Exchange thresholds in dichromats

t’tfon Rcs.Vol. 13,pp. 1993-2002. FeraaxnonPrru 1973.Printedin Great Britain.

EXCHANGE

THRESHOLDS

IN DICHROMATS

W. A. H. RUSHTON,DIANE SPITZER POWELL and IL D. WHITE Institute of Molecular Biophysics, The Florida State University, Tallahassee, Florida 32306, U.S.A. (Receiued 2 February 1973; in revised form 13 April 1973)

A V~Y important property of the photoreceptors in the eye is that whatever energy or wave length of light excites them, there is only one dimension of response. This Princz$e of Unioariunce was already implicit in THOMASYOUNG’S(1802) famous formulation of trichromacy. He postulated three resonators thrown intovibration by light waves. The response of each was defined by the amplitude of the resulting vibration which depended both upon the energy of incident light and upon how close its frequency lay to the natural frequency of that resonator, but these combined to produce a single dimension of output, namely the resulting amplitude-uniuariunce. In terms of visual pigments and their quantum catch we may state the Principle of Univariance as follows : “The intrinsic response of a receptor dependi upon its effective quantum catch but not upon what quanta are caught”. The words “effective” and “intrinsic” need explaining. Not all the quanta caught by a visual pigment lead to bleaching. With rhodopsin about l/3 appear to be degraded into heat without visutaf effect (Wm and BROWN, 1953;SCHNEIDER, GOODE%? and LYIXGOE,1939; KROPF A., 1967). The fraction is independent of wave length, and is without significance for the questions of this paper. In what follows the word “effective” will be-omitted, but by “quantum catch”, we imply “effective quantum catch”. The immediate or intrinsicchange produced by the catch of a quantum does not depend upon its “wave length”. But if light falls upon more than one kind of cone, the combined output will generally depend upon the wave length, since the quantum catch will not be the same for, say, “red” and “green” cones, and the combined outputs interact. Now it appears that this interaction can feed back into the cones themselves (FUORTE~, SCHWARTZ and SIMON,1973)so that intracellular records from cones show the effect, not only of the quantum catch in this cone (the intrinsic response) but also the conducted influence of the catch in another kind of cone. Consequently it is only the intrinsic response that can exhibit univariance. This univariant spectral relation, therefore, will appear either when the conduction from other receptors is abofished, or when only one kind of receptor is excited. It is well known that in scotopic vision, where rods are the only receptors involved, lights of every wave length appear the same in colour and all produce an identical sensation when adjusted simply in energy to look equally bright. This condition is when rhodopsin, the visual pigment of the rods, absorbs quanta as fast from one light as from the other (CRESCITELLIand DARTNALL,1953 and CRAWFORD, 1949). It is also found that a neat exchange of one for the other of these matched lights is undetected by the rods. It appears that a change in the rate of quantum catching is the only luminous event which causes receptors to change their response. Thus when the exchange involves no alteration in the rate of quantum catch, the rods do not “know” that the light has changed. What has just been said of rods appears to be true for each class of cone. Normally in daylight vision there is no circumstance where one class of cone alone is excited. But lights in the red-green spectral range of the common dichromats do excite only one type. Here protanopes have only green-sensitive cones, deuteranopes only red-sensitive cones. From 1993 V.R.13/11-A

W. A. H.

1994 Univa~ance twilight-that

we should

RUSHTON.

expect

DIANESPKZER POWELLAND

these subjects

aillights look thesame

K.

to experience

D. WHITE

what normals

in colour and vary only in brightness,

match can be made simply by adjusting

the light intensities.

experience

in

so that a perfect

This has long been known to

be true.We should also expect that two lights that match should catch quanta at equal rates. This has recently

been confirmed

by MITCHELL and RUSHTON (1971)

any two different lights that appeared the one pigment

(chlorolabe)

identical

to a protanope,

that he possesses,

The same was found for the deuteranope

sensitive

who showed that

bleached

in the red-green

at the same rate spectral

where any two lights judged identical

green spectral range were found to bleach his pigment bleaching rate was measured by a special technique

range.

in the red-

(erythrofabe) at the same rate. The with our “Florida Densitometer”

(HOOD and RUSIITON, 197 1). These considerations mixed contributions

open an important

of “red” and “green”

possibility

in the difficult task of analyzing

cones in the perception

of thresholds

For, if we neatly change the light from one wave length to another

in the red-green

and adjust the relative energies so that one class of cones does not “know” has occurred,

the

and coluor. range

that any change

then whatever is perceived must be due solely to the activity of the other class

of cones. How this “exchange

threshold”

may be developed

to give useful information

will be

described in this and the following papers. METHOD The inset of Fig. 1 shows the essential presentation of this paper-a 2” field I, (X,) of luminance Zt and wave length .& which is suddenly replaced by Z, (A3) of different luminance and wave length, but with no change in size or position. Both fields are superposed upon a steady changing background which is usually a mixture of lights at Xr and &. Figure 1 shows diagrammatically how these lights are delivered to the eye.

l30. 1. Diagram of optical arrangement (& text). A, light source delivering two beams Ai, At polarized at right angles. P, exchange polaroid operated by pulling a string. It changes the field of view (shown in inset) from one to the other. Pt, rotatable polaroid to adjust the proportions of Xr and Aain background. Inset: field presented to the eye. Its center changes from intensity ZSat wave Iength A,, to Z2 at wave length h,. These are presented on a steady background where r\, is a mixture of lights at A1and hl.

Exchange Thresholds

in Dichromats

199s

The tungsten-iodide light source A provides two beams which are united in the mixing cube Ct. One beam passes through the interference filter h2 and the sheet polarizer PZ which transmits horizontally polarized light. The other beam passes through /\r and PI which transmits vertically polarized light. Lenses, not shown in the figure, bring the filament A to a focus at P,, a polarizing sheet which can be pulled by a string against a spring, so that either vertically or horizontally polarized light is transmitted. Thus, on pulling the string (to the left) the light passed will change from wave length A, to X2, and since this substitution occurs at PJ, the focal point, the exchange is sharp. Light from P3 is focussed onto the subject’s pupil by lens L, which brings the 2’ stop Sr, into sharp focus on the retina. Thus the subject saw this stop filled with light that changed from XI to h, on pulling the string. and the change could be reduced to threshold by interposition of the neutral photometric wedge W. Light passing straight from the cube C, to CZ constitutes the background. The optical distance along this path from A to L is equal to that from P3 to L so the background also focussed the filament A on the pupil. The background field was limited by the large stop S1. The rotatable polarizer P4 permitted lights hr, and XZ to be admitted to the background in any desired proportion. The light paths through P3 and through P4 are adjusted so that when II and I, are equal as judged by backgrounds (P4 being set either vertically or horizontally), then they are also equal as judged by pulling the string that operates P3. RESULTS

1. No wave length change First consider the case where all lights are of the same wave length, so that A, = A, = A, = 540 nm. Then the exchange will simply be a brightness,change f (Zi - Z,) seen against a background Za of the same colour. Suppose Z, to have a fixed intensity, and Zz to be varied in intensity by wedge R so that 12 = I, lo-’

(1)

where I,, is the fixed intensity falling on wedge R and r is the interposed wedge density. The luminance difference at exchange is f (Zi - Z,, lo+) and this, seen through wedge W, is attenuated to f (Z, - IO 10-r) 10-w

(2)

where w is the interposed density of wedge W. The exchange is seen projected on a background ZS which is the present experiment is a(Z, + I,), P, being set at 45”. Hence from equation (1) background = +(Z1+ I,, lo+)

(3)

In the experiment, the operator sets Z, to a series of values by adjusting the wedge R. For each r-value of the wedge the subject attenuates the exchange signal, equation (2), by means of wedge W until the change lies at the threshold for detection. Figure 2 gives a typical result on a normal subject where w, the density of W wedge interposed, is plotted downwards as ordinate (i.e. log threshold increasing upwards), against r, the density of R wedge. The most striking feature of this curve is that when r has a certain value ro, the curve rises so steeply that the threshold lies above the strongest exchange intensity available. This is what would be expected of equation (2) if r. was the value which made

zt =

IO lo-‘0

or r. = log (lo/Z,).

(4)

For at this setting the lights Zi and Z, (= Z, lo+) are identical and there is no change to detect. Physical measurement verified that at this r. value, in fact, Z1 and Z2were equal as

W. A. Ii. RUSHTON,DIANESPITZERPOWELLAND

1996

t

i

K.

D. Wm

_

0

I*0 -ii

540354c

0.6

I

0.8

l-0

I

I

I.2

I

l-4

l-6

I-6

2-O

1m log attenuation

fo

is

of

X, (r)

when 1,(X,) and &&A~ IO-‘ore

identical

Fro. 2. Exhchange thresholds

when h, = X2and background is the average of the two changing lights, Abscissae: r, the density interposed by wedge R in the red beam. Ordinates: w, the density interposed by wedge W in the exchange beam, (plotted increasing downward). Theoretical cuves from equation (6).

judged by visual photometry or with a photocell. So the infinite Iog threshold at r,, is a property of the equipment. But the two symmetrical branches of the theoretical curves on either side of r. are properties of the eye. They follow from the Weber-Fechner Law, dJir = K. In this formula &is the threshold change in brightness. It is given by equation (2). I is the background given by equation (3), thus AI

-= I

K

=

5

(II -I,

IO--) lo-”

g(zl + IO 10-7

(9

Introducing the relation of equation (4) gives &2~1()“~

I - lore-r. 1 + l(Yo-’

From this it is easy to plot the relation between w and (r. - r). It is shown by the curves in Fig. 2. They are symme~i~l about the ordinate through r. as is easily seen from equation (6). Changing (r. -r) into (r-ro) only alters the sign not the size of the expression. This means that the threshold is the same but if on one side of the axis of symmetry the string had to be pulled for lowest exchange threshold, on the other side it had to be released. The simple formula of equation (6) makes two justified assumptions. First that the eigengruu {I,,) is negligible compared with the backgrounds used, so we may say that Al/cl+ 1,) is nearly Al/J = K’. Second that K, the Fechner fraction, is so small that the addition to the background of the exchange light, at threshold, is a negligible increment. The squares in Fig. 2 show the exchange thresholds (plotted as w) for various r settings, found by a normal subject where all lights were of wave length 540 nm. The results fit well the theoretical expectations.

Exchange ‘lluesholds

in Dichromats

1997

No doubt both “red” and “green” cones of the normal fovea were excited, but each would be expected to give the same theoretical curve, one shifted vertically relative to the other. So the lower would define the threshold throughout. These curves are very important for the analysis of thresholds in more complex situations. We cut out a template from transparent plastic, and, always plotting w and r on the same scale, we used this template by sliding without rotation to define pigments and excitabilities. This template applies only when P, is at 45” so that the background is the average of the two lights used for the exchange threshold. The ordinate through r0 is impo~ant in defining the position of the curve. It is the axis of symmetry and we shall refer to it as “the axis” for short. The position of r. defined by equation (4) is when the pigment takes an equal quantum catch from each exchanging light and therefore cannot detect the change. We call this point r,, the idept (Greek = equal taken).

A. Protanopes. As mentioned earlier, protanopes and deuteranopes have no colour discrimination in the red-green spectral range. As in scotopic vision, they only distinguish brightness. For them, therefore, exchanges between any two lights are similar to the colourless change of Fig. 2, and we should expect their thresholds to be predictable in the same way from the Weber-Fechner law, and lead to the 2-branched curve with axis at ro, the isolept for their pigment. When the wave length did not change (as in Fig. 2), r. was defined by our instrument, but when h changes from I, at 540 nm to I, at 640 nm as in Fig. 3(a), rD is defined by the energy ratio Ir/Z, at which the cone pigment catches quanta at an equal rate before and after the exchange. In Fig. 3(a) the black circles give the exchange t~esholds in the pro~nope (w-values) for the whole range of r settings, (2 runs). The appropriate isolept value was found by flicker photometry. A rotating Polaroid driven by a variable speed motor was substituted for Pa, Fig. 1, and wedge R adjusted for minimal flicker. In this position the change in quantum catch by the protanope’s pigment in changing from 540 to 640 nm was nearly zero and hence this r setting is the isolept (ro) for that exchange in the protanope. Our template was placed with its axis at this to value and slid vertically to give a good fit (by eye). The continuous 2-branched curve shown, marks the template’s position; it fits the protanope thresholds (black circles) reasonably well. This was to be expected from the principle of univariance, and our results support it. The black circles in Figs. 3(b), (c), (d) and (e) show similarly the protanope log thresholds with exchange between 540 and 620,600, 580 or 560 nm. The values of ro, determined in each case by flicker, define the axis of our template curves, which fit the threshold curves about as well as experimental error justifies. B. Deuteranopes. Many who accept that protanopes simply lack the “red” pi_ment erythrolabe, do not accept the symmetrical statement that deuteranopes simply lack chlorolabe. Into this ancient and difficult controversy we cannot here embark. We regard it as pretty certain that deuteranopes do not contain the normal pigments erythrolabe and chlorolabe in normal amounts, their disability arising from mixed nerve signals, etc. For, if a deuteranope’s eye is bleached to equilibrium first with a strong red light, and then with a green light that looks the same to him, no further change in his pigment density is recorded by densitometry at any measuring wavelength as a result of the second bleach. (RUSHTON,

%‘. A. I-I. ihM%TON,DUNE SPITZER POWELL ANXJ K. D. %‘m

1998

w

0 I I -0.2

! 0

I

I

t 0.2

0.4

540=640 I

I

O-6

0.6

I

I

I

1

1‘0

t-2

I.4

I.6

f&

rcs*

(a)

\ W

0.6

O-6

:

i \

1999

Exchange Thresholds in Dichromats

I

I

I

I

I

I

0.2

0.4

0.6

0-B

I.0

I

I

I

I

r

(4 0.2

-

0.4

-

0.6

-

w

I

5402560 I 0.2

I

I

I

0.4

0.6

0.6

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I

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I

I

(e) FIG. 3(a-e). Exchange thresholds between 540 MI and 640.620,600, 580 or 560 ML Results plotted as in Fig. 2: black circlea with protanopes; white circles, deuteranopes; squares, with normal subjects. Curves are the theoretical “template curvea” from Fig. 2 with isolept axis placed at r-value found by flicker photometry with that subject and those Xlights. Circles lie close to the template curves; squares lie close to their lower envelope.

1963, 1965). But the normal eye always shows a marked further bleaching in the green and RUSHTON, 1963). This difference in pigment behaviour could not exist if both subjects had the same pigments in the same amounts. The behaviour is consistent with the view that the deuteranope has only erythrolabe but the normal has also chlorolabe. At any rate, this is the view we now assume. Erythrolabe is the only pigment active in the deuteranope in conditions of Fig. 3 and it is seen to act in a manner altogether analogous to chlorolabe in the protanope. The exchange thresholds of the deuteranope in Fig. 3 are indicated by white circles, the value r. was determined by flicker, and the template curves are shown by interrupted lines with axis set to that r. value, and with vertical displacement suitably judged by eye. The circles lie not far from the theoretical curves through not so close as with the protanope. (BAKER

2ooo

W. A. H. RUSHTON, DLG~ SPIIZER POWELL AXDK. D. WHITE

C. 1Vormal eyes. If normal eyes contain both the chlorolabe of the protanope and the erythrolabe of the deuteranope as Kijnig claimed (K~MG and DIETWCI, 1886, 1893), we might expect the normal threshold to be the same as that of whichever dichromat saw best. In Fig. 3 the normal threshold is plotted as squares which are seen to lie close to whichever dichromat threshold is the lower. In a region where the continuous and interrupted lines cross, there is an equal chance of either “red” or “green” cones detecting the changeover. So the chance that one or other will detect is better than that for either alone. This “probability summation” must make the threshold for normal eyes lower than that of either dichromat, in the region where the lower branches of the curves cross. These lower thresholds correspond to expectations from Stiles’s “line element” (WYSZECKIand STILES,1967). Taking this roughly into account, the results are fairly consistent with Konig’s view that normal eyes contain both the protanope’s cones and the deuteranope’s cones. 3. Spectral sensitivity of dichromats The isolept values in Fig. 3 tell us the lights of different wavelengths that stimulate equally the receptors of each dichromat. If we know the quantum energies of these lights we may obtain the spectral sensitivity curves. This is shown in Fig. 4 where black circles show the log spectral sensitivity in the protan-

-1.21

540 560 560 600

I_

I

620 640

Wavelength, Exchange threshold

nm for

dichromats

FIG. 4. Spectral sensitivity measurements derived from isolepts for various X exchanges: protauopes, black circles; deuteranopes, white circles. Curves: spectral scnsitivitesfrom matching (Prrr, 1935)= pigment bleaching rates(Mrrmand RUSHTON,1971corrected,set Erratum).

Exchange Thresholds in Dichromats

2001

ope, white circles in the deuteranope. The curves are from MITCHELLand RUSTON(1971) who measured the quantum ener,oy at various wave lengths for a fixed rate of bleaching of the pigment in the dichromat. The results coincided with the wee-mown values of Prrr (1935). These results are nothing new. We determined our r&values by flicker, and Fig. 4 simply confirms the work of many others by similar methods. It is, however, satisfactory to see that the body of observations in this paper can be predicted from Fechner’s law and Pitt’s spectral sensitivity. It encourages us towards the more difficult applications which follow. Erratmn-Owing to a pIotting error, the Mitche~-Rushton curves are slightSy misplaced. The correspondence with Pitt’s results and between brightness and bleaching are correct, but the curve should have been plotted a little narrower. The present Fig. 4 shows the correct shape.

Acknowledgemen&---This work was supported by AEC Contract No. AT-(40-l)-2690, by an NSF. Grant GU-2612 and by a Grant from N.I.H.-lRO1 EYOO-684-Ol-VIS. The writing of this paper was greatly assisted by a Fogarty whole-in-Residence Award to Dr. Rushton, at the National Institute of Health, Bethesda, Maryland. REFERENCES BAKER,H. D. and RUSHTON. W. A. H. (1963). Erythrolabe in the normal eye. J. Physiol., Land. 169,91-92P. CRXWFORD, B. H. (1949). The scotopic visibility function. Proc.phys. Sot. B. 62,321-334. CREXITELLI,F. and D~~ALL, H. J. A. (1953). Human visual purple. Nature, Lund. 172,195-197. FIJORTES, M. G. F., SCHWARTZ, E. A. and SIMON,E. J. (1973) Depolarization of retinal cones by light. J. Pfrysfol. (Lo&) (in press). HOOD,C. and RUSMON,W. A. H. (1971). The Florida Retinal Densitometer. J. Physiol., Lmd. 217, 2I3229. K~NIG,

A. and DIETERICI, C. (1886). Die Grundemp8ndungen und ihre IntensitHts-Vertheilung im Spectrum.

S.B.Acad. wiss. Berlin 805-829.

K~xG, A. and DIETERICI, C. (1893). Die Grundempfindungen in normalen und anormalen Farben Systemen und ihre intensit~ts-Ve~heilung im Spectrum. Z. Psychol. Physioi. Sinnesorg. 4,241-347. UOPF, A. (1967). Intra-molecular energy transfer in rhodopsin. Vision Res. 7,81 l-818. MXHELL, D. E. and RUSHTON, W. A. H. (1971). Visual pigments in dicbromats. Vision Res. 11,103~1044. Prrr, F. G. H. (1935). Characteristics of dichromatic vision with an appendix on anomalous trichromatic vision. Med. Res. Council Special Report No. 200. RUSHTON,W. A. H. (1963). A visual pigment in the deuteran0pe.J. PhysioZ.,Land. 169,31-32P. RUSHTON,W. A. H. (1965). The Newton Iecture. Chemical basis of colour vision and colour bhndness. Nature, Land. 206,1087-1091.

SCH\IEIDER, E. E., G~~DEVE,C. F. and Ln-r-rooa, R. J. (1939). The spectrai variation of the phot~~~itivity of visual purple. Proc. R. Sot. A. 170,102-l 12. WALD,G. and BROWN,P. K. (1953). The molar extinction of rhodopsin. J. Gen. Physiol. 37,189-200. WYSZECKI, G. and STILES,W. S. (1967). Color Science. Wiley, New York. YOUXG,T. (1802). On the theory of light and colours, Phil. Trans. R. Sot. 1802,12-48.

Abstract-Light of intensity Zr at wave length XI is suddenly exchanged for Z, at hr. This exchange is presented upon a background of HZ$ f Z,). The exchange is attenuated to threshold by a photometric wedge. When I, is kept tixed and Z2varied in intensity, the relation between threshold and Zzfor dichromuts fits the curve expected from Weber’s law and the principle of univariance. For normal eyes the threshold is nearly the same as that for the protanope or deuteranope, whichever is lower.

R&u&-On &change b~~uement une lumi&re d’intensito Z, et de longueur d’onde Xt pour Zz et Al. L’&hange est p&en& sur un fond t(fr 4 Z,). On ram&e P&change au se&i par un coin photometrique. Si I, reste fixe et Zt varie, la relation entre le seuil et Z, pour les dichromates suit la courbe prevue par la loi de Wever et le principe d’univariance. Pour les yeux rwrmam, Ie seuil eat a peu p&s le meme que pour un protanope ou un deutiranope, selon celui qui est le plus has.

2002

W.A.H.Rusriro~.

DIANESPITZER POWELLANDK.D.WH~

~-Licht der kite&tit I, und der Weitenknge Ar wechseit plZitzIich mir I2 und ht bei einer ~~eidieuchtdichte won t/2 (I, i fl). Die Mcssung wurd bis an die Schweile mit einem Photometerkeil durchgeffihrt. Wenn I, festgehalten wird und sich I2 k&den, so entspricht dcr Zusammenhang zwischen dem Schwelknwert und 1, fiir Didrromaren dem Weberschen Ges%z und dem Prinzip der Univarianz. &i NormuLvichtigen ist die Schwelie ungeKhr die gkiche wk die fiir Protanope und Deuteranope (und zwar die, die gerade niedriger ist). PeNOM6--~efDie EiiiTe@xnuWxi II c AJI3iHO& BOfiHblAt Cpa3y 3i3MemCTCII 1~ npE AI. 3~a 3aMexa npoecxormr ua @one HiI + II). Mexnrottmecx aMyremix ocna6nsIoTci iI0 a It 83Mekmenx nopora t$OTOMeTpiriw KAIHOM. Korea 1, 0CTaeTCRIIOCTORHIIMM,

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