The name Stereoscope, derived from the Greek words στερεός, solid, and ὁράω, to see, has been given to a binocular optical instrument of modern invention, by which plane representations of figures or landscapes, or any objects whatever, as seen separately by each eye, are combined into one picture, which appear solid or in relief. Unlike other optical instruments, it cannot be used by persons who see only with one eye.
As in all important inventions, the principle of the instrument, as well as its construction, has been claimed for different persons. The fundamental principle of the stereoscope is, that the pictures of any solid object, as seen by each eye, are different; that is, if an artist draws any solid object, as seen with each eye separately, the pictures will be different. Every body knows this that chooses to inquire into the matter; the right eye sees the right side of the nose only, as Gassendi said long ago, and the left eye the left side of the nose. The right eye sees only one glass of a pair of spectacles before the right eye, and the left eye sees only the other glass, which is before it; or, to state the fact more generally, the right eye sees more of the right side of all solid objects than the left eye does, and the left eye sees more of the left side of the same objects than the right eye. In vision these two pictures, the right and left eye pictures, are united into one. The second principle of the stereoscope is, that the pictures thus united, though flat or plane upon the retina, have the appearance of solidity or relief, and, therefore, two dissimilar pictures, like those on the retina, united by means of the two eyes, or by any method whatever, will also appear in relief.
The first of these principles was known to Euclid 2000 years ago, and is distinctly explained in his Treatise on Optics. Fifteen hundred years ago, Galen clearly proves that in viewing solid objects, with each eye and with both, we see three different pictures. "Standing near a column," he says, "and shutting each eye in succession, when the right eye is shut, some of those parts of the column which were previously seen by the right eye on the right side of the column, will not now be seen by the left eye; and when the left eye is shut, some of those parts which were formerly seen by the left eye on the left side of the column, will not now be seen by the right eye. But when we at the same time open both eyes, both these will be seen."
Baptista Porta illustrates these views of Galen by the following figure, in which we see not only the principle of the stereoscope, but the binocular slide with the right and left eye picture united and producing solidity (fig. 1). Let A, he says, be the pupil of the right eye, B that of the left, and DC the body to be seen. When we look at the object with both eyes we see DC. But if it is seen with one eye it will be seen otherwise, for when the left eye B is shut, the body CD, on the left side, will be seen in HG; but, when the right eye is shut, the body CD will be seen in FE; whereas, when both eyes are opened at the same time, it will be seen in CD.
That we have here the representation of the right and Jacopo Chimenti's drawing.
This, doubtless, is the invention of the ocular stereoscope, deduced from Baptista Porta's work. In the year 1593, when Porta's work was published in Naples, Jacopo Chimenti was in the 39th year of his age, and therefore very likely to have availed himself of the binocular theory of the Neapolitan philosopher.
Leonardo da Vinci knew the same fact, and in 1613 Aguilonius, in his work on optics, wrote a whole book on the vision of solids (vid. στερεός, το στερεό). And Dr Smith of Cambridge, Mr Harris of the Mint, and Dr Porterfield of Edinburgh, were all acquainted with the dissimilarity of the pictures as seen by each eye separately. Mr Harris, who wrote in 1775, tells us that we distinguish prominences of small parts by the prospect we have round them; and he adds, "By the parallax, on account of the distance betwixt our eyes, we can distinguish besides the front part of the two sides of a near object not thicker than the said distance, and this gives a visible relievo to such objects, which helps greatly to raise or detach them from the plane in which they lie. Thus, the nose on the face is the more remarkably raised by our seeing both sides of it at once." Hence it is obvious that optical writers in every age knew the two facts, that the pictures on the retina of the two eyes were dissimilar, and that by the union of these two flat dissimilar pictures we obtain the vision of solidity, the union of the two nearest similar points on the two pictures, placing that point at the shortest distance; and the union of the two most remote similar points, placing that point at the greatest distance from the eye.
In order to see objects in relief from plain representations of them, it was required only to obtain accurate
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1 De Refractionibus Opticis parte, lib. v., p. 132; of lib. vi., pp. 143, 145; Neap. 1593. 2 We have taken measures to obtain photographs of Chimenti's drawings. pictures of them as seen by each eye, and a method of uniting these pictures. By means of photography and the binocular camera we obtain two dissimilar pictures, and by the method of Chimenti we can unite these pictures.
So early as 1823 Professor Elliott of Liverpool, when a student at the logic-class in Edinburgh, was led to study the subject of binocular vision, and sometime afterwards he invented a method of uniting the two dissimilar pictures of objects as drawn by himself. He had resolved in 1834 to make the instrument, but delayed doing this till the year 1839, when he constructed an instrument for uniting two dissimilar pictures. This simple stereoscope had neither mirrors nor lenses, and consisted of a wooden box 6 inches long, at the end of which he placed two dissimilar pictures of a landscape (fig. 3) drawn by himself, as seen by each eye. These pictures were then united, and appeared in relief by converging the eyes to a point beyond the pictures. If he had reversed the pictures, as in fig. 3, he would have obtained the same effect by converging the optic axis to a point between the pictures and his eye. Owing to the difficulty of obtaining right and left eye pictures of landscapes and figures, Professor Elliott proceeded no farther with his invention.
In 1836 Mr George Maynard, M.A., of Caius College, Cambridge, who had been previously studying the phenomena of binocular vision, published an article on the subject in a Toronto newspaper, in which he described the principles of the stereoscope, or the Bathroscope (from Bathos, depth, and eros, loses), as he called it.
In June 1838 he communicated to the Royal Society of London an interesting paper on the physiology of vision, in which he described an instrument called a stereoscope for uniting the two dissimilar pictures of solid bodies as seen by each eye. This instrument, which is represented in fig. 5, he describes in the following manner:
"A A' are two plain mirrors about 4 inches square, inserted in frames, and so adjusted that their backs form an angle of 90° with each other; these mirrors are fixed by their common edge against an upright B or against the middle of a vertical board, cut away in such a manner as to allow the eyes to be placed before the two mirrors. C, C', are two sliding boards, to which are attached the upright boards D, D', which may thus be removed to different distances from the mirrors." In order to keep the two upright boards at the same distance from its opposite mirror, Mr Wheatstone "employs a right and left-handed screw, r, l; the two ends of this compound screw pass through the nuts e, e', which are fixed to the lower parts of the upright boards D, D', so that by turning the screw-pin p one way the two boards will approach, and by turning it the other, they will recede from one another; one always preserving the same distance as the other from the middle line f; E, E', are panels to which the pictures are fixed, so that their corresponding horizontal lines shall be on the same level; these panels are capable of sliding backwards or forwards in grooves on the upright boards D, D'."
In using the apparatus "the observer must place his eyes as near as possible to the mirrors, the right eye before the right hand mirror, and the left eye before the left hand mirror, and he must move the sliding panels E, E', to or from him till the two reflected images coincide at the intersection of the optic axis, and form an image of the same apparent magnitude as each of the component pictures,"... the entire effect of relief being produced by the simultaneous perception of the two monocular projections, one on each retina."
The figures to which Mr Wheatstone applied this apparatus were pairs of outline representations of objects of three dimensions, such as cubes, cones, and frustums of pyramids, like those shown at E, E', in the figure; but though the effect produced by the apparatus was new and startling, it did not excite any general interest, and was known only to Mr Wheatstone's friends, or to one or two professors as a portion of their optical apparatus.
Having had one of these stereoscopes constructed for him by the late celebrated optician, Andrew Ross, Sir David Brewster saw its imperfections, and its inapplicability as a general and popular instrument, and he was led to the construction of the lenticular stereoscope, now in universal use in every part of the world. The instrument was exhibited to the British Association at Birmingham in 1849, and a finely executed one by Mr Loudon of Dundee was exhibited by its inventor in Paris in 1850 to the Abbé Moigno. M. Dubosq devoted himself to the manufacture of the instrument, and executed for it the most beautiful daguerreotypes of living individuals, statues, and objects of all kinds. "The stereoscopes of M. Dubosq," says the Abbé Moigno, "are constructed with more elegance, and even with more perfection than the original English instrument; and while he is showing their wonderful effects to natural philosophers, and amateurs who have flocked to him in crowds, there is a spontaneous and unanimous cry of admiration."
On the 30th December M. Dubosq exhibited the lenticular stereoscope to the Imperial Institute of France, and MM. Babinet, Pouillet, and Regnault were appointed a committee to examine it. Although Sir David Brewster had offered the free use of his invention to opticians in Birmingham and London in 1849, yet not a single instrument was made by English artists, and it was not till a year after its introduction into France that it was publicly exhibited in England.
In the beautiful collection of optical instruments which M. Duboscq contributed to the Great Exhibition in 1851, he placed a lenticular stereoscope, with a fine set of binocular daguerreotypes. The instrument attracted the particular attention of the Queen, and before the crystal palace was closed, M. Duboscq executed one of his finest stereoscopes, which was presented to her Majesty by Sir David Brewster in the artist's name. M. Duboscq having received many orders from England, sent over a number of stereoscopes; and in a short time they were manufactured in all parts of the world, and artists dispatched into every country to take binocular pictures of its buildings, monuments, and scenery.
The lenticular stereoscope consists of two convex lenses, or two semi-lenses, or two quarter-lenses, placed 2½ inches distant, through which the observer views what is called a binocular picture, held in the hand, or placed in a box at such a distance from the lenses that it may be seen distinctly, and magnified.
In the earliest instruments two whole lenses were used, in order to save the trouble of halving them, but in this case the two outermost halves were useless, as the eyes of the observer only looked through the inner halves. But in order to make the instruments cheaper, the lenses were cut into halves, or into quarters, and each half or quarter cut into a round disc, so that a single lens could make one semi-lens stereoscope, or two quarter-lens stereoscopes. These different forms of the lenses are shown in the annexed diagram (fig. 6), where L is the lens opposite the left eye, and R the lens opposite the right eye, each eye looking through the part of the lens marked by a dotted circle the size of the pupil of the eye. If the eye is close to the lens it will see the object which it views as distinctly as if the lens were a foot in diameter; but as it cannot be advantageously placed close to it, the lenses are always made larger than is necessary. Beyond the size of lens which allows the pupil to see every part of the object, everything additional is superfluous. The two lenses L, R have been made so large as to meet, and sometimes the shape of a Gothic window has been given to them; but whatever be their size or shape, whether whole lenses, as they have been ignorantly made, or any other size, the eyes must look through two small circular portions equidistant from the centre, and placed at the distance of 2½ inches, as shown in the above figure.
It is hardly necessary to point out to the optical reader the peculiar advantages of semi or quarter lenses. It is impossible to give two separate lenses, L, R, the same focal length and magnifying power, however nearly we may approach to it; but two semi-lenses cut from the same lens, and the two quarter-lenses cut from the same semi-lens, have necessarily the same focal length and magnifying power.
The general form of the instrument in which these lenses are placed is shown in fig. 7. The instrument consists of a pyramidal box, or a box of any form, on the top of which are placed two eye-tubes containing the lenses R, L, which can be separated from one another in a variety of ways, to suit the distance between the eyes of the observer. They may also be drawn out so as to produce distinct vision of the picture, but they are prevented from turning round by a brass pin in the fixed tubes, which runs in a groove cut through the movable tubes. Immediately below the eye-tubes, at G, there should be a groove for the introduction of a pair of convex or concave spectacles, when necessary, or for coloured glasses, or other purposes.
If we now take a binocular slide containing two pictures of a person, or a landscape, as seen by each eye, or as drawn by the rules of perspective from two points 2½ inches distant, and put it into the horizontal opening at AB, and look into the instrument with the right eye at R and the left at L, we shall see the two pictures united into one, and having the same relief as the living person if it is a portrait, or as a scene in nature if it is a landscape; every part being no longer on a plane surface, but at its proper distance from the eye. If we shut the right eye R, and look only with the left eye L, we shall see only the picture 1, which will sink into a comparatively flat representation of the object, with only monocular relief. In like manner, by closing the left eye L, we shall see only the picture 2 comparatively flat; but when both eyes are opened the pictures 1 2, when combined, will start into all the roundness and solidity of life or nature.
The bottom of the stereoscope should be left open, so as to admit binocular pictures on glass, but in this case the open bottom must be covered either with ground glass or transparent paper, unless when the binocular slide has one of its surfaces made of ground glass. The lid CD, which is left open to throw light on opaque binocular slides like those on paper, card-board, or silver plate, must be shut when the pictures are either upon glass or transparent paper.
When the instrument is placed on a stand, as in the figure, it moves round a joint at E, and is raised or depressed by a stop-screw at F. A reflector GH is some-
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1 Comptes Rendus, &c., tom. xxxi., p. 897. 2 See the article Microscope, vol. xiv., p. 770. times added to the stereoscope for throwing different levels upon transparent pictures, and its position is regulated by a pulley P.
In order to explain why the stereoscope combines the two pictures, we shall do it most simply by desiring the reader to look at any object with his left eye through the centre C of any convex lens such as L, fig. 8, so as to see it distinctly. The object will appear directly opposite C; but if, keeping the object and the eye stationary, he draws the lens gradually to the left, the object will advance towards S, just as the parts of the lens between C and E are opposite to the eye, the displacement of the object being greatest or equal to CS, when the eye looks at it through the part nearest the edge E. If the reader looks at a similar object with his right eye through the lens R, he will, in like manner, by moving it, displace the object from E to S. Hence it follows that if he looks with his left eye at one of the pictures of a binocular slide placed opposite the lens L, and with his right eye at the other picture placed opposite the lens R, he will see the two pictures combined in one when the left eye looks through the aperture close to E, and the right eye through the aperture close to E'. The lenses thus perform simultaneously two important functions: While they displace the pictures, they also magnify them. This is all that the stereoscope does. It simply magnifies and unites two pictures, but it does not give them binocular relief. This is done by a beautiful property of two eyes, as will be seen when we treat of the Theory of the Stereoscope. If the two eyes, however perfect be their vision, had not the power of converging their axes to any other distance but that of the surface of the pictures, no relief whatever would have been seen.
The lenses of stereoscopes cut out of semi-lenses, or quarter-lenses, and are placed in tubes so that the line LE or RE' (fig. 6) is parallel to the line joining the two eyes, and they are prevented from turning round by a pin sliding in a groove, as already mentioned. Frequently, however, the pin gets out of the groove, and when the line LE or RE', or CE, CE', is not parallel to the line joining the eye, the picture viewed through the lenses rises above S (fig. 8), or falls below it, so that the instrument becomes useless. To prevent this the lenses have often been fixed, so that their distance cannot be altered to suit different distances in eyes, nor can they be adjusted to distinct vision by a motion of the tubes R L (fig. 7). The adjustment to distinct vision has in some instruments been obtained by making one half of the pyramidal box move within the other half; but, to avoid all these risks, whole lenses such as L, R' (fig. 8), should be placed in tubes as at R, L (fig. 7), having neither pin nor groove, and they may be pulled out, or pushed in, or turned round without affecting the performance of the stereoscope, which is the only possible use of whole lenses. In a whole lens every radius CE (fig. 8), when it is brought opposite the eye-hole, has the same displacing power, and must always displace the picture in the same direction; that is, the two pictures must always be united at the middle point S, and will be equally magnified if the two lenses have the same focal length, which is never so certain as when semi-lenses are used.
Among the various forms which have been given to the lenticular stereoscope, those invented and manufactured by Messrs Smith, Beck, and Beck, 6 Coleman Street, London, hold a high place. These gentlemen received a medal of the first class from the jury of the Paris Universal Exhibition of 1855, for their unrivalled achromatic microscopes, and if their stereoscopes had been exhibited on that occasion they would have been equally distinguished. The following is a brief description of their achromatic stereoscopes.
This instrument is shown in fig. 11, as taken out of its Smith and case A, and resting upon it as a stand, to which it is secured by the hooks C. It has a joint at B, and can be fixed in a vertical, horizontal, or any intermediate position by the brass arm D, which is made tight by the milled head E. Two other positions, namely, when the instrument is horizontal and the person sitting, and when the person is in a standing position, may be obtained by an additional cabinet, which may be used for holding the slides.
The two semi-lenses, which, being rounded, have the appearance of whole lenses, nearly an inch in diameter, are shown at HH. They are placed in tubes, which turn round in their fittings at G, and are in their proper position when the two arrows on the brass arms HH point to one another. In order to adjust the instrument to different eyes, the part of it containing the semi-lenses is moved nearer to, or farther from the stereographs or binocular picture or slide by two milled heads F. The distance of the semi-lenses from the picture may also be increased for aged persons, by drawing them out from their fittings at G. The slides are placed outside and under the two springs I, I.
When opaque slides are used, such as daguerreotypes, or those made of card-board, light is thrown upon them by the mirror O on the inside of the door, which moves round a hinge at P.
When transparencies are used the door O is closed, and the picture illuminated by a removable reflector K, packed in the case, but which, when in use, is held by two brass arms and springs M, and is turned into different positions round the hinge B. "The silvered, or other side, is used according to circumstances; but occasionally some kind of tinted paper, or other reflecting substance, is preferable for giving a tone to the picture; but, whatever it may be, it has only to be placed above the reflector or under the springs, or in place of the reflector, if it is of a sufficiently stiff material."
In order to exhibit paper stereographs or slides, either when mounted in the ordinary way, or when they are given as illustrations in books—such as those in the Stereoscopic Magazine—Messrs Smith, Beck, and Beck have contrived the following ingenious form of the lenticular stereoscope.
This instrument is intended to be held in the left hand by the handle A, as shown in fig. 10, the right hand being left at liberty either to shift the stereographs, or make the requisite adjustments. The semi-lenses are placed in the tubes C, C, and they are in their proper position when the arrow heads, or the brass rims D, D, point to each other. The adjustment to distinct vision is obtained by the milled head B, and a rack and pinion, and also by the motion of the tubes C, C.
The principal feature in this form of the stereoscope is the application of a mirror EE in such a position that, when the instrument is held facing the light, the stereograph is illuminated by reflected as well as direct light, so as to obliterate the shadows of irregularities on the surface of the paper. This mirror is shown at FF, in fig. 11, which is a front view of the instrument when placed above the stereograph in a book, the springs E, E being turned up to allow the brass frame H to rest upon the back. When a separate stereograph is to be examined, the springs E, E are turned round, and the stereograph placed between them and the frame. The two pictures in the stereograph are separated by a division G, which is made of ground glass, to prevent any shadow from being formed on the picture.
In this stereoscope, as well as in the other, the tubes C, C can be turned round slightly from their proper position as determined by the arrows, in order to correct errors which occasionally exist in the stereographs, or in order to unite the pictures when seen by individuals whose eyes are imperfect.
Various improvements have been made upon the reflecting stereoscope, for an account of some of which we must refer to Sir David Brewster's Treatise on the Stereoscope. The most ingenious and important of these, and one which is not described in that work, was invented by Mr Walter Hardie of Edinburgh, who has favoured us with the following description of it.
In this instrument the planes of reflexion are vertical instead of horizontal, as in Mr Wheatstone's. The pictures are placed head to foot, and inverted towards the observer (see fig. 14). The reflectors (either silvered glass or reflecting prisms) are fixed side by side over them, and at such an inclination to each other and to the pictures that the reflected image of the upper picture in the right-hand mirror, and that of the lower picture in the left-hand mirror, are both visible in the same direction ei, and appear to coincide in position. When these images are viewed together, each by its appropriate eye looking into the mirror which reflects it, they are binocularly united; and if the pictures are stereoscopic, the stereoscopic illusion is produced.
The precise relative positions of the mirrors and pictures may be stated thus: the smaller angle of the mirrors must be equal to half the difference between that of the pictures and 180°; and the line of intersection of their surfaces must coincide with that of the two planes which are respectively perpendicular to the surfaces of the pictures at their horizons. The pictures being head to foot with their horizons parallel, their central perspective vanishing-points ought respectively to lie 1½ inches (or half the width between the observer's eyes) on each side of the plane perpendicular to both picture-surfaces, and which passes through the point of contact of the inner edges of the mirrors. If the pictures are separate, by sliding one of them sideways, Mr Wheatstone's experiments in altering the inclination of the optic axes may be repeated. For ordinary use, however, it is more convenient to have both pictures on one piece of card-board, with a flexible fold or hinge between them, and with a thread stretched across from one to the other on each side, to hold them at the proper angle when in use (see fig. 13, which shows the most convenient mode of constructing the instrument).
The stereoscope is adapted for pictures of any size, from that usually made for the lenticular stereoscope up to the largest that can be conveniently used in Mr Wheatstone's; and it has this advantage over the latter, that it easily allows of both pictures being equally illuminated. The distance of the pictures from the mirrors is adjusted to their size (height) by sliding the frame which carries them (upwards for the smaller pictures, or downwards for the larger ones) upon the vertical stem which supports the reflectors (see fig. 13). To facilitate this adjustment, a divided scale of inches may be marked on the upright stem; and the height on this scale, at which each particular picture requires to be placed, may be noted on the back of it. The breadth of the field of view may be further extended, so as to admit broader pictures by interposing refracting prisms (thin edges inwards) between the eyes and the reflectors. For small pictures requiring to be placed at short distances from the reflectors, lenses or lenticular prisms may be used in the same way with advantage.
The stereomicroscope, invented by Mr Claudet, is an instrument which, as its name implies, exhibits an image of the apparently single, presenting the most complete stereoscopic illusion.
This instrument is founded on the principles of the phenomenon of relief of the image formed on the ground glass of the camera obscura, and which Mr Claudet seems to have been the first to notice and explain. Having tried to discover the cause of that phenomenon, he found that the image seen on the ground glass is not the same for both eyes; that when looking only with one eye it continually changes as we move the head, and, consequently, that the image visible for one eye is invisible for the other. The cause of this singular fact is, that the eye sees on the ground glass only the rays which are refracted by the lens in the direction of the optic axis, and that all the other rays are invisible.
This is owing to the perfect transparency of the ground glass, and to the arrangement of the molecules of its surface, by which the rays of light can—nearly all—pass through it without diverging from the surface, as it would be entirely the case if, instead of glass, the focussing screen was of paper or any other opaque substance, which, on account of this property of stopping the refracted rays on the surface, from which they diverge in all directions, present to both eyes at once all the different images produced by every part of the lens.
As regards the ground glass, it is evident that if each eye can see only the image produced by rays refracted in the direction of the optic axis, these rays must be those which, crossing each other on the ground glass, emerge from two opposite sides of the lens, consequently each eye having the perception of an image of different perspective, the result is perfectly stereoscopic. From the same cause, the effect is the converse of relief if we look with a pseudoscope.
The stereomonomoscope is only an application of this property peculiar to the ground glass, to present to each eye only the image which is refracted in the oblique direction of the optic axis. If, instead of the natural objects, we place before the camera the two pictures of a stereoscopic slide, and have each of these images refracted by a separate lens, in such a manner that they coincide on the ground glass of the camera obscura, each eye seeing one of the two images and not the other, we have the same relief as when looking at the slide in a common stereoscope.
If, by inverting the position of the two images before the camera, we place the right picture on the left, and the left picture on the right, we have the converse of relief, or the pseudoscopic effect; but it becomes again stereoscopic by looking with a pseudoscope.
The slide must be cut in two parts, in order to be able to give them the separation by which each picture can be refracted in the oblique direction capable of bringing its image on the centre of the ground glass. The two lenses also must be able to slide in a groove, in order to adjust their position according to the separation of the two pictures, and according to the focal distance of the lenses, which of course varies as we wish to increase or diminish the size of the image on the ground glass, and it can be increased to a considerable dimension, which is one of the greatest advantages of the stereomonomoscope. Nothing is more beautiful than the effect of one of these magnified pictures in perfect relief, and it can be examined by several persons at once.
The apparatus must be placed in a dark room, and the light of a window or lamp is admitted only through the openings of the pictures, if they are transparent views on glass, which are the best suited to the experiment. Views on paper, on silver plates, or positives on glass, requiring to be lighted by reflection, would necessitate a more complicated apparatus, and for this reason it is preferable to confine the stereomonomoscope to the exhibition of transparent pictures, which can be easily lighted by transmitted light.
Fig. 14 represents the arrangement of the lenses A, A', and pictures B, B', by which the pictures coincide in one at C. Fig. 15 is a view of the whole apparatus. DD DD, is the camera, and EE EE, a sliding frame containing the pictures, by which they can be placed before the lenses at the distance required for the size of the compound image on the ground glass, which is fixed on a box sliding in the camera for the adjustment of the focal distance.
In order to understand the theory of the stereoscope, the reader must be acquainted with the phenomena and theory of binocular vision, in which we obtain single vision with two eyes, and see objects in relief, or differences in distance from flat pictures upon the retina.
1. In all stereoscopic slides or double pictures, viewed through the stereoscope, the left-hand picture, when rightly taken, which it seldom is, is a correct representation of an object as seen with the left eye, and the right-hand picture a correct representation of it as seen by the right eye; or they are correct drawings of the object as taken by the rules of perspective, from two points whose distance is 2½ inches, or that of the two eyes. These two pictures, though almost perfectly similar to one another, are essentially different; and if the one was laid upon the other, so that any one point of the one, the tip of the nose, for example, coincided with a similar point in the other, no other points in the two pictures would coincide.
2. When we look at a solid object—at a marble bust, for example—the tip of the nose, the eye, and the ear, are at different distances from the observer's eyes. When we see distinctly the tip of the nose, we see it single, and the eye and the ear are seen indistinctly and double. We see, in short, only one point of any object distinct and single, and when we thus see it, the optic axes, as they are called, or lines passing through the centre of the pupil and the centre of the crystalline lens, are converged upon or meet at that point, and the visible distance of the point thus viewed is the distance of the point of convergence of the optic axis from the eye. Although we cannot see distinctly and singly the nose, the eye, and the ear at the same moment, yet such is the rapidity with which the two eyes converge their optic axes upon each of these points in succession, and upon every other point in succession, that every point of the bust is seen distinctly and singly, and at the distance corresponding to the distance of the point of convergence. The bust is, therefore, seen in relief.
3. We have already seen that the stereoscope simply displaces each picture, carrying the left-eye one to the right, and the right-eye one to the left, and laying the one above the other at a point half-way between each. It does nothing more, the stereoscopic effect, or the relief, being produced solely by the movements of the two eyes.
If the refractive displacement of the two pictures has been such as to unite the two corresponding points at the tip of the nose, whose distance we call 2½ inches, it will not have united the two corresponding points in the two eyes, the distance of which we may suppose to be 2½ inches; and still less will it have united the two corresponding points at the tip of the ear, which we may suppose to be 2½ inches, the eye and the ear points being respectively one-tenth and two-tenths of an inch distant.
When the two pictures thus combined by the lenses are viewed with both eyes, the tip of the nose will be seen distinctly at the distance of the point of convergence. The eyes will instantly, by means of their power of convergence, unite the separated points of the eyes, and then the still more separated points of the ears, running over every 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. The effect thus described may be represented as in fig. 16, where the points R, L
represent the two corresponding points in the nose united by the lenses; L'R' the corresponding points of the eye not united, but distant \( \frac{1}{3} \)th of an inch; and L'R" the corresponding points of the ear not united, but distant \( \frac{2}{3} \)th of an inch.
When the corresponding points united by the lenses are those of the eye, 2.5 inches distant, the effect upon the other points of the bust will be as shown in fig. 17, where
R'L' are the eye points united; R"L" the ear points brought nearer by \( \frac{1}{3} \)th of an inch, but still \( \frac{2}{3} \)th distant; and RL the nose points, the right-eye point having passed the left-eye point by \( \frac{2}{3} \)th of an inch.
When the corresponding points united by the lenses are those of the ear, the effect upon the other points of the bust will be as in fig. 18, where R"L" are the ear points united; R'L' the eye points, distant \( \frac{1}{3} \)th of an inch, the two having passed one another; and RL the nose points, distant \( \frac{2}{3} \)th of an inch, having passed one another still farther.
Now, in all these cases the points L'R", L'R' (fig. 16), R"L" (fig. 17), where L and R have not come up to one another, will be united by the eyes directing their axes to a point beyond the plane of the picture; while the points RL (fig. 17), and R"L", R"L" (fig. 18), which have passed one another, will be united by the eyes directing their axes to a point nearer the eye than the plane of the picture.
By whatever means the two pictures are laid upon one another,—whether by the straining of the eyes—directing their axes to points beyond the picture, or between the picture and the eye; by reflexion from mirrors or prisms, or by the refraction of prisms or lenses,—the relief, or stereoscopic effect, is produced in the manner we have now explained.
This theory of the stereoscope, or rather this explanation of the production of relief by the union of two dissimilar pictures, was first given by Sir David Brewster in the Transactions of the Royal Society of Edinburgh, where he has pointed out the incorrectness of the explanation given by Mr Wheatstone.
As no artist, however skilful, is capable of executing two pictures of any individual object, or group of objects, as they are seen by each eye separately, the stereoscope was of little value before the art of photography enabled us to take such pictures with the most perfect accuracy. If these pictures are not perfectly correct when taken upon a plane surface, their incorrectness, when combined so as to reproduce the object in relief, must be increased. In the exercise of the stereoscopic art, therefore, we must ascertain what is a true representation, of a statue for example, as seen with one eye through a pupil \( \frac{1}{3} \)th of an inch in diameter. It is doubtless a photograph taken with a lens \( \frac{1}{3} \)th of an inch in diameter. Every larger lens will give a photograph showing parts of the statue not visible to the eye, and consisting of a number of coincident pictures as seen from every point of the lens. But notwithstanding this defect, the artist is obliged to use a larger lens than this, in order to accelerate the process; but it is to be hoped that more sensitive materials may soon enable him to use a lens of the smallest size, and thus obtain perfectly correct right and left eye pictures. With the large lenses now in use, 2, 3, and even 4 inches in diameter, no correct stereoscopic pictures can be obtained.
But the right and left eye pictures must not only be taken with apertures as nearly as possible equal to that of the pupil, they must be taken by apertures placed at the same distance as that of the two pupils, that is, at the distance of 2\( \frac{1}{2} \) inches. All pictures taken otherwise are false, incorrect, and out of all accurate proportion. With this essential property, the stereoscopic camera cannot have lenses more than 2\( \frac{1}{2} \) inches in diameter, for they would just touch one another when of this size. With this information, we are now prepared to describe the binocular camera.
The camera must consist of two perfectly similar lenses, binocular in order to give two pictures of the same size; but as it is difficult for the most skilful optician to make two lenses of the same focal length and magnifying power, Sir David Brewster, who was the first to describe a binocular camera, proposed to construct it of achromatic semi-lenses, that is, of an achromatic lens cut in two, and so placed that the distance of the centres of the apertures may be 2\( \frac{1}{2} \) inches.
Several of these cameras were made in London, and give the most perfect stereoscopic photographs; but professional artists have not found it their interest either to use small lenses, to make each single photograph as perfect as possible, or to place lenses at the distance of 2\( \frac{1}{2} \) inches, in order to combine these pictures into proper relief. Their object has been to use lenses of such a size as to make the time of taking the picture as short as possible, and produce a startling degree of relief by placing the lenses at great distances. Although these stereoscopic pictures may please persons of neither taste nor judgment, yet they are most incorrect representations of nature, which men of science instantly discover. In all stereoscopic pictures taken at angles above that which corresponds to a distance of 2\( \frac{1}{2} \) inches, the distances are all drawn out, as it were. A street is made twice as long; and all buildings or objects stretching from the eye are enormously increased in length. The head of a portrait is drawn forward from the neck, and the dress of a lady is made to project forward from her bust.
As every artist places his lenses at the distance he pleases, and as very few employ the proper distance, the thousands of stereoscopic photographs, nay, the millions now circulating in Europe, have no real artistic or geometrical value. If we knew for certain that the distance of the lenses employed were correctly 2\( \frac{1}{2} \) inches, or even if we knew that it was 4, 6, 8, or 10 inches, we could deduce from each pair of pictures, by nice micrometrical measures, the actual forms of the statue or person, or building or landscape, which it represents, as the actual distances of the corresponding points in the two pictures would thus give us a measure of the distances of these parts from the eye; the distance between the tips of the nose, for example, and the points of the ears, and the pupils of the eyes, being measures of the distances of these points from any plane perpendicular to the eye, provided the distance of the lenses was known. A sculptor could thus obtain, even from one stereoscopic photograph, assistance in modelling a bust, and a surveyor might make an approximate plan of a landscape from even one correct stereoscopic representation of it.
A very great improvement in the art of taking single as well as binocular photographs has been made by Mr Thomas.
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1 Vol. 15, p. 349, 1843, or Phil. Magazine, vol. xxv., pp. 355, 479, May and June 1844. 2 This is demonstrated in a more popular manner in Sir D. Brewster's Treatise on the Stereoscope, chap. v. 3 See our art. Optics, vol. xvi. 4 For further information on this subject, see Sir David Brewster's Treatise on the Stereoscope, chap. viii.