STEREOSCOPE is an optical instrument for representing in apparent relief and solidity all natural objects by uniting into one image two representations of these objects as seen by each eye separately. That the two eyes form different images of any objects which are near enough to have dissimilar perspective projections has been long known, and may be readily tested by any one. Euclid proved it geometrically with reference to a sphere (26th, 27th, and 28th theorems of his Treatise on Optics); Galen showed how the demonstration might be made. [537-1] PORTA (q.v.), in his work on Refraction, also writes on the subject, and Leonardo da Vinci adduced the want of correspondence between the parts of the background intercepted by a near object seen by the two eyes singly "as the reason why no painting can show a rilievo equal to that of natural objects seen by both eyes within a moderate distance." [537-2] In 1613 Aguilonius, a Jesuit, in his work on Optics, attributed the union of the two unlike pictures into a clear image to a "common sense" which gave its aid equally to each eye,—this common sense being specially exerted when the object is placed much nearer to one eye than to the other, so that the sizes as well as the forms of the two retinal pictures are sensibly different. The subject was merely touched by various other writers after Aguilonius until 1775, when Harris [538-1] observes: "We have other helps for distinguishing prominences of small parts besides those by which we distinguish distances in general, as to their degrees of light and shade, and the prospect we have round them. Again, by the parallax, on account of the distance betwixt our eyes, we can distinguish, besides the front part, the two sides of a near object not thicker than the said distance, and this gives a visible rilievo to such objects, which helps greatly to raise or detach them from the plane in which tney lie. Thus the nose on a face is the more remarkably raised by our seeing both sides of it at once." This was undoubtedly a con-siderable step towards a sound theory of binocular vision, but it cannot be said to have anticipated the invention of the stereoscope. This instrument owes its origin entirely to the experimental researches of Sir Charles Wheatstone on binocular vision, and the following passage from Mayo's Outlines of Human Physiology, p. 288, published in 1833, is the first clear enunciation of the principle on which it is constructed:— "A solid object, being so placed as to be regarded by both eyes, projects a different perspective figure on each retina; now if these two perspectives be actually copied on paper, and presented one to each eye, so as to fall on corresponding parts, the original solid figure will be apparently reproduced in such a manner that no effort of the imagination can make it appear as a representation on a plane surface." Sir Charles Wheatstone's "Contributions to the Physiology of Vision, Part the First" appeared in the Philosophical Transactions of 1838, but this paper was the result of investigations extending over a period of years, and there is evidence that reflecting stereoscopes were constructed for Wheatstone by Newman, a well-known philosophical instrument maker, so early as the winter of 1832. Wheatstone no doubt also, as early as 1845, employed photographic pictures for his reflecting stereoscope. The subject was taken up by Sir David Brewster, and was developed more particularly in two papers read to the Royal Society of Edinburgh in January 1843 and April 1844. These re-searches led Brewster to the invention of the lenticular or refracting stereoscope. The discoveries of Daguerre and Talbot, and the rapid development of the art of photography, enabled photographs to be taken suitable for the stereoscope, thus superseding the geometrical drawings previously employed, and in 1849 Duboscq, a Parisian optician, began the manufacture of lenticular stereoscopes and executed a series of binocular daguerrotypes of living individuals, statues, bouquets of flowers, and objects of natural history. For many years the refracting stereoscope of Brewster was one of the most popular of scientific instruments, and was to be found, along with an appropriate collection of pictures, in every drawing-room, but of late years it has somewhat fallen into the background, and the manufacture by photographers of stereoscopic views now forms but a small portion of their work. Whilst much credit is due to Brewster for his writings on binocular vision, and for the efforts he made to introduce the stereoscope to the public, there is no doubt that Wheatstone was not only the real inventor of the instrument but he also laid down in his paper published in 1838, and in a second contribution which appeared in the Philosophical Transactions in 1852, the true principles of binocular vision. [538-2]





When we look at an external object with both eyes it is seen generally as a single object, although there must be two retinal pictures, one for each eye. This depends on the fact that the excitation of certain associated spots on the two retinae is referred to the same point in space, or, in other words, that the luminous impression which originates by the irritation of two associated points appears as one point in the visual field. Such associated points or areas of the retina are said to be corresponding or identical. When an object is seen single by two eyes, the two images must fall on corresponding points of the retina. If one eye be pushed to the side, the image on the retina of that eye is displaced from its appropriate identical point, and a double image is the result. Now the term horopter is applied to represent an imaginary surface containing "all those points of the outer world from which rays of light passing to both eyes fall upon identical points of the retina, the eyes being in a certain position." The horopter varies with the different positions of the eyes (see EYE, vol. viii. p. 826). But it is a familiar experience that we not only see a single object with two eyes, but the object, say a cube or a book lying on the table, is seen in relief, that is, we take cognizance of the third dimension occupied by the body in space, although the two retinal pictures are on a plane. It is clear that the two images of the object which do not coincide with the horopter cannot be completely united so as to furnish one single visual impression. Further, it can readily be demonstrated that the two retinal pictures are dissimilar, and yet the two images are fused into one and give the impression of a single object occupying three dimensions. To explain these phenomena, Wheatstone put forward the theory that the mind completely fused the dissimilar pictures into one, and that whenever there occurs such complete mental fusion of images really dissimilar, and incapable of mathematical coincidence, the result is a perception of depth of space, or solidity, or relief. The objection to this theory as stated by Wheatstone is that complete fusion does not take place. It is always possible by close analysis of visual perceptions to distinguish between the two retinal pictures. Further, if the fusion is mental, as stated by Wheatstone, it is an example of unconscious cerebration. Another explanation has been suggested by Brücke. [538-3] When we look at objects near at hand the optic axes are converged strongly, and they become less and less converged as we gaze at objects farther and farther away. There is thus a series of axial adjustments, the necessary muscular movements giving rise to definite sensations, by which we estimate the relative distance of objects in the field of view. A man with one eye cannot judge by this method. We habitually depend upon binocular vision for the guidance of all such movements as require an exact estimate of the respective proximity of two or more objects. "A very good test experiment is to suspend a curtain ring in such a manner as to present its edge at the distance of four or five feet from the eye, and then to try to push sideways through its hoop the curved handle of a walking stick held by the lower end; in this feat, which can be readily accomplished under the guidance of binocular vision, large odds may be laid that success will not be attained when one eye is closed, until a suc-cession of trials shall have enabled the experimenter to measure the distance of the ring by the muscular movements of his arm." [539-1] According to Brücke, the two eyes are continually in a state of motion, and their position of convergence, now greater now less, passes from one side to the other, so that the observer combines successively the different parts of the two pictures, thus giving rise to sensations of depth of space and of subjects standing out in relief. Brücke's theory, in short, is that our perception of depth depends on the fusion of muscular sensations, or rather of nervous impressions arising from the muscles of the eyeballs. It was, however, pointed out by Dove that the sensation of relief, solidity, or perspective is perfect even when natural objects or stereoscopic pictures are seen momentarily by an electric flash lasting only 1 / 24,000 a second, during which time it is inconceivable that there can be any change in the degree of convergence of the optic axes. This experiment is fatal to Brücke's theory, and Wheatstone was right in asserting that the sensation of relief is instantaneous. A third theory is that of Joseph Le Conte, advanced in 1871, and thus stated by himself:— "All objects or points of objects either beyond or nearer than the point of sight are doubled, but differently,—the former homonymously, the latter heteronymously. The double images in the former case are united by less convergence, in the latter case by greater convergence, of the optic axes. Now, the observer knows instinctively and without trial, in any case of double images, whether they will be united by greater or less optic convergence, and therefore never makes a mistake, or attempts to unite by making a wrong movement of the optic axes. In other words, the eye (or the mind) in-stinctively distinguishes homonymous from heteronymous images, referring the former to objects beyond, and the latter to objects this side of, the point of sight." [539-2] Thus, according to Le Conte, the mind perceives relief instantly but not immediately, and it does so by means of double images. This theory does not possess the merit of simplicity, and, whilst it may explain the phenomenon of relief as experienced by those who have been specially trained to the analysis of visual perceptions, it does not satisfactorily account for the experience of everyday life. We are therefore obliged to fall back on the theory of Wheatstone, somewhat modified, namely, that there are, behind the phenomena referred to the retina, psychical operations, unconsciously performed, which fuse together the results of the retinal impressions. In the language of Hermann, "corresponding points are therefore such points as furnish images, which, as experience teaches, are habitually combined or fused. But, as it appears necessary to effect these combinations in order to obtain correct impressions of objects, we get into the habit of fusing also the images of the two not perfectly corresponding points which, under ordinary circumstances, we should perceive as double. It can easily be demonstrated that simultaneous images which fall upon corresponding points are not united, although it is true that they do not form second images. When the mind must unite images which do not fall upon corresponding points, the process must be associated with the conception that the corresponding points in the object occupy the situation for which the eye would have to be arranged, in order that the image should coincide." [539-3]

To obtain binocular pictures suitable for the stereoscope, the camera must be placed successively in two points of the circumference of a circle of which the object is the centre, and the points at which the camera is so placed must have the angular distance representing the convergence of the optic axes when the object is to be viewed in the stereoscope. For example, if the pictures are to be seen in the stereoscope at a distance of 8 inches before the eyes, the convergence will be 18°, and the camera must be stationed at two points on the circle at the same angular distance. This distance of the camera from the object only affects the magnitude of the picture. Usually two cameras are employed, fixed at the proper angular positions. Wheatstone gives the following table of the inclination of the optic axes at different distances, and it also shows "the angular positions of the camera required to obtain binocular pictures which shall appear at a given distance in the stereoscope in their true relief."

== FORMULA ==

"The distance is equal to

== FORMULA ==

denoting the distance between the two eyes and B the inclination of the optic axes" (Wheatstone, Scientific Papers, p. 270).

== IMAGE==

FIG. 1. -- Stereoscopic figures. A, cone; B, ten-sided pyramid.

Suppose two stereoscopic pictures thus taken are presented to the two eyes; it is possible by an effort so to converge the eyes as to throw the images on corresponding points, and when this is done the objects are seen in relief (fig. 1). Such an effort, however, soon causes fatigue, and few persons can so control their eyes and keep them the forced position as to view the pictures in their natural perspective with any comfort. The object of all stereoscopes is to throw the two pictures on corresponding points with the eyes in an ordinary position.

The principle of Wheatstone's reflecting stereoscope is illustrated in fig. 2. It consisted of two plane mirrors, about 4 inches square, fixed in frames and so adjusted that their backs form an angle of 90° with each other. These mirrors are fixed to an upright against the middleline of a vertical board cut away so as to allow the eyes to be placed before the mirrors. On each side there is a panel bearing a groove above and below into which the corresponding pictures can be slid. Mechanical arrangements also exist for the purpose of moving the pictures to or from the mirrors and also for inclining the pictures at any angle (fig. 3). There is one position in which the binocular image will be immediately seen single, of its proper size, and without fatigue, "because in this position only the ordinary relations between the magnitude of the pictures in the retina, the inclination of the optic axes, and the adaptation of the eye to distinct vision at different distances are preserved " (Wheatstone). Although somewhat cumbrous, the reflecting stereoscope is a most useful instrument, and enables one to perform a greater variety of experiments on binocular vision than can be carried out easily with the more common form.

== IMAGE ==

FIG. 2 -- Diagram of Wheatstone's Reflecting Stereoscope ______

== IMAGE ==

FIG. 3. -- Wheatstone's Reflecting Stereoscope.

Wheatstone also invented a form of stereoscope in which the pictures were brought on corresponding points of the retina by refraction instead of by reflexion. This had a form very like the ordinary stereoscope, but, instead of lenses in the apertures to which the eyes are directed, it had "a pair of glass prisms having their faces inclined 15° and their refractive angles turned towards each other. ... A pair of plate-glass prisms, their faces making with each other an angle of 12°, will bring two pictures, the corresponding points of which are 21 inches apart, to coincide at a distance of 12 inches, and a pair with an angle of 15° will occasion coincidence at 8 inches."[540-1]





The form of stereoscope generally used is that invented by Sir David Brewster, and is known as the refracting stereoscope. The arrangement is shown diagrammatically in fig. 4. Let the left eye be at A and the right at B; let a and b be the corresponding pictures for each eye, and p₁, p₂, two prisms of glass. A prism refracts rays of light so that the object seen through the prism appears to be nearer to the refracting edge; the prism p₁ therefore refracts the ray ap₁ in the direction p₁a, as if it proceeded from c. The prism p₂ refracts the ray bp₂ so that to the eye at B it also appears to proceed from c. The effect of this is that the object really appears to be at c. And as the points a and b combine to form the point c, so d and e unite to form the point f, and g and h to form the point i (Weinhold). This stereoscope consists of a pyramidal box blackened inside and having a lid for the admission of light (fig. 5). At the narrow end of the box are two tubes carrying the lenses. The tubes move up and down to suit eyes of different focal lengths, and sometimes convex or concave lenses are inserted over the prisms to meet the wants of long-sighted or short-sighted persons. Fig. 6 shows the upper end of the stereoscope, with the lenses in position.

== IMAGE==

FIG. 4.--Diagram of the Refracting Microscope.

== IMAGE==

FIG. 5.--Sir David Brewster's Stereoscope.

A. Stroh (without knowing that H. Grubb had described the essentials of the apparatus in 1879) has recently invented a new form of stereoscope based on the well-known effects of the persistence of vision. Two stereoscopic pictures are simultaneously projected by two lanterns on a screen so as to overlap, and disks having suitable slits are rotated in front of the lanterns and also in front of the eyes of the observer, in such a way that only one picture is thrown on the screen at a time, and also that the view of the picture is seen with the right and left eyes alternately. Further, the connexion between the disks is so arranged that the time of obscuring the view of the observer's right eye or left eye coincides with the time when the light is shut off from the right or left lantern, and thus the left eye sees the picture of the left lantern and the right eye that of the right lantern. The two eyes never see at the same time, and each eye views its picture after the other, but the impressions come so fast as to be fused in consciousness, and the result is, the image stands out "in solid relief" (Proc. Roy. Soc., No. 244, vol. xl., April 1, 1886).


== IMAGE==

FIG. 6.--Lenses in Refracting Stereoscope.

== IMAGE==

FIG. 7.

During his researches into the physiology of vision, Wheatstone was led to study what he termed conversions of relief. Sometimes when we look at a geometrical figure such as a cube or rhomboid it may be imagined to represent one of two dissimilar figures. In fig. 7 the rhomboid AX is drawn so that the solid angle A should be seen nearest, and solid angle X farthest, and face ABCD foremost, while XDC is behind. Look steadily and the position will change: X will appear nearest, solid angle A farthest; face ACDB will recede behind XDC. [540-2] The effects are most obvious when seen with one eye, and "no illusion of this kind can take place when an object of three dimensions is seen with both eyes while the optic axes make a sensible angle with each other, because the appearance of two dissimilar figures, one to each eye, prevents the possibility of mistake'' (Wheatstone). The conversion of a cameo into an intaglio and of an intaglio into a cameo is a well-known instance of this illusion. Wheatstone observed the conversion of relief exhibited by binocular pictures in the stereoscope when they are transposed, reflected, or inverted, and this led him to the invention of the Pseudoscope, an instrument which conveys to the mind false perceptions of all external objects." Two rectangular prisms of flint glass, the faces of which are 1.2 inch square, are placed in a frame with their hypothenuses parallel and 2.1 inches from each other ; each prism has a motion on an axis corresponding with the angle nearest the eyes, that they may be adjusted so that their bases may have any inclination towards each other" (Wheatstone's Scientific Papers, p. 275). In fig. 8 there is a diagram of the instrument. If a spherical surface be examined with this instrument, it will appear hollow; whilst a hollow surface will appear convex. It is remarkable, however, that the converting powers of this instrument are greatest where the new forms can be conceived without effort. Thus a cameo and an intaglio, a plaster cast in relief and its mould, or any object similar in its opposite reliefs is at once changed by the pseudoscope into the converse form. As pointed out by Dr Carpenter, by gazing we can reverse the interior of a mask so as to see the countenance stand out in relief; it is more difficult to throw the features of a bust into the shape of a mould; whilst it is impossible to effect any conversion upon the features of the living face. "The opitical change is identically the same in its nature in every one of these cases; and there is nothing in the form of the features which refuses to present a converse, this converted shape being presented by the mask; but the mind, which will admit the conception of the converted form when suggested by the inanimate mask or bust, is steeled by its previous experience against the notion that actual flesh and blood can undergo such a metamorphosis "(Carpenter, Edinburgh Review, 1858, p. 460).

== IMAGE==

FIG. 8.--Diagram of Wheatstone's Pseudoscope _______


== IMAGE==

FIG. 9.--Diagram of Von Helmholtz's Telestereoscope.

A little consideration will show that the pic-tures of objects placed at a great distance from the eye are practically if not wholly identical. Here there is scarcely any stereoscopic effect, and the landscape may appear to he flat, as in a picture. To obtain a stereoscopic view of a landscape Von Helmholtz invented the Telestereoscope, an instrument which places as it were the point of view of both eyes wide apart. It consists of two mirrors L and R, each of which projects its image upon I and r, to which the eyes O and o are directed. The eyes O and o are placed as it were at O₁ and o₁, according to the distance between L and R; consequently two dissimilar pictures are obtained; these are mentally combined, with the result that the landscape is seen like a stereoscopic view.

The principle of the stereoscope was successfully applied by Wenham in 1854 to the construction of the binocular microscope. See MICROSCOPE (vol. xvi. p. 272), and also two papers in the Jour. Boy. Micr. Soc, 1884 :—(1) "On the Mode of Vision with Objectives of Wide Aperture," by Prof. E. Abbe, p. 20; and (2) "On the Physiology of Binocular Vision with the Microscope," by Dr Carpenter, p. 486. Prof. Abbe shows, however, that "oblique vision in the microscope is entirely different from that in ordinary vision, inasmuch as there is no perspective, so that we have no longer the dissimilarity which is the basis of the ordinary stereoscopic effect, but an essentially different mode of dissimilarity between the two pictures." In the microscope there is no per- spective foreshortening. There is no difference in the outline of an object viewed under the microscope by an axial or by an oblique pencil. There is simply a lateral displacement of the image—an entirely different phenomenon to that which occurs in non-micro- scopic vision. Thus, whilst the mode of formation of dissimilar pictures in the binocular microscope is different from the production of ordinary stereoscopic pictures, the brain mechanism by which they are so fused as to give rise to sensations of solidity, depth, land perspective is the same. (J. G. M.)


Footnotes

537-1 De Usu Partium Corporis Humani, Lyons, 1550, p. 593.

537-2 Trattata delta Pictura, Scultura, ed Architettura, Milan, 1584.

538-1 Opticks, vol.. ii. pp. 41 and 245.

538-2 See Brewster on the Stereoscope, 1856; Wheatstone's Scientific Papers, published by the Physical Society of London, 1879; and an article by the late Dr William Carpenter in Edinburgh Review for 1858.

538-3 The theory is usually attributed to Brücke, but something very similar to it was taught by Brewster. Brewster, however, did not attach importance to muscular sensations as an element in the question, and was content in pointing out that, in looking at the stereoscopic pictures of a bust, for example, "the eyes will instantly, by means of their power of convergence, united the separated points of the eyes, and then the still more separated points of the ears, running over each part of the bust with the rapidity of lightning, and uniting all the corresponding points in succession, precisely as it does in looking at the bust itself." See his article "Stereoscope," in Encyc. Britan.,8th ed., vol. xx. p. 689.

539-1 Carpenter, Edinburgh Review, 1858.

539-2 American Journal of Science and Arts, vol. ii, 1871.

539-3 Hermann's Physiology, translated by Gamgee, p. 430.

540-1 Wheatstone's Scientific Papers, p. 267.

540-2 Necker, Phil. Mag., 3d series, vol. i. p. 357.



The above article was written by: Prof. J. G. McKendrick.