designed human densitometer that we have now built at Florida State University appears to be simpler in construction and better in performance

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1 J. Phyaiol. (1971), 217, pp With 5 text-ftgurew Printed in Great Britain THE FLORIDA RETI NAL DENSITOMETER BY C. HOOD AND W. A. H. RUSHTON From the Institute of Molecular Biophysics, Florida State University, Tallahassee, Florida 32306, U.S.A. (Received 24 March 1971) SUMMARY 1. In Part I the principles of reflexion densitometry are discussed in relation to the measurements of visual pigments in man. 2. In Part II the new Florida densitometer is described in some detail, and records are shown of the instrument's performance with pigment in equilibrium or changed by bleaching. 3. With an artificial eye the fluctuations are of the order to be expected from quantum noise and limit the precision of one measurement to of 'double density' which corresponds to some 2 % of total pigment. 4. Part III treats of the reliability and significance of the measurements in living man. It needs ten repeated measurements to attain the reliability of 1 with the artificial eye. 5. The measuring light used bleaches cone pigments by 04 % in the 6 sec required to make a measurement. 6. The interpretation of the measurements is briefly discussed. INTRODUCTION During the past 15 years we have designed and built five retinal densitometers in Cambridge University, two for animals (Rushton, 1952; Rushton, Campbell, Hagins & Brindley, 1955; and Lewis, 1957) and three for man (Campbell & Rushton, 1955; Rushton, 1956, 1961). The newly designed human densitometer that we have now built at Florida State University appears to be simpler in construction and better in performance than earlier models, and in this paper we give briefly, first the main principles of densitometer design as applied to man, and then a short description of our new instrument with some of its physical performance.

2 214 C. HOOD AND W. A. H. RUSHTON PART I Principle of retinal den8itometry As in the ophthalmoscope, light is shone into the eye and is reflected from the fundu8 oculi to re-emerge from the pupil. Some of this emergent light is separated from the in-going beam by a small mirror and falls upon a photomultiplier cell with which it is analysed. Since most of this light has been reflected from behind the retina, it will have passed twice through the receptor layer, and hence have suffered absorption in the photo pigments of the rods and cones. Consequently the photomultiplier signal will give information about the amount of light absorbed by the photopigments and hence about their density. Unfortunately the information is not quite simple. The lining of the human eye is very black; therefore most of the light absorbed is lost, not in the photopigments of the rods and cones, but in the black granules of the pigment epithelium behind the retina. The first problem is to distinguish between these two kinds of absorption so that we may measure only the light loss in the pigments of the rods and cones. We can do this because the visual pigments are photolabile and bleach nearly to transparency in strong light, whereas (in mammals) the pigment epithelium is photostable and absorbs (and reflects) as much after exposure to strong light as before. Consequently, if measurements are made in light of any wave-length before and after bleaching, the difference will be due entirely to changes in absorption by the photolabile pigments and will measure the extent of the change at that wave-length. The measuring light. A further consequence of the blackness of thefundus is that very little of the measuring light that enters the eye is returned to the photocell for measurement (about 1/40,000 from the fovea in our experiments). We may not remedy this smallness of signal by increasing indefinitely the intensity of the incident light, for then we should bleach away the pigment as we tried to measure it. This is the condition that limits the amount of information obtainable. We may either spread the information over a large number of wave-lengths as in the densitometer of Weale (1959) and Carr & Ripps (1967). Or we may use one wave-length at a time which naturally permits greater accuracy at the wave-length chosen (Campbell & Rushton, 1955; Rushton, 1961). Both densitometers are good instruments. Control. The total 'double density' change measured is about 0-2, and we need to make measurements reliable to 0.01 or less. Fortunately it is not necessary that the light or the electric signal be stabilized over long periods to this accuracy, because all that is needed is to compare the measuring light with some control light that is insensitive to change of the

3 THE FLORIDA RETINAL DENSITOMETER 215 visual pigment. Weale divides his beam and sends one part into an artificial eye, as control. We use as control a part of the beam that has passed through a deep red filter and consists only of wave-lengths too long to suffer appreciable absorption in the visual pigments. This red control beam enters the eye along the same path as the measuring beam. In both systems the measuring light alternates with the control light and their ratio measures the pigment density, free from errors due to fluctuations of the light source or photocell. Eye tremor is more serious. Our control system has the advantage that this type of fluctuation is much reduced because control and measuring lights follow the same path and are equally subject to tremors. Bleaching. It is very valuable to be able to bleach with one light while 'simultaneously' measuring the pigment change with another. In this way it is possible (though not easy) to analyse more than one pigment in a retinal mixture. We bleach with a flickering light and measure during its dark phase. Only the measuring light (not the bleaching light) is allowed to reach the photomultiplier cell. The details will be described in Part II. PART II The instrument Measuring pathways. Fig. 1 shows an optical diagram of the 'Florida densitometer'. A is a 6 V 5 A tungsten lamp with a vertical straight filament, powered from a stabilized supply. (If a simple mains transformer is used, however, the performance seems just as good.) Two beams from A after reflexions in mirrors M1 and M2 are united by reflexion and transmission in the plain glass plate G set at the polarizing angle so that the reflected beam from M1 is completely polarized perpendicular to the plane of the Figure; the beam from M2 is polarized in the plane of the Figure by the sheet polarizer P1. A rotating polarizer Pr, mounted in a ball race and driven by a pulley, transmits the two beams in sinusoidal alternation, their energies being proportional to sin2pt and cos2pt respectively (where pt is the angle at time t). The control beam passes through the photometric wedge W1, neutral filters and the deep red filter R (R. G. 650, Schott & Gen. that passes only A > 650 nm). The measuring beam passes through one of several alternative interference filters A (mounted on a wheel) thus defining the wave-length at which the pigment density is measured. The lens L1 focuses the filament A (much reduced in size) upon the subject's dilated pupil after reflexion in the small ophthalmoscopic mirror M3. The subject thus sees in Maxwellian view the lens L1 uniformly illuminated by a mixture ofa and R lights, and limited by the interchangeable stop S1 fitted with cross hairs for fixation (in foveal measurements). These

4 216 C. HOOD AND W. A. H. RUSHTON are set so as to be seen sharply, and are movable in the vertical plane by two rack-and-pinion motions. The measuring beam falls near the edge of M3 and after deflexion enters the left eye just temporal to the centre so that the corneal reflexion passes back to the left and does not contaminate the fundal signal emerging on the right. B LI]L W2 -: C-S2 -~~~53. Fig. 1. Optics of the Florida densitometer, diagrammatic and not to scale (see text). Instead of a mirror that half-covers the pupil, a half-silvered mirror covering all may be used. In principle both arrangements are equivalent, but when only 1/40,000 of the incident light reaches the photocell, very little scattered light will cause grave contamination. We have therefore never allowed in- and out-going lights to fall upon the same path except in the retina itself where coincidence is inevitable. The light reflected from each illuminated point of the emmetropic subject's retina emerges from the pupil as a parallel beam, and the portion that leaves through the right half of the pupil falls upon the lens L3 and is focused on to the stop S3. The operator, placing his eye in the position of P.C. 1 can see at S3 the sharp image of the cross hairs S1 refocused from the retina. The iris stop S3 is now closed down so that only so much of the illuminated retina is exposed as is to be measured. Centring is achieved either by fine movements of the stop at S1 or of the lens L3. Nearly all retinal reflexion except that from the selected region is thus excluded by S3, and the light admitted falls upon an E.M.J. photomultiplier cell P.C. 1.

5 THE FLORIDA RETINAL DENSITOMETER 217 Bleaching. The bleaching light source B is a tungsten filament grid fitted with a concave reflector that brings the grid to a focus that fills the small circular hole S4 drilled in the wall of the light housing. The lens L2 focuses this hole upon the pupil, after the beam has been brought into concurrence with the measuring light by the beam-splitting cube C. The 6 mm bright disk formed would nearly fill the dilated pupil but for the fact that M3 intercepts only half of the disk. The image, therefore, fills the temporal half of the pupil, leaving the nasal half clear for returning rays. The stop S2 (with cross hairs like Sl), is seen sharp by the subject, the aperture of S2 being a little larger than S1, and concentric. It is important that the powerful bleaching light B should not reach the photocell P.C. 1 and contaminate the weak measuring signal. The axis D of a constant velocity motor bears three vanes like a clover leaf spaced at 1200 and occupying 630 each so that the path of the bleaching light is chopped as the vanes rotate at about 10 interruptions/sec. The vanes also interrupt the path to the photocell P.C. 1, but since their number is odd, the bleaching path and the photocell path are blocked alternately, hence the light can never pass from B to P.C. 1. The vanes occupy 630 in order to avoid edge escape, and careful screening precautions are taken to eliminate cross-scatter. Filters and the neutral wedge W2 control the colour and intensity of the bleaching light. Optical performance. Fig. 2a shows a d.c. oscilloscope record of the output of the photomultiplier P.C. 1. The bleaching light is off, the clover leaf vanes are still; only the measuring light falls on the subject's eye and its retinal reflexion reaches P.C. 1 and generates a downward deflexion. The conditions are those used in the normal measurements of cone pigments; the measuring light is of wave-length 580 nm, Pr rotates at about 20 rev/sec (so sine waves repeat at 40/sec). Total volts across the EMI tube are 1000, peak-to-peak output 0 4 V, time = 10 msec/square. Four records are superposed in Fig. 2a. (i) The upper horizontal (H1) is when a black card was interposed in both the A beam and the R beam: only stray light falls on P.C. 1 (ii, iii) Each sine wave is when only the A or only the R beam is occluded; (iv) the lower horizontal (H2) is when neither is occluded. Just before these records, the wedge W1 had been adjusted so that sine wave R was brought equal in amplitude to A, thus the lower line, which is the sum of the equal and opposite sines, is nearly straight. The effect of bleaching on these equal and opposite sine waves is seen in Fig. 2b (with a different subject from that in Fig. 2a). Here two pairs of sine records are superimposed one taken shortly before and the other shortly after a 30 sec exposure that bleached away most of the cone pigments. The red control is seen to be unaffected by bleaching and the superimposed sine waves coincide except for noise. The 580 nm signal on the

6 218 C. HOOD AND W. A. H. RUSHTON other hand is increased in amplitude on bleaching by about 50 %. This corresponds to a 'double density' of 0 17 of cone pigment being removed. In Fig. 2 the photocell output produces a downward deflexion, thus crests mark the zero output (with crossed polarizers), and peak photocell outputs are measured at trough. In practice we do not measure the amplitude of the A sinusoid; we neutralize it with an equal R amplitude in antiphase. In that condition the H, (a) 7,..... I. I H2 (b) t 111HH -0' Ḣ b4-sm.,.. _-umuuuru~j Mod (C) (C) I......,...,....,,,, h2 Fig. 2 (a). Four records of reflexions from human eye. Oscillograms of output from photocell P.C. 1 operated at 1000 V. Deflexions downward, each square corresponding to 0-2 V. Sine-wave frequency at 40/sec. Top horizontal H1 is when A path and control R path are both blocked (zero output); the two sine waves are when either A or R are blocked. The lower horizontal H2 is when R and A are both open and the two sine waves (whose amplitudes are here equal) sum in antiphase. Fig. 2 (b). The two sine waves R and A (580 nm) are recorded as in Fig. 2 a, first just before, and then soon after a full bleaching exposure. The red control sine-wave is unaffected (superimposed waves coincide) but the 580 nm wave increases in downward amplitude after bleaching. Fig. 2 (c). Al shows the photocell output in steady darkness; h2 the output in steady weak light adjusted to give the same mean output as H2 in Fig. 2 a.

7 THE FLORIDA RETINAL DENSITOMETER 219 lower horizontal H2 of Fig. 2a (which is the sum of the R and A sinusoid) will be restored to a straight line. The R amplitude so adjusted is determined by the setting of the wedge W1. If W1 is always set so that the summed output is a straight line (with zero sinusoidal component), then we know for each setting what is the amplitude of the A sinusoid, because that must be equal to the amplitude produced by the R beam which is defined by the calibration of W1. The level and noise of the upper horizontal (H1) was not changed by extinguishing nearly all lights (and screening the photocell from the rest). It therefore corresponds to the dark current of the photocell. H2 is much noisier as would be expected from a signal that might carry various fluctuations in addition to those inherent in the greater steady light. Fig. 2c shows records taken in precisely comparable conditions except that the photocell was now removed from the optical equipment, wrapped in a loose black cloth and put in a part-covered box. The upper line (h1) of Fig. 2c was recorded when the box and coverings were made as light-tight as possible in a dark room. The lower record (h2) was made when enough of a steady flash lamp light was allowed to filter through, to produce a lowering of d.c. level about equal to that of H2 in Fig. 2a. Since when the average light is the same the noise is the same in Fig. 2a and 2c, densitometry measurements in these conditions appears to be limited by the quantum fluctuations of the 'steady' light. Photometry confirms that this is of the right order of magnitude. Fig. 3 shows records made while the clover-leaf vanes are running at 10 interruptions per sec. Record A monitors the bleaching light; at the troughs it fell on the eye. B records the photocell output. It might be expected also to exhibit a battlement form, swinging between H1 and H2 of Fig. 2a as the vanes periodically extinguished all light to the photocell. We are indebted to Dr J. G. Robson for the design of a small transistor element (operated by a commutator on the motor axis) which converts the battlement records into B, Fig. 3. While the measuring light is falling on P.C. 1 we get the (noisy) output which may be brought to balance by the wedge W1. But just before the vane intercepts light falling on the photocell its output is clamped at that instantaneous level. Thus Fig. 3B shows an alternation of signal and silence, suitable for measurement. Fig. 3 C is a repetition of B but now in equilibrium under a strong bleaching light which has removed most of the cone pigments. This has no effect on the deep red signal but the 580 nm light is now less absorbed, so that its sine-wave amplitude is increased (see Fig. 2b) and slightly more than 1 cycle of this increase is seen added to the noise in record C. If W1 is now readjusted, the noise signal may be straightened out to appear like B, and the amount by which the wedge was changed measures the double-

8 220 C. HOOD AND W. A. H. RUSHTON density change caused by the bleaching. However, there is a very much more precise way of reaching the end point. It will be noted that though the bleaching light is enormously stronger than the measuring light nothing of it contaminates our record; nothing leaks through with our maximum bleaching intensity which is 7-5 log td of retinal illumination, a light which will bleach half the cone pigments away in 100 msec - the duration of one cycle. C. A - Fig. 3. Records from photocell when the bleaching and measuring lights are in operation (10 c/s). A, monitor of bleaching light which falls on the eye when the trace sinks. B, the measuring signal in balance; a noisy horizontal when the bleaching light is not falling on the eye. C, repeat of B when some pigment has been bleached; the signal now contains a sinusoidal element that needs balancing out. Electrical processing. In principle our signals are two sine waves of frequency 40 c/s in antiphase which we wish to adjust to equal amplitudes so that a horizontal straight line (H2, Fig. 2a) results. In the presence of noise we can do this efficiently by means of a third beam from the light source A, Fig. 1 (shown as a dashed line). This beam simply passes through the rotating polarizer Pr and falls on a photocell P.C. 2 through a sheet polarizer window P2 which may be rotated to bring the P.C. 2 output into phase with P.C. 1 when the A beam is blocked. Now if the R and A beams (assumed noise-free) were not properly balanced, the P.C. 1 output would be a sine wave of small amplitude, in phase with P.C. 2 when R is too strong; in antiphase when too weak. The presence of noise is not so serious when we know exactly what and where the signal is, and we can increase the signal/noise ratio some hundredfold

9 THE FLORIDA RETINAL DENSITOMETER 221 by using a lock-in amplifier (Princeton Applied Research). Much of the noise is removed by passing the P.C. 1 output through an amplifier tuned to 40 c/s. The resulting signal is then in effect multiplied by the signal from P.C. 2 and the product integrated. The result is to diminish all components of noise except those close in frequency and phase with the signal. The output of this process approximates to the noise-free magnitude of wedge imbalance. This is recorded in Fig. 4 (time: 1 square = 2 sec). At the graduated vertical line a fairly strong bleaching light was applied and left on. Measurements were made as in Fig. 3, but now the results are smoothed and the Fig. 4. Output of phase-sensitive demodulator (over-smoothed) which records the change in the R-A balance 2 sec per square. Bleaching light applied at break in the trace causes a substantial change in balance level. change of balance displayed. The gap in the tracing indicates when the bleaching started, and the trace indicates roughly the time course of bleaching. When too much smoothing is employed (as in this record) the output is slow to follow changes; we get the best results with less smoothing, and an output which rapidly responds to change in setting of the wedge W1, but inevitably with more noise. Sensitiveness of measurement. In practice this is limited by movements, etc., of the subject's eye which will be considered later. Here we are concerned with the physics of the equipment, and it will suffice to show that

10 222 C. HOOD AND W. A. H. RUSHTON this does not limit appreciably the sensitiveness of measurements which can be obtained from man. For the subject we substituted an artificial eye consisting of a little cylinder with lens at one end and 'retina' in its focal plane at the other. The lens was stopped down to give an 8 mm pupil, the cylindrical walls were black, the 'retina' was white and the measuring light reduced so that the output of photocell P.C. 1 had the same amplitude as in normal human measurements. Table 1 shows five runs each consisting of ten successive settings of the wedge W1, Fig. 1, required to bring the photocell signal into balance. The wedge scale was graduated in units of transmittance, thus each reading TABLE 1. Measurement of light transmitted using the artificial eye Glass Wedge readings Run plate (transmission) 1 Out 406± In Out In 35*8±031 5 Out Ten readings at each run; mean + S.D. of one reading. measures (in some fixed unit of flux) the amount of light reflected from the eye and received upon the photocell P.C. 1. The final column in Table 1 gives the average and the S.D. of one measurement in the ten repeated readings of that run. In runs 2 and 4 a plain glass plate was interposed in the 560 nm measuring beam to mimic some regeneration of pigment absorbing in the green but not in the deep red. The glass reduced the reflected light by 8 % (if perfectly clean) which is 0-03 equivalent density for single passage. This gives an easily measurable change in wedge reading slightly variable due to the exact placing of the glass, very constant at its removal. Table 1 shows that the S.D. of one measurement is in a reading of 4; we need to know what uncertainty this means in the percent of total pigment measured. The change from full bleach to full regeneration on the human fovea is from 4 to 2-4 in units of reflected light (the less-than-full change of Fig. 2b is from 4 to 2.6). Thus the in 4 of Table 1 is that uncertainty in a total of = 1-6 or %. Thus if all uncertainty lay in the instrument, each human measure would be correct to /. Unfortunately the frailty of man raises this figure.

11 THE FLORIDA RETINAL DENSITOMETER 223 PART Reliability of measurements in man (a) Repeatability. When the reflexion measured comes from the living eye, results are not nearly so dependable as those from an artificial eye. This is probably due mainly to movement of the eye which causes small changes in the ratio of signal to deep red control light, returned from the eye Ṫhe head is clamped with bite-bar and brow rest, both moulded out of dental wax. Sometimes we use, instead of the brow-rest, a clamp moulded to the bridge of the nose (as recommended by Safir &1Hyams, 1969). Some subjects seem to be set more firmly and comfortably with one clamp, some with the other. Eye fixation is maintained by the subject looking steadily at a fixation point suitably placed for rhodopsin measurements, or for foveal pigments at the cross hairs centred in measuring and bleaching beams. For runs which may take 20 min for completion, continued exact fixation is neither necessary or desirable. The subject looks all the time near the fixation mark, but only fixates exactly when so directed during 5-7 sec when wedge settings are actually being made. Usually fixation is satisfactory. Difficulties are experienced immediately after a great change in brightness (e.g. switching on or off a strong bleaching light) when the cross hairs may be temporarily invisible. Sometimes, in a long run, involuntary pendular eye movements set in. The subject afterwards -says that the light kept floating away and he could not hold it still. The wedge balance is seen to swing in consort, and often that run must be abandoned. Pupil size should remain fixed no matter how strong the bleaching light. This needs dilatation by a mydriatic of the type which paralyses the oculomotor nerve. When this is not strong enough, or the effect partly worn off, variation of pupil with illumination may produce errors of two kinds: (a) the bleaching light may fall upon the iris and hence retinal illumination be less than expected, (b) the measuring light will leave the eye through a smaller aperture than normal. If signal and deep red control were equally reduced this should make no change in the balance setting of the wedge, but in fact it does change this balance. Experiments without a fixed pupil must be rejected. Drooping eyelids. Most eyelids droop somewhat and the small measuring light is best sent in a little below mid level. Experienced subjects learn to open wide their eyes when asked to fixate for measurement. But the flickering lights have a hypnotic effect and this is sometimes accompanied by loss of muscle tone, drooping of the eyelids and of the skeleton, with some change of head position. Blinking is no trouble, it is easily recognized 8 PHY 217 I

12 224 C. HOOD AND W. A. H. RUSHTON as a flick in the balance needle and ignored. Tears are sometimes formed in prolonged fixation but appear to have little effect on wedge settings. The chief trouble is that we sometimes are unaware that any of these things have occurred, only that something has gone 'wrong' with the measurements, so single measurements can only be accepted with caution. Since, however, these defects are very unlikely to obtrude in the same way from one experiment to the next, a well-repeated sequence commands respect. (b) Experimental precision. In Part II an example was given of the precision of settings when repeated measurements were made on the artificial eye. Now for comparison we make repeated measurements on a human eye first in the dark, and then in equilibrium under steady illumination with light of 560 nm at various levels. TABLE 2. Measurements of light transmission using the human eye Steady bleach (log td) Wedge transmission S.E. of mean (10) - co(dark) * The results are shown in Table 2 where column 1 gives the bleaching intensity in log td. Columns 2 and 3 give the mean + S.E. of ten readings of the densitometer wedge brought to balance during the equilibrium. The wedge is calibrated in units of transmission so the numbers are proportional to the light flux reflected from the eye, which for dilute pigment is proportional to the change in density. The total change in column 2 is from full regeneration to full bleaching. Thus ( ) represents 100 % pigment bleaching, and other levels in column 2 are proportionally interpolated. These values with + 1 S.E. are plotted in Fig. 5 as p (fraction of pigment unbleached) against log I (the bleaching intensity in trolands). The curve is derived from the fundamental kinetic equation (Rushton, 1958, 1963; Rushton & Henry, 1968). - to dp = /Io-(- (1) where t is time and to, Io constants. In equilibrium dp/dt = 0 hence,/o = (I-p)/p- (2) This is the curve of Fig. 5. It is slid horizontally to the place of best fit which is where Io, the intensity for 50 % bleaching lies at 4-7 log td. This is a usual figure (somewhat higher, it appears, in Florida than in Cambridge).

13 THE FLORIDA RETINAL DENSITOMETER 225 The scatter of points about the curve suggests fluctuations in the sequence of measurements from one point to the next which lie outside those of repeated measurements at one point shown in Table 2 (e.g. due to small head movements, etc., during the whole course of the experiment). Bleaching by the measuring light. The brighter the measuring light the greater the signal/noise ratio and in general the more precise and quick the measurement. But the cost is that some pigment is bleached by the measuring light itself and this, if too large, may complicate or even invalidate the results. Clearly we must know the bleaching produced by our measuring light to evaluate this complication. We have measured this as follows _.... 0, I' Dark logtd Fig. 5. Fraction of pigment (p) present at equilibrium under bleaching by green light of various intensities (I). Abscissae, log I in trolands. Experimental points show mean + s.e. from Table 2. Curve represents II1 = (1 -p)/p, where 10 (the light which bleaches to 50 %) is found to be 4*7 log td. With our densitometer set for foveal application, the subject sees the bleaching light with the measuring light superimposed. Thus it is easy to introduce a card from the left, half way across the circular bleaching-light stop, so that only the right semi-circle shines; and from the right across the measuring-light stop so that only the left half shines. This arrangement then presents a bipartite field permitting direct measurement of the two lights. In the measuring beam was a 560 nm interference filter and no neutrals; in the bleaching beam another 560 nm filter, and as much of the neutral wedge W2 (Fig. 1) as gave an exact match. Now if these two half fields match, they will bleach equally, and Fig. 5 shows how much. For the bleaching beam which matched the measuring light is that shown by the arrow at 4X2 in Fig. 1 which at equilibrium bleached 25 %; thus the measuring light (with the 0X6 density removed) would eventually bleach 8-2

14 226 C. HOOD AND W. A. H. RUSHTON up to this amount. With 0-6 in place, the bleach at equilibrium is 7-5 % as follows from eqn. (2) where log I = = 3-6, and log lo = 4-7. Hence (1-p)/p = IIo = antilog ( ) = I -p = = 7.50/. Thus if our measuring light is left on indefinitely it will bleach a dark adapted eye up to 8 %. But it is usually left on only 5-10 sec for a measurement. The maximum bleaching rate is when p = 1 and from eqn. (1) it is ({dp\ d _ 1 1I \dt max to lo Now to is the time constant of regeneration in the dark which is 2 min and I/IO we have seen is 0-08, thus the maximum bleaching rate is 4 % per min or 0-4 % per 6 sec which is about the time it takes to make a sound wedge setting. The photosensitivity of rods is about 0 4 times that of cones, so they bleach correspondingly less. On the other hand they regenerate more slowly and hence accumulate more the effects of repeated measurements. Interpretations of the wedge settings. When densitometry is performed upon solutions, the simplifying principle of 'additivity ofdensities' applies. If the measuring light passes in series through a set of similar troughs 1, 2, 3,... each containing solutions of densities D1, D2, D3,..., then the density of the whole set (by definition) will be D1 + D2 + D If now the contents of all the troughs are poured into a large vessel and mixed (without chemical interaction) and the troughs refilled with the mixture, the density of the set is found to be the same as before, namely D1 + D2 + D This is the sense in which we may say that the density of the mixture is the sum of the densities of the individual ingredients. It has played an important part in studying exactly the changes which occur when rhodopsin is bleached. An essential for this additivity to apply is that all the measuring rays are similar and pass through similar pigment mixtures. This certainly is not the case with rays passing through the mosaic of receptor pigments in the retina. Some measuring rays pass through one kind of cone, some through another and some rays pass between them. How are we to interpret the photocell output from this assortment of rays, variously attenuated, which fall upon it? A different additivity principle applies, not of densities, but of transmitted lights. If the measuring light passes in parallel through a mosaic of receptors 1, 2, 3,... each of them transmitting light quantities I,, I2, I3,... then the total light transmitted T will be I There is here plainly some similarity with electric resistors in series and in parallel; in series it is the resistances (densities) which add, in parallel it is the conductances (trans-

15 THE FLORIDA RETINAL DENSITOMETER 227 missions) which add. To put a whole retina into an instrument which measures density and then without comment to publish the instrument's plot as the measure of changes in the quantity of various pigments, appears to be a defect of understanding exactly analogous to using the formula for resistances in series in a situation where they are in parallel. Transmissivity measurements. In dealing with light passing through the retinal mosaic a useful formula is eqn. (3) derived by Rushton (1965b). Where J, the transmissivity change from complete bleaching is To - T me+nx To m+n+a+b/p (3) In this formula Greek symbols are wave-length dependent; Roman not. Our wedge (W1, Fig. 1) whose setting indicates the pigment level, is calibrated in units of transmission so the readings are proportional to the light reflected from the eye. To is the wedge reading in the fully bleached state, T at any other stage of bleaching using the same measuring light. The light absorbed by double passage through erythrolabe (or chlorolabe) cones is me, (nx), where m (n) is a factor depending upon the proportion of red (or green) cones on the fovea. From the fully bleached fovea the total light returning is proportional to the denominator of eqn. (2) and consists of m units from empty red cones, n from empty green, a from the spaces between the cones and b/p from superficial light reflected anterior to the fundus (whose reflexion fraction is p). Formula (3) has a very important property. Any change in J results from the change due to e added simply to that due to x. If the 'density' rather than the light returning is measured, this 'density' change when one pigment only alters is a horrible involvement between the pigment that changes and those which do not. On the other hand it is not easy in eqn. (3) to measure a and b/p, and thus get absolute values. Moreover, the important quantity e which represents the absorption by erythrolabe raises the question of self-screening if the cone density is high as argued convincingly by Brindley (1953) and others who have followed him. There is also some doubt as to the path followed by reflected rays. Do they mainly retrace their course through the outer segments of the cones or do they pass back between the cones? And does the proportion of retracers depend upon the region of the pupil from which returning rays are collected, as the Stiles-Crawford effect might suggest (see the paper following)? If the density of cone pigment is small, results expressed as p, the fraction of pigment unbleached will hardly be affected by these considerations and for most purposes e may be taken as proportional to p. This is the case in two recent investigations, Alpern on cone pigments and Alpern (1971) on rhodopsin. Both of these used a densitometer which is almost an exact replica of the instrument 8-3

16 228 C. HOOD AND W. A. H. RUSHTON described in this paper and provide an independent demonstration of its performance. There is one class of measurement which avoids altogether the difficulties of interpreting the transmission measurements. It is when conditions of bleaching and regeneration are adjusted so that the wedge reading is the same in one state as in another. If only one pigment is involved or if both erythrolabe and chlorolabe may be treated as a single pigment (as in bleaching and regeneration with white light), then when in two states the wedge balance is the same, the pigment level must also be the same whatever that level may actually be expressed as % bleach. In this way the deuteranope was shown to have only one cone pigment in the red-green range (Rushton, 1965 a), since a bleach by red or by bluegreen light that both gave equal wedge transmission values measured at one wave-length, gave equal values measured at all other wave-lengths. Another application was to the threshold rise produced by glare (Rushton & Gubisch, 1966). A glaring surround field produced the same threshold rise as a much weaker background field directly applied to the test area, when the two fields bleached equally the pigment at the test area as measured by equal wedge settings. Thus glare acted entirely by light scatter and not by nervous lateral inhibition. A recent application, this time with the Florida densitometer, is the demonstration (Mitchell & Rushton, 1971) that in dichromats lights, which appear to them equally bright, bleach their pigment equally. One more example, also using the Florida instrument, is presented in the paper which follows this. Here the Stiles-Crawford effect, the inefficiency of light which enters near the edge of the dilated pupil, is studied both subjectively by matching brightness (as usual) and objectively by matching the bleaching rates, when the bleaching light enters the pupil at various points. The two are found to correspond. This work was supported by the U.S. Atomic Energy Commission, N. AT.-(40-1) and a National Science Foundation Grant GU REFERENCES ALPERN, M. (1971). Rhodop8in kinetic8 in the human eye. J. Phy8iol. (In the Press.) BRINDLEY, G. S. (1953). The effects on colour vision of adaptation to very bright lights. J. Physiol. 122, CAMPBELL, F. W. & RUSHTON, W. A. H. (1955). Measurement of the scotopic pigment in the living human eye. J. Phy8iol. 130, CA.RR, R. E. & RiPPs (1967). Rhodopsin kinetics and rod adaptation in Oguchi's disease. Invedtve Ophth. 6, LEWIS, D. M. (1957). Retinal photopigments in the albino rat. J. Phy8iol. 136,

17 THE FLORIDA RETINAL DENSITOMETER 229 MITCHELL, D. E. & RUSHTON, W. A. H. (1971). Visual pigments in dichromats. Vision Res. (In the Press.) RUSHTON, W. A. H. (1952). Apparatus for analysing the light reflected from the eye of the cat. J. Phy8iol. 117, P. RUSHTON, W. A. H. (1956). The difference spectrum and the photosensitivity of rhodopsin in the living human eye. J. Physiol. 134, RU5HTON, W. A. H. (1958). Kinetics of cone pigments measured objectively on the living human fovea. Ann. N.Y. Acad. Sci. 74, RUSHTON, W. A. H. (1961). Dark adaptation and the regeneration of rhodopsin. J. Phy8iol. 156, RUSHTON, W. A. H. (1963). Cone pigment kinetics in the protanope. J. Physiol. 168, RUSHTON, W. A. H. (1965a). A foveal pigment in the deuteranope. J. Phy8iol. 176, RUSHTON, W. A. H. (1965b). Stray light and the measurement of mixed pigments in the retina. J. Physiol. 176, RuIrHTON, W. A. H., CAMPBELL, F. W., HAGINS, W. A. & BRINDLEY, G. S. (1955). The bleaching and regeneration of rhodopsin in the living eye of the albino rabbit and of man. Optica Acta 1, RUSHTON, W. A. H. & GuBIsCH, R. W. (1966). Glare: its measurement by cone thresholds and by the bleaching of cone pigments. J. opt. Soc. Am. 56, RUSHTON, W. A. H. & HENRY, G. H. (1968). Bleaching and regeneration of cone pigments in man. Vision Res. 8, SAFIR, A. & HYAMS, L. J. (1969). Distribution of cone orientation as an explanation of the Stiles-Crawford effect. J. opt. Soc. Am. 59, 757. WEALE, R. A. (1959). Photosensitive reactions in fovea of normal and cone-monochromatic subjects. Optica Acta 6,