These two perceptions correspond to two functions of the visual system, whose characteristics are highly different, and whereas this duality was ignored by the discourses about persistence, in the course of time, it imposed its demands to the movie technique. Thus, if a 24-frame-per-second filming, and therefore projection frequency, allows, still today, to perceive the movements on the screen at their natural tempo, in a jerkless continuity, the brightness and the area of the screens increasing, this frequency of 24 illuminations per second of the retina, applied in the years 1928–1930, became too low to avoid an unpleasant flicker.

To obtain a smooth perfectly steady visual sensation, one passed, later on to 48, then most often, to 72 illuminations per second. Consequently, when sitting in a movie theatre, we receive 24 frames per second, but each frame appears two or three times.

Thus in the cinematic conditions it is easier to obtain image continuity and apparent movement than brightness steadiness. The aim of the present paper is to study some characters of the history of the flickering brightness studies after examining the problem of the continuity of the cinematic images which can be perceived as static or as moving.

The difference between images continuity and brightness steadiness is obvious in the experiment by van de Grind et al. [6]. A simple ring intermittently illuminated was presented on a dark background. Its brightness was modulated rectangularly in time, light and dark times equal. One determined the frequency at which the ring reached persistence of its contours. This frequency varied from about 3.8 to 4.8 Hz as the relative brightness varied from 1 to 1000. At these low frequencies, the brightness inside the contours continued flickering, the brightness fusion frequencies (not given) varying most likely from about 15 to 45 Hz, whereas the persistence of the pattern was not, or only slightly, dependent on the brightness level. Obviously, the two mechanisms seem very different.

Another case of static image persistence is the toy created by J.A. Paris in the late 1820s in London. His thaumatrope – as it was then called – is none other than the cardboard circle on which one draws on one side, for instance a cage, and on the other side a bird, so that, during the whirling of the card, the two images become superimposed and the bird appears inside the cage. In this toy as in the previous experiment the system results in a single static image or in superimposed static images, easily obtained, and in both cases, visual persistence is probably the main factor at play. Visual and not retinal: pattern or object identification is a cortical, not a retinal function.

Subsequently, the duration of the light impression was actually measured by the method of the red-hot coal by various individuals also quoted by Helmholtz [3] among whom one has to single out, ‘the knight’, Patrice d'Arcy, who presented to the ‘Académie royale des sciences’ of Paris in 1765 [14] a Memoir on the Duration of the Sensation of the Sight. Speaking as a physicist, he remarked that the duration of the visual sensation “may have an influence on the accuracy of our observations” and that it is thus interesting to know it. With this aim in view, he built a machine animated by a clockwork that rotated a steel rod, at the end of which he fastened the ember. He then determined the rotation speed for which an observer saw a closed circle of fire. The experiments were made in a garden by night, the observer watching from a dark room 50 m away. The result was 8/60s or 133 ms as duration of one rotation. By varying the conditions of observation, he then came to “direct experiment which will remove all uncertainty”: he put a light behind the machine that rotated a large cardboard disc with an opening through which the light appeared at each rotation. In this experiment, one had a continuous sensation of light for a duration of about 145 ms between successive appearances. D'Arcy thus achieved what was probably the first experiment of intermittent luminous stimulation and we can say today that this frequency, in the order of 7 Hz, corresponds fairly well to what the device and the conditions allow to hope for.

In his doctoral dissertation, Plateau [15] in 1829, says that he used first an implement similar to that used by d'Arcy, a piece of white cardboard replacing the ember. But he then wanted to measure the total duration of the sensation “up to the moment when the impression gets barely perceptible”, he obtained 350 ms. In one of his other experiments, he used a disc with 12 white and 12 black sectors of equal width and rotated it in daylight. When a uniform grey was obtained, the duration of one revolution was 191 ms and he wrote that if one wanted to know “the duration of one undiminished impression”, one just had to divide 191 by 24. Curiously he does not do the division, the result of which, 8 ms, is surprisingly low (it corresponds to a frequency as high as 62.5 Hz, for a white paper in daylight... certainly in summer with a shining sun).

In the chapter headed Duration of the sensation of light in his Physiological Optics, Helmholtz [5], like Plateau, measured this duration with a rotating sectored black-on-white disc. He recalled Plateau's experiment, but probably confusing the duration of one revolution and the duration of the transit of a black sector, he commented that Plateau's result is “strikingly large” and he gave his own results: about 21 ms for the disc illuminated by the strongest lamplight and 50 ms in “the dim light of the full moon”.

When d'Arcy wrote, “[...] if the impressions of objects are all the more lasting as they are more illuminated, the result will be [...]” he had scarcely any doubt about the answer, it had to be positive. But Plateau, then Helmholtz, had to notice that the duration measured with the rotating discs was, on the contrary, shorter when the stimulation was stronger. Helmholtz added: “[...] yet on the whole the effect persists longer”, whereas Plateau was more cautious when he wished that rigorous experiments showed that the total duration of the impression is longer when the impression is stronger. Since this time, a great number of these experiments have been performed, but, considering the great diversity of the procedures, it is impossible to draw a clear and definitive conclusion. In any case, with the flicker-technique it is evident that one certainly did not measure what one intended to measure. Augustin Charpentier, a physicist of Nancy, distinguished in 1891 total persistence from what he called “apparent persistence” [16].

In 1887, Charpentier used a rotating disc alternating opaque and cut out sectors in front of an adjustable light field and he claimed to have shown that the persistence duration varied inversely to the square root of the “luminous intensity” [20]. But his procedure was far from the classical one, he fixed one constant light time and 4 dark times and thus 4 frequencies and adjusted the light level so that the flicker ceased. In these conditions, the light-time fraction of the period varied from 0.0625 to 0.50. Unfortunately, these results were sometimes presented as if they had been obtained for a light-time fraction of 0.50.

Erwin Ferry, in New York, some years later, in 1892, in order “to determine the principal factor producing persistence in vision”, plotted “curves showing the relation between the duration of the retinal impression of eye and the wave-length of light observed for spectra of different intensities” [21]. He used a diffraction-grating spectrometer and a rotating disc with two cut out opposite sectors of ninety degrees interposed between the lamp and the collimator.

He determined for each wavelength its relative luminosity and for a same wavelength he varied the luminosity. From the speed of rotation of the disc he deduced “the duration of the maximum impression on the retina”. He presented the tables of results and concluded “that color is at most a slight factor in retinal persistence and that luminosity is the all-important factor” and he proposed an approximate empirical law: “The duration of retinal impression is inversely proportional to the logarithm of the luminosity, or in the form of an equation: D=1/klogL”, adding that “it is interesting to note the similarity with Fechner's law [...]”.

From the equation of D one has drawn D=T/2 and F=1/T whence F=alogL (where a=k/2), the critical flicker frequency (CFF) is proportional to the logarithm of the luminosity. This is “Ferry's law” which Ferry, interested only in persistence, has never propounded. Additionally, he never plotted any curve showing the relation he proposed. His data, which covered less than two log units, if plotted on graphs of D in function of 1/logL in all cases show some curvature.

Convinced that the phenomenon was related to Fechner's law, he preferred to follow this idea rather than linger over the experimental results; thus his name was given to a law that he had neither formulated in terms of frequency, nor actually demonstrated.

The flicker logarithmic law was really established by the works of the Englishman T.C. Porter, published in 1898, 1902 and 1912 [22]. He used a rotating half-black, half-white disc whose illumination can vary in the range of a little more than 5 log units. Also he provided information that made it possible to calculate the absolute value of the stimulations and to compare his results with those of subsequent works. In 1902, he presented the table and the graphs of his data and proposed the equation F=alogL+b. We have reproduced in Fig. 1 his 1912 graph, which included several data obtained after 1902, particularly in the range of low levels of illumination of the disc, where the slope of the curve is lower. Porter gave for this slope a=3.5 and for the slope of the main segment a=12.6.

His new data had fully confirmed the reality of two different slopes and Porter, who did not use an artificial pupil, verified that the break was not due to a lack of expansion of the pupil at the low illumination. Such was not the case and he left the problem unsolved.

It is interesting to note that in 1898, he was still calculating the duration of the impression on the retina. And when in 1902 he still commented about “The actual ‘last’ undiminished of the impression”, he used Plateau's (and Ferry's) vocabulary, he still belonged to the 19th century. However, when in the same text he gave his results as the number of revolutions per second, he belonged to the 20th century. Grünbaum had already adopted the term ‘frequency’ in 1898.

The transition from duration of the persistence to frequency was not motivated by theory only, because, with the appearance of the ‘cinematography’, the problem of the choice of the projection frequency was becoming important from a practical point of view. Porter had perfectly understood it. In 1902 he wrote: “Although the primary object of this research is to throw light upon the process of vision [...] we can easily determine [...] the number of pictures that must be projected on the screen per second in order that there may be no trace of flicker”. He roughly estimated it at 50 “where the arc light is used for projection, though half this number would probably be sufficient to prevent the flicker from being distressing”.

Apparently more physicist than physiologist, Porter had not made the link between the two slopes on his graph and the retinal ‘duplicity’ established some years earlier. One of the numerous contributions of Selig Hecht and his collaborators, in New York, from the 1920s to the 1940s, was to show that the first segment results from the activity of the rods and that the steeper segment results from the activity of the cones.

Fig. 2 assembles the curves that condense the results of the works of Hecht's school [23] on the variations of the Ferry–Porter law as a function of different parameters, eccentricity (in A), diameter of the test patch (in B) and wavelength (in C). For this last graph, the luminances of the different wavelengths have been equalized in photopic conditions (cones vision) and they become different in scotopic conditions (rods vision), this causes a separation of the curves at low values of I, although they are coincident at higher values.

Calculations show that the coordinates of the point of break on Porter's curve and on Hecht's curve d=19° in B are not far from each other. This break is not always observed and, from Porter's plots, it would be possible to draw a smooth transition from scotopic to photopic conditions. One also has to notice that at 60 Hz, Hecht's curve reaches its horizontal asymptote while Porter's plot at 65 Hz is still on the straight segment.

In 1952, the Dutchman Hendrik de Lange, an electronic engineer, published the first article about his experiments on flicker [26]. He presented in Delft, in 1957 in his dissertation [27], a synthesis of researches whose spirit was at complete odds with former works. He was writing in 1952: “Considering the fact that the eye retains the received image for a moment, the disappearance of flicker at a high rate of intermittence is normally explained by the ‘filling in’ of the dark phases. However, this approach to the explanation of the phenomenon does not lend itself to calculations and closer formulation.”

As a good engineer, he thus applied to the visual system the method classically used in the study of systems, the setting up of input–output relations. The task becomes simpler if one is lucky enough to be dealing with a linear system (one in which the input–output relations are described by linear equations) because, in such a case, if the input varies following a sine function, the output is also a sine wave of same frequency, but whose amplitude and phase are a function of the frequency.

We shall confine ourselves to variations of amplitude. If for various frequencies, we measure the attenuation, the ratio between the input and output amplitudes, on plotting attenuation values as a function of frequency, both on a logarithmic scale, as is usual in electric filter technique, we obtain the Bode diagram of the system or, in our particular case, its temporal modulation transfer function.

But we cannot generate an input sin ωt (positive–negative oscillation) with a luminous flux, contrary to what is possible with an electric current and the visual sinusoidal stimulus (Fig. 3) can be described as L(t)=La(1+msinωt) with a ‘dc’ component, La, and an ‘ac’ component of amplitude mLa, and frequency F=ω/2π. La is the time-average value and therefore the adaptation level of the eye. One can deduce from the figure that La=(Lmax+Lmin)/2 and that the amplitude mLa=(Lmax−Lmin)/2 and thus that the ratio of the ac-to-dc components, called here modulation m=(Lmax−Lmin)/(Lmax+Lmin).

Now, two questions remain: about the linearity and about the output, which is not a sine wave but the perception of a flicker.

Is the visual system or more specifically the brightness system, linear?

According to the Ferry–Porter law, the response is no. However, the situation is not hopeless: according to the Talbot–Plateau law, the luminance of a dark and light alternation at and above fusion is proportional to the light-time fraction of the period, not to its logarithm, that is to say that the system works then linearly.

The output amplitude problem is solved by de Lange [28], as follows: “The need for estimating the amplitude of the brightness variation as psychological output quantity is avoided by using the eye as zero instrument.” The result is given by the modulation value corresponding to the disappearance of the flicker. We thus proceed at constant output and it is the input amplitude that varies according to frequency.

In many traditional works as in the experiments of Ferry, of Porter and in those of Hecht concerning the curves of Fig. 2, the light-time and the dark-time fractions were equal. Fig. 3a shows the luminance variation over time thus obtained: a square wave modulation of 100%. It is obvious that, in this type of experiment, the mean luminance or adaptation level La and the absolute amplitude of the light stimulus are linked. The dc and ac components of the stimulation are not dissociable and therefore in the classical procedure it is impossible to analyse the respective role played by each component.

But it becomes possible if one uses de Lange's procedure of which the sequence of graphs c, d, e on Fig. 3 shows the principle: mean luminance and modulation amplitude are independent and by choosing a value for the mean La, one can apply a sinusoidal modulation varying in amplitude and determine the corresponding frequencies. By repeating the operations, with different values of La, one obtains a family of curves from which it is possible to analyse how the system works.

After using the sectored rotating discs, de Lange had opted for Polaroids (one fixed and one spinning). His test field of only 2° diameter was surrounded by a 60° field having the same brightness La. He used a 2.8-mm-diameter artificial pupil.

Fig. 4 shows the results obtained with one observer for seven levels of mean retinal illumination. As is usual for the attenuation characteristics of linear systems in control and communication engineering, the rate of modulation m (called here r%) on Y axis grows downwards (thus the sensitivity grows upwards). The 0.375-trolands (called here photons) level stands at the limit usually established between mesopic vision (cones and rods) and scotopic vision (rods only), which accounts for the position of the curve on the graph.

In the lowest frequency region the curves run horizontally and for the 3.75-td to 1000-td curves, the value r at 1.5 Hz varies little, from 1.1 to 1.7%. With a period as long as 0.67 s, perception is more like simple detection of luminance variation than the perception of flicker. The quasi-equal relative threshold amplitude for various luminance levels illustrates the Weber law (1846), according to which the relative threshold amplitude ΔL/L vs. logL is constant (at least for medium levels). Thus it is obvious that up to 2 or 3 Hz, the brightness system is not linear.

As the frequency increases for the curves above 1 td, a peak appears, increasing towards higher sensitivity and slipping towards higher frequencies as the mean luminance increases. Above 2 or 3 Hz, the frequency increase results in an increased sensitivity of the system. At 375 and 1000 td, the amplification increases up to about 9.10 Hz, for higher frequencies it decreases and only then does a smoothing effect occur. At first, de Lange called the peak phenomenon a resonance effect and later a pseudo resonance.

After the peak, as the frequency increases, the attenuation increases very markedly for a small change in frequency, and de Lange considers that this part of the curves can be regarded as giving attenuation characteristics, for the brightness system, of a low-pass filter.

We have seen that, as early as 1922, Ives had to come to the conclusion that for the various light stimulation temporal profiles that he was using, the CFF was determined by the fundamental frequency amplitude. It is not impossible that this assertion rather than to turn the flicker studies towards the right way, is partly responsible for the harmonic analysis being neglected until de Lange's work, whose importance was, once more, not always understood.

Thus, in 1961, Henri Piéron [24] to whom de Lange had sent a copy of his dissertation, wrote: “We have just mentioned the research of de Lange who employed sinusoidal stimulation. This is a method that has been used more and more frequently.” He was sceptical about explanations that would be based on the wave form and the harmonics, according to him, these problems “are to be sought in the distribution of the amount of photons delivered and not in the wave theory”, adding in a footnote: “Ives appealed to Fourier analysis, but, in a practical sense, only the fundamental is operative.”

If such is the case, why trouble oneself about harmonic analysis? All the more so, as according to some authors, the classical stimulation abruptly alternating dark and light may have seemed the simplest method: the sinusoidal modulation, more difficult to carry out seemed uselessly complex and harmonic analysis seemed a superfluous luxury. As Horace Barlow [37] reminds us, it is not easy to accept the fact that one can represent a transient event, such a sharp click, by a set of superimposed sine waves of indefinite duration, and leading mathematicians disbelieved Fourier, in 1807, when he stated the principle of harmonic analysis which was to prove so useful in a great variety of fields.

Fig. 7 from the excellent Visual Perception, by Tom Cornsweet [38], intends to show that harmonic analysis is not a useless luxury. It allows us to understand the behaviour of the brightness system when the intermittent stimulus is the classical square-wave with equal duration of light and dark. In this case the square wave can be represented by the sum of the odd harmonics:

The square-wave synthesized by the full series has an amplitude 0.785 (i.e. π/4) times that of the fundamental sine wave and thus the amplitude of the fundamental is 1.273 times that of the square wave.

As the frequency of the stimulation increases, the frequencies of the harmonics also increases and, the cut-off frequency at 7.1 trolands being about 40 Hz, only at the lowest frequency, 10 Hz, the second harmonic is present in the output spectrum (with a very small amplitude). At frequencies of 20 and 30 Hz, there is only the fundamental, and nothing at 40 Hz.

With the sectored rotating disc, it was easy to vary the angular value of the white or the cut-out sector, and a considerable number of studies were devoted to the influence of the rectangular pulse-to-cycle-fraction (PCF) on the CFF. Bartley [39], Landis [40] and others had commented on the chaos resulting from the whole, chaos in the data and in the attempted explanations.

Once more, harmonic analysis was the right way to clarify the situation, as shown by Kelly [41] in a short but pertinent and useful paper.

In this article, Kelly explained how the form of the function relating CFF (i.e. high-frequency flicker threshold) to PCF “can be understood in a very simple manner.” It consists in analysing the rectangular waveforms into their fundamental frequency components.

Fig. 8 shows the essential results of Kelly's analysis. The two curves represent the lower and upper bounds for the first harmonic amplitude L1 as a function of the pulse-to-cycle fraction R.

The lower curve represents the usual case of a constant maximum illuminance Lmax, guaranteed by a small artificial pupil. The equation of L1 is then:

The upper curve represents the case of a time-average illuminance La held constant and for that Lmax=La/R. The equation of L1 becomes:

From these equations we can calculate first the absolute amplitude of the fundamental frequency L1 and then predict the CFF from, for instance, Hecht's curves.

The upper curve could also represent the case of Lmax constant and the time-average retinal illuminance held constant thanks to the pupillary reaction. But actually the compensation is not complete and the true curve would fall within the intermediate shaded area. In this area are also the numerous curves in the literature which are neither perfectly symmetrical nor exactly in accordance with the upper curve, the conditions Lmax=constant (with an artificial pupil) or La=constant not having been strictly respected.

Plateau [15] rotated the discs A and B reproduced on Fig. 9 and he is probably the first to observe that – in terms of today – complementary PCFs have the same CFF. For him, this result confirms that a weak impression (the one produced by the narrow white sectors) decreases more slowly than a strong one. The constant illumination of both discs is the same and the case is the one of Eq. (2) and lower curve Fig. 8: R=0.15 in A and 0.85 in B on the approximate drawing and L1/Lmax=0.29 for A and B.

Because of a certain ambiguity in Plateau's text, Helmholtz [5] misinterpreted it: “Plateau noticed, by the way, that when the ratio between the width of the white and black sectors is changed without altering the number of sectors, the period of revolution needed to get a uniform impression is the same.” And he thought he had demonstrated it with the third disc on Fig. 9. “With increasing the speed of revolution, the flicker ceases all over almost at the same time.”

Actually, on the three concentric rings on his disc the white sectors respectively took, from the centre to the edge, 1/4, 1/2 and 3/4 of the period. We are also in the case of Eq. (2), constant maximum illuminance and for R=0.25, 0.50 and 0.75, the corresponding ratios L1/Lmax are 0.450, 0.637, and 0.450. Between the middle ring and the two others, the difference is therefore of 0.15 log unit and not more than 1.5 Hz for a probable coefficient of about 10. Considering also the conditions of observation, it was certainly difficult to perceive some difference in the CFFs. Thus Helmholtz was right in saying he did not really see any difference, but he was wrong when he asserted that the difference did not exist. [In the edition of Physiological Optics by the Optical Society of America [5], p. 214 a cross-reference to Fig. 42 (the disc with the three values of R) instead of Fig. 40 (a disc with one period of 360°, two of 180° and four of 90°) makes the text completely incoherent].

Porter [22] noticed in 1898 and exposed in details in 1902 that, in his experiments – with our symbols – CFF=0 when R=0 and when R=1 and therefore, for constant illumination, CFF “is likely to be a function of the product” R(1−R) and he showed that his experimental curves of CFF in function of R were symmetrical, with a maximum for R=0.5.

Ives [42] in 1922, although he was the initiator of the use of harmonic analysis to deal with the problem, accepted Porter's empirical expression and admitted that R(1−R) “is practically equivalent” to (sinπR)/π. Nevertheless, the first formula is the result of an abstract mathematical game, whereas the second concerns the concrete amplitude of a sine wave as we have seen with Kelly.

About this symmetrical lower curve of Fig. 8, but referring to Porter, Piéron [43], in 1928 made the curious claim that he was still sustaining in the 1961 [24], that it is “a fundamental error” to admit the equivalence between the rapid succession of black and white areas (alternation) and the periodic interruption of the vision of a luminous area (intermittence). With the black and white disc, “there is an alternation of perceptual qualities [...], this is not at all identical to the flickering light perceptions.” For him, the symmetric curve is only valid when a black and white disc is used.

Periods of uncertainty are not lacking in hazardous assertions: Porter, in his first paper, in 1898, on observing that the curves that he was obtaining were not perfectly symmetrical, wrote: “The writer believes that this is due to the fact that the black sector is not completely black.”

We shall end with the case which gave to Kelly [41] the opportunity to explain his statement on the relation between PCF and CFF. It concerned a paper in which Howard Bartley with Thomas Nelson [44], in 1961, presented experiment with Lmax constant at four levels, but without an artificial pupil. The curves of CFF in function of PCF were quasi-symmetric at low level and more and more asymmetric as the level of Lmax increased. The authors explained the diversity of the curves by Bartley's theory, which brings into play the responses of the retinal ‘off’ ganglion cells; an electronic model confirmed this hypothesis. They concluded: “As a total, the present findings and the interpretations made solve many puzzles inherent in the diverse results reported during the past several decades.”

Actually, Kelly showed that is it possible to reproduce the Bartley–Nelson curves by including the effect of pupillary adaptation in the calculation of the retinal illuminance amplitude of the fundamental harmonic. This effect attempts to keep constant the retinal illuminance (La) when the stimulus luminance increases, but the compensation is not complete and the shape of the resulting curves, falling in the shaded area of Fig. 8, are intermediate between those of the extreme limits of this shaded area. And Kelly commented: “These results appear to indicate that the main features of PCF data, which Bartley and Nelson regarded as a ‘decisive theoretical test’ of a rather involved neurophysiological hypothesis, are primarily artifacts of the stimulus waveform chosen for the experiments.”