This may be stated mathematically in the form AL, = f;(L) :4fJL1.
iii
The values of k and L, used for the curves in Fig. 7 are given in Appendix I. As a guide to the exact position of each curve a vertical marker has been placed at the adapting luminance for which L= 1I 2k. Successive curves are displaced horizontally by one log unit for clarity. The points for each frequency were fitted with reference only to the data at that frequency. and it shouId be noted that this produced a marked regularity aeross curves, with the intersection of the two functions becoming deeper as frequency was increased. Stiles (1949) showed that for his data a function with a more gradual transition between the horizontal and 45’ asymptotes may be observed for each mechanism. If the luminance functions of physiological mechanisms had a shallower transition between the asvmptotes. a good fit might be obtained with fewer Stiles-type functions. It should therefore be noted that at several points they(l) function itself is hardly abrupt enough to fit the data (e.g. at 5, 20 and JOHz). This suggests that the use of the f(L) hmction is warranted by the data. An alternative possibility is that the data might conform to a square root relationship between dL and L. .A line with the slope of -0-j is shown in Fig. 3 (dashed line), as predicted from the square root law of fluctuation theory. Clearly when shifted it would not provide a good fit to the data at any luminance. De Lange’s data (and indeed Stiieii were obtained with a fovea1 increment which had a sharp boundary. Other flicker data have been measured with a large. homogeneous flickering field (Kell>, 1961). It is of in-
frequencies. the assumption 41 he made that the same two mechanisms are responsible for the NO branciiss ot the curves at all frsquencies. -This mukss it possible to consldsr the sensitivities of each mxhunism ssparately. The sensitivity of sach mechanism can be plotted over the bvhole range of frequencies and background luminances by extrapolation from the region where it determined overall sensitivity. For convenience the mechanism that dstsrminrd oLeraIl sensitivity predominantly at low adaptation luminances will be called the low luminance mechanism. and similarly for the 3c -A : / high luminance mechanism. (For frequencies at which , 4’ 4” 4. 4. 4 z liop ldl the data xvas fitted bv only ons_/‘(Lf function. this curve Fio=. 2. hlodulation sensitivity data from Ktliy { 1961) re- will be arbitrarily assigned to the 10% Iuminance plottsif ;1sin Fig 2. Frequtnctes of 40, 20. 10, 5 and 1.5 Hz mechanism.) ;irs displactd success~vtll; to the right by one toy unit. Before replotting ths derived srnsitivities oi the two mechanisms. the rationale for differsnt axis scales must tetest to compare the luminance function analysis for be considered. The most characteristic aspect of flicker fovea1 and large-lield flicker. Figure 3 presents the data is ths form of the high frequency asymptote. Kell! iuminance function anaiysis of Kelly’s data in a similar (1969a. l97la. 197lb) has established that the high frequency asymptote of absolute modulation of much manner to Fig. 2. It appears that a single component Ricker data conforms to a d#usion model in which is sr&icient to fit all the data. sensitivity is a linear function of the square root of freA numerical indication of the conformity of theory to data is desirable. since it was impractical to fit the quency. This contrasts with the earlier electrical analog curves by a standard formula. The log standard devi- of de Lange ( 1957)in which the high frequency asympation of the points from the curves in the vertical direc- tote ivas a linear function of log frequency determined by the number of cascaded integrators involved. The tion was computed both for the present analysis and sensitivities of the two mechanisms derived by b>-measurement from pubIish~d figures for the mod& described by Van Nes (1968) and Kelly (I971a). The luminance function analysis have therefore been plotf‘(L) functions tit de Lange’s data with G’ = IGO dB. tsd in accordance kvith the diffusion model (Fig. -la) De Lange did not attempt to model all his data. SO no and the cascaded integrator model (Fig. 4b). In Fig. 4~. ahsolute modulation sensitivities on a logarithmic fit can be calculated. The fit of the square root relationship to his data has G’ = 360 dB (from Van Nes. 1968). scale are plotted as a function of modulation frequency The i.(L) functions fit Keliy’s data with 0’ = 0.70 dB, on a square root scale with adaptation luminance as whereas Kellv’s (1971a) theoretical functions fit the a paramsttr. It is apparent that the sensitivity of the same points with 0’ = 2.75 dB. Clearly the f(L) func- low luminance mechanism (filled symbols) does not tions fit the data with smaller error variance than the show any tendsncy to asymptote for different theories of either of the other authors. A mathematical adaptation luminances, whereas the sensitivity of the curve-fitting procedure might improve the fit still high luminance mechanism (open symbols) clearly further. and certainly should not degrade it. Note that approaches a straight line asymptote with a slope of Van Nes and Kelly require two degrees of freedom (d,) -0.75. as fitted by inspection at all luminances. The for their theoretical curves. The use of two possiblef(l) plot of the same values in terms of logarithmic relative functions at each frequency requires four parameters. modulation versus frequency coordinates I Fig. 4b) sugbut they have the constraint that sensitivity is deter- gests an explanation for the non-asymptotic behavior mined by the most sensitive mechanism throughout of the low luminance component. While the sensitivi[squation (?)I. This gives three degrees of freedom at ties of the high luminance mechanism (open symbols) each frequency. now sprsad considerably, the sensitivitv of the low Each curve fit is determined to the same number of luminance mechanism (filled symbols) -is essentially degrees of freedom (J,) as it has points, since a11points constant for three adaptation luminances. while the are independent. The number of degrees of freedom fourth approaches them at high frequencies. The accounted for by each theoretical curve is therefore straight line asymptote fitted by inspection has a slope ti, - tl,. The sum of these E(d, - d,) over all de Lange’s of - 5 corresponding to five cascaded integrators. The frequencies is 33 for d, = 2 and 27 for d, = 3. In the data are not suficiently extensive to determine the case of Kelly’s data E(d, - d,) is I7 for d, = 2 and 12 slope with any great accuracy, but the number ford, = 3. The variance is redxed in proportion to the required seems to vary little tvith luminance level. It reduction in number of degrees of freedom. Thus tz should be noted that sensitivities of the low and high should be reduced by a factor of 080 for de Lange’s luminance mechanisms are each we11 determined at data and 0.70 for Kelly’s when the d, is increased fcom high frequencies of modulation. so that the difference 7 to 3. The l‘(L) functions reduce C? by factors of 0.28 in asymptotes cannot be due to inaccuracies of extraand 0.25 respectively. in comparison to the alternative polatlon. Description of the curves in terms of twoI‘ theory, so they still provide a better fit to the data functions. shifting relative to each other as frequency even when the extra degree of freedom is taken into of modulation is changed. corresponds to the irreguaccount. larity of the spacing of de Lange’s originai frequent! The principal result of the analysis is to show that response functions. This irregularity is particularly evit\s-of(L) functions are required to fit flicker sensitivity dent on the high frequency slopes of the functions of at many frequencies in the 2’ field data of de Lange. both‘subjects but was not commented upon by de In view of the regularity of the differences in fit across Lange himself. ,A
I
i?rminonce
I”
,1
,
i-
I I
I
2
5
-1
10 20 (IOQ 5cole)
Modulation
frequency
50
100
U4rI
Fig. It. Frequency characteristics of the two mechanisms identified in the dam of Fig. 2. FilIed symbols --low luminance com~nent, open symbols-high luminance component; circles--3.0, pyramids-20. squares-1.0, fuIcra-O~Olog td. (a) Sensitivities of both mechanisms are plotted in terms of iog absolute modulation threshold as a function of the square root of frequency. Asymptotes to a slope of -0.73 (solid line) are drawn by inspection for the high luminance mechanism (open symbols) onI>. as the sensitivities low luminance mechanism do not appear to asymptote. (b) Sensitivities of both mechanisms replotted in terms of log relative modulation as a function of log frequency. Asymptotes fdashed lines) to a slope of -5 (solid line) are now drawn by inspection for the low luminance mechanism (filled s,ymbols) only, as the high luminance mechanism fails to asymptote here. Since only onef(Q function was sufficient for Kelly’s (1961) data, the frequency response of that function is approximated by Kelly’s original smooth curve, and need not be redrawn. l-liehas shown (Kelly, 1969a) that the high frequency asymptotes of these data conform to the diffusion model. 111.DISCUSSION What mechanism might be producing the alternative sensitivities in Fig. 4? Since one predominates at low and the other at high luminance, the first hypothesis to be considered is that they result from rod and cone activity respectively. This hypothesis must be rejected for two reasons. Firstly, de Lange’s stimulus was specifically designed to eliminate rod activity. The 7” flickering area was fovea1 and the large equiluminant surround should have eliminated any effect of stray light in the periphery. Secondly, the analysis of Kelly’s (1961) data should have shown evidence of two mechanisms, since the 65’ field should adequately stimulate both rod and cones at appropriate luminance levels. Since only one mechanism contributed to 65” field sensitivity, it is most unlikely that rods in the periphery could contribute to the 2” field sensitivity. The other salient difiierences between the two stimulus configurations are that de Lange’s contained flickering edges, whereas Kelly’s was uniform and of greater area. Kelly (1969a, 1969b) has shown that the presence of flickering edges greatly alters the shape of flicker sensitivity. Flickering edge sensitivity is greater at low frequencies, whereas the uniform field shows a reduced low frequency sensitivity and a sharper peak. Comparing these results with Fig. 4b reveals a remarkable similarity in shape. The high luminance curves (open circles) appear to correspond with the uniform field sensitivity (Kelly. 1969b. Figs. 1 and 9) and the
low luminance curves (filled circles) with his flickering edge sensitivity. This identification is supported by the fact that both the high luminance curves and the uniform field sensitivity conform to a square root asktnptote (Fig. 4a). Note that the shape of the latter was essentially invariant with the number ofedgespresent. This correspondence suggests that the two components in Figs. 4a and b utilize uniform field and edge information, respectiveIy. Kelly (1969b) chose conditions which optimally select one or the other mechanism as the determinant of threshold. His results require only that the retina contains a single type of detection mechanism with area1 summation in which lateral inhibitory conncctions may or may not be stimulated, according to the stimulus configuration. On the other hand. the results of the analysis presented here conform to the assumption that the uniform field and edge sensitive mechanisms operate simul~neous1~ on the same stimulus input and that flicker threshold is determined by the response of the most sensitive mechanism. Iv.
RETINAL
MECH.C.3StlS
Having eliminated rods and cones as a possible explanation of the two mechanisms. it is of interest to
speculate on other physiotogical mechanisms which might explain the psychophysical data. The two main cell types projecting up the optic nerve may be referred to as “sustained and “transienr” ganglion cells (Cleland, Dubin and Levick. 197 1. 1973: Dowling, 1970; Enroth-Cugell and Robson. 1966: Ikeda and Wright, 1972). However, --sustained” cells also show an initial transient response. For the purpose of this paper the relevant distinction is between sustained and transient responses which may or may not occur in the same cell or fibrs but which must have different retinal substrates. It w-ill he assumed that the
517
Viji;al modularion jznsm\it! major eRects reported for the two cell-t!-pes derivs from their predominant response characteristic. Sustained responses may be identified with the edge sensitive mechanism and transient responses with the uniform field mechanism on the basis of five characteristics.
relatively faithful11 to the ganglion cell Ictsl. On the other hand. the edge-ssnsitive sustained response appears to be subject to a neural adaptation process which limits the response in the manner ofa series of cascaded integrators. REFERESCES
noise and absolute threshold. J. opt. Sot. Am. 36, 63-1-639. Cleland B. G.. Dubln bl. LV. and Levick W. R. I 1971) Sustained and transient cells in the cat’s retin,! xnd lateral gcniculate nucleus. J. Pi~Moi. Lord. 217. -L;T--196. Clcland B. G.. Levick LV. R. and Sanderson K. J. II9731 Properties ofsustainedJnd transient ganglion cells m the cat retina. J. Plryswi.. Lorul. 228, 649-680. de Lange H. I 1952) Euperim=znts on Hickcr and borne calculations on an electrical analogue of rhe fo\sal systems. Physicu 18. 935-950. de Lange H. (19571 Attenuation characterisrics ,Ind phaseshift charactsristlcs of the human fovea-cortex s!stcms in relation to Hicker-fusion phenomena. Doctoral dissertation, Tech. Hog.. Delft. dc Vries H. (1943) The quantum character of ljght and its bearing upon the threshold of vision. the differential sensitivity and the visual xuity of the elc. PI~ysw 10, 553-564. Dowling J. E. (1970) Oreanlzation of vertebrst? retinas. [)Iwsr. Ophtltai. 9, 65C6YO. Enroth-Cugell C. and Robson J. G. (19661 The contrast sensitivitv of retinal ganglion cells of the cat. J. Ph)~iol.. Lo&187. 5 I7-552. _ Fcchner G. T. ( 1860) Elrrw~rr drr Ps~honh~sk ITrans. bk ;\dler H. E.. 1966). Holt. Rinehart & W&on. New Yori. Fukada Y. (1971) Receptive field organization of cat optic nerve tibrcs with special reference to conduction velocity. 1’isiorz Rrs. 11, 209-226. Graham C. H. and Kemp E. H. (193s) Brightness discrimination as a function of the duration of rhc increment in intensity. J. yen. Ph~siol. 21. 63%650. Ikeda H. and Wright Xl. J. 11972) Differential effects of refractive errors and receptive field organization of the central and peripheral ganglion cells. I~isron Rrs. 12, 146%-1~36. Kelly D. H. (1961) Visual responses to time dependent stimuli--I: Amplitude sensiti\ity measurements. J. opr. sot. .4m. 51. -122-1’9. Kelly D. H. (1969a) DitTusion model of hnssr Bicker rssponses. J. opt. SOC..4rtz. 59, 16651670. Kelly D. H. (1969b) Flickering patterns and lateral inhibition. J. opt. Sot. .4m. 59, 1361-1370. Kelly D. H. (197la) Theory of Hicker and trsnsrsnt responses-1: Uniform fields. J. opr. Sot. .4m. 61. 53--546. Kelly D. H. (197lb) Theory of Hacker and tracsxnt responses-11: Counterphase gatings. J. opr. Sot. .4/n. 61. 633640. Mueller C. G. (1950) Quantum concepts in \isuA intensity discrimination. ,+n. J. Ps)chol. 63, 92-11X. Mueller C. G. (1951) Frequent) of seeing funstlons for intensit) discrimination at various levels of adapting intensity. J. ytm. Physiol. 31, -16N7-I. Rushton LV. A. H. (1965) The Ferrier Lecturs to the Royal Societ!. Visual Adaptation. Proc. R. Sot. B. 162, Z&-16. Sperling G. and Sondhi 51. bI. (1965) Model for visual luminance discrimination and flicker detection. /. opt. Sot. .4m. 58, I l33- I 145. Stiles W. S. (1939) The dirxtional sensitivity of the retina and the spectral sensitivities of the rods and cones. Proc. Barlou
(I) Rrcepticr-firld
orgmkatim
Sustained responses have a marked centre-surround organization. whereas transient responses do not. (Cleland. Levick and Sanderson, 1973). Sustained responses should therefore respond better to flickering edges. and transient responses better to a uniform field flicker. (1) Receptice-field
si:e
Sustained responses tend to have smaller receptive fields than transient responses (Cleland ef al.. 1973). Correspondingly, the edge-sensitive mechanism appeared with small field stimulation and the uniform field mechanism predominated with a large field.
The sustained response should by definition show little low frequency reduction, as was found for the edge-sensitive mechanism. The transient re>Tonse should be much reduced at low frequencies. as was found for the uniform field mechanism, since the high luminance sensitivity must fall below the low iuminante sensitivity in the region below 5 Hz (Fig. la).
Enroth-Cugell and Robson (1966) show that sustained responses change little with luminance level. reporting a variation of only threefold with a thousand-fold decrease in luminance in a typical sustained cell. Winters and Hamasaki (1972) show similarly that optic tract responses have different intensity rebszonse functions for the sustained and transient components of the response. With a two log unit variation in intensity. the sustained spike rate varies by a factor of 4 whereas the initial transient changes by a factor of IO. This difference is in accord with the insensitivity- of the edge-sensitive mechanism to luminance changes relative to the uniform field mechanism. (5) Rerir~al disrrihrriot~ Sustained cells predominate in the fovea and perifovea whereas transient cells are widely distributed across the retina (Fukada. 1971; Ikeda and Wright, 1972). Correspondingly. the edge-sensitive mechanism appeared only with a flickering edge close to the fovea, whereas the uniform field mechanism was present with stimulation both of the fovea and of the whole retina. Thus information gleaned from the psychophysics agrees at every point with an identification of the two mechanisms with the two major response types of ganglion cells of the retina. The different as>-mptotic behaviour of the two components is a final point for which there is no corresponding physiological information. If the identification with retinal cell tl;pes is correct, it suggests that the transient uniform field response has a limit determined by diffusion across the receptor membrane (Kelly, 1969a) which is transmitted
H. B. (1956) Retinal
R. Sot.
127B. 6-L-105.
Stiles W. S. (1919) The detxmination of rhe spectral sensirlvlties of the retinal mechanism bq sensor); metbdds. .Ved. Tijtischr. .Yatuwk. IS. l25- l-16. T>ler C. W. f 1970) A psychophysical study of the dynamics of color vision using wavelength-modulated light. Doctoral dissertation. University of Keele.
San .Nrs F. L. (t968) Experimental studies m spatiowmporal contrast transfer by the human eye. Doctoral dissertation. University of Utrecht. Weber E. H. (1833) De P&u. Resorptione. Auditu rr Tmt~c Annotatiunrs hxotnicar er Physioiogicae. C. F Koehler. Leipzig. Winters R. W. and Mamasaki D. I. 119i3) Comparison oi LGN and optic tract intensity-response functions. Cisiorr
APPEVD~S
1
Table I. Frsquenc]. I Hzr
i (log td) High Lou
i, cloy tdl tow High
Rzs. 12, W-608.
Values of k 2nd L,, [equation (I)] at ezch frequency for low and high luminance mechanisms, obtained as descrzbed in text for the data ofdr Lange (Fig 3!.
