The stereoscope

by David Brewster

In Mr. Wheatstone’s ingenious paper of 1838, the subject of binocular vision is treated at considerable length. He gives an account of the opinions of previous writers, referring repeatedly to the works of Aguilonius, Gassendi, and Baptista Porta, in the last of which the views of Galen are given and explained. In citing the passage which we have already quoted from Leonardo da Vinci, and inserting the figure which illustrates it, he maintains that Leonardo da Vinci was not aware “that the object (c in [Fig. 2]) presented a different appearance to each eye.” “He failed,” he adds, “to observe this, and no subsequent writer, to my knowledge, has supplied the omission. The projection of two obviously dissimilar pictures on the two retinæ, when a single object is viewed, while the optic axes converge, must therefore be regarded as a new fact in the theory of vision.” Now, although Leonardo da Vinci does not state in so many words that he was aware of the dissimilarity of the two pictures, the fact is obvious in his own figure, and he was not led by his subject to state the fact at all. But even if the fact had not stared him in the face he must have known it from the Optics of Euclid and the writings of Galen, with which he could not fail to have been well acquainted. That the dissimilarity of the two pictures is not a new fact we have already placed beyond a doubt. The fact is expressed in words, and delineated in drawings, by Aguilonius and Baptista Porta. It was obviously known to Dr. Smith, Mr. Harris, Dr. Porterfield, and Mr. Elliot, before it was known to Mr. Wheatstone, and we cannot understand how he failed to observe it in works which he has so often quoted, and in which he professes to have searched for it.

This remarkable property of binocular vision being thus clearly established by preceding writers, and admitted by himself, as the cause of the vision of solidity or distance, Mr. Wheatstone, as Mr. Elliot had done before him, thought of an instrument for uniting the two dissimilar pictures optically, so as to produce the same result that is obtained by the convergence of the optical axes. Mr. Elliot thought of doing this by the eyes alone; but Mr. Wheatstone adopted a much better method of doing it by reflexion. He was thus led to construct an apparatus, to be afterwards described, consisting of two plane mirrors, placed at an angle of 90°, to which he gave the name of stereoscope, anticipating Mr. Elliot both in the construction and publication of his invention, but not in the general conception of a stereoscope.

After describing his apparatus, Mr. Wheatstone proceeds to consider (in a section entitled, “Binocular vision of objects of different magnitudes”) “what effects will result from presenting similar images, differing only in magnitude, to analogous parts of the retina.” “For this purpose,” he says, “two squares or circles, differing obviously but not extravagantly in size, may be drawn on two separate pieces of paper, and placed in the stereoscope, so that the reflected image of each shall be equally distant from the eye by which it is regarded. It will then be seen that notwithstanding this difference they coalesce and occasion a single resultant perception.” The fact of coalescence being supposed to be perfect, the author next seeks to determine the difference between the length of two lines which the eye can force into coalescence, or “the limits within which the single appearance subsists.” He, therefore, unites two images of equal magnitude, by making one of them visually less from distance, and he states that, “by this experiment, the single appearance of two images of different size is demonstrated.” Not satisfied with these erroneous assertions, he proceeds to give a sort of rule or law for ascertaining the relative size of the two unequal pictures which the eyes can force into coincidence. The inequality, he concludes, must not exceed the difference “between the projections of the same object when seen in the most oblique position of the eyes (i.e., both turned to the extreme right or the extreme left) ordinarily employed.” Now, this rule, taken in the sense in which it is meant, is simply a truism. It merely states that the difference of the pictures which the eyes can make to coalesce is equal to the difference of the pictures which the eyes do make to coalesce in their most oblique position; but though a truism it is not a truth, first, because no real coincidence ever can take place, and, secondly, because no apparent coincidence is effected when the difference of the picture is greater than what is above stated.

From these principles, which will afterwards be shewn to be erroneous, Mr. Wheatstone proceeds “to examine why two dissimilar pictures projected on the two retinæ give rise to the perception of an object in relief.” “I will not attempt,” he says, “at present to give the complete solution of this question, which is far from being so easy as at first glance it may appear to be, and is, indeed, one of great complexity. I shall, in this case, merely consider the most obvious explanations which might be offered, and shew their insufficiency to explain the whole of the phenomena.

“It may be supposed that we see only one point of a field of view distinctly at the same instant, the one, namely, to which the optic axes are directed, while all other points are seen so indistinctly that the mind does not recognise them to be either single or double, and that the figure is appreciated by successively directing the point of convergence of the optic axes successively to a sufficient number of its points to enable us to judge accurately of its form.

“That there is a degree of indistinctness in those parts of the field of view to which the eyes are not immediately directed, and which increases with the distance from that point, cannot be doubted; and it is also true that the objects there obscurely seen are frequently doubled. In ordinary vision, it may be said, this indistinctness and duplicity are not attended to, because the eyes shifting continually from point to point, every part of the object is successively rendered distinct, and the perception of the object is not the consequence of a single glance, during which a small part of it only is seen distinctly, but is formed from a comparison of all the pictures successively seen, while the eyes were changing from one point of an object to another.

“All this is in some degree true, but were it entirely so no appearance of relief should present itself when the eyes remain intently fixed on one point of a binocular image in the stereoscope. But in performing the experiment carefully, it will be found, provided the picture do not extend far beyond the centres of distinct vision, that the image is still seen single, and in relief, when in this condition.”[22]

In this passage the author makes a distinction between ordinary binocular vision, and binocular vision through the stereoscope, whereas in reality there is none. The theory of both is exactly the same. The muscles of the two eyes unite the two dissimilar pictures, and exhibit the solid, in ordinary vision; whereas in stereoscopic vision the images are united by reflexion or refraction, the eyes in both cases obtaining the vision of different distances by rapid and successive convergences of the optical axes. Mr. Wheatstone notices the degree of indistinctness in the parts of the picture to which the eyes are not immediately directed; but he does not notice the “confusion and incongruity” which Aguilonius says ought to exist, in consequence of some parts of the resulting relievo being seen of one size by the left eye alone,—other parts of a different size by the right eye alone, and other parts by both eyes. This confusion, however, Aguilonius, as we have seen, found not to exist, and he ascribes it to the influence of a common sense overruling the operation of physical laws. Erroneous as this explanation is, it is still better than that of Mr. Wheatstone, which we shall now proceed to explain.

In order to disprove the theory referred to in the preceding extract, Mr. Wheatstone describes two experiments, which he says are equally decisive against it, the first of them only being subject to rigorous examination. With this view he draws “two lines about two inches long, and inclined towards each other, on a sheet of paper, and having caused them to coincide by converging the optic axes to a point nearer than the paper, he looks intently on the upper end of the resultant line without allowing the eyes to wander from it for a moment. The entire line will appear single, and in its proper relief, &c.... The eyes,” he continues, “sometimes become fatigued, which causes the line to become double at those parts to which the optic axes are not fixed, but in such case all appearance of relief vanishes. The same experiment may be tried with small complex figures, but the pictures should not extend too far beyond the centre of the retinæ.”

Now these experiments, if rightly made and interpreted, are not decisive against the theory. It is not true that the entire line appears single when the axes are converged upon the upper end of the resultant line, and it is not true that the disappearance of the relief when it does disappear arises from the eye being fatigued. In the combination of more complex figures, such as two similar rectilineal figures contained by lines of unequal length, neither the inequalities nor the entire figure will appear single when the axes are converged upon any one point of it.