Alfred Wilhelm Volkmann on stereoscopic vision

ABSTRACT

Wheatstone’s demonstration of binocular single vision and depth with stimulation of non-corresponding points reverberated throughout mid-nineteenth century German visual science. It challenged the received view that single vision was a consequence of retinal correspondence otherwise objects were seen double. Wheatstone also argued that stimulation of corresponding points could yield double vision. He interpreted his experimental observations in psychological rather than physiological terms, as did Helmholtz later. Volkmann addressed both of these challenges in a long article on stereoscopic vision published in 1859. While he accepted the first of the questions Wheatstone posed Volkmann was more cautious with regard to the second. Volkmann was an experimentalist who applied psychophysical methods to determine thresholds for stereoscopic depth perception. In line with many of his colleagues in Germany, he took issue implicitly with Wheatstone’s approach: how can the detailed quantitative experiments supporting Vieth and Müller’s interpretation of binocular single vision be derailed by simple observations with a stereoscope? Unlike most of his colleagues, Volkmann was swayed in Wheatstone’s favor through his own experiments: both physiological and psychological processes are involved in stereoscopic depth perception.

KEYWORDS:

• stereoscopic vision
• Volkmann
• Wheatstone

Alfred Wilhelm Volkmann¹ (1801–1877) presented his theoretical and experimental response to Wheatstone’s² (1838) analysis of binocular vision in 1859. The impact of Wheatstone’s stereoscopic investigations on German visual science was seismic. Müller’s³ elegant analysis of binocular single vision, linking the Vieth-Müller circle with identical (or corresponding) retinal points, was challenged by the perception of singleness and depth from stimulating non-corresponding retinal points and many of Müller’s countrymen sprang to its defense.⁴ Five articles in recent issues of Strabismus present translations into English by H. J. Simonsz from Volkmann’s¹ examination of stereoscopic vision and his attempts to reconcile the disparate views. Volkmann is shown in Figure 1 together with the title page of his article.

Figure 1. Detail of a portrait of Alfred Volkmann and the title page of his article on stereoscopic vision.

In Part 1⁵ of the translation (pp. 1–32 of Volkmann’s¹ article) Volkmann assesses the approaches of Brücke⁶ and Panum⁷ to accommodate stereoscopic phenomena without abandoning the doctrine of identical retinal points. Part 2⁸ (pp. 32–59) presents the results of Volkmann’s experiments determining fusional thresholds in the three dimensions of space – horizontal, vertical and torsional. Part 3⁹ (pp. 59–72) presents Volkmann’s attempt to reconcile the seemingly incompatible approaches of German physiologists and the empiricist interpretations of Wheatstone. Volkmann’s considerations and experiments on Wheatstone’s observation that stimulation of corresponding points can lead to double vision are presented in Part 4¹⁰ (pp. 72–86). The final translation (Part 5,¹¹ pp. 86–100) addresses some paradoxical aspects of stereoscopic vision.

Two years after Volkmann’s article, Nagel^12–15 published a book on vision with two eyes parts of which have also been translated in Strabismus. The starting points for both Volkmann and Nagel were the implications of Wheatstone’s stereoscopic phenomena for Müller’s theory: “If Wheatstone were right on this point, the doctrine of vision was threatened to be overturned completely”^1(p2). What did Wheatstone demonstrate that stirred visual scientists, particularly those in Germany, so dramatically? First, he showed that points that are not on the Vieth-Müller circle can be seen as single and in depth; secondly, he presented a figure that stimulated identical retinal points and was seen as double. Volkmann addressed both aspects of vision with two eyes.

A portrait of Wheatstone is shown in Figure 2 together with the first page of his article introducing the stereoscope and stereoscopic depth perception^{2 (p.371).}

Figure 2. A portrait of Charles Wheatstone and the title page of his first article on stereoscopic vision.

Wheatstone was a pioneer of research on stereoscopic vision. Indeed, stereoscopic vision was not appreciated until 1838, when he demonstrated the synthesis of depth from the binocular combination of two plane drawings mounted in his stereoscope. Wheatstone not only invented the stereoscope, but he also carried out many ingenious manipulations with stereograms. He also adopted philosophical empiricism to interpret how these various factors combine. That is, he conceived of perception as a mental process in which previous exposures to patterns of stimulation were related to one another. Wheatstone demonstrated that dissimilar pictures on the two retinae could be seen singly and in depth. For example, two vertical lines at different distances could be projected onto a flat surface between the eyes and the object: when each eye was presented with a single projection the impression of depth was reproduced. He also showed that paired three-dimensional outline cubes, when viewed in his stereoscope, induced the same impressions of depth as those produced by flat projections of them. Moreover, when the cubes were placed so as to project identical images to the eyes then depth was no longer seen. Similar changes in the perception of depth could be produced with paired skeleton figures as with outline drawings. Thus, representing the appropriate perspective projections of an object to each eye yielded the perception of solidity. In the set of stereograms that Wheatstone published, outlines were used for the specific purpose of reducing any reliance on monocular cues to depth. When he transposed the stereograms the direction of depth reversed. However, when the projections were of a symmetrical solid, like a cube, there were changes in apparent size attendant upon the reversal of depth. This relationship between perceived size and distance was one to which Wheatstone was to return in his second paper on binocular vision.¹⁶ He adopted the empirical methods of the physicist to unravel the independent contributions of factors like accommodation, convergence, retinal size and disparity in determining perceived size.

A summary of Wheatstone’s article¹⁷ was soon translated into German and a full translation was provided later¹⁸; Volkmann cited the English version rather than the translations into German. William James shrewdly observed that Wheatstone’s paper “contains the germ of almost all the methods applied since to the study of optical perception. It seems a pity that England, leading off so brilliantly the modern epoch of this study, should so quickly have dropped out of the field. Almost all subsequent progress has been made in Germany, Holland, and, longo intervallo, America”^{19 (pp. 226−227)}.

The first of the German physiologists to bridle at the attack by Wheatstone on Müller’s doctrine of identical retinal points was Brücke⁶ (Figure 3); his article was published in the Archiv für Anatomie und Physiologie edited by Müller. Brücke argued that detailed vision is restricted to a small foveal region so that any object will be scanned rapidly. In the case of binocular vision the eye movements involve variations in vergence as well as version, with the ensuing perception based on a synthesis of these different retinal impressions. According to this hypothesis, stereoscopic depth could not be perceived if the eyes did not move.

Figure 3. A portrait of Ernst Brücke and the title page of his article on stereoscopic vision.

Wheatstone^{2 (p. 392)} had already considered and rejected this hypothesis: “Another and a beautiful proof that the appearance of relief in binocular vision is an effect independent of the motion of the eyes, may be obtained by impressing on the retinæ ocular spectra [afterimages] of the component figures.” Volkmann reached the same conclusion using a novel method. In the same year as his article on stereoscopic vision, he invented the tachistoscope²⁰ to examine precisely this question; the instrument enabled brief presentation of paired stimuli, one to each eye, to determine whether depth was still seen – it was. Dove²¹ had reached the same conclusion using paired afterimages produced by illumination with an electrical spark. Thus, the evidence against Brücke’s eye movement hypothesis was strong.

Volkmann noted that Panum⁷ (Figure 4) also rejected Brücke’s analysis of stereoscopic depth perception and adopted a position supporting both psychological and physiological factors involved in it. Panum made a more nuanced attempt to salvage Müller’s theory from the attack on it by Wheatstone: he replaced points of retinal correspondence by circle of correspondence in what came to be referred to as ‘Panum’s fusional areas’. However, the logical consistency of this hypothesis was questioned by Volkmann who reported a number of related experiments. Volkmann was principally an experimentalist. Interest in theory needed to be empirically supported and 39 experiments are described in the whole article.

Figure 4. A portrait of Peter Ludvig Panum and the title page of his book on seeing with two eyes.

Panum devoted much of his book to examining another aspect of binocular vision highlighted by Wheatstone – binocular rivalry.^22–24 When radically different stimuli are presented to each eye in a stereoscope, they are not combined but compete, resulting in dynamically changing patterns of visibility. Wheatstone² examined rivalry between the letters A and S each surrounded by similar circles. Letters were recognized as complex patterns and simpler stimuli were soon enlisted. One of the first systematic studies of rivalry was published by Panum.⁷ The orthogonal grating stimuli he introduced have dominated the study of rivalry ever since. Panum drew attention to the dynamic variations and to the mixtures or composites that are seen and he sought to interpret the phenomenon in physiological terms rather than the psychological factors proposed by Wheatstone² and later by Helmholtz.²⁵

Volkmann’s mastery of experimental vision was displayed in Part 2 of the translation. He had been a colleague of Fechner in Leipzig and he determined the thresholds for the detection of stereoscopic depth using line stimuli in a variety of orientations.

It is in Part 3 of the translation that Volkmann cites Wheatstone’s¹⁶ second, and much neglected, memoir in binocular vision. In it Wheatstone described and illustrated an adjustable mirror stereoscope, a prism stereoscope, and a pseudoscope for reversing disparities. The main purpose of these was to extend the range of conditions under which the two eyes could be stimulated. Wheatstone used the stereoscope with adjustable arms to vary retinal size, convergence, accommodation, and disparity. He found that “The perceived magnitude of an object, therefore, diminishes as the inclination of the axes becomes greater, while the distance remains the same; and it increases, when the inclination of the axes remains the same, while the distance diminishes. When both of these conditions vary inversely, as they do in ordinary vision when the distance of an object changes, the perceived magnitude remains the same”^16(p3). On the basis of these experiments, as well as his own Volkmann appreciated that stereoscopic depth involves psychological as well as physiological processes: “The psychological influences are very important in the theoretical consideration because they make any explanation of the discussed fusion process through innate relations impossible”^9(p189).

Wheatstone’s second line of attack was that stimulation of corresponding retinal points can result in double vision. This was examined experimentally by Volkmann in Part 4 of the translation.¹⁰ The stimulus Wheatstone used was a thick tilted line and a thin vertical in one eye and a single thick vertical in the other. The reproduction of this figure by Volkmann^{10 (Fig. 15)} does not show the differences in thicknesses of Wheatstone’s stimulus^{2 (Fig. 13)}, although Volkmann does describe them as thick and thin lines. When Volkmann^{26 (Fig. 34)} returned to this issue the illustration distinguished more clearly between the thick and thin lines. He was not able to replicate Wheatstone’s observations, nor were others before and after him.^6,12,25,27 However, the stimulus combinations used were rarely like those employed by Wheatstone. For example, the squares surrounding the lines to aid binocular alignment were often not included, and there was little consensus in the alternative observations described. For these reasons, Ono and Wade²⁸ tried to stay as close as possible to Wheatstone’s arrangement: a replica of Wheatstone’s mirror stereoscope was used with photographic copies of his stimuli at the size and viewing distance he described. The results of three experiments were not conclusive as there were large individual differences. The Wheatstone stimulus is itself complex as different predictions would be made for the upper and lower halves of the display and Volkmann’s results could be taken as reflecting this.

Volkmann^1,26,29,30 wrote about binocular vision both before and after Wheatstone announced the stereoscope to the public in 1838 and it is instructive to compare his final analysis with the earlier accounts. A brief chapter on single vision with two eyes is included in his first book.²⁹ His chapter on Seeing in Wagner’s handbook³⁰ contains a section on single and double vision illustrating the Vieth-Müller circle. Wheatstone’s stereoscopic experiments are described but Volkmann’s sympathies remained with the theory of identical retinal points. It would seem that this initial engagement with Wheatstone’s ideas was the goad to his experiments reported in 1859.¹ As would be expected, there is a lengthy appraisal of vision with two eyes in his second book on optics.²⁶ It is based largely on the long article that has been translated in the recent issues of Strabismus. This chapter has been overlooked largely because (as pointed out by Strasburger, Huber and Rose³¹) it was omitted from the table of contents!

Volkmann was an experimentalist who applied the psychophysical methods of Fechner to determine thresholds for stereoscopic depth perception. In line with many of his colleagues in Germany, he took issue implicitly with Wheatstone’s approach: how can the detailed quantitative experiments supporting Vieth and Müller’s interpretation of binocular single vision be derailed by simple observations with a stereoscope? Unlike most of his colleagues, Volkmann was swayed in Wheatstone’s favor through his own experiments. While he accepted the first of the questions Wheatstone posed (that stimulation of non-corresponding points can yield singleness and depth) he was more cautious with regard to the second (that stimulation of corresponding points can lead to double vision).

An index of the significance of Volkmann’s 1859 article is that in the section on stereoscopic vision, Helmholtz²⁵ (1867) provides relatively little empirical data of his own but uses that from Volkmann.¹ Indeed, Volkmann is accorded more citations than Wheatstone.

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The author(s) received funding from the University of Dundee for publishing this article.