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STEREOSCOPE (Gr. orepeos, solid, (TKOTTCIV, to see) - 1 The fundamental property of stereoscopic vision, or simultaneous vision with both eyes, is the direct perception of the relative distances of near objects. Of course, ideas of the different distances of objects also occur in vision with a single eye, but these are the result of other experiences and considerations. These representations are also not always unequivocal (see fig. i). For instance they may arise from the former knowledge of the shape and size of a distant object, from the partial covering of one object by FIG. i. another; and they very often occur where stereoscopic observation fails; this latter is involuntary, i.e. the observer is unconscious of it. We will now investigate the conditions necessary for the perception of depth.

If the head is held still only one portion of space can be observed stereoscopically. The single eye, when moved, surveys, including indirect vision, a field which measures 180 in a horizontal direction, and 135 in a vertical direction. The two fields overlap and a smaller conical space is formed, with the nose as vertex (B V S in fig. 2), in which both eyes can see simultaneously; and outside this space stereoscopic vision is impossible. The shape and size of this space are very different in men and animals. According to Armin Tschermak the horizontal extent of the space surveyed with both eyes is only 34 in a rabbit as compared with 90 in man, 1 5 in a fowl and about 5 in a carp (measured in water). There is a further difference between the eyes of men and animals. The optic axis of the eye is the line joining the centres of the curves, but the direction in which the eye can see most clearly does not always coincide with this, being determined by the spot on the retina which is most susceptible to light, the so-called yellow spot (Fovea, F in fig. 2). In man this spot is still near the axis, although not always exactly on it. It is not perfectly known how it is situated in animals, but in many the axes o: the eyes diverge (especially strongly in geese), and the portions of the retina utilized in stereoscopic vision lie far distant from the axis, as in many animals the eyes are only slightly movable. Every time that the eyes are directed on one spot (P in 1 The subject of stereoscopy has been extensively developed by the author of this article, who, curiously enough, having lost the sight of one eye through an accident, could no more enjoy the beautier of stereoscopic sight. ED.

fig. 2) this point is seen simply, together with a number of other points which together form the so-called " horopter." According to Joh. Miiller, Helmholtz, Hering, Volkmann and others, these are those points of the object-space (e.g. Q and R n fig. 2), whose images fall on identical or corresponding spots on the retina, by which are meant those points on the retina whose nerve filaments are united and which are equidistant in the same direction from the centre of the yellow spot (see EYE; VISION). The horopter varies according to the position of the fixed spot in the object-space; for example, it is the ground FIG. 2.

itself for a man standing erect and looking straight ahead. All object-points situated outside the horopter fall on points of the retina which are not identical, but the two images are only seen as real double images in exceptional cases. As a rule the effect is that these points are also seen simply, but at other distances than that of the fixed point P. The differences of the images arise in the moving of the image-points in the direction of the connecting line of the two eyes. For this reason the eyes cannot recognize the space between parallel shining telegraph wires if the connecting line of the two eyes be parallel to the wires, whilst the perception of the depth occurs involuntarily if the connecting line of the eyes is more or less perpendicular to the wires. These differences of images which have been mentioned are therefore necessary and are sufficient for the perception of depth. The explanation that the perception of depth was due to a difference between the two retinal images was first given by Ch. Wheatstone in 1833; but it was contradicted by E. Briicke (1841), Sir David Brewster (1843) ar >d others, who stated that when observing an object the angle of convergence of the axes of the eyes continually changed, and through this and also by the exertion of the muscles and the accommodation of the eye there was a simultaneous touching of the object, which gave rise to the perception of its depth. This latter theory, however, was contradicted by H. W. Dove, who showed that a stereoscopic viewing was also possible with momentary illumination of the object; and still less does it agree with the fact, to which Wheatstone first called attention, that facsimiles also have a stereoscopic influence, in spite of the fact that the images retain their position on the retina unchanged. Numerous experiments show the same result, and it follows that even a change of the angle of convergence is not always observed as a change of depth.

There are two kinds of stereoscopic vision, direct and indirect, according to whether the point seen indirectly, e.g. H in fig. 3, is compared with the fixed point P, or with another point seen indirectly, e.g. ] in fig. 3. In both kinds of stereoscopic vision the exactness of the observation of the depth is greater as the point J approaches H, and the point H approaches P. As a matter of fact a man's eyes are naturally never perfectly still. They move in their sockets, and the point P, where the axes intersect, is continually changing. Direct stereoscopic vision arises from indirect stereoscopic vision and vice versa, and the accuracy of the discernment of the depth increases and decreases. As in this the eye does not revolve round its lens but round the centre of the Sphere situated 10 mm.

FIG. 3.

behind it, the entrance-pupil of the eye moves slightly to and fro and up and down, and many experiments have been made to produce a perception of depth for a single eye from the relative movements of the images consequent on this motion. As these movements of the images only occur in indirect vision, it can be understood they are not seen by most people. This, however, cannot be regarded as an actual perception of depth, because these viewings necessitate a consideration for each individual interpretation, which is quite foreign to stereoscopic vision.

Indirect stereoscopic vision is of great importance. It makes it possible to recognize any sudden danger or obstacle outside the direction in which one is looking. Even with the stereotelemeter (see below) the position of the range through which, for example, a bird flies, could not always be accurately given, if one were solely dependent upon direct stereoscopic vision. If the attention and eyes are directed upon a certain object, as, for instance, in manual labour and in measuring the imagespace with the so-called " travelling mark " on the stereocomparator, then direct stereoscopic vision only is concerned.

Stereoscopic vision is in many ways similar to the monocular observation of a preparation under the microscope, and yet there is a great difference. In an unchanged focused microscope it cannot be distinguished which of the indistinct objects are above and which are below the plane focused for. In stereoscopic vision, however, this can be seen directly. How does this happen? Why does the point H in fig. 3 appear behind and the point V in front of the point P when both eyes are fixed on the point P? As is shown in fig. 3 the image-points on both sides lie further apart for H or nearer together for V than the image-points for P, and for all the points on the horopter (Q, R, S, T etc.), whether the points H and V are situated inside or outside the horopter. In other words, if the point H be formed in the object-space by the moving of the related points Q (or R) towards H, then a movement of the image-point takes place in the right eye (or the left), in both eyes in the direction of the nose, so long as the point H is outside the horopter. On the contrary an external movement of the imagepoint, i.e. towards the temples, takes place when the points S and T are substituted by the point V situated inside the horopter. This differentiation of the retinal images of the points H and V respectively inside and outside the horopter must suffice, and the question as to how the idea of space is conveyed to the brain is a physiological and psychological subject.

If the images of the line PH in both eyes (or of the line PV) are very different in length, the double images of the point H (or V) are seen without great attention. But the stereoscopic effects are in these cases always the same as before. There is, however, an exception in which the observer sees only two images and in which stereoscopic observation is completely excluded. This exception is important because it occurs in the space in the immediate proximity of P. If for example the second point (H' in fig. 3) is situated behind or in front of the point P, so that it falls between the two optic axes^or on one of them, then only double images can be seen, either of P or of H', according to whether the optic axis cuts at P or H', or double images of both points if the optic axes intersect at any other point of the line PH', but the representation of the difference of depth of the two points P and H' is never obtained.

This fact can be easily realized if a stick, e.g. a lead pencil, be held before the eyes of an observer with good stereoscopic sight so that its lengthwise axis falls exactly on a point between the eyes or in the middle of one of the two eyes. The double images can be seen still more clearly if two small balls on thin threads are suspended behind one another so that their connecting line retains the position mentioned above. In this experiment it can be seen directly how inconvenient these double images are to the observer. He involuntarily tries to evade them by moving the head. The reason for this is that, when P (or H') is fixed, the images of H' (or P) are always separated from one another by the centre of the yellow spot. The distances of the two images from the yellow spot have consequently opposite signs, whilst for all other objects (e.g. H) which lie outside the two axes the distances have the same signs. The difference of the sign is, however, not alone decisive, for if the connecting line PH' is moved a little higher or lower out of the plane FPF the signs remain different, but the stereoscopic effect is immediately regained. Therefore in all cases in which the connecting line PH' is seen with one eye as a point and with the other as a line, or with both eyes as a line, but from two diametrically opposite sides, there is no stereoscopic effect, but double images are seen ; and that for stereoscopic observation it is essential to see the connecting line PH' with both eyes simultaneously from one and the same side, from above or below, from the left or the right. This condition is provided for in the stereotelemeter by the arrangement of a zigzag measuring scale, so that the connecting-line of the marks slightly ascends. Care must be taken when using this instrument (as also when using any stereoscopic measuring instrument) that the index hangs close to or above the object to be measured, so that the latter is only touched and in no way covered by the mark.

The power of perception of depth in man is most accurate. This has been ascertained by the approximately equal keenness of vision of all normal-sighted people and by the interpupillary distance. The angle which serves as a measure for the keenness of vision is that under which appear two neighbouring points of the object-space which are still seen by the single eye as a double point; according to the older experiments of Helmholtz, this angle is about i'. When measured on the retina the keenness of vision is determined by the diameter of the nerve filaments situated in straight rows close to one another in the fovea (fig. 4). The diameter of these filaments amounts to roughly 0-005 mm., or in angular measure i'. More recent experiments for keenness of vision and power of perception of depth have given considerably higher values (Wiilfmg, Pulfrich, Heine and others); thus Pulfrich in 1899, when first introducing stereoscopic instruments for measuring distance, proved that as a rule persons with normal eyes have a power of perception of depth of 10" and still less in unrestricted vision . This is explained as follows (Hering, Heine) :

It is unimportant for perception where the filament mentioned above is illuminated. In order to see two objects lying close to one another it is not essential that the two image-points should be separated from one another by the distance of the two nerve filaments of the eyes. This happens whenever the line separating two objects passes through the two points (see fig. 4). It is natural that the perception of depth has no fixed limits, for the position of the images shown in fig. 4 changes with the movement of the eyeball, and the closer the two points are to one another, the more FIG. 4. ' rarely it occurs. If the angle of convergence of the optic axes = A, the (average) distance between the eyes 6=65 mm., 5 = j' relatively = 1 17000 (the perception of depth easily attained by normal sight) and E=the normal distance of the point P from B in fig. 2, then from E = B/A, the change of depth dE gives:

dE = B . S/A 2 = E . 8/A = E" . S/B.

If the angle A has the value 5 then all perception of depth ceases. At this distance objects are only still distinguishable from those lying behind them, which together form a surface but cannot always be seen as a surface because our representations of the depths of distant objects are not conclusively controlled by stereoscopic sight. This distance is called the radius of the stereoscopic field, and is calculated by the formula R = B/8, whence R=45O metres. From the above formulae it can be directly seen that the variation dE increases with E 2 , and the proportional variation dE/E increases with E. The numerical values can be easily calculated when either A or E is given thus:

dE/E = a/A or dE/E = E/R.

The limits of stereoscopic vision defined above can be extended and under the name of " stereoscope " every binocular instrument is included which serves this end. Those instruments should first be mentioned which have restored the more or less lost power of stereoscopic vision. It is necessary for those with normal sight to wear spectacles when the eyes cease to accommodate themselves to objects near at hand. Spectacles which only cover he lower half of the eye and leave the upper A! A! FIG. 5.

half free to look out into space are the best. FOF those who have been operated on for cataract, and for excessively shortsighted persons, the " telescope-spectacles " devised by M. v. Rohr (of Zeiss, Jena) are a great assistance. There are two xxv. 29 methods of extending the limits of stereoscopic vision and of increasing the accuracy of the perception of depth, (i) by augmenting the keenness of sight by the aid of a telescope or microscope, and (2) by increasing the interpupillary distance by several reflections after the plan shown by Helmholtz in his mirror stereoscope (1857) (see fig 5). When binocular telescopes and microscopes are used, erect images are formed when the two instruments are contiguous. If this is not the case, the order of depth is reversed and the same false or pseudoimages are formed as when the pictures in a stereoscopic view are interchanged or a correctly combined stereoscopic picture is observed in a so-called pseudo-stereoscope. If, however, in this case the axes of both instruments intersect in front of the eyes, then reversed pictures are obtained, but the correct order of depth is recovered.

Telescope magnification (m times) and base magnification (n times) bring the radius R of the stereoscopic field to m or n times respectively the value above given, and if both are simultaneously active to mn times. The errors for a certain distance E are accordingly reduced to l/mn. Of course these expedients do not increase the capability of the observer, but the values of the convergence angle A and 8 in the object-space are different. It is therefore quite natural that the three-dimensional images, which appear in the binocular vision-space of the observer, vary with reference to their dimensions and the distance of the separate parts from each other. In this respect the action of the base magnification is fundamentally different from that of the telescope magnification. Both bring the objects m or n times respectively nearer to the observer, but in the first case the areal dimensions are diminished in the same proportion as the distances are lessened, whilst in the other case the real dimensions remain unchanged. In the first case the threedimensional image is a model proportionately diminished in all its dimensions and brought nearer to the observer: in the other case the objects appear pushed together to the front like the wings of a theatre. The remark made in Helmholtz's Physiological Optics that when m = n the three-dimensional image would look like the object seen without any instrument at a distance of i/ is consequently not correct. What is remarkable is that this observation, to which as a so-called " Helmholtz rule " great importance was for a long while attached, and to a certain extent still is, does not correctly express the views of Helmholtz, which he states very clearly in his earlier essay on the tele-stereoscope, and which agree with the explanation here given.

Spectacles and binocular telescopes were the first binocular instruments (see BINOCULAR INSTRUMENTS). The latter with chromatic lenses had already been constructed in the 17th and 18th centuries. The Dutch double-telescope (opera. glasses), which were almost exclusively used up to the 'nineties of the i pth century, were introduced in the 'thirties by Fr. Voigtlander. The binocular microscope appeared in the early 'fifties. The introduction of the Porro prism (four reflections with reversion of the picture and lateral transposition of the rays) by Abbe in 1893 was of great importance for the binocular telescope and microscope. It led to the construction of the prism field-glasses and other telescopes which, in comparison with the Galileo binocular telescopes till then in use, not only had a considerably increased perception of depth but also a substantially larger field of vision. Similarly by inserting the Porro inverting system between the eyepiece and the objective, the binocular microscope constructed by H. S. Greenough and S. Czapski was produced. Recently binocular glasses (after Fritsch and Zeiss) have come into use for slight magnifications, in which, following the example given by Wenham (1853), the interpupillary distance and the angle of convergence are diminished by four reflections (the course of the rays reversed as in fig. 5).

All of the instruments mentioned above v l pi ^1 Vi PI h, ""R FIG. 6.

are used exclusively for the observation of three-dimensional objects with two eyes. Wheatstone (1838) first showed that the same spatial impression could be produced by two views of the object taken from two different points and he called the instrument a stereo scope. Let us imagine in fig. 6 a plane Fi' Fi between the twc eyes Ai and A2 and the points P, H and V in the object-space and on this plane the perspective projections of P, H and V ' produced towards AI and A ? as, for example, by photographing on the plates Fi and F 2 with objectives Oi and O 2 at Ai and A 2 then th> object can be taken away and we obtain from the projections th< same spatial effect as when observing the object itself. The change of accommodation of the eye which, however, has no influence on the power of perception of depth, is excluded, and a furthe difference (according to I. I. Oppel, 1854) is that in unrestrictec vision the image-points not situated on the yellow spot undergo slight displacement in consequence of the difference of the position of the pupil and of the centre of rotation of the eye, which is taken as the centre of projection. This can in no way be imitatec in the pictures. In order to obtain a stereoscopic effort from such pictures apparatus is not always necessary. When the pictures L and R in fig. 6 are at a distance equal to that of distinct vision, the stereoscopic effect can be obtained by observing them when the optic axes of the eyes are parallel, and if the pictures are interchanged, when the axes intersect. The second of these methods, which were discovered by Whcatstone, was later widely used for the stereoscopic observation of large wall pictures.

The 1852 model of the Wheatstone stereoscope is shown diagrammatically in fig. 7. This differs from the original model in that the pictures L and R can be placed at different inclinations to the mirrors Si and 52 and at different distances from them in order to observe the pictures under exactly the same inclination of the image and the same angle of convergence as when the picture was taken. Photographs with a large base line and converging axes were then often taken (in Germany first by L. Moser). This mirror stereoscope had no practical result worth mentioning on account of its awkward shape and of the difficulty in obtaining equal illumination of both pictures. It was also inconvenient that the pictures had to be placed separately and reversed in the apparatus. These difficulties are for the greater part avoided in the L. Pigeon R (Nancy, 1905) new mirror-stereoscope for large pictures, which can be purchased in book form. Fig. 8 shows diagrammatically the arrangement by which one picture is seen direct and the other in a mirror (H. W. Dove, Sir David Brewster and W. Rollmann). The disadvantage attached to this, that the picture observed in the mirror must be reversed, can according to Pulfrich 1 be obviated by rotating the correct picture through 180' T' T T" /**""-. / fi, H H'"" 7^><^., h ' ^*^ f, plane of the picture ^v^j FIG. 7.

A, A, FIG. 8.

in its own plane and placing it in the position of the picture L and by using a so-called roof-prism in the place of the mirror.

Incorrect stereoscopic effects easily arise when using pictures. If for instance the distance of a picture from the centre of projection is different at the time of observation from what it was when the photograph was taken (see fig. 9), objects appear to be either too much in relief or too flat even in monocular vision, just as when looking first through the objective of a telescope and then through the eyepiece. An excellent example is provided by the stereoscopic observation of the Moon, first performed by Warren de la Rue (1858) to show that the three-dimensional image is modified by altering the angle of convergence and by placing the pictures obliquely. If the pictures obtained with converging axes are placed further apart on the same plane, the stereoscopic image of the moon has the shape of an egg; this, however, immediately disappears and changes into an approximate Sphere, if the picture be broken in the middle and both sides bent back. If the pictures are observed, as by Warren de la Rue, in a Wheatstone stereoscope under exactly the same conditions as when the photographs were taken, the impression of a Sphere is obtained.

M. von Rohr (Die binocularen Instrumente, 1907) drew attention to che optics of the older stereoscopists and in particular to the works of Wheatstone, and it is to be regretted that so 1 This fact is published here for the first time.

little notice was taken of these older works during the recent development of most binocular instruments. It would, however, be erroneous to demand that the above-mentioned conditions for the observation of three-dimensional images should always be considered. This is impossible, for example, in the stereocomparator in which the three-dimensional image is only seen in portions, and never all at once. Neither does it concern stereoscopic measuring instruments, and it is a curious coincidence that the stereo-planigraph (see fig. 15) constructed after Wheatstone's stereoscope, and correct as to the so-called orthomorphy of the three-dimensional image, was of no use as a measuring instrument.

A lens-stereoscope invented in 1849 by Sir David Brewster and constructed by J. Duboscq is very largely used. The causes of its success were its convenient form and the fact that a series of adjusted stereoscopic pictures (landscapes, machines, FIG. 9.

etc.) could be observed in rapid succession. The Brewster stereoscope, by making an easy observation of stereoscopic pictures possible when the distance between identical points on both pictures was considerably greater than that between the observer's eyes, supported to a certain extent the inclination of photographers not to detract from the pictures. If the lenses shown in fig. 10, on the focal plane of which JT/_ llj the stereoscopic image is * formed, are large enough, and the distance between the image-points hi and h 2 is not greater than the distance between the centres of the two lenses (avoiding the divergence of the axes of the eyes), ;hen the distance between the eyes is secondary and .he observer sees the distant points with the axes of the eyes parallel. These apparent advan- FIG. 10.

ages, however, are counteracted by the defect that the picture seen through the lenses is eccentric, and consequently an ncorrect impression of the picture is obtained, and an alteration n the three-dimensional image occurs.

Wheatstone showed later in his controversy with Brewster that his disadvantage in the lens-stereoscope could be avoided by v t fi h g i...

v, P.IU f ' ' R f f \ \ * P, h.

v t p, h, h, p, vi hj pa Vf n ' ' > > h,p,v, FIG. n.

djusting the lenses and distant points to the distance between he observer's eyes. This same condition was fulfilled in the double-verant " constructed by v. Rohr and A. Kohler (1905), in which the lenses, in accordance with A. Gullstrand's rule, arc so arranged that the centre of rotation of the eye always coincides with the nodal point of the lenses. If every one had the same interpupillary distance there would be nothing more perfect than this stereoscope.

_ If in fig. 6 the two pictures L and R are interchanged in both pictures (a or b in fig. n), then the image-points for H are closer together than those for V; thus in stereoscopic vision H appears in front of P, and V behind it. No change is made to the reliel by turning the picture upside down (c and d in fig. 11). In fig. lid, the pictures are in the same positions as when the photographs are taken (Fi, Fj in fig. 6). Obviously transparent pictures can be easily reversed ; in other cases it must be effected by mirrors ( Wheatstone, Dove and others) or by an erecting reflection prism. The original unbroken plate (fig. I id) can be seen in the pseudo-stereoscope shown in fig. 12, and the correct relief is obtained if it is rotated about the connecting line of the two pictures before placing in the stereoscope. If a symmetrical body be observed in the pseudo- stereoscope, for example a pyramid, the relief is still reversed. But if a prism be dispensed with the object appears flat, and a plane drawing appears in relief.

These pseudo-stereoscopic phenomena are of the greatest importance for the study of the principles of stereoscopy, for they demonstrate that the perception of depth can be aided by a direct presentation and hindered by a reverse presentation. If a plate of the dolomites, for example, with a large base line, arranged as in I ia and I ib is taken, and the apparatus and the eyes are directed upwards, then the pseudomorphic image in space looks like the roof of a stalactite cave. On the other hand, when arranged as I ic and I id the image appears correctly represented, but it is a little more difficult to see the horizon in the foreground of the pseudomorphic image. Reference can only be made here to the physiologically interesting phenomena of colour-tones, which are a result of the chromatism of the eye and occur in monocular and binocular vision (Dove and, more recently, A. Bruckner).

A comparatively simple solution to the problem of putting pictures seen in a stereoscope in motion is provided in the mutoscope for a single observer. The other problem to make one stereoscopic picture visible to several people simultaneously can be met in various ways, most simply (according to Rollmann [1853] and D'Almeida [1858]) by portraying the two stereoscopic pictures in different colours one over the other, and giving each observer spectacles of different coloured glass for each eye, with which it is only possible to see one picture with each eye. Another method suggested by I. Anderton (1891), in which polarization and a Nicol prism must be used to separate the pictures, has met with little success, and F. E. Ives's novel proposal (1903) to separate the pictures when being taken and also observed by a ruled grating placed immediately in front of the photographic plate is not practicable. A method devised by D'Almeida, which depended upon the alternate visibility of the two pictures, demands a mechanism for each observer, exactly synchronous with the intermittent illumination. This principle was successfully adopted by J. Mackenzie Davidson and H. Boas (1900) for a direct stereoscopic observation of Rontgen radiographs. Immediately after the discovery of the Rontgen rays in 1895, E. Mach made stereoscopic investigations of these radiographs.

The development of stereoscopy has in no way been uniform; on the contrary, a long period, during which practically no interest was taken in stereoscopy or stereoscopic phenomena, was preceded during the middle part of the 19th century by a period of universal interest. The reason for this was not so much the realization of the defects of the stereoscopes in themselves, and the trivial manner in which they were put on the market, as, for example, a closing stereoscope containing confectionery, as the fact that the public did not know how to make use of the pictures seen in the stereoscope. This state of affairs was altered when Zeiss, of Jena, as a result of the investigations of E. Abbe and C. Pulfrich, succeeded in constructing apparatus which made it possible to measure the three-dimensional images.

The stereotelemeter, constructed after H. de Grousilliers' idea, appeared in 1899. This is a double telescope with the distance between the objectives increased, and a number of rows of marks placed in the plane of the image which appear as ' M in <x> i real objects floating at fixed distances above the landscape, from which the distances of the objects in the view can be easily read. In 1905 Pulfrich devised a method of stereoscopic measurement which is specially interesting from a physiological point of view, but which can only be employed for isolated objects, such as beacons, signals, etc. This method has the peculiarity that no marks are necessary for the measurement. The binocular telescope is so arranged that it always produces two three- dimensional images of the object which is to be measured close to one another, which as a rule are seen as though they were at different distances and of different sizes. The measurement is made by causing the difference of relief of c- the two images to disappear either by bringing the instrument nearer to the object or by readjusting the apparatus. The equal size of the two three-dimensional images can be regarded as a criterion of their equal distances; and it is of further advantage to the method that the images to be compared are equal as to definition andfj colour.

A consequence of these instruments, which are chiefly important for military surveying, was the Pulfrich stereocomparator devised in 1901. The stereoscopic measuring machine invented by H. G. Fourcade of Capetown (1902) is similar to this in many points. These instruments inaugurated the successful measurement of the distances of distant objects and the uses of stereoscopy were consequently increased. Measurement is not made of the objects themselves, but on photographic plates which are taken with special instruments field- and stand-phototheodolites at the extremities of a baseline which is always selected according to the distance of the object (Y,=E.-f)

o, > ,. P/ o, ll Jtereo - Com par a fo! fuifA the marfo Jtli *nd ffli A, A, FIG. 14.

and the exactitude of measurement needed. For measuring the pictures a binocular microscope, adjusted to the dimensions and the listance between the two plates, is used, and a fixed mark is placed in each image plane which combine in binocular view to a virtual mark in the three-dimensional image. If the plates are correctly adjusted, by moving the plates perpendicular to one another and by altering the distance of the plates from one another, this so-called " travelling mark " can be placed on any point of the landscape, and then used for the measurement of solidity of the objects, or the production of plans and models, just as formerly, for example, the measuring staff was used for geodetic observations, with the difference that in the stereocomparator the mark is regulated by the observer only and is not hindered in its movements by any undulations, etc., of the land.

Fig. 13 shows how the lateral movement of the mark m 2 is transformed in a movement towards and away from the observer in the three-dimensional image M. Fig. 14 shows the theory of measuring a stereophotograph. The axes are horizontal when the photograph is taken, and the plates are in one plane. It shows the method of calculating the position of the point P in the object-space from the co-ordinates Xi and yi of image-point on the left plate and the so-called parallel axis a = xi x 2 ; the last is constant for all points in the vertical plane GG through P at right angles to Mid. The two microscopes in fig. 14 really produce erect pictures, and the two^ plates ^are so placed in the stereocomparator as to be seen from Pi' and Pj'.

The use of the stereocomparator is unlimited for the measurement of relief. It is extended similarly to all objects and phenomena, large and small, distant and near, in motion or stationary, to those which retain their shape for a long period or which are constantly changing, or to those which are only visible for a short time. For a large number of experiments of this sort mountain photography (Von Hiibl, etc.), coastal measurements, photographing a battle from a ship, geodesy, study of the waves (Kohlschutter, Laas), the trajectory of a shot (Neuffer, Krupp, Neesen), the use in building railways or on voyages of discovery, etc. the stereocomparator has given proofs of its uses and new fields are being constantly opened up for it. A further advance has been made in the sterepphotogrammetric method by providing the stereocomparator with a drawing apparatus (F. V. Thomson, E. v. Orel and Carl Zeiss), with which contours can be automatically drawn from the stereophotogrammetric photographs. E. Deville's (1903) stereoplanigraph (fig. 15), designed for the same purpose, is only used as The mirrors are transparent for the observation of a source of light, etc., which is moved in the object-space.

The stereometer may be regarded as a modification of the stereocomparator, and is constructed for the measurement of men and animals, and also for sculpture, and for the observation of complete stereoscopic photographs. The motion of the mark is effected by a lateral movement of one of the two objectives forming the picture. Pulfrich has recently provided the Greenough binocular microscope with a point or a circular mark situated exactly in the centre of the field of view for the purpose of the direct gauging of small preparations which cannot be directly brought into contact with a mark. This contact with the preparation is effected by displacing either the preparation or the microscope, and the separate distances are read with a vernier.

The earlier suggestions for making the stereoscope a measuring instrument were not realized though decisive improvements were made. Brewster was unconsciously near the solution of the problem when he prepared ghosts or vistas by placing one transparent picture over another. More important than these trivial pictures are the superposed pictures (of conic sections, machines, anatomical preparations, etc.) contrived by E. Mach (1866) in which sections of the same solid object are successively photographed on one plate so that in a stereoscope one can see, as it were, through the opaque surface of the solid into the interior. To A. Rollet (1861) is due the merit of constructing the first stereoscopic measuring. scale. It was a sort of ladder, whose rungs gave the distances of objects. Shortly after Mach suggested using the mirror image of a wire model observed in a transparent mirror for the measurement of the dimensions of a body placed behind the glass plate.

The works of I. Harmer (1881) and F. Stolze (1884 and 1892) are of importance for the history of the development of stereoscopic measurement. Harmer used a scale of depth consisting of a series of squares arranged one behind the other in order to measure in the stereoscope a picture of the clouds taken with a large base-line (about 15 metres). Stolze placed gratings in front of the two semi-pictures of a mirror stereoscope, one of FIG. 15. a demonstration apparatus.

which could be moved by a micrometer, and he thus discovered the device called the " travelling mark." Apparently independent of all earlier experimenters T. Marie and H. Ribaut had the idea of the " travelling mark " in 1899 and 1900 and used it for measuring the Rontgen radiographs.

Of the applications of stereoscopy we may notice the utilization of spatial effects and troubles in stereoscopic vision (agitation and lustrous appearances) in the discovery of differences and alterations in pictures. The method was first used by Brewster to recognize irregularities in carpet patterns, and later by Dove and others for distinguishing the original from a copy, for testing coins, cheques, etc. Moreover, with the development of celestial photography, the stereoscope came to be applied to the discovery of planets, comets, variable stars, errors in plates, the proper motions and parallaxes of the fixed stars (Harmer, Kummel, Wolf and Lenard, Forster and others).

The stereocomparator has also been employed in astrometry, and a planetoid discovered by its aid was named Stereoscopia in recognition of this application. Since 1904 binocular observation of stellar plates to determine differences in the images of the objects reproduced has been gradually discarded for the method devised by Pulfrich, which consists in the monocular observation of the two plates in the stereocomparator with the assistance of. the so-called " blink " microscope (fig. 16). In this microscope the two pictures are seen simultaneously, or individually by alternately opening the screens BI and 82. In the second case all differences of the two images are immediately distinguished by a sudden oscillation of the image-point or by a sudden appearance and disappearance of single points like flash lights at sea or the modern illuminated sky lights in towns, and there is now no merit in discovering new planets, comets and variable stars by this method.

The blink microscope is far more useful than the stereomicroscope for such purposes, for there is not one special direction in which differences can be best distinguished. It is better therefore for the stereo method to be restricted to the work for which it is specially suitable, and for which it will never be replaced, and for such experiments as we have just discussed to be solely performed with the aid of the blink microscope. (C. P.*)

Note - this article incorporates content from Encyclopaedia Britannica, Eleventh Edition, (1910-1911)

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