0*521. (see Fig. 5, p. 43 in Denton & Pirenne, 1954) was mounted in front of the source. The

Transcription

1 369 J. Physiol. (I959) I45, THE MINIMUM FLUX OF ENERGY DETECTABLE BY THE HUMAN EYE F. H. C. MARRIOTT,* VALERIE B. MORRIS AND M. H. PIRENNE From the University Laboratory of Physiology, Oxford (Received 20 August 1958) The threshold for a steady, effectively point, source of light presented against a zero intensity background, which represents the smallest energy flux detectable by the human eye, has apparently not been recently determined. Walsh (1953) gives a value of 750 quanta/sec entering the eye. This value is based on the review of measurements made with white light published by Stiles, Bennett & Green (1937). It is calculated on the basis of photopic (cone) vision, and is intended to give a safe estimate rather than an absolute lower limit for the energy flux detectable (see Pirenne, 1956). Some authors have given lower values (see Table 2), but all these experiments were done many years ago, and the technique is sometimes open to criticism. Preliminary experiments were carried out with an apparatus in which the test field was about 1 m from the eye. Values of the order of 100 quanta/sec were obtained. However, very small light leakages in the apparatus would have invalidated the results, owing to the exceedingly low luminance of the test field. It was decided, therefore, to carry out experiments using a much brighter source placed at a considerable distance from the eye. Fortunately a light-proof tunnel over 40 m in length was available under the laboratory, and this was used for the experiments. METHODS The light source consisted of a 12 V, 12 W tungsten filament opal bulb, mounted in a light-proof box and underrun at the constant voltage of 10*3 V. At this voltage the diaphragmed part of the bulb gave a luminous intensity of 1-2 cd at a colour temperature of K. The bulb was exposed through a diaphragm 1-9 cm in diameter, and at the distance used this subtended about 1-8' of arc at the eye. An Ilford 604 colour filter, transmitting a band of wave-lengths centred at about 0*521. (see Fig. 5, p. 43 in Denton & Pirenne, 1954) was mounted in front of the source. The intensity was controlled by neutral wedges (Ilford, colloidal carbon in gelatine). The source and colour filter were calibrated by the National Physical Laboratory. The wedge densities were measured by comparison with sector disks (Pirenne, Marriott & O'Doherty, 1957). The energy values were calculated as explained in Pirenne et al. (1957). * Nuffield Biological Scholar. 24 PHYSIO. CXZLV

2 370 F. H. C. MARRIOTT AND OTHERS The subject sat at a distance of 36-9 m (Subject P.E.H. at 36-7 m) and viewed the source with his right eye, using a circular artificial pupil 2-1 mm in diameter. The position of the head was fixed by a dental impression. The light was exposed for 15 sec periods. A red fixation point about 70 from the source was used to give an idea of the position of the test light. The subject did not attempt to maintain fixation, and the fixation point was usually covered during the test exposure. The subject had been dark-adapted in complete darkness for at least half an hour before the experiment. The threshold was determined by the method described in detail by H. K. Hartline and P. R. MacDonald (Pirenne et al. 1957). This gives a value corresponding to about 50% seen. In these experiments, however, the range of uncertain seeing was not large, amounting as a rule to about 0-3 log. unit. The subject indicated that he was ready for each exposure and was then told when the light was uncovered and covered again. Exposures were presented in groups of six or seven at intensity steps of 0-2 log. unit, this range covering intensities which were never seen and intensities which were always seen. The different intensities were presented in random order, and one 'blank' was included in each group-the subject being given the usual signals for 'on' and 'off' but no light being in fact shown. Blanks were never reported 'seen' except in the one instance shown in Table 1. The groups were given in pairs 0.1 log. unit apart, so that each pair of groups consisted of exposures at intervals of 0.1 log. unit and two blanks. RESULTS Table 1 shows the results of seven measurements of the threshold energy flux. The second column shows the energy flux passing through the pupil, in ergs x 10-10/sec. The third column gives this energy as equivalent quanta of 0-507,u, taking account of the relative scotopic efficiencies of the different wave- TABLE 1 Threshold Equivalent quanta (0-507IL) Subject Ergs x 10-10/sec per second M.H.P V.B.M V.B.M A.C.C. 3.8* 89* A.C.C F.H.C.M P.E.H * One blank reported seen. lengths in the band transmitted by the filter. The quantum of light of wavelength 0-507,, the wave-length giving maximum scotopic efficiency, has energy 3-92 x ergs. The third column is obtained from the second by dividing by this value and multiplying by a factor (0-906) to correct for the relative scotopic efficiencies of the wave-lengths transmitted. Each of the values in columns two and three is the mean of about six groups of exposures at 0-2 log. unit intervals. The standard error of each value is roughly + 6%.

3 MINIMUM DETECTABLE LIGHT FLUX 371 DISCUSSION Table 2 gives the results of previous determinations of the threshold energy flux. Only investigations in which a narrow spectral band was used have been included. The first investigation of the problem was made in 1889 by Langley (1889), using a narrow band from the solar spectrum. His definition of threshold, ' a light which is observed to vanish and reappear when silently occulted and restored by an assistant without the observer's knowledge', would give rather a higher value than the definition used in the present paper-a light near 'threshold' as defined in our experiments is not continuously visible. TABLE 2 Mean effective Threshold wave-length r ^ Author wfv) Ergo x 10-10/se Quanta/sec Langley (1889) Von Kries (1907) and Eyster Chariton & Lea (1929) Barnes & Czerny (1932) Von Kries and Eyster (von Kries, 1907) appear to have used a technique very close to that which would be used in the best experiments to-day. Their value is within the range given by our subjects. Chariton & Lea (1928) were mainly concerned with the perception of flashes, and concluded 'for longer flashes the limit approaches the value of 200 quanta'. In fact, the longest flashes used were 1 sec, giving a threshold value of 150 quanta. Barnes & Czerny (1932) used a spectral band, mainly between 0 50 and. 0 55,, considerably broader than that used for our experiments. Their method of presentation involved several point sources viewed simultaneously, with no system of fixation. Apart from Langley's result of 70 years ago, these authors all give values close to those obtained in our experiments. Hecht, Shlaer & Pirenne (1942) found a threshold for sec flashes of quanta, using a field 10' of arc in diameter placed 20 from the fovea. Possibly a somewhat lower value might have been found at 100 (Stiles & Crawford, 1937). Barnes & Czerny (1932) give quanta. Thus the energy required for perception of a flash is 50% or more of the energy per second for perception of a continuously exposed small source. Graham & Margaria (1935) suggest that the threshold flux for a field 2' of arc in diameter placed 150 from the fixation point becomes constant for times over 0 5 sec at a value about six times the flash threshold energy per second. However, they did not use exposures longer than 0*5 sec for this area, and the 24-2

4 372 F. H. C. MARRIOTT AND OTHERS position of the asymptote is not very well determined. Our result, a threshold flux for long exposures of about twice the flash threshold energy per second, does not agree with their conclusion, but the conditions were not identical. Graham & Margaria were maintaining fixation throughout the exposure time, whereas in our experiments the eye was free to move. This may have made it possible to use the most sensitive parts of the eye, and altered the conditions for summation. It is well known that complicated phenomena take place under conditions of prolonged fixation (see e.g. Pirenne et al. 1957, pp ). Barlow (1958), using a field 7-1' of arc in diameter 6.50 from the fixation point, found the threshold energy increased by only about a factor of 2 when the exposure time increased from to sec. This suggests that much longer temporal summation is possible in this part of the retina, in which, however, the flash threshold value may be higher (Stiles & Crawford, 1937). Accounts have been given elsewhere of the role of eye movements (Pirenne, 1948, p. 73) and of the problems of physiological and probability summation (Pirenne et al. 1957, p. 49). The interpretation of the present experiments involves many complications, and it is not clear how the flash threshold, the summation time, and the threshold for long exposures are related. It is presumably necessary that at some time during the long exposure a number of quanta at least equal to that acting at the flash threshold should act upon the retina within the summation time, but this may not be a sufficient condition for a positive response. Suppose, for the sake of argument, the flash threshold is taken as 60 quanta, of which one-tenth act on the retina, and the 15 sec exposure time is regarded as consisting of 150 separate 'flashes' of 0.1 sec. This may be a reasonable approximation taking account of the duration of fixation pauses ( sec), and a retinal summation time of 0.1 sec. Then a flux of 120 quanta/sec gives a mean of 1-2 quanta absorbed per 'flash', and from Poisson's equation this leads to the expectation that in 80% of trials the necessary 6 or more quanta per 'flash' will not be absorbed in any one of the 150 'flashes' of the 15 sec exposure. But the results of Table 1 show that 120 quanta/sec were seen in about 50% of trials, so it is likely that some units must be capable of summing over more than 01 sec. An increase to 0-13 sec is found to be sufficient. The calculation is rather sensitive to changes in the parameters, but the assumptions that only one supraliminal 'flash' is necessary for a positive response, and that the threshold for these elementary 'flashes' making up the 15 sec exposure time is the same as the threshold for an instantaneous flash with fixation presented to the subject at a known moment, would probably lead to an under-estimate rather than an over-estimate of the summation time. In any case, the theory underlying the calculations, at best, constitutes only an approximation to a highly complex situation.

5 MINIMUM DETECTABLE LIGHT FLUX 373 SUMMARY 1. Measurements were made of the threshoid for an effectively point source of light continuously exposed. 2. Using a spectral band centred at 0 52,t, the threshold was about 4-7 x ergs/sec. 3. This is equivalent to about quanta/sec of maximum scotopic efficiency (0.507,). 4. This result is compared with earlier published results and with results for the flash threshold for small sources. 5. The temporal summing properties of the eye are discussed in the light of these findings. The apparatus used in these experiments was obtained through a grant from the Medical Research Council. One of the authors (V. B.M.) also received a personal grant from the Medical Research Council. REFERENCES BARLOW, H. B. (1958). Temporal and spatial summation in human vision at different background intensities. J. Physiol. 141, BARNES, R. B. & CzERNY, M. (1932). Lasst sich ein Schroteffekt der Photonen mit dem Auge beobachten? Z. Phys CmATrrON, J. & LEA, C. A. (1928). Some experiments concerning the counting of scintillations produced by alpha particles. Proc. Roy. Soc. A, 122, DENTON, E. J. & PrRENNE, M. H. (1954). The absolute sensitivity and functional stability of the human eye. J. Phy8iol. 123, GRAHAM, C. H. & MARGARIA, R. (1935). Area and the intensity-time relation in the peripheral retina. Amer. J. Physiol. 113, HECHT, S., SHLAER, S. & PRENNE, M. H. (1942). Energy, quanta, and vision. J. gen. Phy8iol. 25, LANGLEY, S. P. (1889). Energy and vision. Phil. Mag. 27, PIRENNE, M. H. (1948). Vision and the Eye. Chapman and Hall: London. PIRENNE, M. H. (1956). Physiological mechanisms of vision and the quantum nature of Iight. Biol. Rev. 31, PIRENNE, M. H., MARRIOTT, F. H. C. & O'DOHERTY, E. F. (1957). Individual differences in nightvision efficiency. Spec. Rep. Ser. med. Res. Coun., Lond., 294. STLES, W. S. assisted by BENNETT, M. G. & GREEN, H. N. (1937). Visibility of light signals with special reference to aviation lights. Review of existing knowledge. Rep. Memor. aero. Res. Comm., Lond., STLES, W. S. & CRAWFORD, B. H. (1937). The effect of a glaring light source on extrafoveal vision. Proc. Roy. Soc. B, 122, VoN KRIES, J. (1907). tber die zur Erregung des Sehorgansw erforderlichen Energiemengen. Z. Sinnesphysiol. 41, WALSH, J. W. T. (1953). Photometry (2nd ed.) p. 80. London: Constable.