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The spectral sensitivity of “red” and “green” cones in the normal eye
THE SPECTRAL SENSITIVITY OF “RED” AND ““GREEN” CONES IN THE NORMAL EYE W. A. H. RUSHTON, DUANESP~TZER POWELL and K. D. WHITE Institute of Molecular Biophysics, The Florida State University, Tallahassee, Florida 32306, U.S.A. (Receiued 2 Fehwy
1973; in revisedform 13 April 1973)
IN THE previous paper we described the technique of “exchange thresholds”.
In the following paper we shall apply this technique to determine the spectral sensitivity of the elusive cone pigment responsible for the abnormal Rayleigh equation with a protanomalous or a deuteranomalous subject. In the present paper we use the method to determine the spectral sensitivity of the two cone pigments active in the red-green spectral range of the normal eye. Our results confirm Konig’s belief (KONIG and DIETERICI,1886, 1893) that protanopes and deuteranopes each lack one of the normal pigments and contain the others unchanged. Thus the normal subject possesses the chlorolabe of the pro&mope and the erythrolabe of the deuteranope. This not unexpected result gives us confidence in the method, and we may apply it to find the unknown pigments in the anomalous trichromats (in the following paper) with more assurance. The method of analysis in this paper is of two kinds. The first is to use the technique of exchange thresholds to find for one visual pigment its isolept, i.e. the relative energies of the two exchanging lights from which that pigment absorbs equally (Greek = equal taken). We exchange light at 540 nm of fixed intensity, for light at 64Onm and adjust this in intensity so that the visual pigment investigated absorbs equally from each light. This condition is the isolept for that pigment, with those lights. The second kind of experiment is to use our Analytical Anomaloscope (MITCI-IELL and RUSHTON, 1971b) to match lights of various wave lengths by a suitable mixture of light at 540 nm and 640 am adjusted in intensity to the isolept for the pigment investigated. We shall prove that when the perfect RAYLEIGH(1881) match is established and the (red + green) mixture matches energy & of wave length h, then at each wave length, Ea is inversely as the spectral sensitivity of the pigment. ~on~uently we have only to adjust the intensity of the red component (640 run) to the isolept value for any visual pigment and make perfect Rayleigh matches, to obtain at once the spectral sensitivity of that pigment, between 540 and 640. For clearness of exposition we shall assume that each type of cone contains just one visual pigment. METHOD Figure 1 shows diagrammatically our equipment which could be rapidly transformed to serve either the exchange threshold measurements or as analytical anomaloscope. The change is made by interposing the oblique mirror M in the beam from DA (for anomalscope) or displacing it clear to the left (for exchange thresholds).
With mirror M interposed, Fig. 1 is a simpIi%iedversion of the anomaioscope actualIy used, which was exactly as described by MITCHELL and RUSK~ON (1971b). The light source, A,isa t~t~i~ide iamp which emitted three beams. Beam 1 passes through an interference filter, &a (transmitting light of 540 rim) arid a 2003
2004
W. A. H. RL’SKTON,&AXE SPITZER POWELL
A.UD
K. D. WHITE
FIG. 1. Diagram of optical arrangement (see text). (a) Analytical Anomaioscope: with mirror M interposed. A, light source with three beams, Z,, 540 nm. vertically polarized; lo, 6&un, horizontally polarized and attenuated by neutral wedge R; E, beam Focussed on slit D, in front of “rainbow interference wedge” that passes mon&hrom&c light of any desired wivelength. This beam, attenuated by wedge W, constitutes the monoc~omatic field of the Rayleigh match. The {red f green) mixture for comparison is the conffuence of lo and 4 in the mixing cube Ct with the R/G proportion adjusted by the rotatable polarizer P+. (b) Exchange Thresholds: with mirror M clear to the left. IO, attenuated by wedge R, has value Z2. Z2 is exchanged for II by interposing one or other half of the polarizer P1, thereby excluding either vertically or horizontally polarised light. These exchanging lights are seen superimposed upon the steady beam through P4, whose angular setting adjusts the proportion of red to green in the background. vertical polarizer P,. Beam 2 passes through filter & (640 run) and P2 which polarizes horizontally. Beam 2 is attenuated by the neutral wedge R. Beam 3 is focussed (by a lens not shown) onto a slit just in front of the “rainbow wedge” DA. This is an interference filter of continuously variable wave length transmission, so by moving it across the slit, any desired wave length could be selected for the Rayleigh match. The transmission EL for each position was calibrated both for wave length and energy. Beams i and 2 are brought together by the mixing cube Cr. The combined beam to the left is blocked by the interposed mirror M and is not used in the anomaloscope. The combined beam running down to Cz constitutes the (red + green) mixture which must match the E, beam through the rainbow wedge. Since beam 1 is polarized vertically, beam 2 horizonally, the mixture may be passed in any desired proportions by suitably adjusting B, the angle of the rotatable polarizer P.+ to the vertical. This allows a colour match between EL and the mixture; adjustment of the neutral wedge W in the El beam allows the brightness match. The two lights to be equated were presented in alternate strips of a grating for easy comparison (see. MTCHELL and RUSKTON1971b). From Fig. 1 it appears that light from P4 falling upon Cz is pofarized at an angle ff to the vertical. Actually, as described in MITCHELLand RUSHTON(1971 b) two quarter-wave plates are interposed between P4 and C2. The first, fixed to P4, converts the adjusted (red + green) mixture into circularly polarized light. The second quarter-wave plate reconverts this into a vertical plane polarized beam. The beam E1 is horizontally polarized (by a Polaroid not shown) and both beams, united in the mixing cube C2, are viewed through a grating of alternate cellophane strips and gaps. The cellophane is a half-wave plate with axis at 45” to the horizontal, thus, on transmission, vertically polarized light becomes horizontal, horizontal becomes vertical. fn front of the eye is the final Polaroid transmitting only vertical light+ Consequently the vertical (red -f- green) mixture (but not the horizontal EA beam) passing through the gaps in the grating are transmitted by the final Polaroid. Thus the grating gaps show onfy (red + green). Similarly the EL fight after passing through the cellophane strip becomes vertically polarized and transmitted by the final Polaroid, but the (red + green) mixture becomes horizontal and is excluded. Thus the cellophane strips are seen lit only by EA, the gaps only by (red f green), and these can be accurately compared and adjusted to a perfect match.
Spearal Sensitivity of “Red” and “Green”
2005
Exchange tiresfrofdr
Whtn mirror M (Fig. 1) was dispiaced to the left, beam 3 (through DJ was not used, but the eye received instead the beam through Ps, The equipment now is exactly as described in Fig. 1 of the previous paper (R-N, POWELLand WHITE.1973 to be referred to as RPWl). Exchange thresholds were operated by interposing either the horizontally or the vertically polarizing element of PO. When, by pulling a string against a spring, the horizontal polarizer was interposed, only 640 nm tight was passed. When, on release, the vertical was interposed, only 540 mu was passed. The neutral wedge W could attenuate these exchange lights to threshold. To view the exchange thresholds, the cellophane grating and “polaroid” were removed from between Cz and L. The exchange light from P, was limited to a 2’ field by a stop S1, and the background from P4 limited by a much larger stop S1. One further important adjustment was necessary to secure that when lights matched by exchange, they also matched in their contribution to the background. Filters X1and A3were removed and wedge R adjusted to give zero change when, by rotating P4, the background alternated between light from beam 1 only or from beam 2 only. With this R-setting we require that there should be zero exchange diierence on puiling the exchange string. This was secured by interposing in the exchange beam an oblique glass plate, rotated from the plane normal to the beam, about either a vertical or a horizontal axis. This will leave the verticaIly and horizontally plane-polarized lights still polarized in those planes, but it will alter the ratio of the two energies transmitted. The angle of the plate was adjusted so that the two transmitted lights were equal. This means that when wedge R is set to the isolept for exchange thresholds (for pigment P) it is also set at isolept for the (red f green) mixture in the Rayleigh match. In this setting, Rayleigh matches give us at once the relative spectral sensitivity of P, as we shall now prove. The proof was given in MITCHELL and RUSHTON(1971b) but as the proof is short and cardinal to our coucIusions, we repeat it here. RAYLEIGH
MATCHES
WITH
ISOLEPT
SETTING
The mirror M (Fig. 1) is interposed and light Elfrom the rainbow wedge DA is attenuated by the neutral wedge W and brought to perfect match with the (red + green) mixture suitably proportioned by rotating the Polaroid P4 to the proper angle 4. When 8 = 0”, only green light is transmitted. Let G be the lu~nan~e of the “mixture field” in this condition. When 8 = 90” only red light is transmitted. Let the luminance now be RIO-‘, where t is the interposed density of wedge R. Let PA,PG,PK be the relative absorptions of pigment P for lights A,G, R. The isolept condition is that the quantum catch from G is the same as from RIO-',or
GPG = RlO-’ PR.
(1)
Now for any position of 8, the total quantum catch from the (red + green) mixture is
GP,cos20+R10-'P,sin20 and substituting from equation (1) Catch in pigment P = GP, (cos2@ + sin2Q) = GPG.
(21
This means that, with r at the isolept for P,the quantum catch in P is the same whatever the 0 setting. We have verified this in protanopes and deuteranopes, (MITCHELL and RUSHTON, 1971b). With r set to their isoIept they say that they can detect no change whatever when 0 is swung between 909 and 0”. Now, in the condition of the Rayleigh match, for each pigment the quantum catch must be the same from the h field as from the (red + green) mixture. So this must apply to pigment P. The luminance of the Xfield is E1attenuated by wedge W. If w is this interposed density the quantum catch in pigment P from the h field. = EA lo-“PA and this must be equal to the catch from the mixture which is given by equation (2). Consequently
2006
W.
A. H.
RUSHTON,
&AS
~PITZER
POWELL
AND
K.
Eli 10-wPI = GPG.
D. WUTE
(3)
In this equation E, is known from calibration, w is the wedge setting made by the subject, and GPc is a constant. Thus the spectral sensitivity PI is inversely as El lo-“, which is known. A great advantage of the analytical anomaloscope is that if r can be set at the isolept for one pigment, then only that pigment is involved in the W wedge settings for the Rayleigh match. The 8 settings are irrelevant and ignored. They are only made to equalize colour in the two fields so that the essential brightness match can be made more exactly. If colour discrimination is weak (as with anomalous trichromats), the 8 setting will be less secure. But that is no calamity since we do not use the B setting. If our subject is not troubled by colour difference and can make a good brightness match, that is all that is asked of him. Since we only have to set r at the isolept of a pigment to obtain its relative spectral sensitivity by Rayleigh matches, it becomes of cardinal importance to be able to make this setting. This can be done by measuring exchange thresholds.
TO
FIND
THE
NORMAL
ISOLEPTS
The equipment was set for exchange thresholds and r adjusted to r0 the isolept for the protanope as described in the previous paper (RPW 1). If one of the normal pigments had its isolept at or near this point, the exchange would cause zero or only a very small change in the quantum catch of this (green) pigment and the observed threshold must result from the other (red) pigment in which the catch changed considerabIy with exchanging lights. This threshold was measured with the exchanging lights superimposed upon a background consisting of the red (640 nm) only, (0 = 903 or the green (540 nm) only, (@= OS). Near the isoiept for the “green” pigment, these backgrounds match for green. But the thresholds are detected by the “red” pigment, and since that is relatively more sensitive to red, the red background is much the stronger. In fact it was found that the log threshold was h higher with a red than with a green background. Weber’s law The backgrounds were bright compared with Fechner’s eigengrau and by placing neutral densities in the &am (C,C, (Fig. 1) it was found that the change in log exchange threshold was equal to the density added or removed. In particular the rise h on changing the background from green to red was neutralized if a density h was interposed in the red background. In this condition the green background raised the exchange threshold as much as did red with density h added. We now assume that two backgrounds GI and R, that raise equally the threshold for pigment P, are equally absorbed by P. This derives powerful support from the work of STILES(1959) who found for each colour mechanism that lights of various wave lengths that were equivalent as threshold flashes against a fixed background, were also equivalent as backgrounds in raising the thresholds of a fixed flash. We assume that this result holds in our very similar experiments, and that the receptor involved in our exchange threshold absorbed equally from each background that raised equally the exchange threshold. Now the red back~ound with density h added, raises the threshold as much as does the green background; and we conclude that each background is equally absorbed by the “red” pigment.
Spectral Sensitivity of “Red” and “Green”
I
4
2007
‘\
FIG. 2. Each horizontal line gives the result of exchange thresholds with red or green background. Vertical placement is arbitrary for clearness of display. Circles give the value of r, the interposed density of wedge R (Fig. 1) when exchange thresholds were measured. Length of horizontal tine to tbe right is the increase in log threshold when the background changes from green to red. Arrowheads should lie on an ordinate corresponding to the isolept for the pigment responding at threshold. Curves show the exchange threshold curves for protanopes (continuous) and deuteranopes (dashed) taken from the previous paper. Arrowheads fall close to their axes (ilepts). Black circles mark average positions. The vertically shaded area is where measurements would be expected to give the wrong answer for reasons explained in the Appendix.
Adding h to the red light can be done by shifting the R wedge from rO to (re + h). If this is the condition where red and green lights are equally absorbed by the “red” cones it is their isolept. Consequently we tid the isolept for red by starting with T set at r. near the isolept for green to ensure that it is the red cone whose exchange threshold is measured, then find h the increase in log exchange threshold in changing backgrounds from the tixed green to this red light. Now set I to (re + h), and this should be the isolept for the red cones that we required to find. RESULTS
Figure 2 displays some results of this experiment, each horizontal line representing a different experiment, their vertical placement being simply for clarity of presentation. The horizontal axis plots r the interposed density of wedge R. The points on the axis marked roe, rox show the isolept values for erythrolabe (deuteranope) and chlorolabe (protanope). The dashed and continuous two-branched curves are the exchange threshold curves obtained in the previous paper (RF’W1) from deuteranopes and protanopes when the background was the average of the exchanging lights. The axis of each coincides with its isolept. The horizontal lines give the results of exchange thresholds made with r set at various values. A perpendicular dropped from a circle onto the horizontal axis marks the r-setting in that experiment. The rise h of log threshold when the background was changed from green to red is plotted in Fig. 2 as the length of the horizontal line to the right from circle to arrowhead. If that background change produced a fall in log threshold, h is negative, and
W. A. H.
2008
Rusino~, DLW-JE SP~ER POWELL ANDK. D.
-i-H
6
x
cl
. -
Wavelength,
k%tlTE
nm
Dichromots
PITT (1938)
FIG. 3. Log
spectral sensitivity curves for the “red” and “green” cones of the normal eye. White circles piot Rayleigh matches at the red isolept; black circles at the green isolept. Dashed curve is the fog spectral sensitivity for deuteranopes, continuous curve that for protanopes. MITCHELL and RUSHTON’S(1971) curves here corrected for their plotring error.
the arrows point to the left. Then, as argued above, the arrowhead should fall on the isolept for the pigment involved in the exchange threshold. For example, the group of four lowest horizontals in the upper part of the figure have circles on the erythrofabe isolept (rob). If the “red” cones have their isolept near here they will not “see” the exchange of tight and onfy green cones can determine the threshold. The change in log threshold with change of background from green to red was (-4) and that brings the arrowhead to a position (r,,c - h) very dose to the axis of the chlorolabe curves (t-,.,x). The position of arrowhead does not depend at all critically upon the position of the circles, provided they do not lie to the left of r+. By the argument given above, however far to the right the circles lie, the arrowheads should still fall upon the isolept, hence in Fig. 2 arrows should all he on the same ordinate, no matter where they start. This is seen to be the case within the limits of experimental error and the average value of this ordinate (black circle) differs by about 0.03 log unit from the isolept of chlorolabe in the protanope. Setting now r to this value or something near it, the experiment was repeated. In this case the “green” cones could not “see” the exchange and the “red” cones determined the threshold. The difference in log threshold @otted as horizontals in the lower part of the figure have arrowheads which nearly coincide with the r,,c, the isolept of erythrolabe in the deuteranope. There are grounds for rejecting the lines in the area of vertical shading (see Appendix).
Spectral Sensitivity of “Red” and “Green”
RAYLEIGH
2009
MATCHES
Knowing the isolepts for the “red” and “green” cones we may now find their spectral sensitivity in the red-green range. The instrument was changed into the analytical anomaloscope and r set to the isolept values given by the mean arrowhead position of Fig. 2, as indicated by the black circles. With each of these r-settings, perfect Rayleigh matches were made for a series of monochromatic lights, h, in the comparison field. As shown in.equation (3), ELPAIO-” = GPG which is constant so that PA is inversely as El lo-“, which is measured. In Fig. 3 the log quantum sensitivity of the two pigments so measured is plotted. Black circles give the “green” pigment, white circles the “red”. The curves shown are the spectral sensitivities of chlorolabe in the protanope (continuous), and erythrolabe in the deuteranope (dashed) as measured from the rate of bleaching by lights of various wave .lengths ~MITC~LL and RUS~ON, 197la), results which coincided with coiour matching functions in dichromats by PITT (1935). There was a plotting error in the (1971) curves that is corrected in the curves of Fig. 3. We agree with Koenig that the “red” and “green” pigments of normal vision are the erythrolabe and chlorolabe of the common dichromats, whose defect is simply the loss of one of them. DISCUSSION
Though the details of our equipment and procedure may be confusing, the underlying idea is simple. It is to reduce the complexity of a dichromatic system to the simplicity of monochromacy.by abolishing the activity of one component. From the principle of univa~ance we conclude that a pi~ent Q will not “see” an exchange from one light to another which is equally absorbed by it. This is the condition at the isolept. At or near the isolept for one pigment Q, then, this pigment will not be able to detect exchange thresholds, which must be registered entirely by the other pigment, P. P’s threshold is raised in proportion to the intensity of background, .and concluding from Stiles’s work that backgrounds which raise P’s threshold equally are equally absorbed by P, we derive that such equal backgrounds give P’s isolept. We found in this way P’s isolept for the red and green lights which, mixed in proper proportions were used for Rayleigh matches. Nowhere is the simplification produced by the isolept more striking than its application to the Rayleigh match. With a protanope, where all lights in the red-green range appear the same in colour, it is simple to match El against (say) a fixed green and for each wavelength h find the energy El that appears identical. With our analytical anomaloscope set at the isolept for pigment P we may do exactly this when two pigments are present. The colour difference between A and green makes a direct match impossible to set or interpret. But in our anomaloscope (Fig. 1) a change of 8 (Pa) alters the colour without any change of absorption by pigment P. Consequently colour difference may be eliminated and a perfect match made with the simplicity found in the protanope, and we may find El the energy at Xwhich is absorbed by P as much as is the fixed green. The spectral sensitivity curves of the two pigments in the normal eye were found in this way, first by determining the isolepts with exchange thresholds, then using these settings for the Rayleigh matches. The results plotted in Fig. 3 coincide with the chlorolabe curve from the protanope, and erythrolabe from the deuteranope, measured subjectively by colour matches (pm; 1935) or objectively by the rate of bleaching of their fovea1 pigments by lights of different wave lengths (MCCALL and RUSHTON,1971a). V.R.13/11--s
2010
W. A. H. RUSHTON, DUNE
SPWZER POWELL AND
K.
D. WHITE
This affords rather strong proof of the correctness of K&rig’s conclusion that protanopes and deuteranopes simply lack each one of the normal pi_gments, the others remaining unchanged. This conclusion is also supported by Fig. 3 of the previous paper (RPWI) where the exchange threshold for the normal eye was found to be nearly the same as that for the protanope or deuteranope, whichever was the lower. From the Principle of Univariance, in the range where the protanope has only the green pigment active, it is plain that a red and a green background that raise the threshold equally, must be absorbed equally. The present observations show that those same backgrounds are equa1 in raising the thresholds for green cones in the norma eye. If then, we accept Riinig’s view that the green pigment is the same in protanopes and normals, we may conclude that red and green backgrounds that are equal in raising the green cone threshold, are equally absorbed by the green cone pigment, even in a retina where red cones are also present. THE SPECTRAL
SENSIflVITY
OF FOVEAL
CONES
IN NORMAL
EYES
THOMAS YOUNG(1802) explained the fact that any spectral light can be matched by a suitable mixture of three fixed coloured lights not by properties of light but by properties of the eye. He supposed three resonators, one most sensitive to red, one to yellow and one to blue (in his first formulation). Ever since then attempts have been made to determine more precisely the spectral sensitivities of these three resonators which must account for the spectral matching functions. The present view is that there are three types of fovea1 cone each with a different visual pigment whose spectral sensitivity (in situ) determines the spectral responsiveness of the cone. If one cone pigment absorbs quanta equally from each of two comparison fields, that pigment cannot distinguish between them (univariance). If this holds simultaneously for al1 three types, the fields are indistinguishable and are said to match. The problem, then, is to find the spectral sensitivity of each cone pigment. This has been attempted in single cones in excised human (or monkey) retinas-a formidably difficult task, for the measuring light always bleaches away some of the pigment to be measured and it is impossible to secure that the measuring light received by the photocell has all passed through the visual pigment -a serious defect. What is the relation between this difference-s~ctrum measured, and the action-spectrum in cone pigments upon which vision depends? What is the effect upon spectral sensitivity of the angle of incidence of light upon the cone (Stiles-Crawford effect of the second kind)? These important difficulties are usually not mentioned by those who measure single cones. Thus single cone measurements though important can hardly be better than fair approximations. Measurements on living man by retinal densitomet~ has many drawbacks, but also some advantages. We may correlate the psycho-physical effect of some light presentation in a particular person with the pigment change produced in his eye by exactly that light presentation. For instance, we can measure in a deuteranope the difference spectrum resulting from bleaching with (a) a red light, (b) a green light which to him looks identical. Since the two resulting difference spectra are the same (RUSHTON, 1965b), deuteranopes can only have one visual pigment (e~hrola~) in the red-green range. More important, it is easy to measure bleaching rates. This alone of all densitometry measurements is independent of stray light. Light that goes elsewhere does not bleach; lights that bleach at equal rates must be absorbed at equal rates, and it is this action spectrum that must be most closely related to visual performance. RUSHTON(1963, 196%) showed with
Spectral Sensitivity of “Red” and “Green”
2011
protanopes and deuteranopes that lights of different wave lengths which looked identical to these subjects, bleached the pigment measured at equal rates. This showed that the pigment measured was that responsible for the subject’s vision. The same work was repeated more accurately by MITCHELL and RUSHTON(197 1a). However none of these objective measurements are nearly so accurate as colour matching in good conditions. Thus the best measurements must be derived from psycho-physics. The C.I.E. photopic measurements are generally accepted as the most satisfactory figures we have, and they refer, of course, to normal vision with light entering centrally through the pupil and encountering macular pi~entation and other transmission losses. It is for these conditions that we generally require the three spectral sensitivity functions. If we knew exactly these three spectral sensitivity functions we could easily deduce the C.I.E. spectral mixture figures. But it is easier to mix than to unmix. From the C.I.E. figures we cannot extract the spectral sensitivity functions without further information, as is very well known. K&rig suggested how this could be done if we assume that protanopes, deuteranopes and tritanopes have normal vision except for the lack of the “red”, the “green” and the “blue” cones. If this were true, each of these dichromats will confuse with a given colour, a whole set of colours which, plotted on the colour triangle, must lie on a straight line. CLARKMAXWELL (1855) was the first to demonstrate this (with his father-in-law who was a protanope), and it has been often coni%-med since with all three dichromatic types. Moreover if, for one type, a set of these confusion lines are plotted, it is found that they al1 meet in a point. This point is rather exactly located, for the lines are defined by many experimental observations all collinear; and their concurrence is defined by many lines. The three concurrence points are rather exactly known. But these three points give us just that additional information that we need to convert the C.I.E. figures into the three spectra1 sensitivity functions. The mathematical transformation and the resulting K&rig Fundamentals are given in WYSZECK~ and STILES (1967, p. 414), upon the expectation that K&rig’s assumptions are true. We have done no experiments in the blue spectral range but in the red-green range we have been able to support K&rig’s assumptions rather strongly. (a) This paper has measured the “red” spectral sensitivity and found it that of the deuteranope; the “green” is that of the protanope. (b) MITCHELLand RUSHTON(197Ia) found in these dichromats.that lights they judged equal, bfeached at equal rates the pigments erythrolabe or chlorolabe measured in their cones. (c) BAKERand RUSHTON(1965) found by partial bleaching that the difference spectrum in the normal was a mixture of the difference spectra from deuteranopes and protanopes. (d) The effect of partial bleaching in the dichromat on the difference spectrum or the colour matching functions, proves that protanopes and deuteranopes have only one pigment in the red-green spectral range. We hope that these observations will strengthen belief in Konig’s penetrating assumptions, and justify his use of the colour matching functions as the most accurate estimate of the three spectral sensitivity functions of the living human eye.
APPENDIX When “green” cones determine the exchange threshold and the background changes from red to green, it will raise the threshold for “green” cones much more than for “red” cones. If it raises the “green” threshold enough, this threshold may lie above that of the “red”
2012
W. A. I% RUSHTON,DLUX
%?lTZER
POWELL
D t
AND
c
E
K.
D. Wr~l!?
\ t \ \
/’
\ \
r
Et// / /
/
\ \
F
/il; FIG. 4. Theoretical dashed, erythrolabe
exchange threshold curves, continuous, for chlorolabe (protanopes); (deuteranopes). Heavy lines when the background is green II, tight lines when it is red 12. The curves in Fig. 4 are not drawn accurately. From equation (5) and (6) the length AB Fig. 4 at abscissa r, is log 10”~ - log 10”1 = log I(Yo-’ = rO-~. This is the distance from AB to r0 the isolept of the active pigment-as we have seen.
cones. If that happened, it would be wrong to interpret the change in log threshold (as we have done), as the change in Iog quantum catch by “green” cones from the two backgrounds. For, in this case the excitability has changed from “green” cones to “red” which entirely invalidates our argument. In fact this complication has been avoided in the experiments of this paper except in the vertically shaded area of Fig. 2. We now explain how we were able to avoid it. The previous paper (RPWI) showed that for various values of r (the R wedge density) the W wedge density w, set for exchange threshold was given by : K
10”
=
l - ltYO-’
HI +
l(yo-‘)
where to is the isolept for the pigment responding at threshold. Experimental results confirmed this theoretical expectation. In the present paper the background is either one or other of the exchanging lights, not their average (as in RPWI), and this gives K
l*wl
=
1 - 1~0-’ for the green background 1, 1
j,(
lowt
=
(9
1 - l@O-’ for the red background iz IfyO_’
Fig. 4 plots these theoretical curves. Dashed curves refer to erythrolabe cones, continuous curves to chlorolabe. Heavy lines are when the background is green, light when it is red.
Spectral Sensitivity of “Red” and “Green”
2013
When in Fig. 2 the circles lie on the chlorolabe isolept, in Fig. 4 likewise the r setting is on the ordinate AB. With green background, the threshold is that of the lowest heavy line to cut AB which is the dashed (erythrolabe) line at B. Changing to the red background we seek the lowest right line. This is the dashed line at A. Both lowest lines are dashed, hence the threshold keeps with the red cones. The distance AB is h which should be the distance from AB to the erythrolabe isolept. But suppose that the circle in Fig. 2 lay at the r-value represented by ED. The lowest heavy line is still on the dashed curve now at E. But on changing to light lines we find that it is now the continuous curve at D that is lowest, so changing backgrounds here involves a switch of threshold cones--L‘ red” to “green”. The line ED is less than half the Iog threshold rise up to the next dashed curve. That is why in Fig. 2 the lines near the centre are so short, and must be rejected from our analysis. If Fig. 4 represents correctly the excitability, it is plain that for r-settings at the isolept or at any point further from the centre of the figure, we are safe in avoiding a switch of threshold cones when the background is changed. But this figure assumes that the two types of cone are equally excitable (have the same Weber fraction). Consider an r-setting on the GF ordinate (Fig. 4). Then, as before, the lowest heavy curve is the dashed curve at F and the lowest light the dashed curve near G. But it only needs chlorolabe cones to be somewhat more excitable than the others-that the whole set of continuous curves should sink 0.3 log units relative to the others-for the thin continuous line to cut the ordinate GF below the dashed curve. This would entail the switch of threshold cones that we seek to avoid. This danger arises when “green” cones are the more excitable and the experiment, as represented in Fig. 2 is an arrow pointing to the right. It does not arise with arrows pointing left (when green is the more excitable). From preliminary threshold measurements we found that “green” cones were in fact slightly more excitable than “red”. Now from Fig. 4 (where green and red are assumed equally excitable) any ordinate to the right of the E isolept must intersect rhin curves, continuous lower than dashed; also thick curves, continuous lower than dashed. If in fact green cones are the more excitable, this lowers further the continuous curve and accentuates this relation--no switch of threshold cones. Consequently, in Fig. 2, all arrows facing left which start on the E isolept or to the right of it should end on the x isolept. The average is very close and those experiments where circles actually lie on E,fall rather accurately on x. Knowing now the x isolept, we may place the circles there and obtain arrows to the right without fear of any cone switch, since at their isolept the x cones are completely inoperative in these measurements, and cannot contaminate our results. Acknowledgements-Thii work was supported by AJX Contract No. AT-(40-l)-2690, by a NSF Grant GU-2612, and by a NIH Grant IROl-EYOO-684-VIS. The writing of this paper was greatly assisted by a Fogarty Scholar-in-Residence Award to Dr. Rushton, at the National Institutes of Health, Bethesda, Maryland.
REFERENCES
BAKER,H. D. and RUSKTON,W. A. H. (1965). The red-sensitive pigment in normal cones. J. Physiof., Lo&. 176,56-72. KOENIG. A. and DIETERICI,C. (1886). Die Grundempfindungen und ihre Intensitgts-Vertheihmg im Spectrum. S.B. Acad. Wiss. Berlin. 805-829. m, J. C. (1855). Experiments on colour as perceived by the eye with remarks on on colour blindness. Trans. Roy. Sot. Edit& 21,2X-298. MITCHELL,D. E. and RUSHTON,W. A. H. (1971a). Visual pigments in dichromats. VisionRes. 11,1033-1044.
W. A. H. RUSHTON,DUNE SP~TZERPOWELLAND K. D. WHITE
2014
MITCHELL,D. E. and RUSHTON,W. A. H. (1971b). The red-green
pigments of normal vision. Vision Res. 11,
1045-1056. Pm,
F. H. G. (1935). Characteristics of dichromatic vision with an appendix on anomalous trichromatjc vision. Med. Res. Council Special Report. No. 200. RAYLEIGH,Lord. (1881). Experiments on colour. Nurure, Lond. 25,64-66. RUSI-ITON, W. A. H. (1963). A cone pigment in the protanope. J. Physiol., Land. 168,345-359. RUSHTON,W. A. H. (1965a). A fovea1 niament in the deuteranooe. J. Phvsiol.. Lund. 176.24-37. RUSHTON;W. A. H. (1965b) Newton I%ure, Chemical basis ofcolourvision and colour blindness. Nuture, Land. 206,1087-1091.
RUSHT~N,W. A. H., POWELL,DIANESPITZERand WHITE, K. D. (1973). Exchange thresholds in dichromats. Vision Res. (In press.) (= RPWl). SOLES, W. S. (1959). Colour vision: the approach through increment theshold sensitivity. Proc. Nut. Acud. Sci. Wash. 45,100-l 14. WYSZECKI,G. and STILES,W. S. (1967). Color Science. Wiley, New York. Yo~G, T. (1802). On the theory of light and colours. Phil. Trans. R. Sot. 1802, 12-48. Abstract-If green light (540 nm) is exchanged for red light (640 nm) with energies so adjusted that each excites the “red” cones equally (their isolept), then only ‘green” cones can respond to the exchange. The exchanging lights are projected upon a steady background light of either 540 or 640 nm with energies so adjusted that they raise the exchange threshold equally. We conclude that this energy ratio is the isolept for “green” cones. The experiment was repeated with exchange energies now at the isolept for “green” cones, and the background ratio now gives the isolept for “red’ cones. Our Analytical anomaloscope is set with the 640 and 540 nrn primaries at the isolept energy values for (say) “green” cones. Then these cones absorb a fixed quantity Q of light from the (red + green) mixture independent of the R/G ratio. So, when a Rayleigh match is made for any wave length h, the fraction of incident energy EL absorbed by “green” cones is the fixed amount Q. Consequently the spectral sensitivity of “green” cones is inversely as EA. The spectral sensitivity of “green” and “red” cones so measured coincides with that of protanopes and deuteranopes. This supports Konig’s views, and justifies the extraction of the “Kiinig fundamentals” from (C.I.E.) colour matching functions using the confusion concurrences of dichromats. R&nm&Si on &change de la lumitre verte (540 nm) pour de la rouge (640 nm) avec i-s energies &glees de facon a exciter egalement les cones “rouges”, les cones “vet-&” sont alors seuls a repondre a cet &change. Les Iurni&es &chat&es sont projetees sur un fond stable de 540 ou 640 nm avec des energies r&glees de facon a augmenter de la mBme quantitt le seuil d’khange. On deduit que ce rapport d’energie excite egalement les c&es “verts”. On rep&e l’experience en 6changeant maintenant les energies de facon a exciter Cgalement les cones verts, et alors le rapport des energies du fond excite egalement les cones rouges. Notre anomaloscope analytique est reg16 avec les primaires 640 et 540 nm aux valeurs d’energies qui excitent 6galement les cones verts, par exemple. Ces cones absorbent alon une quantite fixe Q de lumiere du melange rouge + vert indipendante du rapport R/G. Done, quand on fait une egalisation de Rayleigh pour une longueur d’onde quelconque X, la fraction d’energie incidente EL absorb&e par les cones verts est la quantite fixe Q. Par consequent la sensibilite spectrale des cones verts est inversement proportionnelle ii EA. La sensibilite spectrale des cones verts et rouges ainsi mesurQ coincide avec celle des protanapes et deut6ranopes. Cela con&me les id&es de Konig et justifie la determination des fondamentales de Kiinig a partir des fonctions de melanges de couleurs de la C.I.E. et des points de confusion des dichromates. Znsammenfassung-Wenn man griines Licht (540 nm) mit rotem (64Onm) vertauscht, wobei die Energien so eingestellt werden. dass die “roten” Zapfen jeweils gleich stark erregt werden (“isoieptisch”), so reagieren nur die “griinen” Zapfen auf den Sechsel. Die wechselnden Lichter werden auf ein Umfeld von 540 nm oder 640 nm oroieziert. dessen Energien seinerseits so eingestellt werden, dass sich die Schwelle wechselweise in gleicher Weise erhiiht. Win folgern nun, dass dieses Energieverhlltnis isoleptiscb fiir die “gr@zen” Zapfen ist. Das Experiment wurde wiederholt mit Wechsellicht, das isoleptisch fin die “griinen” Zapfen war; das Verhgltnis der Energien im Umfeld ist dann isoleptisch ftir die “roted’ Zapfen.
2015
Spectral Sensitivity of “Red” and “Green”
Unser AnaIytisches ~o~loskop wird ki den Prim%rvalenzen 646 nm und 530 nm auf die isoleptischen Energiewerte fiir (beispiefsweise) “grrine” Zapfen eingestelh. Dann absorbieren diese Zapfen eine bestimmte Lichtmenge Q aus dem Rot-Grtin-Gemisch unabhringig von deren VerhPltnis, d.h. bei einer Untersuchung am Anomaloskop bei einer beliebigen WellenIHuge X ist dcr Anteil der ausgesandteri Energie E,, der von den “grtinen” Zapfen absorbiert wird, die bestimmte Menge Q. Die spektrale Empfindlncjkeit der “grtinen” Zapfen ist damit invers zu El. Die so gemessene spektraie Emptindhchkeit der “griinen” und “toten” Zapfen koinzidiert mit der von Protanopen und Deuteranopen. Dies entspricht den Vorstellungen Koenigs und rechtfertigt die Ableitung der Koenig’schen Grundvalenzen BUSden C.I.E.-Normspektralwerten, die auf den Verwechslungsgeraden von Dichromaten beruhen.
Pesto~e-ECXM 3errexti cBeT 1540 KM) 3aMemteTcs na rrpacmift CBCT(640 uM) c ~arroli xiepraett, ~TO aiixm& eo36maeT “irpacnbre” ironfiovglr ommatrono (8x 33onenTbr), TorAa Tomso “3enexbxe” ~0~16orrca xory-r pearapoaaTb na 3aMeny. SaMeu.sioitmecst RuIyrerizn rIpoeKT&ipytoTcr ria uOCTOrrartb& $Oti 540-646 RM c TtiX3iM cooTriotIxe?meM 3aeprRB. mo omi O~naKono ywniwuiaio~ nopor nprr 3ahfese. Mu !xm.mo'Iilehf, wo
Torna 3~0 oniomemie
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3KcnepHMenT 6bm noBTopetf c u3Menenue.o s?tep.?uriumyuenuii 06ecnewiaarommi
Am “3enenbIx" xon6orer, a oTHomewe 3Hepraff E3npetma QoHa ruonerrry AJIR “icpactibtx” Kon6oreK. Ham anansiTwwIurti axow3~1oc~0n ricrtonb3yer B xarec-ree ocxo~~bxx Ei3n~emfeR 640 si 540 WM, npn saeprrmx 06ecrtemmatomux a3onemy (nanp3iMep) “3enerrbxx” iron6oqek. %TeM ?rn Koniionxn nOrnomamT onpeneneiinoe KonmeciBo Q cBeTa OT cMecrr/Xpacrroe+ 3enefioe/,He3amicfIFrlo0T cooTHomemin RIG. Mra~, npri ycrarioee ypanuetiur Penes anff mo608 A?dHM ~on8b1, h norur naAaIomeil3iieprEllE, IlOrnOaiaeMasi “3eneHbnd’ ~on6oaa?.m fumxem nocronrmo~ 3en1~33~0& Q. CnenoisaTenbzio, cneirrpazbmu q9crmrreAbaocrb L‘3eiWSX" xon6orer ~pa~o~o~op~o~~bHa EA. &eKrpanbrras q~~~~~ “3enesibIx" a "Kpacmsx" xon6oveK, OnpeAenemw Tax%iM 06pa3obr, coBnaAaeT c ~~~~H~ob~ ~~~T~HOIIOB H $wepaHoizoB. 3~0 noAAep=&zeT B3rnxAbI Khjra H noAw2pxcAae-r onpawuiwxzb s~crpa~mi3 DCXOBB~~: ~IB~TOB (MK~)IIo~Y~~~~M ~~B~~OBO~OC~~B~~I~HIICRC~~~~~~RB~MA~~A~~O ux?woprunWYeH3fX AHXpOMaTOB.
1973; in revisedform 13 April 1973)
IN THE previous paper we described the technique of “exchange thresholds”.
In the following paper we shall apply this technique to determine the spectral sensitivity of the elusive cone pigment responsible for the abnormal Rayleigh equation with a protanomalous or a deuteranomalous subject. In the present paper we use the method to determine the spectral sensitivity of the two cone pigments active in the red-green spectral range of the normal eye. Our results confirm Konig’s belief (KONIG and DIETERICI,1886, 1893) that protanopes and deuteranopes each lack one of the normal pigments and contain the others unchanged. Thus the normal subject possesses the chlorolabe of the pro&mope and the erythrolabe of the deuteranope. This not unexpected result gives us confidence in the method, and we may apply it to find the unknown pigments in the anomalous trichromats (in the following paper) with more assurance. The method of analysis in this paper is of two kinds. The first is to use the technique of exchange thresholds to find for one visual pigment its isolept, i.e. the relative energies of the two exchanging lights from which that pigment absorbs equally (Greek = equal taken). We exchange light at 540 nm of fixed intensity, for light at 64Onm and adjust this in intensity so that the visual pigment investigated absorbs equally from each light. This condition is the isolept for that pigment, with those lights. The second kind of experiment is to use our Analytical Anomaloscope (MITCI-IELL and RUSHTON, 1971b) to match lights of various wave lengths by a suitable mixture of light at 540 nm and 640 am adjusted in intensity to the isolept for the pigment investigated. We shall prove that when the perfect RAYLEIGH(1881) match is established and the (red + green) mixture matches energy & of wave length h, then at each wave length, Ea is inversely as the spectral sensitivity of the pigment. ~on~uently we have only to adjust the intensity of the red component (640 run) to the isolept value for any visual pigment and make perfect Rayleigh matches, to obtain at once the spectral sensitivity of that pigment, between 540 and 640. For clearness of exposition we shall assume that each type of cone contains just one visual pigment. METHOD Figure 1 shows diagrammatically our equipment which could be rapidly transformed to serve either the exchange threshold measurements or as analytical anomaloscope. The change is made by interposing the oblique mirror M in the beam from DA (for anomalscope) or displacing it clear to the left (for exchange thresholds).
With mirror M interposed, Fig. 1 is a simpIi%iedversion of the anomaioscope actualIy used, which was exactly as described by MITCHELL and RUSK~ON (1971b). The light source, A,isa t~t~i~ide iamp which emitted three beams. Beam 1 passes through an interference filter, &a (transmitting light of 540 rim) arid a 2003
2004
W. A. H. RL’SKTON,&AXE SPITZER POWELL
A.UD
K. D. WHITE
FIG. 1. Diagram of optical arrangement (see text). (a) Analytical Anomaioscope: with mirror M interposed. A, light source with three beams, Z,, 540 nm. vertically polarized; lo, 6&un, horizontally polarized and attenuated by neutral wedge R; E, beam Focussed on slit D, in front of “rainbow interference wedge” that passes mon&hrom&c light of any desired wivelength. This beam, attenuated by wedge W, constitutes the monoc~omatic field of the Rayleigh match. The {red f green) mixture for comparison is the conffuence of lo and 4 in the mixing cube Ct with the R/G proportion adjusted by the rotatable polarizer P+. (b) Exchange Thresholds: with mirror M clear to the left. IO, attenuated by wedge R, has value Z2. Z2 is exchanged for II by interposing one or other half of the polarizer P1, thereby excluding either vertically or horizontally polarised light. These exchanging lights are seen superimposed upon the steady beam through P4, whose angular setting adjusts the proportion of red to green in the background. vertical polarizer P,. Beam 2 passes through filter & (640 run) and P2 which polarizes horizontally. Beam 2 is attenuated by the neutral wedge R. Beam 3 is focussed (by a lens not shown) onto a slit just in front of the “rainbow wedge” DA. This is an interference filter of continuously variable wave length transmission, so by moving it across the slit, any desired wave length could be selected for the Rayleigh match. The transmission EL for each position was calibrated both for wave length and energy. Beams i and 2 are brought together by the mixing cube Cr. The combined beam to the left is blocked by the interposed mirror M and is not used in the anomaloscope. The combined beam running down to Cz constitutes the (red + green) mixture which must match the E, beam through the rainbow wedge. Since beam 1 is polarized vertically, beam 2 horizonally, the mixture may be passed in any desired proportions by suitably adjusting B, the angle of the rotatable polarizer P.+ to the vertical. This allows a colour match between EL and the mixture; adjustment of the neutral wedge W in the El beam allows the brightness match. The two lights to be equated were presented in alternate strips of a grating for easy comparison (see. MTCHELL and RUSKTON1971b). From Fig. 1 it appears that light from P4 falling upon Cz is pofarized at an angle ff to the vertical. Actually, as described in MITCHELLand RUSHTON(1971 b) two quarter-wave plates are interposed between P4 and C2. The first, fixed to P4, converts the adjusted (red + green) mixture into circularly polarized light. The second quarter-wave plate reconverts this into a vertical plane polarized beam. The beam E1 is horizontally polarized (by a Polaroid not shown) and both beams, united in the mixing cube C2, are viewed through a grating of alternate cellophane strips and gaps. The cellophane is a half-wave plate with axis at 45” to the horizontal, thus, on transmission, vertically polarized light becomes horizontal, horizontal becomes vertical. fn front of the eye is the final Polaroid transmitting only vertical light+ Consequently the vertical (red -f- green) mixture (but not the horizontal EA beam) passing through the gaps in the grating are transmitted by the final Polaroid. Thus the grating gaps show onfy (red + green). Similarly the EL fight after passing through the cellophane strip becomes vertically polarized and transmitted by the final Polaroid, but the (red + green) mixture becomes horizontal and is excluded. Thus the cellophane strips are seen lit only by EA, the gaps only by (red f green), and these can be accurately compared and adjusted to a perfect match.
Spearal Sensitivity of “Red” and “Green”
2005
Exchange tiresfrofdr
Whtn mirror M (Fig. 1) was dispiaced to the left, beam 3 (through DJ was not used, but the eye received instead the beam through Ps, The equipment now is exactly as described in Fig. 1 of the previous paper (R-N, POWELLand WHITE.1973 to be referred to as RPWl). Exchange thresholds were operated by interposing either the horizontally or the vertically polarizing element of PO. When, by pulling a string against a spring, the horizontal polarizer was interposed, only 640 nm tight was passed. When, on release, the vertical was interposed, only 540 mu was passed. The neutral wedge W could attenuate these exchange lights to threshold. To view the exchange thresholds, the cellophane grating and “polaroid” were removed from between Cz and L. The exchange light from P, was limited to a 2’ field by a stop S1, and the background from P4 limited by a much larger stop S1. One further important adjustment was necessary to secure that when lights matched by exchange, they also matched in their contribution to the background. Filters X1and A3were removed and wedge R adjusted to give zero change when, by rotating P4, the background alternated between light from beam 1 only or from beam 2 only. With this R-setting we require that there should be zero exchange diierence on puiling the exchange string. This was secured by interposing in the exchange beam an oblique glass plate, rotated from the plane normal to the beam, about either a vertical or a horizontal axis. This will leave the verticaIly and horizontally plane-polarized lights still polarized in those planes, but it will alter the ratio of the two energies transmitted. The angle of the plate was adjusted so that the two transmitted lights were equal. This means that when wedge R is set to the isolept for exchange thresholds (for pigment P) it is also set at isolept for the (red f green) mixture in the Rayleigh match. In this setting, Rayleigh matches give us at once the relative spectral sensitivity of P, as we shall now prove. The proof was given in MITCHELL and RUSHTON(1971b) but as the proof is short and cardinal to our coucIusions, we repeat it here. RAYLEIGH
MATCHES
WITH
ISOLEPT
SETTING
The mirror M (Fig. 1) is interposed and light Elfrom the rainbow wedge DA is attenuated by the neutral wedge W and brought to perfect match with the (red + green) mixture suitably proportioned by rotating the Polaroid P4 to the proper angle 4. When 8 = 0”, only green light is transmitted. Let G be the lu~nan~e of the “mixture field” in this condition. When 8 = 90” only red light is transmitted. Let the luminance now be RIO-‘, where t is the interposed density of wedge R. Let PA,PG,PK be the relative absorptions of pigment P for lights A,G, R. The isolept condition is that the quantum catch from G is the same as from RIO-',or
GPG = RlO-’ PR.
(1)
Now for any position of 8, the total quantum catch from the (red + green) mixture is
GP,cos20+R10-'P,sin20 and substituting from equation (1) Catch in pigment P = GP, (cos2@ + sin2Q) = GPG.
(21
This means that, with r at the isolept for P,the quantum catch in P is the same whatever the 0 setting. We have verified this in protanopes and deuteranopes, (MITCHELL and RUSHTON, 1971b). With r set to their isoIept they say that they can detect no change whatever when 0 is swung between 909 and 0”. Now, in the condition of the Rayleigh match, for each pigment the quantum catch must be the same from the h field as from the (red + green) mixture. So this must apply to pigment P. The luminance of the Xfield is E1attenuated by wedge W. If w is this interposed density the quantum catch in pigment P from the h field. = EA lo-“PA and this must be equal to the catch from the mixture which is given by equation (2). Consequently
2006
W.
A. H.
RUSHTON,
&AS
~PITZER
POWELL
AND
K.
Eli 10-wPI = GPG.
D. WUTE
(3)
In this equation E, is known from calibration, w is the wedge setting made by the subject, and GPc is a constant. Thus the spectral sensitivity PI is inversely as El lo-“, which is known. A great advantage of the analytical anomaloscope is that if r can be set at the isolept for one pigment, then only that pigment is involved in the W wedge settings for the Rayleigh match. The 8 settings are irrelevant and ignored. They are only made to equalize colour in the two fields so that the essential brightness match can be made more exactly. If colour discrimination is weak (as with anomalous trichromats), the 8 setting will be less secure. But that is no calamity since we do not use the B setting. If our subject is not troubled by colour difference and can make a good brightness match, that is all that is asked of him. Since we only have to set r at the isolept of a pigment to obtain its relative spectral sensitivity by Rayleigh matches, it becomes of cardinal importance to be able to make this setting. This can be done by measuring exchange thresholds.
TO
FIND
THE
NORMAL
ISOLEPTS
The equipment was set for exchange thresholds and r adjusted to r0 the isolept for the protanope as described in the previous paper (RPW 1). If one of the normal pigments had its isolept at or near this point, the exchange would cause zero or only a very small change in the quantum catch of this (green) pigment and the observed threshold must result from the other (red) pigment in which the catch changed considerabIy with exchanging lights. This threshold was measured with the exchanging lights superimposed upon a background consisting of the red (640 nm) only, (0 = 903 or the green (540 nm) only, (@= OS). Near the isoiept for the “green” pigment, these backgrounds match for green. But the thresholds are detected by the “red” pigment, and since that is relatively more sensitive to red, the red background is much the stronger. In fact it was found that the log threshold was h higher with a red than with a green background. Weber’s law The backgrounds were bright compared with Fechner’s eigengrau and by placing neutral densities in the &am (C,C, (Fig. 1) it was found that the change in log exchange threshold was equal to the density added or removed. In particular the rise h on changing the background from green to red was neutralized if a density h was interposed in the red background. In this condition the green background raised the exchange threshold as much as did red with density h added. We now assume that two backgrounds GI and R, that raise equally the threshold for pigment P, are equally absorbed by P. This derives powerful support from the work of STILES(1959) who found for each colour mechanism that lights of various wave lengths that were equivalent as threshold flashes against a fixed background, were also equivalent as backgrounds in raising the thresholds of a fixed flash. We assume that this result holds in our very similar experiments, and that the receptor involved in our exchange threshold absorbed equally from each background that raised equally the exchange threshold. Now the red back~ound with density h added, raises the threshold as much as does the green background; and we conclude that each background is equally absorbed by the “red” pigment.
Spectral Sensitivity of “Red” and “Green”
I
4
2007
‘\
FIG. 2. Each horizontal line gives the result of exchange thresholds with red or green background. Vertical placement is arbitrary for clearness of display. Circles give the value of r, the interposed density of wedge R (Fig. 1) when exchange thresholds were measured. Length of horizontal tine to tbe right is the increase in log threshold when the background changes from green to red. Arrowheads should lie on an ordinate corresponding to the isolept for the pigment responding at threshold. Curves show the exchange threshold curves for protanopes (continuous) and deuteranopes (dashed) taken from the previous paper. Arrowheads fall close to their axes (ilepts). Black circles mark average positions. The vertically shaded area is where measurements would be expected to give the wrong answer for reasons explained in the Appendix.
Adding h to the red light can be done by shifting the R wedge from rO to (re + h). If this is the condition where red and green lights are equally absorbed by the “red” cones it is their isolept. Consequently we tid the isolept for red by starting with T set at r. near the isolept for green to ensure that it is the red cone whose exchange threshold is measured, then find h the increase in log exchange threshold in changing backgrounds from the tixed green to this red light. Now set I to (re + h), and this should be the isolept for the red cones that we required to find. RESULTS
Figure 2 displays some results of this experiment, each horizontal line representing a different experiment, their vertical placement being simply for clarity of presentation. The horizontal axis plots r the interposed density of wedge R. The points on the axis marked roe, rox show the isolept values for erythrolabe (deuteranope) and chlorolabe (protanope). The dashed and continuous two-branched curves are the exchange threshold curves obtained in the previous paper (RF’W1) from deuteranopes and protanopes when the background was the average of the exchanging lights. The axis of each coincides with its isolept. The horizontal lines give the results of exchange thresholds made with r set at various values. A perpendicular dropped from a circle onto the horizontal axis marks the r-setting in that experiment. The rise h of log threshold when the background was changed from green to red is plotted in Fig. 2 as the length of the horizontal line to the right from circle to arrowhead. If that background change produced a fall in log threshold, h is negative, and
W. A. H.
2008
Rusino~, DLW-JE SP~ER POWELL ANDK. D.
-i-H
6
x
cl
. -
Wavelength,
k%tlTE
nm
Dichromots
PITT (1938)
FIG. 3. Log
spectral sensitivity curves for the “red” and “green” cones of the normal eye. White circles piot Rayleigh matches at the red isolept; black circles at the green isolept. Dashed curve is the fog spectral sensitivity for deuteranopes, continuous curve that for protanopes. MITCHELL and RUSHTON’S(1971) curves here corrected for their plotring error.
the arrows point to the left. Then, as argued above, the arrowhead should fall on the isolept for the pigment involved in the exchange threshold. For example, the group of four lowest horizontals in the upper part of the figure have circles on the erythrofabe isolept (rob). If the “red” cones have their isolept near here they will not “see” the exchange of tight and onfy green cones can determine the threshold. The change in log threshold with change of background from green to red was (-4) and that brings the arrowhead to a position (r,,c - h) very dose to the axis of the chlorolabe curves (t-,.,x). The position of arrowhead does not depend at all critically upon the position of the circles, provided they do not lie to the left of r+. By the argument given above, however far to the right the circles lie, the arrowheads should still fall upon the isolept, hence in Fig. 2 arrows should all he on the same ordinate, no matter where they start. This is seen to be the case within the limits of experimental error and the average value of this ordinate (black circle) differs by about 0.03 log unit from the isolept of chlorolabe in the protanope. Setting now r to this value or something near it, the experiment was repeated. In this case the “green” cones could not “see” the exchange and the “red” cones determined the threshold. The difference in log threshold @otted as horizontals in the lower part of the figure have arrowheads which nearly coincide with the r,,c, the isolept of erythrolabe in the deuteranope. There are grounds for rejecting the lines in the area of vertical shading (see Appendix).
Spectral Sensitivity of “Red” and “Green”
RAYLEIGH
2009
MATCHES
Knowing the isolepts for the “red” and “green” cones we may now find their spectral sensitivity in the red-green range. The instrument was changed into the analytical anomaloscope and r set to the isolept values given by the mean arrowhead position of Fig. 2, as indicated by the black circles. With each of these r-settings, perfect Rayleigh matches were made for a series of monochromatic lights, h, in the comparison field. As shown in.equation (3), ELPAIO-” = GPG which is constant so that PA is inversely as El lo-“, which is measured. In Fig. 3 the log quantum sensitivity of the two pigments so measured is plotted. Black circles give the “green” pigment, white circles the “red”. The curves shown are the spectral sensitivities of chlorolabe in the protanope (continuous), and erythrolabe in the deuteranope (dashed) as measured from the rate of bleaching by lights of various wave .lengths ~MITC~LL and RUS~ON, 197la), results which coincided with coiour matching functions in dichromats by PITT (1935). There was a plotting error in the (1971) curves that is corrected in the curves of Fig. 3. We agree with Koenig that the “red” and “green” pigments of normal vision are the erythrolabe and chlorolabe of the common dichromats, whose defect is simply the loss of one of them. DISCUSSION
Though the details of our equipment and procedure may be confusing, the underlying idea is simple. It is to reduce the complexity of a dichromatic system to the simplicity of monochromacy.by abolishing the activity of one component. From the principle of univa~ance we conclude that a pi~ent Q will not “see” an exchange from one light to another which is equally absorbed by it. This is the condition at the isolept. At or near the isolept for one pigment Q, then, this pigment will not be able to detect exchange thresholds, which must be registered entirely by the other pigment, P. P’s threshold is raised in proportion to the intensity of background, .and concluding from Stiles’s work that backgrounds which raise P’s threshold equally are equally absorbed by P, we derive that such equal backgrounds give P’s isolept. We found in this way P’s isolept for the red and green lights which, mixed in proper proportions were used for Rayleigh matches. Nowhere is the simplification produced by the isolept more striking than its application to the Rayleigh match. With a protanope, where all lights in the red-green range appear the same in colour, it is simple to match El against (say) a fixed green and for each wavelength h find the energy El that appears identical. With our analytical anomaloscope set at the isolept for pigment P we may do exactly this when two pigments are present. The colour difference between A and green makes a direct match impossible to set or interpret. But in our anomaloscope (Fig. 1) a change of 8 (Pa) alters the colour without any change of absorption by pigment P. Consequently colour difference may be eliminated and a perfect match made with the simplicity found in the protanope, and we may find El the energy at Xwhich is absorbed by P as much as is the fixed green. The spectral sensitivity curves of the two pigments in the normal eye were found in this way, first by determining the isolepts with exchange thresholds, then using these settings for the Rayleigh matches. The results plotted in Fig. 3 coincide with the chlorolabe curve from the protanope, and erythrolabe from the deuteranope, measured subjectively by colour matches (pm; 1935) or objectively by the rate of bleaching of their fovea1 pigments by lights of different wave lengths (MCCALL and RUSHTON,1971a). V.R.13/11--s
2010
W. A. H. RUSHTON, DUNE
SPWZER POWELL AND
K.
D. WHITE
This affords rather strong proof of the correctness of K&rig’s conclusion that protanopes and deuteranopes simply lack each one of the normal pi_gments, the others remaining unchanged. This conclusion is also supported by Fig. 3 of the previous paper (RPWI) where the exchange threshold for the normal eye was found to be nearly the same as that for the protanope or deuteranope, whichever was the lower. From the Principle of Univariance, in the range where the protanope has only the green pigment active, it is plain that a red and a green background that raise the threshold equally, must be absorbed equally. The present observations show that those same backgrounds are equa1 in raising the thresholds for green cones in the norma eye. If then, we accept Riinig’s view that the green pigment is the same in protanopes and normals, we may conclude that red and green backgrounds that are equal in raising the green cone threshold, are equally absorbed by the green cone pigment, even in a retina where red cones are also present. THE SPECTRAL
SENSIflVITY
OF FOVEAL
CONES
IN NORMAL
EYES
THOMAS YOUNG(1802) explained the fact that any spectral light can be matched by a suitable mixture of three fixed coloured lights not by properties of light but by properties of the eye. He supposed three resonators, one most sensitive to red, one to yellow and one to blue (in his first formulation). Ever since then attempts have been made to determine more precisely the spectral sensitivities of these three resonators which must account for the spectral matching functions. The present view is that there are three types of fovea1 cone each with a different visual pigment whose spectral sensitivity (in situ) determines the spectral responsiveness of the cone. If one cone pigment absorbs quanta equally from each of two comparison fields, that pigment cannot distinguish between them (univariance). If this holds simultaneously for al1 three types, the fields are indistinguishable and are said to match. The problem, then, is to find the spectral sensitivity of each cone pigment. This has been attempted in single cones in excised human (or monkey) retinas-a formidably difficult task, for the measuring light always bleaches away some of the pigment to be measured and it is impossible to secure that the measuring light received by the photocell has all passed through the visual pigment -a serious defect. What is the relation between this difference-s~ctrum measured, and the action-spectrum in cone pigments upon which vision depends? What is the effect upon spectral sensitivity of the angle of incidence of light upon the cone (Stiles-Crawford effect of the second kind)? These important difficulties are usually not mentioned by those who measure single cones. Thus single cone measurements though important can hardly be better than fair approximations. Measurements on living man by retinal densitomet~ has many drawbacks, but also some advantages. We may correlate the psycho-physical effect of some light presentation in a particular person with the pigment change produced in his eye by exactly that light presentation. For instance, we can measure in a deuteranope the difference spectrum resulting from bleaching with (a) a red light, (b) a green light which to him looks identical. Since the two resulting difference spectra are the same (RUSHTON, 1965b), deuteranopes can only have one visual pigment (e~hrola~) in the red-green range. More important, it is easy to measure bleaching rates. This alone of all densitometry measurements is independent of stray light. Light that goes elsewhere does not bleach; lights that bleach at equal rates must be absorbed at equal rates, and it is this action spectrum that must be most closely related to visual performance. RUSHTON(1963, 196%) showed with
Spectral Sensitivity of “Red” and “Green”
2011
protanopes and deuteranopes that lights of different wave lengths which looked identical to these subjects, bleached the pigment measured at equal rates. This showed that the pigment measured was that responsible for the subject’s vision. The same work was repeated more accurately by MITCHELL and RUSHTON(197 1a). However none of these objective measurements are nearly so accurate as colour matching in good conditions. Thus the best measurements must be derived from psycho-physics. The C.I.E. photopic measurements are generally accepted as the most satisfactory figures we have, and they refer, of course, to normal vision with light entering centrally through the pupil and encountering macular pi~entation and other transmission losses. It is for these conditions that we generally require the three spectral sensitivity functions. If we knew exactly these three spectral sensitivity functions we could easily deduce the C.I.E. spectral mixture figures. But it is easier to mix than to unmix. From the C.I.E. figures we cannot extract the spectral sensitivity functions without further information, as is very well known. K&rig suggested how this could be done if we assume that protanopes, deuteranopes and tritanopes have normal vision except for the lack of the “red”, the “green” and the “blue” cones. If this were true, each of these dichromats will confuse with a given colour, a whole set of colours which, plotted on the colour triangle, must lie on a straight line. CLARKMAXWELL (1855) was the first to demonstrate this (with his father-in-law who was a protanope), and it has been often coni%-med since with all three dichromatic types. Moreover if, for one type, a set of these confusion lines are plotted, it is found that they al1 meet in a point. This point is rather exactly located, for the lines are defined by many experimental observations all collinear; and their concurrence is defined by many lines. The three concurrence points are rather exactly known. But these three points give us just that additional information that we need to convert the C.I.E. figures into the three spectra1 sensitivity functions. The mathematical transformation and the resulting K&rig Fundamentals are given in WYSZECK~ and STILES (1967, p. 414), upon the expectation that K&rig’s assumptions are true. We have done no experiments in the blue spectral range but in the red-green range we have been able to support K&rig’s assumptions rather strongly. (a) This paper has measured the “red” spectral sensitivity and found it that of the deuteranope; the “green” is that of the protanope. (b) MITCHELLand RUSHTON(197Ia) found in these dichromats.that lights they judged equal, bfeached at equal rates the pigments erythrolabe or chlorolabe measured in their cones. (c) BAKERand RUSHTON(1965) found by partial bleaching that the difference spectrum in the normal was a mixture of the difference spectra from deuteranopes and protanopes. (d) The effect of partial bleaching in the dichromat on the difference spectrum or the colour matching functions, proves that protanopes and deuteranopes have only one pigment in the red-green spectral range. We hope that these observations will strengthen belief in Konig’s penetrating assumptions, and justify his use of the colour matching functions as the most accurate estimate of the three spectral sensitivity functions of the living human eye.
APPENDIX When “green” cones determine the exchange threshold and the background changes from red to green, it will raise the threshold for “green” cones much more than for “red” cones. If it raises the “green” threshold enough, this threshold may lie above that of the “red”
2012
W. A. I% RUSHTON,DLUX
%?lTZER
POWELL
D t
AND
c
E
K.
D. Wr~l!?
\ t \ \
/’
\ \
r
Et// / /
/
\ \
F
/il; FIG. 4. Theoretical dashed, erythrolabe
exchange threshold curves, continuous, for chlorolabe (protanopes); (deuteranopes). Heavy lines when the background is green II, tight lines when it is red 12. The curves in Fig. 4 are not drawn accurately. From equation (5) and (6) the length AB Fig. 4 at abscissa r, is log 10”~ - log 10”1 = log I(Yo-’ = rO-~. This is the distance from AB to r0 the isolept of the active pigment-as we have seen.
cones. If that happened, it would be wrong to interpret the change in log threshold (as we have done), as the change in Iog quantum catch by “green” cones from the two backgrounds. For, in this case the excitability has changed from “green” cones to “red” which entirely invalidates our argument. In fact this complication has been avoided in the experiments of this paper except in the vertically shaded area of Fig. 2. We now explain how we were able to avoid it. The previous paper (RPWI) showed that for various values of r (the R wedge density) the W wedge density w, set for exchange threshold was given by : K
10”
=
l - ltYO-’
HI +
l(yo-‘)
where to is the isolept for the pigment responding at threshold. Experimental results confirmed this theoretical expectation. In the present paper the background is either one or other of the exchanging lights, not their average (as in RPWI), and this gives K
l*wl
=
1 - 1~0-’ for the green background 1, 1
j,(
lowt
=
(9
1 - l@O-’ for the red background iz IfyO_’
Fig. 4 plots these theoretical curves. Dashed curves refer to erythrolabe cones, continuous curves to chlorolabe. Heavy lines are when the background is green, light when it is red.
Spectral Sensitivity of “Red” and “Green”
2013
When in Fig. 2 the circles lie on the chlorolabe isolept, in Fig. 4 likewise the r setting is on the ordinate AB. With green background, the threshold is that of the lowest heavy line to cut AB which is the dashed (erythrolabe) line at B. Changing to the red background we seek the lowest right line. This is the dashed line at A. Both lowest lines are dashed, hence the threshold keeps with the red cones. The distance AB is h which should be the distance from AB to the erythrolabe isolept. But suppose that the circle in Fig. 2 lay at the r-value represented by ED. The lowest heavy line is still on the dashed curve now at E. But on changing to light lines we find that it is now the continuous curve at D that is lowest, so changing backgrounds here involves a switch of threshold cones--L‘ red” to “green”. The line ED is less than half the Iog threshold rise up to the next dashed curve. That is why in Fig. 2 the lines near the centre are so short, and must be rejected from our analysis. If Fig. 4 represents correctly the excitability, it is plain that for r-settings at the isolept or at any point further from the centre of the figure, we are safe in avoiding a switch of threshold cones when the background is changed. But this figure assumes that the two types of cone are equally excitable (have the same Weber fraction). Consider an r-setting on the GF ordinate (Fig. 4). Then, as before, the lowest heavy curve is the dashed curve at F and the lowest light the dashed curve near G. But it only needs chlorolabe cones to be somewhat more excitable than the others-that the whole set of continuous curves should sink 0.3 log units relative to the others-for the thin continuous line to cut the ordinate GF below the dashed curve. This would entail the switch of threshold cones that we seek to avoid. This danger arises when “green” cones are the more excitable and the experiment, as represented in Fig. 2 is an arrow pointing to the right. It does not arise with arrows pointing left (when green is the more excitable). From preliminary threshold measurements we found that “green” cones were in fact slightly more excitable than “red”. Now from Fig. 4 (where green and red are assumed equally excitable) any ordinate to the right of the E isolept must intersect rhin curves, continuous lower than dashed; also thick curves, continuous lower than dashed. If in fact green cones are the more excitable, this lowers further the continuous curve and accentuates this relation--no switch of threshold cones. Consequently, in Fig. 2, all arrows facing left which start on the E isolept or to the right of it should end on the x isolept. The average is very close and those experiments where circles actually lie on E,fall rather accurately on x. Knowing now the x isolept, we may place the circles there and obtain arrows to the right without fear of any cone switch, since at their isolept the x cones are completely inoperative in these measurements, and cannot contaminate our results. Acknowledgements-Thii work was supported by AJX Contract No. AT-(40-l)-2690, by a NSF Grant GU-2612, and by a NIH Grant IROl-EYOO-684-VIS. The writing of this paper was greatly assisted by a Fogarty Scholar-in-Residence Award to Dr. Rushton, at the National Institutes of Health, Bethesda, Maryland.
REFERENCES
BAKER,H. D. and RUSKTON,W. A. H. (1965). The red-sensitive pigment in normal cones. J. Physiof., Lo&. 176,56-72. KOENIG. A. and DIETERICI,C. (1886). Die Grundempfindungen und ihre Intensitgts-Vertheihmg im Spectrum. S.B. Acad. Wiss. Berlin. 805-829. m, J. C. (1855). Experiments on colour as perceived by the eye with remarks on on colour blindness. Trans. Roy. Sot. Edit& 21,2X-298. MITCHELL,D. E. and RUSHTON,W. A. H. (1971a). Visual pigments in dichromats. VisionRes. 11,1033-1044.
W. A. H. RUSHTON,DUNE SP~TZERPOWELLAND K. D. WHITE
2014
MITCHELL,D. E. and RUSHTON,W. A. H. (1971b). The red-green
pigments of normal vision. Vision Res. 11,
1045-1056. Pm,
F. H. G. (1935). Characteristics of dichromatic vision with an appendix on anomalous trichromatjc vision. Med. Res. Council Special Report. No. 200. RAYLEIGH,Lord. (1881). Experiments on colour. Nurure, Lond. 25,64-66. RUSI-ITON, W. A. H. (1963). A cone pigment in the protanope. J. Physiol., Land. 168,345-359. RUSHTON,W. A. H. (1965a). A fovea1 niament in the deuteranooe. J. Phvsiol.. Lund. 176.24-37. RUSHTON;W. A. H. (1965b) Newton I%ure, Chemical basis ofcolourvision and colour blindness. Nuture, Land. 206,1087-1091.
RUSHT~N,W. A. H., POWELL,DIANESPITZERand WHITE, K. D. (1973). Exchange thresholds in dichromats. Vision Res. (In press.) (= RPWl). SOLES, W. S. (1959). Colour vision: the approach through increment theshold sensitivity. Proc. Nut. Acud. Sci. Wash. 45,100-l 14. WYSZECKI,G. and STILES,W. S. (1967). Color Science. Wiley, New York. Yo~G, T. (1802). On the theory of light and colours. Phil. Trans. R. Sot. 1802, 12-48. Abstract-If green light (540 nm) is exchanged for red light (640 nm) with energies so adjusted that each excites the “red” cones equally (their isolept), then only ‘green” cones can respond to the exchange. The exchanging lights are projected upon a steady background light of either 540 or 640 nm with energies so adjusted that they raise the exchange threshold equally. We conclude that this energy ratio is the isolept for “green” cones. The experiment was repeated with exchange energies now at the isolept for “green” cones, and the background ratio now gives the isolept for “red’ cones. Our Analytical anomaloscope is set with the 640 and 540 nrn primaries at the isolept energy values for (say) “green” cones. Then these cones absorb a fixed quantity Q of light from the (red + green) mixture independent of the R/G ratio. So, when a Rayleigh match is made for any wave length h, the fraction of incident energy EL absorbed by “green” cones is the fixed amount Q. Consequently the spectral sensitivity of “green” cones is inversely as EA. The spectral sensitivity of “green” and “red” cones so measured coincides with that of protanopes and deuteranopes. This supports Konig’s views, and justifies the extraction of the “Kiinig fundamentals” from (C.I.E.) colour matching functions using the confusion concurrences of dichromats. R&nm&Si on &change de la lumitre verte (540 nm) pour de la rouge (640 nm) avec i-s energies &glees de facon a exciter egalement les cones “rouges”, les cones “vet-&” sont alors seuls a repondre a cet &change. Les Iurni&es &chat&es sont projetees sur un fond stable de 540 ou 640 nm avec des energies r&glees de facon a augmenter de la mBme quantitt le seuil d’khange. On deduit que ce rapport d’energie excite egalement les c&es “verts”. On rep&e l’experience en 6changeant maintenant les energies de facon a exciter Cgalement les cones verts, et alors le rapport des energies du fond excite egalement les cones rouges. Notre anomaloscope analytique est reg16 avec les primaires 640 et 540 nm aux valeurs d’energies qui excitent 6galement les cones verts, par exemple. Ces cones absorbent alon une quantite fixe Q de lumiere du melange rouge + vert indipendante du rapport R/G. Done, quand on fait une egalisation de Rayleigh pour une longueur d’onde quelconque X, la fraction d’energie incidente EL absorb&e par les cones verts est la quantite fixe Q. Par consequent la sensibilite spectrale des cones verts est inversement proportionnelle ii EA. La sensibilite spectrale des cones verts et rouges ainsi mesurQ coincide avec celle des protanapes et deut6ranopes. Cela con&me les id&es de Konig et justifie la determination des fondamentales de Kiinig a partir des fonctions de melanges de couleurs de la C.I.E. et des points de confusion des dichromates. Znsammenfassung-Wenn man griines Licht (540 nm) mit rotem (64Onm) vertauscht, wobei die Energien so eingestellt werden. dass die “roten” Zapfen jeweils gleich stark erregt werden (“isoieptisch”), so reagieren nur die “griinen” Zapfen auf den Sechsel. Die wechselnden Lichter werden auf ein Umfeld von 540 nm oder 640 nm oroieziert. dessen Energien seinerseits so eingestellt werden, dass sich die Schwelle wechselweise in gleicher Weise erhiiht. Win folgern nun, dass dieses Energieverhlltnis isoleptiscb fiir die “gr@zen” Zapfen ist. Das Experiment wurde wiederholt mit Wechsellicht, das isoleptisch fin die “griinen” Zapfen war; das Verhgltnis der Energien im Umfeld ist dann isoleptisch ftir die “roted’ Zapfen.
2015
Spectral Sensitivity of “Red” and “Green”
Unser AnaIytisches ~o~loskop wird ki den Prim%rvalenzen 646 nm und 530 nm auf die isoleptischen Energiewerte fiir (beispiefsweise) “grrine” Zapfen eingestelh. Dann absorbieren diese Zapfen eine bestimmte Lichtmenge Q aus dem Rot-Grtin-Gemisch unabhringig von deren VerhPltnis, d.h. bei einer Untersuchung am Anomaloskop bei einer beliebigen WellenIHuge X ist dcr Anteil der ausgesandteri Energie E,, der von den “grtinen” Zapfen absorbiert wird, die bestimmte Menge Q. Die spektrale Empfindlncjkeit der “grtinen” Zapfen ist damit invers zu El. Die so gemessene spektraie Emptindhchkeit der “griinen” und “toten” Zapfen koinzidiert mit der von Protanopen und Deuteranopen. Dies entspricht den Vorstellungen Koenigs und rechtfertigt die Ableitung der Koenig’schen Grundvalenzen BUSden C.I.E.-Normspektralwerten, die auf den Verwechslungsgeraden von Dichromaten beruhen.
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