The stereoscope

In order to understand the theory and construction of the stereoscope we must be acquainted with the general structure of the eye, with the mode in which the images of visible objects are formed within it, and with the laws of vision by means of which we see those objects in the position which they occupy, that is, in the direction and at the distance at which they exist.

Every visible object radiates, or throws out in all directions, particles or rays of light, by means of which we see them either directly by the images formed in the eye, or indirectly by looking at images of them formed by their passing through a small hole, or through a lens placed in a dark room or camera, at the end of which is a piece of paper or ground-glass to receive the image.

In order to understand this let h be a very small pin-hole in a shutter or camera, mn, and let ryb be any object of different colours, the upper part, r, being red, the middle, y, yellow, and the lower part, b, blue. If a sheet of white paper, br, is placed behind the hole h, at the same distance as the object rb is before it, an image, br, will be formed of the same ray and the same colours as the object rb. As the particles or rays of light move in straight lines, a red ray from the middle part of r will pass through the hole h and illuminate the point r with red light. In like manner, rays from the middle points of y and b will pass through h and illuminate with yellow and blue light the points y and b. Every other point of the coloured spaces, r, y, and b, will, in the same manner, paint itself, as it were, on the paper, and produce a coloured image, byr, exactly the same in form and colour as the object ryb. If the hole h is sufficiently small no ray from any one point of the object will interfere with or mix with any other ray that falls upon the paper. If the paper is held at half the distance, at b′y′ for example, a coloured image, b′y′r′, of half the size, will be formed, and if we hold it at twice the distance, at b″r″ for example, a coloured image, b″y″r″, of twice the size, will be painted on the paper.

As the hole h is supposed to be so small as to receive only one ray from every point of the object, the images of the object, viz., br, b′r′, b″r″, will be very faint. By widening the hole h, so as to admit more rays from each luminous point of rb, the images would become brighter, but they would become at the same time indistinct, as the rays from one point of the object would mix with those from adjacent points, and at the boundaries of the colours r, y, and b, the one colour would obliterate the other. In order, therefore, to obtain sufficiently bright images of visible objects we must use lenses, which have the property of forming distinct images behind them, at a point called their focus. If we widen the hole h, and place in it a lens whose focus is at y, for an object at the same distance, hy, it will form a bright and distinct image, br, of the same size as the object rb. If we remove the lens, and place another in h, whose focus is at y′, for a distance hy, an image, b′r′, half of the size of rb, will be formed at that point; and if we substitute for this lens another, whose focus is at y″, a distinct image, b″r″, twice the size of the object, will be formed, the size of the image being always to that of the object as their respective distances from the hole or lens at h.

With the aid of these results, which any person may confirm by making the experiments, we shall easily understand how we see external objects by means of the images formed in the eye. The human eye, a section and a front view of which is shewn in Fig. 5, a, is almost a sphere. Its outer membrane, abcde, or mno, Fig. 5, b, consists of a tough substance, and is called the sclerotic coat, which forms the white of the eye, a, seen in the front view. The front part of the eyeball, cxd, which resembles a small watch-glass, is perfectly transparent, and is called the cornea. Behind it is the iris, cabe, or c in the front view, which is a circular disc, with a hole, ab, in its centre, called the pupil, or black of the eye. It is, as it were, the window of the eye, through which all the light from visible objects must pass. The iris has different colours in different persons, black, blue, or grey; and the pupil, ab, or h, has the power of contracting or enlarging its size according as the light which enters it is more or less bright. In sunlight it is very small, and in twilight its size is considerable. Behind the iris, and close to it, is a doubly convex lens, df, or ll in Fig. 5, b, called the crystalline lens. It is more convex or round on the inner side, and it is suspended by the ciliary processes at lc, lc′, by which it is supposed to be moved towards and from h, in order to accommodate the eye to different distances, or obtain distinct vision at these distances. At the back of the eye is a thin pulpy transparent membrane, rr o rr, or vvv, called the retina, which, like the ground-glass of a camera obscura, receives the images of visible objects. This membrane is an expansion of the optic nerve o, or a in Fig. 5, a, which passes to the brain, and, by a process of which we are ignorant, gives us vision of the objects whose images are formed on its expanded surface. The globular form of the eye is maintained by two fluids which fill it,—the aqueous humour, which lies between the crystalline lens and the cornea, and the vitreous humour, zz, which fills the back of the eye.

But though we are ignorant of the manner in which the mind takes cognizance through the brain of the images on the retina, and may probably never know it, we can determine experimentally the laws by which we obtain, through their images on the retina, a knowledge of the direction, the position, and the form of external objects.

If the eye mn consisted only of a hollow ball with a small aperture h, an inverted image, ab, of any external object ab would be formed on the retina ror, exactly as in Fig. 4. A ray of light from a passing through h would strike the retina at a, and one from b would strike the retina at b. If the hole h is very small the inverted image ab would be very distinct, but very obscure. If the hole were the size of the pupil the image would be sufficiently luminous, but very indistinct. To remedy this the crystalline lens is placed behind the pupil, and gives distinctness to the image ab formed in its focus. The image, however, still remains inverted, a ray from the upper part a of the object necessarily falling on the lower part a of the retina, and a ray from the lower part b of the object upon the upper part b of the retina. Now, it has been proved by accurate experiments that in whatever direction a ray aha falls upon the retina, it gives us the vision of the point a from which it proceeds, or causes us to see that point, in a direction perpendicular to the retina at a, the point on which it falls. It has also been proved that the human eye is nearly spherical, and that a line drawn perpendicular to the retina from any point a of the image ab will very nearly pass through the corresponding point a of the object ab,[31] so that the point a is, in virtue of this law, which is called the Law of visible direction, seen in nearly its true direction.

When we look at any object, ab, for example, we see only one point of it distinctly. In Fig. 5 the point d only is seen distinctly, and every point from d to a, and from d to b, less distinctly. The point of distinct vision on the retina is at d, corresponding with the point d of the object which is seen distinctly. This point d is the centre of the retina at the extremity of the line aha, called the optical axis of the eye, passing through the centre of the lens lh, and the centre of the pupil. The point of distinct vision d corresponds with a small hole in the retina called the Foramen centrale, or central hole, from its being in the centre of the membrane. When we wish to see the points a and b, or any other point of the object, we turn the eye upon them, so that their image may fall upon the central point d. This is done so easily and quickly that every point of an object is seen distinctly in an instant, and we obtain the most perfect knowledge of its form, colour, and direction. The law of distinct vision may be thus expressed. Vision is most distinct when it is performed by the central point of the retina, and the distinctness decreases with the distance from the central point. It is a curious fact, however, that the most distinct point d is the least sensitive to light, and that the sensitiveness increases with the distance from that point. This is proved by the remarkable fact, that when an astronomer cannot see a very minute star by looking at it directly along the optical axis dd, he can see it by looking away from it, and bringing its image upon a more sensitive part of the retina.

But though we see with one eye the direction in which any object or point of an object is situated, we do not see its position, or the distance from the eye at which it is placed. If a small luminous point or flame is put into a dark room by another person, we cannot with one eye form anything like a correct estimate of its distance. Even in good light we cannot with one eye snuff a candle, or pour wine into a small glass at arm’s length. In monocular vision, we learn from experience to estimate all distances, but particularly great ones, by various means, which are called the criteria of distance; but it is only with both eyes that we can estimate with anything like accuracy the distance of objects not far from us.

The criteria of distance, by which we are enabled with one eye to form an approximate estimate of the distance of objects are five in number.

1. The interposition of numerous objects between the eye and the object whose distance we are appreciating. A distance at sea appears much shorter than the same distance on land, marked with houses, trees, and other objects; and for the same reason, the sun and moon appear more distant when rising or setting on the horizon of a flat country, than when in the zenith, or at great altitudes.

2. The variation in the apparent magnitude of known objects, such as man, animals, trees, doors and windows of houses. If one of two men, placed at different distances from us, appears only half the size of the other, we cannot be far wrong in believing that the smallest in appearance is at twice the distance of the other. It is possible that the one may be a dwarf, and the other of gigantic stature, in which case our judgment would be erroneous, but even in this case other criteria might enable us to correct it.

3. The degree of vivacity in the colours and tints of objects.

4. The degree of distinctness in the outline and minute parts of objects.

5. To these criteria we may add the sensation of muscular action, or rather effort, by which we close the pupil in accommodating the eye to near distances, and produce the accommodation.

With all these means of estimating distances, it is only by binocular vision, in which we converge the optical axes upon the object, that we have the power of seeing distance within a limited range.

But this is the only point in which Monocular is inferior to Binocular vision. In the following respects it is superior to it.

1. When we look at oil paintings, the varnish on their surface reflects to each eye the light which falls upon it from certain parts of the room. By closing one eye we shut out the quantity of reflected light which enters it. Pictures should always be viewed by the eye farthest from windows or lights in the apartment, as light diminishes the sensibility of the eye to the red rays.

2. When we view a picture with both eyes, we discover, from the convergency of the optic axes, that the picture is on a plane surface, every part of which is nearly equidistant from us. But when we shut one eye, we do not make this discovery; and therefore the effect with which the artist gives relief to the painting exercises its whole effect in deceiving us, and hence, in monocular vision, the relievo of the painting is much more complete.

This influence over our judgment is beautifully shewn in viewing, with one eye, photographs either of persons, or landscapes, or solid objects. After a little practice, the illusion is very perfect, and is aided by the correct geometrical perspective and chiaroscuro of the Daguerreotype or Talbotype. To this effect we may give the name of Monocular Relief, which, as we shall see, is necessarily inferior to Binocular Relief, when produced by the stereoscope.

3. As it very frequently happens that one eye has not exactly the same focal length as the other, and that, when it has, the vision by one eye is less perfect than that by the other, the picture formed by uniting a perfect with a less perfect picture, or with one of a different size, must be more imperfect than the single picture formed by one eye.