following paper deals with a very limited range of parameters but the

Transcription

1 J. Phyeiol. (1969), 202, pp With 13 text-figure8 Printed in Great Britain ROD INCREMENT THRESHOLDS ON STEADY AND FLASHED BACKGROUNDS BY P. E. HALLETT From the Department of Physiology, University of Alberta, Edmonton, Alberta, Canada (Received 27 November 1968) SUMMARY 1. This paper presents increment threshold data for a fairly wide range of parameters but certain of the relationships are slightly complicated by what may amount to large differences in the observers' criterion. The following paper deals with a very limited range of parameters but the measurements are more precise and the analysis more simple. 2. Increment thresholds have been measured for a small, brief duration test viewed against large steady and pulsed backgrounds, using the technique of Aguilar & Stiles (1954) which is intended to isolate rod vision. Under these circumstances it is shown that the test is seen by the rods and that the cones do not disturb the sensitivity of the rods. 3. The relative positions of increment threshold curves for steady and pulsed backgrounds are usually consistent with an integration time of r = ca. 0-1 sec. 4. Backgrounds of less than 0-1 sec duration are effectively impulse inputs in the sense that the magnitude and time course of the test threshold disturbance ('impulse function') is dependent only on background energy. 5. Functions of the impulse function may be substituted for the classical integration time r. The exact form of the impulse function and its theoretical treatment is pursued in the next paper. 6. The threshold disturbance caused by switching on a background light settles to a steady value within 2 to 3 times T. INTRODUCTION The threshold for the perception of a test flash added to a steady background is one measure of the effects of background light on visual sensitivity and has been much investigated (reviews by Barlow, 1957; Pirenne & Marriott, 1962; Brindley, 1960; Rushton, 1965). One concept of import-

2 356 P E. HALLETT ance is that the eye can integrate the light from a testing signal fort = ca. 0X1 see, the classical integration time of the eye, and in this paper T is shown to provide a useful description of the effects of pulsed backgrounds on the rod threshold. In the next paper an analysis of the impulse functions of rod vision will be used to derive both r and the dark light of the eye. METHODS Apparatus. Figure 1 illustrates the optical arrangements. Light for the test beam is taken from one side of the vertical filament 6 V 36 W motor car headlamp bulb (S) and light for the background beam is taken from another side of the same filament. The two beams are guided by lenses (L1, L2) through neutral attenuating wedges (W), interference filters (V), masking slits (S) and fast shutters (Sh) before recombination by the half aluminized plate glass mirror M' and delivery to the observer's eye. The slit in the background beam is imaged in the centre of the dilated pupil of the observer's left eye and the slit in the test beam is imaged more towards the nasal edge of the pupil. The headlamp bulb is run from a ripple free, stabilized DC power supply at such a voltage that it matches the colour of a Source A standard lamp (C.T. = K). The neutral wedges are colloidal carbon filters (Simpl Ltd.) cemented in glass, with compensators arranged so that the attenuation is spatially even. The densities corresponding to the various settings were measured for each pass band with a Baldwin vacuum cell photometer (MND Mark 6, A type cathode) on more than one occasion. The interference filters are of the sort which allows the peak of the pass band to be adjusted (Schott Veril B60, half width = nm). The characteristics of these filters have been checked independently of the maker's calibrations and specifications with a good recording spectrophotometer. A computer program was used to calculate the luminous efficiency and mean wave-lengths of filtered source A light according to the weights of the rod mechanism, Stiles's cone mechanisms and the vacuum cell photometer. The contributions of parasitic light are easily detected by comparing the mean wave-lengths and efficiencies on the basis that the stray light is either zero or is the maximum allowed by the calibrations. Supplementary glass filters prove necessary in the red and in the blue. The background and test pass bands for rod isolation were chosen from the computed data in accordance with the principles described by Aguilar & Stiles (1954). The shutters are light bamboo flags attached to galvanometer type movements (Elliott Bros torquemotor 130 (600 ma) A1). These robust motors are driven by overloading them briefly. The motors are in series with power transistors across a current limited power supply. When sufficient current is drawn from the bases of the power transistors the full 20 V of the supply are applied to the motor which in the parallel arrangement needs only 2 V for full deflexion. Burn out is prevented by cut out of the power supply. The power transistors are activated by the amplified output pulses of a Devices 5 figure Digitimer. In this way the 1 mm wide slits ST and SB are uncovered in 0 3 msec and it is easy to adjust the synchronous action of the two shutters to 0-1 msee. The half mirror AM' is chosen from a set with various degrees of aluminization so as to ens ire the best combination of the maximum brightnesses of the test and background beams. The fixation point consists of a small red point with 1 deg subtense blue background (Gregory, 1959). During steady fixation the blue background is not visible but shows immediately if fixation shifts. This precaution might be thought to be important since the eye might shift during the long interval (up to 1 see) which sometimes occurs between the test and background flashes. In practice the observers seem able to fixate quite well for 1 see without any such reminder.

3 ROD THRESHOLDS 357 Photometric calibrations. The apparatus beams were calibrated with the Baldwin photometer at the beginning and end of each session and the photometer was calibrated against a standard lamp every other session. The observer'8 view. The fully dark-adapted observer bites his dental impression in Kerr compound and when ready fixates on a small red fixation point at 12 ft. distance, and triggers the apparatus. The iris of his left eye is paralyzed with cyclopentolate hydrochloride. He F.P. * (a) FT F B (b) F.P. IST M ShV L2 Li (c) Fig. 1. (a) The observer's view: F.P. is the fixation point, B the background and T the test. (b) The entry positions of the test and background beams in the plane of the dilated pupil: FT and FB are umnagnified images of the 3 x 1 mm slits ST and SB and are 2*5 mm apart. (c) The plan of the apparatus. Light from the source S is collimated by L1, attenuated by the neutral wedges W, and is focused by L2, via the interference filter Veril B 60 on the 3 x 1 mm slit S, which may be uncovered by the shutter, Sh. This slit is then focused in the observer's eye at E. The test and background beams are recombined by the half mirror M'. M represents full mirrors. L, and L4 are large achromats. T is the diaphragm which governs the size of the test; it is in the back focal plane of L4. The transmission characteristics of the interference filters are scarcely affected by converging light of the angle used. 12 Phy. 202

4 358 P. E. HALLETT sees in his nasal field an 18 degree subtense red background and added to the centre of this is a 1*5 msee 13 min subtense 530 nm test flash. P8ychophy8ical technique. The method of constant stimuli with blanks was used, following the practice of Pirenne, Marriott & O'Doherty (1957) and Hallett (1969c). The nature of the variations in threshold measurements is discussed in the latter paper and it is argued that something like the observer's criterion is very stable for the 5-6 min required to measure a threshold but tends to jump to some new level when the viewing conditions are slightly changed. The ob8erver8. The observers were between 16 and 29 years of age and wore their distance spectacles during the experiments. This does not make much difference to the clarity of peripheral vision but does ensure that the fixation point is nicely visible. The false positive rates for these observers and the within sample threshold variations are roughly the same as those given in Hallett (1969c). RESULTS In all the present experiments the observer simply has to say whether or not he can detect the small short duration testing signal which falls on his peripheral retina 18 degrees from the fovea. The threshold energy for 0*5 probability of detection in a single presentation of the test is roughly 100 quanta (507 nm) at the cornea for all the observers when no background is present but the necessary threshold energy may be considerably elevated by a bright steady or transient background. The edges of the background do not contribute to the threshold disturbance because the background is sufficiently large (18 degree subtense) for these effects (Westheimer, 1965) to be unimportant. The spectral distribution of the test and background lights has been chosen by special calculation and their entry at the pupil arranged so as to ensure that the test is visible only to rods of the retina, even when the threshold is very high. The dimensions of the test (13 min subtense, 1*5 msec duration) have been chosen to ensure the closest possible approach to noise-limited vision (Barlow, 1957). Increment threshold experiments Checks on rod isolation. The rod isolation technique of Stiles (Aguilar & Stiles, 1954) employs a deep red background which enters via the centre of the dilated pupil and a green test which enters at the edge. The background by virtue of its colour and perpendicular incidence on the retinal cones is bright to the cones and elevates the cone threshold considerably but is less bright to the rods. The test by reason of its colour and oblique incidence on the retina is less bright to the cones than it is to the rods. As a result the threshold of the rods is always well below that of the several cone mechanisms, at least until near rod saturation, and the test when just visible is seen only by the rods. Now these conditions work very well when the background is steady, but conceivably problems arise when the background is transient. The

5 ROD THRESHOLDS 359 observer's task may at times be so difficult that he prefers to work well above the rod threshold, in which case the cones might assist in the detection of the test, or complicated interactions between the rod and cone mechanisms may occur, such as those demonstrated between the cone mechanisms in special circumstances by Stiles (1949). There can be no 4 "0 -I 0A,W 3 I To bo I a a a 0 -co Logl0 background in scotopic trolands Fig. 2. Observer P.E.H., left eye. Increment threshold curve for a small 1 5 msec test and temporally coincident 1-5 msec large background (0) for the usual rod isolation conditions of this paper (green 530 nm test entering at the nasal edge of the dilated pupil, red 635 nm background entering at the centre; test and background centred 18 degrees from the fovea). Effect of changing test to blue 440 nm which enhances its brightness for Stiles's it 1 and ff3 cone mechanisms but reduces the brightness for T 4, ft 5 and the rods (0). Effect of shifting background entering to the edge of the pupil ([1), which reduces background brightness to the cones but is likely without effect on the brightness to the rods. The heel of this curve is at log scotopic trolands (-5 3 log scotopic troland sec) which is much lower than that usually found for other observers (-4 log scotopic troland sec). doubt that the observer's task is difficult when the background is transient and that his (cone) sensation is quite complicated. Not only does the brightness of the background vary with time but its colour seems to vary spatially from red to yellow with evidence of white lace-like structures in certain areas. Not all observers can agree on the appearance of a transient I2-2

6 360 P.E.HALLETT red background but it is fortunately possible to show that the responses of the cones do not affect the responses of the rods. The experiments of Figs. 2-4 and 11 suffice to exclude the possibility that rod isolation breaks down when the background is transient. If the spectral compositions of the test and background are varied then the relative brightness of the test and background beams to the rods and the cone mechanisms varies, as is shown in Table 1, yet this has no effect on the experimental results, which are expressed in the scotopic units appropriate 2- I 0 -c Logl0 background intensity in scotopic trolands Fig. 3. Observer J. L., left eye. Increment threshold relation for a 1-5 msec green (540 nm) test which enters at the nasal edge of the pupil. The background enters centrally and is either red 635 nm (open symbols) or green 545 nm (filled symbols). The increment threshold curves coincide if scotopic scales are used; change of background from red to green increases its brightness to all the mechanisms but particularly to the rods and ff3. Background is either steady (left: [l, *) or a 1-5 msec flash coincident with the test (right: A, A); the horizontal separation of the steady and flashed increment threshold curves is 2-1 log which is somewhat larger than the simple expectation (1.8 log). Each point is the average of 4 days' measurements. to rod vision. Of course certain combinations of test and background pass bands should lead to the failure of rod isolation and the appearance of a rod-cone break at some appropriately high intensity but there are no indications of this in the present experiments. It does seem that for the usual rod isolation conditions of this and the next paper the test is always seen by the rods and the responses of the cones to the background do not influence the sensitivity of the rods. Alpern (1965) and Alpern & Rushton (1965) have also demonstrated the complete independence of the rods and the various cone mechanisms in essentially similar experiments with transient illumination. The integration time for background light. The integration time T for rod vision has usually been measured by increasing the duration of the test

7 ROD THRESHOLDS 361 signal and finding the longest time r for which the threshold energy is constant. The indications are that the integration time is smaller when the eye is light-adapted than when it is fully dark-adapted (Barlow, 1958) (although this is not a substantial change when one is working in the usual logarithmic scales) and in his signal/noise analysis of rod increment thresholds Barlow (1957) has assumed that the light from a steady background TABix 1. Changes in the brightness of the apparatus on shifting the pass band Test beam Background beam (shift from (shift from Mechanism 530 to 440 nm) 635 to 545 nm) vr log log fr log (+2 47?) log ff log log V5-1S89 log log Rods (SA)2-1-02log og Photopic function (VA) log log Calculated from (1) the illustrations of Stiles (1953), (2) the C.I.E. scotopic luminosity function (Le Grand, 1957), (3) the C.I.E. photopic luminosity function (Le Grand, 1957), (4) the spectral energy distribution at K, and (5) the measured spectral transmissions of the filters. The bracketed valve is based upon an extrapolation of Stiles's (1953) data. is also integrated for T sec. This is a very reasonable and practical assumption. The test is generally not very bright in comparison with the background, except at rod saturation (Aguilar & Stiles, 1954), and even if the test were bright enough to change the integration time of the local region on which it falls it would not be easy to show this. The experiments of Figs. 3-6 are by and large consistent with an integration time oft = ca. 0 1 sec. The abscissae of the graphs are in intensity units and the left-hand curves represent the increment threshold curves for a small short test ( sec, except in Fig. 6 which is 0 01 sec) on a steady background, whereas the right-hand curves represent increment threshold experiments in which the test is synchronous with a brief background of the same duration. The pulsed background can be considered as illuminating the dark-adapted eye since the repetition rate of the background flashes is about once every 6 see and the threshold recovers to very near the dark-adapted value within 1 sec of a background flash. The horizontal separation of the steady background and pulsed background curves is just about what one would expect if the light from the steady background is integrated for r sec, for if the pulsed backgrond is exposed for T < r sec then it will be weaker than the steady background by log (-rt). In Fig. 5 the flashed background curve at the top right is for a sec test and synchronous background and that at the bottom is for a 0 1 sec

8 362 P. E. HALLETT test and synchronous background; the increment threshold curve moves from the one position in the Figure to the other by sliding down the test scale for log 0.1/ = 1-8 log and along the background scale for 1-8 log to the left, as the effectiveness of the test and background is increased by increasing the exposure time. 5 I I I Al I 4._Q._W 20-P - H.V.S IO lh W 0o 2 a I R.F.W. 11 I0 I Il Log10 background intensity in scotopic trolands Fig. 4. Increment threshold curves for a 1-5 msec 13' subtense test centred on a steady background of 18 degrees subtense. Observer H.V. S. *, observer R. F.W. A. Similar curves but for a 1.5 msec background coincident in time with the test and viewed by the dark-adapted eye, H.V. S. 0, R.F. W. A, -l. Thesame arbitrary curve has been used to illustrate the four experiments. The horizontal separation of the steady and flashed background curves is 1-7 log for H.V.S., and 1-4 log for R.F.W., as compared with a simple expectation of 1-8 log. Conditions analogous to Aguilar & Stiles (1954); nasally entering green (530 nm) test (except E1 which is blue 440 nm) and centrally entering red (635 nm) background. 18 degrees eccentricity of view. The lines marked 'O' indicate background illuminations of 0 by scotopic trolands. The plots of Figs. 3 to 6 suggest that at moderate brightnesses the points on a steady background curve are nearly related to those on a pulsed background curve by B05 qb (S.S.) = O (qq (0) T'-5), (1) 1 I I

9 d._ 02 04a 2 10 to X X E ROD THRESHOLDS V I I I I I a Log1o background intensity in scotopic trolands I I I co Fig. 5. Observer G.D.H. Increment threshold relation for a 1-5 msec 13' subtense test on a steady background (0). The same arbitrary curve shifted laterally by log illustrates the increment threshold curve obtained when the background is synchronous with the test, illuminating the dark-adapted eye for only 1-5 msec (0). If test and background durations are now increased to 100 msee the curve shifts log horizontally and vertically (E), as expected. Rod isolation technique. The slopes of these curves are unusually steep but the integration time concept still applies. _* I ' boo _ Log1o background intensity in scotopic trolands Fig. 6. A similar experiment to Figs. 4 and 5 for observer E. K. S. Increment threshold curve for a 10 msec test on a steady background (*), and for a test coincident with a 10 msec background (0). The horizontal separation of the curves is 1 log as expected. Rod isolation technique. Other parameters as usual.

10 364 P.E.HALLETT where qb(8.s.) is the threshold energy in quanta at the cornea for a small brief test added to a steady background of intensity B quanta deg-2 sec'1, after time has been allowed for the eye to settle to a steady state (8.8.), and qq (0) is the threshold energy in quanta at the cornea for a small brief test coincident (time difference t = 0) with a brief background of energy Q quanta dega. Equation (1) is an empirical approximation, but is of considerable importance in understanding the impulse functions of rod vision (Hallett, 1969b). It may be quickly derived from a small extension of the signal/ noise argument of Barlow (1957). Let ax be the sample area (integration area) of rod vision, r be the sample time (integration time) of rod vision, K be the signal/noise ratio which is the observer's criterion, F be the fraction of corneal quanta which is effective for vision, then, if the dark light of the eye is small compared with the real backgrounds of interest, and with the other symbols as before, FqB(s.s.) = K(BFaTr)05 (2) means that the mean increase in the sample count of acting quanta due to the signal must significantly exceed the standard deviation of the sample count arising from the background alone. A similar statement for a brief background synchronous with the test is FqQ(0) = K(QFa)0-5 (3) and division of (2) by (3) and rearrangement gives (1). In brief the increment threshold curve for a small brief test synchronous with a large brief background illumination of the dark-adapted eye has much the same shape on log. plots as the more familiar increment threshold curve for a steady background, at least for all but the brightest backgrounds. The important difference is that the flashed background curve is usually displaced along the log. background intensity axis according to the extent that the exposure T is shorter than the integration time r = 01 sec. This rule of displacement may fail in two ways. The first is that failure will be expected if something like the observer's signal/noise criterion K assumes two different values, KB and KQ, according to whether the observer views a steady or a transient background. Examination of (2) and (3) shows that if K assumes a higher value in the second equation then one must substitute for ro.6 in equation (1) the smaller quantity KBIKQ 7O05 i.e. the lateral displacement of the flashed background curve is less than is consistent with a value for T of 0-1 sec. This is what is seen in Fig. 2 for

11 ROD THRESHOLDS P. E. H. whose flashed background curve has its foot at log Q = log T = log scotopic troland sec, instead of at the more usual value of log Q = ca. -4. Similarly for observer R. F.W. in Fig. 4 the flashed background curve is only 1-4 log to left of the steady background curve instead of the 18 log expected if T = 0 1 sec. Now it will be shown below that there are two other ways of estimating T (from impulse functions) which do not depend upon comparison of flashed backgrounds with steady backgrounds. I I I, J. L I- ~ ~ Log1o background in scotopic trolands Fig. 7. If the 1-5 msec test occurs 50 msec later than the 1 5 msec background (0) the threshold is lower than when the test and background are coincident (A), showing that some recovery must have taken place. 13 min test, 18 degree background, rod isolation conditions. Each point is average of 4 days' measurements. In these cases it scarcely matters what KQ is, provided it is consistent, and it suffices to say that there is other evidence that T for P. E. H. and R. F.W. is about 0-1 sec (see below under 'Integration time for background light' and 'Integration time from qq (t) '). The second failure of the displacement rule may occur for very bright backgrounds. It is possible that flashed backgrounds more readily saturate the rods than do steady backgrounds (Fig. 5, compare the lower curve for 0-1 sec background with the upper curve for a steady background) but this point has not been much investigated. It is reasonable to ask how rapidly the rod threshold can change. This can be explored in experiments in which the time interval between the test and background flashes is varied, and this approach should reveal something of the inertial characteristics of the test-background system. Numerous experiments have been performed (e.g. Baker, 1963; Sperling, 1965) but the present state of knowledge has not changed much since the experiments of Crawford (1947). Figure 7 shows an increment threshold curve obtained when the test follows a brief background by 0 05 sec; some recovery has evidently occurred in this short time.

12 366 P. E. HALLETT Impulse functions These experiments are very much the same as the more familiar increment threshold experiments except that the background parameters (e.g. flash energy) are fixed for the duration of the experimental session and the log threshold is measured by the method of constant stimuli for various time intervals t between the beginnings of the test and background flashes. 4 I. I I I I I I - t 0 0 o R.F.W A L f -A - co -O." L oq Time interval between the beginnings of test and background flashes in seconds Fig. 8. Impulse functions for a small brief test for two observers. Top, for observer R.F.W. the threshold disturbance created by 1-5 msec (0) and 100 msec (0) duration backgrounds of energy 0-6 log scotopic troland sec. Bottom, for observer H. V. S., the lesser disturbance caused by weaker 1-5 msec (A) and 100 msec (A) backgrounds of energy I0 log scotopic troland sec. Backgrounds of these durations give the same effect, provided they deliver the same number of quanta, and for this reason may be regarded as impulse inputs, at least for experiments of this accuracy. Rod isolation conditions. 18 degree eccentricity. The beginning of the background is reckoned as time zero so qq (t < 0) is the threshold energy when the test precedes an impulse background of energy Q, and so on. Integration of background light. Figure 8 illustrates the first experiments. The top curve for observer R. F.W. shows that the time course of the log threshold disturbance is much the same for a sec background as

13 ROD THRESHOLDS 367 it is for a 0 1 see background, provided the background energy is the same. This is, of course, the expected result if the integration time of the eye is about 0-1 sec. The lower curve in Fig. 8 shows the same thing but the height of the response is smaller because the background energy is smaller. Clearly backgrounds of less than 0 1 see are very short compared with the duration of the log response and are more or less completely integrated. 4 to 0 0 -ax w Time interval between test and background in seconds. Time course of sensitivity disturbance produced by a brief background flash Fig. 9. Observer P.E.H. Impulse functions for a small brief test for various strengths of input. The 15 msec duration backgrounds increase in energy from the lowest value of log scotopic troland sec. in steps of 0 9 log, in the order 0. /, A, *, 0. Rod isolation technique. 18 degree eccentricity. Such backgrounds can be considered to be effectively impulse inputs, and it will prove appropriate to call the log. threshold disturbance the log. impulse function. Figure 9 shows log impulse functions for various magnitudes of input, and Figs. 10 and 11 (top curves) again show that the response is much the same provided the background energy is constant and its duration 0-1 sec or less. The time of the peak response. In 120 experimental sessions in which impulse functions have been measured for various conditions it has been consistently observed that the test threshold begins to rise at t = ca see and that the peak threshold is close to t = 0 ( sec). This is what would be expected if the test and background entered a network, the constants of which are unaffected by the test. If the test enters before

14 368 P. E. HALLETT the background some of its later effects will need to be distinguished from the response to the background, and if the test enters at t = 0 the difficulty of recognizing the test will be greatest because all of the effects of the test will be obscured by the response to the background, but will be recognized if the strength of the test is sufficiently increased. The effect of later illumination on the earlier sensitivity of the eye is well known. It is shown in the optical illusion of Bidwell, in experiments on human thresholds (Crawford, 1947; Baker, 1963; Sperling, 1965) and in an experiment on Limulus eye (Ratliff, Hartline & Miller, 1963). Integration time from qq (t). It will be shown in the next paper that if the test and background enter a linear filter, and if the test is detected when its mean effect significantly exceeds the fluctuation in the response arising from the quantum fluctuations in the background, then thresholds on a steady background qb (s.s.) are related to the threshold disturbance qq (t) due to an impulse background by BO.sr+ 0-5 qb(88.) = 5+ q2(t) dt (4) provided the dark noise of the filter can be neglected and all signal/noise decisions are of the same constant fallibility. If the form of (4) is compared with that of (1) it will be obvious that the integral of the squared threshold disturbance relative to peak is the integration time, +00 q2 Q(t dt = T.(5 This is necessarily so because the linear filter model does not differ mathematically from Barlow's 'discrete sample' model except for the use of time functions instead of the integration constant r. The twenty-two impulse functions used in this paper give a value for r of 041 sec. It can be argued that a better estimate is about 0-07 sec; the impulse functions have usually been measured as log qq (t) in intervals of At = 0*025 see but this step width is very coarse in comparison with the spread of q2 (t) so numerical integration is in some error. A value for r of 0 07 see is really quite close to the customary but not very precise figure of 0.1 sec (e.g. Barlow, 1958; Baumgardt, 1961), derived from experiments at the absolute threshold of vision in which the duration of the test is varied. The agreement between the very different approaches is striking and would likely be better if it were practical to evaluate (5) for very weak inputs. It should be noted that (5) is relatively insensitive to the observer's criterion, provided it is reasonably consistent. For some observers on some occasions the height of the impulse function relative to absolute threshold

15 ROD THRESHOLDS 369 is excessively large. It is as if the criterion K is about 3 times larger when the threshold is raised by the impulse background. Expression of the threshold disturbance relative to the peak permits one to demonstrate that for all observers on all occasions the left hand side of (5) is consistent with r = ca. 01 sec. Step functions Figures 10 and 11 illustrate for observer E the effects of increasing the duration of the background whilst its energy is held constant. These Figures also illustrate some of the problems which may be encountered in visual threshold work. In Fig. 10 the log. threshold disturbance due to 01 sec backgrounds is of a height which is consistent with the log. impulse functions for the three observers of Figs. 8 and 9. The response to the on-step of the longer duration backgrounds is not complete at t = 0, as is appropriate if this response represents something like the convolution of a step input with an impulse function which is not finished by t = 0. The responses to the off-step are most remarkable-there is a very large, definite increase in threshold. Figure 11 shows later experiments on the same observer. The log. impulse function (top curve) is now smaller by about 0 5 log. at the peak, the step responses are generally smaller and the peculiar off-response has disappeared leaving a process of simple decay at 'off'. The wave forms of Fig. 11 are fairly simple and in shape are not unlike the logarithm of the voltage response of a high order lag network to voltage square waves of various durations, i.e. for these simpler wave forms the linear threshold disturbance at 'on' would be more or less the opposite of the disturbance at 'off'. It may also be noted that the time required for the system to settle is about 2 to 3 times the integration time r which is of some interest in view of the use in the next paper of negative exponentials for the system impulse function. Figure 12, which is also from the later data of observer E, shows a log impulse function which is smaller than the comparable experiment on observer R. F.W. in Fig. 8. Also shown is the response to a long duration square wave which displays on initial overshoot with the peak at t = 0. This type of response was observed by Crawford (1947) and subsequently by many others, usually for conditions in which the cones are active. The overshoot in Fig. 12 was measured, however, for the usual rod isolation conditions of the present paper. There are no reasons to suppose that overshoots of this sort represent 'receptor potentials', although this has been suggested (Baker, 1963), and the main point is that this non-linearity of the rod mechanism is only apparent when the rod threshold is forced very high by very bright backgrounds. The simpler on-response (Figs. 10 and 11) is in some ways more typical.

16 370 P. E. HALLETT 2~~~~ I I,,,, I 2 0 1~~~~00 A X Time interval between the beginnings of test and background flashes in seconds Fig. 10. Experiments in which background energy was held constant at - 2 log scotopic troland sec, while background duration was varied, for an observer who subsequently changed his characteristics. Data for observer E before December 3rd, 1966, 18 degree left temporal retina. Top, the response to short duration backgrounds is of the typical magnitude of the impulse response functions of observers, R.F.W., H.V. S., P.E.H. Lower three curves, for longer durations of square wave a very large definite elevation is seen at 'off'. Small brief test. Rod isolation technique.

17 ROD THRESHOLDS 371 I I I, A A ok ~ L Ae A ] 4'5 0 i 0L A d5 flashes in seconds Fig. 11. Experiments in which background energy was held constant at -12 log scotopic trolands sec, while background duration was varied, for an observer who had changed his characteristics. Data for observer E after 3 December 1966, 18 degree left temporal retina. Top, the responses to 1-5, 30 and 100 msec backgrounds are now smaller than the comparable results of Fig. 7, top. Lower curves. The anomalous 'off' effect, shown for the longer duration backgrounds in Fig. 7, has disappeared, leaving much simpler wave forms reminiscent of low pass filter responses. The recovery at 'off', however, sometimes anticipates the off-step and sometimes does not. Small, brief test. Rod isolation conditions, except for the 350 msec background experiment where the [1 points are for a blue 440 nm test instead of the usual green 530 nm test.

18 372 P. E. HALLETT Steady state If equation (2) is rewritten, substituting X the dark light of the eye for B, and calling qx (s.s.) the absolute threshold q(abs) for clarity, then Barlow's (1957) approach gives Fq(abs) = K(XFT)0,5 (6) 0~~~~~~~~ li I I I I I I I bte0 n of Time interval btentebgnisofthe test and background flashes in seconds Fig. 12. Observer E after 3 December The effect of varying test-background interval for an effectively impulse background of 100 msec (*) and for a longer duration (300 msec) background of the same intensity (0. LO: 1*6 log scotopic trolands. The impulse function (S*) does not display any late undershoot but the step function (Q[.C1) displays an overshoot at t = 0. Small brief test. Rod isolation technique. q~bs V} = 05JO>q(as)d% 8 and if (6) is divided into (2), the resulting statement qb(s.s.) _ B\0.5 q(abs) vx) 7 amounts to Barlow's description of the increment threshold, when the sensitivity of the eye is in the steady state and B > X. Hitherto it was only possible to test the exponent of (6) because X could not be measured independently of steady-state data. Impulse functions permit independent measurement of X, provided the signal/noise criterion K is the same in impulse function experiments as it is in steady-state experiments. From (4) and (7) we have for B > X, qb(s.s.) (B)05 = b5 +i:{± qg (t) )dt (8

19 ROD THRESHOLDS 373 which shows that the integral of the square of the linear threshold disturbance qq (t), over the limits - x < t < + cx and relative to Q and q2(abs), plays the same role as 1/X in earlier theory. Unfortunately statement (8) presents two considerable difficulties: the first is that it is not quite true, as is well known (Barlow, 1957, 1958) simple linear signal/noise theory does not provide a complete account of the steady-state increment threshold q (s.s.) for a small brief test; the second is that for some observers on some occasions the right-hand side of (8) is found to be considerably greater than the left-hand side. This is because qq (t) is at times excessively large. The next paper (Hallett, 1969b) demonstrates that usually linear signal/noise theory is nearly true and that the impulse functions of human rod vision give information about T, X and the deviations from simple signal/noise theory which occur as the input magnitude increases. An account of the failure and successes of the first twenty-two tests of (8) is not without interest. The top and left-hand scales of Fig. 13 show the experimental steady-state increment threshold relation. Clearly linear signal/noise theory cannot be exactly true because the slope of the log. plot exceeds 0 5 as the background intensity B increases towards values which saturate the isolated rod mechanism. In the triangular inset of Fig. 13 are shown values of the root integral of the square of the threshold disturbance qq(t) related to the absolute threshold q (abs). Following Barlow (1957) the dark light X of the eye is assumed additive to the real background B. The contribution of X to the observed threshold is incorporated, and the calculation simplified, by rewriting (8) as shown in Fig. 13 (Hallett, 1969 b). If linear signal/noise theory were exactly true for all observers at all times this inset would contain a single curve which, apart from a small region of transition at log Q = ca. -3, would consist largely of a horizontal asymptote of ordinate zero at low Q,where the contribution of the dark-light dominates, and an asymptote of slope 0 5 at high Q, where the contribution of the dark light is trivial. The displacement of this ideal curve into the co-ordinate system of the top and left-hand scales can bo done quite simply, without any arbitrariness, by leaving the numerical values of the co-ordinates of the curve unchanged. These simple expectations are not realized. The top curve in the triangular inset is based upon the first seventeen impulse functions of the twenty-two used in this paper. The position of this curve, predictor 1, is grossly higher than the observed steady-state data and this is because of the excessive height of the impulse functions-such behaviour has been seen also in three recent (unpublished) experiments on another observer. The bottom curve, predictor 2, is based upon five impulse function experiments on observer E obtained after 3 December These impulse functions are of smaller height than those plotted as predictor 1, and predictor 2 does give a plausible account of the available oddments of steady-state data for observer E, which for clarity are shown in the lozenge of Fig. 13. It does appear that this is, in fact, typically the case; similar behaviour has been observed in fifty-one impulse functions of the dark-adapted eye obtained from five further observers. In addition predictors 1 and 2 show roughly the same departure from the signal/noise ideal as that observed in steady-state experiments. The slope exceeds 0 5 slowly, at first and the more rapidly for the brighter backgrounds.

20 374 P. E. HALLETT Log1O steady background B in scotopic trolands -co ;~~~I a C 0~~~~~~~~~~~~~~~~~~~ to log. / Predictor 1 and pooled results for all observers 4o E's acua reslt (bt /66 O4,d Predictor2aandobservers \u TriangulaEs actual results (both io 2-4a~~~9 r displaced vertically other int for illustration) E's l d o 0 M~~~~~~~~ -~ Log10 impulse background Q in scotopic trolands sec Fig. 13. A first attempt at predicting the rod increment threshold for a small brief test on a large steady background by applying linear signal/noise theory to the threshold disturbances created by 'impulse' backgrounds of between -i5 and 100 msec duration. Rod isolation technique. Triangular inset: integrals of seventeen impulse response functions for various background energies are shown as *, grouped around the curve 'Predictor 1' (data of R.F.W., H V.S. and P.E.H. and E's early data from Fig. 10, top). Five other integral, based on E's later data (e.g. Fig, 1.1, top) are shown as, grouped around the curve 'Predictor 2' which lies 0-9 log below Predictor 1. The theoretical expectation is that the 'predictors' be straight lines of slope 0-5. In fact the evaluated integral is non-linear withqnr5 but this non-linearity has roughly the same shape as that ofqe(e.8) with Bo-5 so that the calculated curves match the observed increment threshold curves in shape but not necessarily in position. Top and left-hand scales: the points (0) show the observed increment thresholds for various steady backgrounds of B scotopic trolands. The slope of the increment threshold curve over 4-5 decades of visible background is the same as that of Predictor 1 but the position is not. Trapezoidal inset: a vertical shift has been applied for clarity. The abscissae are given by the top scale. The points show miscellaneous steady-state increment threshold data for observer E: incrementet thresholds on steady backgrounds; *0 thresholds from the level parts of the responses to long duration square waves shown in Figs. 10 and 11. Predictor 2 gives a reasonable description of both the shape and the position of this section of observer E's steady-state increment threshold relation. Subsequent experience is that good prediction is typically observed for other observers (Hallett, 1969 b).

21 ROD THRESHOLDS 375 DISCUSSION Integration time. The experiments of this paper do demonstrate in a number of ways the value of integration time concept and it is particularly interesting that functions of the impulse function of the dark adapted eye can be so clearly related to the integration time r. These relationships are developed further in the next paper in which a more precise description of impulse functions and their mathematical properties is given. Optimum performance and criterion. One of the difficulties presented by several of the experiments of this paper is that the threshold disturbances due to transient illumination can at times be excessively great. A very clear example is provided by observer E who changed his performance characteristics in a fairly abrupt fashion from generally high thresholds (Fig. 10) to generally low thresholds (Figs. 11 and 12). This sort of discrepancy, and the fact that the impulse functions of some observers may be larger for the same input than those of others, is possibly due to a variation in something like the observer's signal/noise criterion. Now there are several reasons for believing that the signal/noise criterion does vary but there does not seem to be any good way of allowing for this variation. Barlow (1956) demonstrated that an observer can change his criterion at the absolute threshold of vision so that the mean threshold becomes slightly smaller (by 0.1 log) and the experimental scatter (the spread of the frequency-of-seeing curve) and false positive rate somewhat larger, although this latter change was not established by a very large sample. In two later papers (Hallett, 1969c, d) it will be shown (a) that for samples of threshold measurements the magnitude of the 'between sample' variation is so large that some characteristic of the observer's performance, possibly his criterion, must change whenever the viewing conditions change, and (b) that the false positive rate due to confusion of noise with a signal is very low and much less than the observed false positive rate, which must therefore largely reflect errors which have nothing to do with the observer's signal/noise criterion. If it is not possible to detect, or allow for, changes in the observer's criterion by examining the false positive rate, or some such quantity, then one is more or less forced to classify the variety of the responses to a fixed manoeuvre and by sheer experimental repetition determine what is most commonly observed. Whether or not causal relations can be discovered between the different common outcomes will depend upon the sensitivity of the outcomes to criterion. It is very fortunate that certain experiments lead to the same conclusion, no matter what the criterion, provided it is

22 376 P. E. HALLETT consistent. One example is the determination of the integration time T from experiments in which the duration of the test is varied. Another is the determination of r from the impulse function according to equation (5); a value of near 0O 1 sec does seem to be observed for all observers no matter what the over-all height of the responses. In other situations, however, when one attempts to relate the data from two situations in which the sensations are very different, e.g. equations (1) or (8) which relate experiments with steady illumination to those with impulse illumination, one has less confidence that causal relations can be demonstrated. It is therefore a matter of some interest that these two situations are usually found to be nearly related by linear system signal/noise theory, as is shown in the next paper. This work was supported by the Medical Research Council of Canada and the Defence Research Board of Canada, grants MRC MA 1981 and DRB REFERENCES AGUTLAR, M. & STILES, W. S. (1954). Saturation of the rod mechanism of the retina at high levels of stimulation. Optica Acta 1, ALPERN, M. (1965). Rod-cone independence in the after-flash effect. J. Physiol. 176, ALPERN, M. & RUSHTON, W. A. H. (1965). The specificity of the cone interaction in the after flash effect. J. Phygiol. 176, BAKER, H. D. (1963). Initial stages of dark and light adaptation. J. opt. Soc. Am. 53, BARLOW, H. B. (1956). Retinal noise and absolute threshold. J. opt. Soc. Am. 46, BARLOW, H. B. (1957). Increment thresholds at low intensities considered as signal/noise discriminations. J. Physiol. 136, BARLOW, H. B. (1958). Temporal and spatial summation in human vision at different background intensities. J. Physiol. 141, BAUMGARDT, E. (1961). Duration and size as determinants of peripheral retinal response. J. opt. Soc. Am. 51, BRINDLEY, G. S. (1960). Physiology of the Retina and the Visual Pathway. London: Edward Arnold. CRAWFORD, H. B. (1947). Visual adaptation in relation to brief conditioning stimuli. Proc. R. Soc. B 134, GREGORY, R. L. (1959). A blue filter for detecting eye movements during the autokinetic effect. Q. Ji exp. Psychol. 11, HALLETT, P. E. (1969b). Impulse functions for human rod vision. J. Physiol. 202, HALLETT, P. E. (1969c). The variations in visual threshold measurement. J. Physiol. 202, HALLETT,P.E. (1969d). Quantum efficiency and false positive rate. J. Physiol. 202, LE GRAND, Y. (1957). Light, Colour and Vision. London: Chapman & Hall. PIRENNE, M. H. & MARRIOTT, F. H. C. (1962). Visual functions of man. In The Eye, ed. DAVSON, H., vol. 2. London: Academic Press. PIRENNE, M. H., MARRIOTT, F. H. C. & O'DOHERTY, E. F. (1957). Individual differences in night-vision efficiency. Med. Res. Coun. Spec. Rep. Ser. no London: Her Majesty's Stationery Office. RATLIFF, F., HARTLINE, H. K. & MILLER, W. H. (1963). Spatial and temporal aspects of retinal inhibitory interaction. J. opt. Soc. Am. 53, RUsHTON, W. A. H. (1965). Visual adaptation. Ferrier Lecture Proc. R. Soc. B 162,

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