1082 L E T T E R S T O T H E E D I T O R Vol. 52

Further Studies of a 9-cps Resonant-Frequency Effect in the Human Fovea-Cortex System*

BRIAN S. SCOTT Defence Research Medical Laboratories, Toronto 12, Ontario, Canada

(Received November б, 1961)

THE response of the human fovea-cortex system to a light varying periodically in intensity as a function of the fre­

quency was examined by de Lange.1-3 His techniques were similar to those used in obtaining the frequency characteristics of an elec­tronic system. He introduced a term r to indicate the sensitivity of the eye to flicker as a function of frequency with r being defined as the ratio

The Fourier representation of the luminance vs time function is given by B( t )=B 0+B 1 cosωt+B2 cos2ωt+ ...BN cosNωt, where ω = 2πf (radians per sec). In the case of a sine wave, modulated luminance B0 is the time average luminance, i.e., dc level of luminance, and B1 = ½A, where A is the peak-to-peak amplitude of the ac modulation. All other terms are zero. Similarly with a square-wave modulated luminance, B0 is the dc level of luminance:

and

The first three Fourier components of a square wave are shown in Fig. 1.

De Lange1 observed a maximum in sensitivity of the eye to flicker at 9 cps under high-dc-level conditions. This phenomenon he termed the "resonance" effect which he later called the "pseudo resonance" effect since the resistance R and capacitance C values necessary for electrical analogues did not adequately describe the frequency characteristics of the visual pathway. De Lange did not attempt to describe the fovea-cortex system as a specific RC circuit but rather tried to represent certain characteristics of the physiological process involved. In support of this method his

FIG. 1. First three fourier components of a square wave.

work indicated that the increase in sensitivity was not due to reciprocal energizing, i.e., asynchronous excitatory and in­hibitory mechanism. He postulated as a possible mechanism a negative feedback system which changes phase so as to be positive in the region of 9 cps. Since this type of system is not likely to be found functionally in the peripheral part of the fovea-cortex system it might indicate involvement of the central nervous system in the "resonance" effect, either with or without the feed­back mechanism.

Talbot's law states that at the critical flicker frequency (CFF) or above, subjective brightness is equal to that of the dc com­ponent of the varying luminance. For frequencies below the CFF there is a shift from the Talbot effect to a state in which inter­mittent light is more effective in terms of sensation than is a con­tinuous fight, the Brücke effect. Bartley4,5 observed a maximum in the brightness enhancement at 9.5 cps. De Lange obtained a maximum at 9.5 cps but at the CFF since r was obtained by in­creasing the amplitude of the ac component until flicker was just perceived at various frequencies and dc levels of illumination.

The object of the study reported here was to examine further the "resonance" effect with particular attention to target size.

In this experiment a Sylvania glow modulator tube served as the light source and produced the dc and ac components simul­taneously. Light waveforms were generated by the modulation of of the current through the tube, which provided square waves with negligible distortion. However, at the dc amperages used, i.e., 30 to 40 mA, the fight output of the tube shifted into the red end of the spectrum. The retinal illuminance of the dc component varied from 1500 to 760 trolands due to a gradual reduction in tube efficiency. The effect of this was to increase the average level of r and decrease the resonance effect; thus day-to-day compari­sons of the data are not reliable. However, during a single session (1½ h) the dc level decreased by not more than 5%, making intra-session comparisons reliable. Maxwellian view was utilized in order to achieve homogenous high-luminance test fields. A series of apertures provided target sizes of 5.73°, 2.86°, 1.43°, and 0.72°. A black surround was used; whereas de Lange used a surround which was at the same dc level as that of the 2° target area. The target was viewed monocularly through an artificial pupil 2 mm in diameter while de Lange used a pupil 2.5 mm in diameter.

Two female observers, having 20-20 vision for both eyes, served in this study. A method of ascending limits was used in which r was increased until flicker was perceived. Threshold values of r were obtained for a series of 13 frequencies in the range 1.0 to 20.0 cps in both ascending and descending orders.

The values of r were established from measurements of the current flowing through the glow-modulator tube and information supplied by the manufacturer of the "relative light output" vs "amperage" of the tube. Experimental values were also obtained

September 1962 L E T T E R S T O T H E E D I T O R 1083

FIG. 2. Sensitivity, various target sizes, one observer, on one day.

photometrically and were in excellent agreement with the manu­facturer's data.

Although differences in experimental conditions preclude quanti­tative comparison with de Lange's data, qualitative analysis has led to several conclusions. In most instances there was a marked minimum in r at a frequency of approximately 9 cps which is in agreement with de Lange's results (see Fig. 2). It would appear that the marked differences in the data collected on the same day are a result of the different target sizes utilized, since the dc light-output level was checked with a photomultiplier tube before and after each test session and showed a decrease of less than 2%. Thus as the target size increases, the value of r occurring at a given frequency decreases, and the peak due to the resonance phenomena becomes less pronounced.

Good agreement was found between the value of r for a square wave, and the value obtained for a sine wave, as shown in Fig. 3. For frequencies greater than 14 cps this agreement is better than 1%. De Lange3 also found this relationship and discusses its sig­nificance in detail. The differences in the two curves at lower fre­quencies are interesting but the data are inconclusive. This dif­ference could be due to higher harmonics having an effect. For example at 4.5 cps the second harmonic (9 cps) may aid in the detection of flicker of a square wave due to the resonance phe­nomena at 9 cps. This hypothesis is strengthened by the fact that these results and those of de Lange are similar in that as the frequency is decreased, the values of r for a square wave become increasingly less than those for a sine wave.

From the excellent agreement of the Fourier analysis at the higher frequencies, one can conclude that the fovea-cortex system is acting linearly. It must be noted that this is true only when de Lange's method is utilized.

There is insufficient evidence to explain the "resonance effect." De Lange1-3 suggests that a negative-feedback system which changes to positive feedback at 9 cps is a likely mechanism and that this process may occur centrally or peripherally. Bartley4,5

concluded that the brightness enhancement at 9.5 cps was a central phenomenon since it occurred in this frequency range for all luminances and all practical bright-dark ratios.

It is known that within certain limits a repetitive visual stimulus can evoke a corresponding cortical electrical response. However the frequency characteristic involved in driving the alpha rhythm does not appear to have been studied.

If the "resonance effect" is a central phenomenon it would seem natural to expect that there might be a similar increase in sensi­tivity at 9 cps for an auditory stimulus. Riesz6 using "beats" around 1000 cps found an increase in sensitivity at 3-cps beat frequency. This writer (in unpublished results) also found a maxi­mum in sensitivity at 3 cps using amplitude modulation. An "auditory resonance" effect does exist but not at the same fre­quency as the visual one. Thus it does not help in determining whether the visual resonance effect is central. It has been sug­gested that the visual "resonance" effect is linked to the alpha rhythm at 9 cps. Another spontaneous cortical rhythm at a fre­quency corresponding to the auditory-resonance effect, i.e., 3 cps is the delta rhythm. The observations of Loomis, Harvey, and Hobart,7 and Davis et al.8 suggest that delta waves are closely associated with auditory stimulation.

Although the evidence is meager, these observations suggest that the mechanism of the visual-resonance phenomenon and probably also the auditory-resonance phenomenon involve the interaction of the output of the sense organ with that of closely associated spontaneous cortical electrical rhythm which produces an increase in sensitivity at the natural frequency of the cortical rhythm.

* This work was done under PCC D77-94-20-46, DRML Project No. 246 and is DRML Tech. Memo. No. 246-2. 1 H. de Lange, Physica 18, 939 (1952). 2 H. de Lange, J. Opt. Soc. Am. 44, 380 (1954). 3 H. de Lange, "Attenuation characteristics and phase-shift cliaracter-istics of the human fovea-center system in relation to flicker fusion phe­nomena", N. V. Philips, Telecommunication Industry (Hilversum, Holland, June 5, 1957). 4 S. H. Bartley. J. Exp. Psychol. 23, 313 (1938). 5 S. H. Bartley, in Handbook of Experimental Psychology, edited by S. S. Stevens (John Wiley & Sons, Inc., New York, 1951). 6 R. R. Riesz, Phys. Rev. 31, 867 (1928). 7 A. L. Loomis, E. N. Harvey, and G. A. Hobart, J. Neurophysiol. 1, 413 (1938). 8 H. Davis, P. A. Davis, A. L. Loomis, E. N. Harvey, and G. A. Hobart, J. Neurophysiol. 2, 500 (1939).

FIG. 3. Sensitivity, two waveforms, one observer, on one day, target size 0.72°.