- Email: [email protected]
Some new aspects in stereoscopic vision
168 SOME NEW ASPECTS IN STEREOSCOPIC VISION by C. A. J. voN FRIJTAG DRABBE, Delft, Holland. Introduction.
The aim of the following study is to afford a deeper insight into the problems of stereoscopy. This cannot be attained without first considering how we "see" the m e n t a l image of the outside world when looking with one eye. Experience has taught us that when seeing binocularly, the rules of observations show a typical deviation with relation to the observation with one eye. The following considerations should therefore be taken into account, which in their turn, illustrate that when seeing binocularly, the mental images of each of our retinal images may occur separately. Let us examine this property more cl9sely, thus obtaining a clear insight into the ways and means of fusing these separated images. We then find that by one of these ways the so-called stereoscopic observation will become possible. At the same time the position as to where we subjectively "observe" the stereoscopic image may be approximately determined. This problem where we observe the stereo image has never, to our knowledge, been quite definitely solved, neither with regard to the distance of observation, nor with regard to its position. Monocular vision or vision with one eye.
When closing one eye and focusing the other upon an object, we get an image of the object on which the eye is focused. This lies for us unchangeable on one spot, viz. in the exact direction where the object is. Without special means we are not able to see the image anywhere else than in that place. By this we get the impression as if we see the object itself in its place in the olitside world. Yet this is only apparent. What is the case, however? We focus our eye on the object and we get on our retina a strongly reduced and at the same time an inverted image. Until this point the relation between us and the object is still merely of an optical nature. The retinal image itself is formed, after the rays coming from the object have passed our eye-lens, according to the normal optical rules (fig. I). After that, the retinal image we caught from "the outside world, comes to our consciousness by a neurological and psychological way by means of a process which has nothing to do and obviously cannot have anything to do with optics. We ourselves take possession of the retinal image and what we make of it need not be completely analogous to reality. Nobody exactly knows, at least with regard to the colour, how our outside world looks. We see'a red colour, but is that the very same colour the object reflects indeed? We do not know this; we only know that the average man experiences this colour as red; but at the same time we know that there are others, viz. the colourblind, who do not experience this colour as such. So becoming aware of the colour is already something subjective. But so is
169 dimension. W e can hardly prove this. The dimensions which an object apparently has. for us is again a matter of experience, for this cannot only b e derived from the dimensions of the retinal image. This is soon to be perceived when various people are asked how large they see the moon. The dimensions which they give differ fantastically. From experience we compare what we see as regards colour and size with what we know and then from this results our personal "observation". Besides these totally personal observations as to the form and the classification of the image, certain rules are to be recognised. We mean this: everyone who fixes his eye upon a ball does not see a square object. When a figure has been drawn on the ball we all see this in the same place on the whole if we turn the eye towards the same place of observing. This fact is very important. Of course little differences in observing the shape are possible as a consequence of variation of our eye-lens; it is also possible to have variations in the shape of the figure in the image, when we make recognition difficult by vague colours and contours or if we observe when it is more or less dark, but wheri the portrait of a cat is pictured on the ball we do not see a dog, as long as the portrait has been duly pictured. The relation between the object itself and the image which we get of that object is so closely tied down with mathematical rules, that we often make the mistake of thinking that the image we form of that object really is the object, that is to say that we really optically observe the object itself. The analogy is deceitful as well. We can aim at every point of the object if we want to shoot at it and hit the mark, supposing that we are good marksmen and have good rifles. We observe the movements of the object as well. This teaches us immediately that other persons, fully independent of us, see the movements in the same way. Yet, reality can already play us a trick now, because we switch on our speed of reaction, which is entirely subjective. It may happen that the one observes a movement in a somewhat different sense than another, even we can see a fact occur differently, if circumstances are too difficult for normal observation. If however we take people of normal psychical condition, who are normally sighted, and we have the observation taking place calmly and without involving difficulties, then the image observed will be the same for several observers, taking into consideration the restrictions mentioned before: variations in lens and colour sensibility. The fact that the relation between the object and the image which we make of it is so accurately tied down by rules, is also the cause of the error made by the unir~itiated, as if we project outside ourselves our image according to the rules of optics. Optics as such does not play a part at all in the creation of our mental image. Now it should be interesting to know whether that close connection between our image and the object (as we stated when viewing with one eye only) also holds good in the case of seeing binocularly. This we shall discuss later when treating binocular vision. Besides being able to fix our eye (that is our eye-axis) upon an object, we can also (once more
170 when we do not intentionally create a difficult case) view that object. That is not all the same. For we can also look aimlessly with one eye at something, without paying attention to it. If, however, we do the latter, then we usually make use of another property of our eye at the same time, viz. accommodation. By this we understand the adjusting of the form of the eyeball and o f the lens in such a manner, that we see the object "clearly", in other words the image is in sharp focus on the retina and especially in its yellow spot.
Binocular vision or vision with two eyes. If we open both eyes and look again at the object which we observed with one eye before, then we get the impression that each of our eyes exactly observes as we described before. When we look at a definite object it is evident that both eyes are directed at the same time at the same object and even at the same spot of the object. This is called the convergence of the eye-axes at that point. One supposes that convergence is at least partly acquired. Thus 'it is thought that a baby has to learn how to converge. In practice the trouble of the baby is that he is not as yet able to fix his attention upon an object. H e has to learn how to focus; consequently we observe that in his first days the baby is squinting or staring and does not really "see" us. However, that has nothing to do with inability to converge. The convergence follows automatically as soon as the baby knows how to focus and that he has to learn. An experiment may make this clear.
Experiment 1. Close one of the eyes and observe a given point. Although we think that with one eye no distance can be fixed and the observed point can only be determined as lying in the axis of the observing eye, it is evident that, if we close that eye and open the other at the same time, the latter, without having observed too, is directed to the same point, in other words, with the given eye-axes, if attention is paid to a given point, we cannot do anything else but converge, as our brain does so automatically. Afterwards we shall see why. A second wrong opinion is that the feeling of the convergence would be decisive for estimating distances. For the moment we know that beyond our will, purely by a psychical action, convergence always takes place faultlessly, notwithstanding closing one eye. Experiment 2. We now take another experiment and shut one of the eyes again. With the open eye we observe points at greater and smaller distances. This involves altering of convergence beyond our will. This altering of convergence we don't perceive; the eye that is closed does hardly move in our feeling. W h a t we feel in fact, is the pulling nearer or the gliding further away of the gaze of the observing eye. With training we can even attain this effect for different distances, without altering the direction of the eye-axes, by thus directing our attention respectively to the space behind the point, to the point itself or to the space before it; one will then clearly feel a kind of strain and relaxing as when breathing. But this feeling we evidently perceive in the viewing eye only.
J f/
- 0 "~'/
_ / t
~
/
-(
C~: ~
\
IC)'. , //
~::~:"
°Z~
~
~
171 From these various points we think we might deduct that convergence of the eyes is an inborn property, connected with "viewing" at something or "focusing" at something. But it is an error too if one thinks that with binocular vision each eye performs the same action as with monocular vision, that is to say, that a direct relation exists between the image that our right eye catches and the reflected image which our brain makes of it and which appears in our world of observation before our right eye. The next experiment serves to illustrate this.
Experiment 3 (fig. II). We take a ruler and put it straight before us against our nose, between both eyes. We now perceive two rulers in a position dependent on the point we focus. Both the rulers "in appearance" are directed towards our point of observation and moreover lie approximately in the line of our eye-axes 1). But if we blink in turn then the left ruler seems to disappear when closing the right eye, and the right ruler when closing the left eye. So it is obvious to assume that the right eye projects the ruler mentally near the left eye-axis and that the left eye does the same near the right eye-axis. The reciprocal relation we know of viewing with one eye appears not to exist with binocular vision, that is to say the image which is projected near our left eye in our field of observation originates from the right retinal image and reversely. This experiment itself is extremely important, for it is evident now that we see projected nearly~on both eye-axes an object which lies in the angle of our eye-axes. We shall show how this property again solves difficulties with stereoscopic vision. Perhaps one is inclined to doubt the existence of that relation between both eyes and therefore we make the following experiment.
Experiment 4 (fig. III). We take a stereoscope either with or without magnifying glasses and put a coin under one of the glasses. Soon we shall perceive that only one of the eyes can see that coin directly and that only one of the eyes receives a retinal image, Another person now can indicate the coin itself as well as the place in which the person looking through the stereoscope, sees t'.e coin, but he c a n indicate it also under the other glass, where there is nothing, and the observer "sees" it essentially and completely in the same shape and position as he observed it the first time under the other glass. So it is a fact that an action of our brain can cause the broadcasting of our mental image originating from the retina of the other eye. But this experiment teaches us something more, viz. when our right eye is better than the left one and we have put the coin under the good right eye, then i) We will speak in this article of the "eye-axis', whereas this is an optical definition. In reality the axes mentioned in this article and fig. II originate from points not far from the eyes and differ slightly for different persons.
172 the coin we observe under the bad left eye is o f the same quality as that which is observed by our good eye. When we do the reverse, then we observe before our right eye a more or less vague image, equal to that normally seen by the left eye. Evidently with binocular vision the one eye receives and the other eye observes this image; in more scientific terms, the perception of the one eye raises the apperception of the other one with binocular vision. As we saw before the point on which we concentrate is beyond our will the point of intersection of the eye-axes, the two mental images meet at this point of concentration and by that we get the "impression" that binocular vision is the combined function of the right and the left eye with monocular vision. That is not the case at all, e.g. exp. 3 shows that the image seen with the left eye, has been formed by the right one and reversed, while with monocular vision the image of the left eye is also formed by the left eye. When viewing an object with both eyes, the combination takes place near the object, but this combination must also be the image seen by the left eye but formed by the right one and the image seen by the right eye should be formed by the left one.
Fhe influence of binocular vision on the forming of a stereoscopic image. Human beings have the capability, when looking with both eyes, not only of evoking an impression of that part of the world that makes an image on the retinas of both our eyes, but also they have the capability of making that image move in a direction parallel to our eye base. So we can, when looking in the direction of a single object, bring this object in focus. Then we only see one sharp image of that object (fig. IVa). But we are also able to bring our eyes in the direction of that object and focus too far. The result is that in view of that object we stare with eye-axes that have a direction to a point that is too far away, so that the object lies within the angle formed by our eye-axes (fig. IVc). In this case we become aware that it is quite impossible to see only one object. An object near F may be seen as a single image, but O can only be seen as a double image, according to fig. II. When shutting the right eye suddenly, the left part of this double image will disappear; when shutting the left eye the right part disappears. If we devote our attention to what is happening, it is also observed that the left part of the image that disappeared when shutting the right eye, is seen in the direction of the left eye-axis; whereas the right part that disappeared when shutting the left eye, is seen in the direction of the right eye-axis. The more F is chosen at a greater distance, the more our eye-axes will have to diverge and so the more both parts of the double image will be separated. When looking to infinity, that is to say with F lying in infinity, both eyeaxes have to be parallel. Persons who practise a good deal can also make their eye-axes diverge. The writer can make his eyes diverge in such a way that the double objects are separated about 15 cm, that is about double the eye base. We discussed, however, that we can also look too short. Now again we see a double image. With relation to point F we are squinting. But now the object is
173 not lying in the angle, given in fig. IV c, but in the angle as is to be seen in fig. IV b. Again we see a double image. When shutting the right eye, the right part of that double image will disappear; when shutting the left eye, the left part will disappear. So, ~vithout solving the problem how we get a double image, we are sure that when looking at an object that is not lying near the intersection of the eye-axes, we always observe a double image of that object, whether we stare or squint. It is that ability of producing a double image that gives us the possibility of getting a stereoscopic image. The only thing we have to do is to choose a stereo-couple and to make from one of these a double image by staring or squinting. We only need to bring the other stereo-photo to the same place, where we see one of the parts of the double image of the first photograph and then we get a stereo-image. What is the solution of that problem? Well, normally each o f our eyes receives a flat reversed image of a given object (fig. V). The image on both retinas will be the same if the object is a flat one. But as soon as we take an object with three dimensions, both images on the retinas will be slightly different. We say that those images show different parallaxes. According to mathematical and physical laws we can know how great these parallaxes will b e . With the help of our brain we make a reconstruction of these two images and the result is that we "see" a three-dimensional object again. H o w these things can happen is beyond our knowledge. The only fact we really know is that the whole ability of men to "see" and "to see threedimensionally", is the possibility that out brain makes that reconstruction in any way. But at the very moment that we make a double image appear from one photograph and we bring an additional stereoscopic photograph in the same place of one of these double images, it is for us just the same as if an object itself were to bring images on our retinas and that our brain made the combination. Here we make that combination "free-handed'. Of course there is a law that we should not neglect, for we know already that staring or squinting has a different result. We know that when staring we see the image that we think is made by our right eye, ~ppear as the left one and when squinting we see it as the right one. So we can understand that in both cases the effect will be different, and so it is. But in both cases, staring or squinting, it is the person himself who has to do the work to make the images double in one way or another. There is still another solution of the same problem and that is that another person brings both images one upon the other. It is the printer of the stereo-photographs who can do this work (fig. VI). He can do this by applying vectographs, that is printing each of them in such a way that, when using eye glasses of polaroid material, the right eye only sees one of both photographs printed together, while the left eye only sees the other one. He can also establish the same effect by printing one of the photographs in blue and the other in r~d. When using a red and blue filter we see only the blue 1 2
174 photograph with the eye, before which the red filter is held and the other eye (blue filter) sees only the red one (fig. VII). So, since the combination has already been made by the printer, we have only to look with adapted eye glasses or filters to get the right stereoscopic image. It will always be necessary that the right eye only receives the image that normally is presented to the right eye when looking at the object as shown in fig. VIII. If we should change the photographs in a way that the left eye receives the image destined for the right and the right eye receives the image, destined for the left one, then all things are reversed. All intersections of rays that belong together, will give reconstructions which are opposite to normal; so we see points farther on that should be nearer and other points nearer, that should be at a greater distance. We call this pseudoscopic effect (fig. IX). With normal binocular vision we can never make any mistake, for it is the object itself that creates the right images in the right eye, and so at the right place. When looking without a stereoscope, it is not difficult to understand that we have the capacity of joining two stereo-photo's and getting a three-dimensional reconstruction, as if we looked normally. But we have to remember that in this case the convergence of our eye-axes has to be incorrect, i.e. nearly parallel. In case that the printer has brought both images together in such a way that we can separate them for the constru&ion of single retinal images, we know that he has created the same situation as when normally looking with two eyes and so the convergence is more or less normal. Still we see considerable difference between a normal binocular image and the three-dimensional image when seeing vectographs or anaglyphs. The difference is that when normally seeing, the object itself is in the place of the mental reconstruction that the brain makes of the object; it is as if the object hides in the image and does its work again and again by sending rays to our retina at the same time that our brain is giving the reconstruction. When seeing a vectograph or an anaglyph, We see the mental three-dimensional reconstruction, but now the object itself is not there; our image only consists of a veil of intersecting points of rays. In binocular vision that results in our mental reconstruction lying on the object itself and being unable to pass that object, while the mental three-dimensional reconstruction of the object by vectographs or anaglyphs is not brought to a standstill by the object itself and so we see it over and through tables, paper and other things. That is the difference. It is as if in the first case our reconstruction is materialized, whereas in the second case it is quite unmaterialized. But" what about the stereoscopic image we get when looking through a stereoscope? The stereoscope is nothing more than an instrument that helps to bring our eye-axes more or less parallel, but always in such a position that we have our object as in fig. 1V c. We already know what must be the result. All constructions of stereoscopes follow the same principle, whether they have magnifying glasses, mirrors to enlarge our eye base, or not. The only thing that is interesting is that the eye-axes have an intersection that does not lie on the combined objects themselves, but at a much larger distance (fig. IVc). So again double images have to appear and it is only the place where the
175 stereoscopic image is lying that we have to discuss now.
Place where we observe the stereoscopic, three-dimensional reconstruction. One of the figures which Wheatstone left us to explain clearly the problem of stereoscopic vision, is the figure with which the eye-axes of a persian have been converged at a fixed point F. He maintains that two points a and h, lying along the respective eye-axes (at practically equal distances from our eye), should raise a fused image in F (fig. X). This assertion is entirely wrong and though this principle was already put forward more than a century ago, the exactness of this seems to be so obvious that nearly everybody has simply accepted this and to-day one is still convinced that the thesis is right. Nevertheless it is completely wrong arid it is an indication of a lack of critical sense that no one has ever checked and rectified the facts. What is the case in reality? Let us take any given point in our field of observation and suppose that point is the point in question F. Now we take two matches and we put them upright before our eyes in such a way that the matches (thus the points a and b) cover the point F before each of our eyes. Far from seeing the Wheatstone phenomenon now and thus seeing in F a fused image of a and b (thus both matches), three images are formed of the two matches, that is to say two single images of one of the matches and one combined image which is in fact not lying in F but is hiding F. We can demonstrate that this fused image (essentially a stereoscopic image) cannot lie in F. For that purpose we have only to make the following experiment. We move the matches towards us in the same position. Undoubtedly we now see the following occur: The fused image comes nearer when moving the matches towards us and the single images do so too. Making the reversed motion with the two matches, that is to say moving them farther away from us, thus nearer to F, then the reverse happens. F being a fixed point, the fused image which is moving nearer or farther cannot lie in F. What is more, it only reaches F at the moment that we h a v e almost reached F with the matches. That last moment we can hardly observe. Too often do we experience how long wrong assertions can remain in currency if only a semblance of truth attaches to them. Let us hope, however, that this time the wrong figure of Wheatstone will be hushed up, once and for all. But we have not yet finished with it, for, of course, we want to know where the fused image is indeed situated. For that purpose let us make another experiment We take two smooth, round pencils, a red and a blue one, instead of the matches. We put them again in a and b, in other words along the lines of the converging eye-axes and we observe that the single images (the outer two) are respectively red and blue, red on the side we hold the red one and blue on the side we hold the blue pencil. The fused image has a combined colour and is evidently composed of red + blue, as we should expect.
176 Now however we let the red pencil make a small quick tumbling motion in the direction of the eye-axis, along which it is situated (if need be several times at a stretch) and after that we stop the red pencil just like the other one. The fused image is, obviously red now. After this we do the same with the blue pencil while keeping the red one still. The fused image now is a blue pencil 1). From this experiment it is obvious that the fused (stereoscopic) image is twofold. What did we do? By turns we compelled the eyes to devote our attention to one of the pencils (that which was moving), i.e. at first we especially observed the red pencil vcith the left eye. After xhis we especially observed the blue one with the other eye by attracting attention for that eye to the moving pencil. From this experiment it appears that we are able to compel ourselves to give priority to a certain eye. The other one then only plays a secondary role. When we move neither of the two pencils, then the fused image looks more red or blue, in accordance with the colour of the pencil which is brought along the eye-axis of our best eye and to which more attention is paid. But with our experiments the distance of a and b from our eye and from F was arbitrary. All the observed phenomena remain however the same, whether we keep the pencils nearer or farther, as long as we do not approach F too much. Thus the object can be put into an infinite number of places between our eye-axis and the point F we pay attention to. It follows that with normal binocular vision we are confronted with the special case, that we pay attention to the point F itself. We only observe a n o r m t l image as we observe this daily, if we have our eyes (at least approximately) converged at the point to which we are devoting attention. From the fact that we see the stereoscopic image lying near the moving pencil thus near the red as well as near the blue one, it should follow that in fact we have to do with two stereoscopic images, but we get the impression to see only one, for the situation of both is the same. Each of the stereoscopic images "appears" to consist of the object to which we pay our attention and a moved or a broadcasted image of the other one. So the explanation would be that we essentially observe four images of two objects but that the inner two, which both are fused images, can be observed by us as one image only (fig. XII A). To explain the things mentioned we revert to our experiment with the stereoscope, by which we put under one of the glasses, only the right one, an object e.g. a photo. We then see this photo lying under the left glass too. If we had brought under the left glass the accessory stereoscopic photo, then under each of the glasses a stereoscopic couple would have been seen. However, we see the whole only as one stereoscopic image and we now know that this phel~omenon has to do with the normal binocular vision, assuming that. we observe objects, which are not placed in the point of intersection or point of convergence of the eye-axes. l) Persons with strongly differing eyes will observe that one of the images is continually inclined to return.
177 From the fact that we observe a direct and a transmitted image covering each other and we then get a three-dimensional impression, we think we may deduce that man has a preferential eye which he uses normally. The second only plays a secondary role; it transmits its retinal image to the other eye. Now we understand why, when gazing at one object, we observe two, of which the left one disappears if we shut the right eye and the reverse. For we then take away the transmitted image, because the eye which should have to transmit does not receive an image and thus is not able to transmit anything. The consequence of this is very remarkable indeed. Between the optical part of forming the retinal image and the psychically observed image which is formed of it by the ego, there is a phase, which takes place in its entirety in our brain and which is of a neurological and psychological nature. For in the process of observation of this by our psycheformed image, the eye, as an optical instrument, no longer performs any duty at all. This implies that when observing with one eye only and shutting, the other one, we have to observe with the shut eye (thus not with the optical device of it, but with that organism which makes us observe the image projected o u t w a r d ) t h e same image indeed. We can only imagine the same with difficulty, but so it is. But because this eye al~o "observes" a mentally outward projected image, in case of normal vision the shut eye is directed at the same point which our viewing eye is directed at. An experiment teaches us that this is the very case. Things are not so, that we converge involuntarily from experience or by certain reactions of the body and focus an eye upon the point upon which the other eye does the same, but we focus both eyes upon that point because the optically non-viewing eye also "observes". Perhaps that is the very explanation of the disposition of our visual faculty, by which the nerve-bundles lie crosswise, but still have a direct connection, too (fig. XI). Presumably the single eye, which acts as perceptor, carries the image inward via the eye nerves and this image proceeds on its way in stimuli to both eyes. This should theri imply that the nerves do not represent both a percepting and appercepting action, but t h a t one- way traffic acts in our eye nerves. It is recommended that more competent persons than we might perhap~ investigate whether the nerve Connections to the cerebellum perform the sole duty of delivering motive p6wer in order to enable the nerves to let their transmitting function perform. The apparently senseless crossing of the eye nerves appears to be, when we make a diagram of it, the only possible solution of the problem of perception of one eye, combined with apperception for both eyes. One might reproach fis for neglecting to give a reconstruction diagram from which the eventual exactness of our solution should appear. In this connection we refer to the fact that the optical course of rays which causes the shaping of the retinal image, in itself, has nothing to do with our image which is mentally projected, so t¢ speak. After the foregoing one may understand in this way that the image has come to us optically on the retina, that it has been transmitted mentally in our brain and that we really "see" this mental image lying in our outside world. 12,
178 The connection of the pencil" of rays of o u r mental image with the optical course of'rays is only this, that the pencil of rays of the x number of points of the object which we observe, is to our eye congruent to the pencils of rays .from the instrument in our orbit to the image that we "observe" projected in the field of observation (except psychical aberrations and except for infirmities of our lenses). Both pencils of rays, that from the image, observed by our right "mental eye" and that from the image observed by our left ~mental eye", produce a system of intersections quite equal to those with normal vision, for in the two cases both the mental images cover each other, as we saw before. The difference with our binocular vision in our normal field of observation is only that in the last case the object itself lies in the place where our mental spatial image forms from the masses if intersections of corresponding rays, while when observing separated objects, placed within or outside our angle of convergence, the spatial intersection image floats near one of the flat stereoscopic photos. Our inborn and developed experience taught us in both cases, without fits and starts, to go fumbling along this whole mental image with our perception or with our "concentration". We want to call special attention to the fact that in our opinion the formed three-dimensional image lies nearly in the plane of the objects presented to our eyes, thus in the Wheatstone case nearly in the plane brought through a and b perpendicularly on our eye-axes. "Nearly", because one cannot speak of a fixed position, neither with normal vision nor with stereoscopic vision. This is not only due to the action of parallaxes, through which part of all the points of the image is nearer to our eyes and another part further away (therefore we cannot speak only of a plane), but also because the ego is brought into action. And this complex of psychical and neurological reactions has raised properties in the mental image which were not present in the original object nor in the perceived retinal image. Here we have discussed, however, the case of normally reacting persons with normally functioning eyes and nerves. Finally we want to point out that in our opinion nothing indicates that amalgamation into a fused image should take place in the brain, but we think that fusion takes place in our field of observation of two images not yet fused. What, among other things, points to this is the fact that we are able to observe the fusion of two images but that the stereoscopic effect, especially for the unskilled, is brought about almost simultaneously and then, as it were, with a shock. Had fusion happened before in the brain, this would not be the case. Now we want to solve from the constructional point of view, too, the position of the stereoscopic image (fig. XII). In figs. a and b we tried to show how observation works. It is certain that fig. a must represent the matter welt in so far as we indeed observe the stereoscopic image in two places and well along both the eye-axes so far they are focussed upon F. It is certain too that we observe the outer by-images with interspaces, which entirely harmonize with the space between the points a and b. Yet it is certain that we d o not observe four images and so we have to believe that fig. b is more correct and consequently the stereoscopic image, psychical and physical disturbances excepted, must lie in the median plane, the plane through our nose perpendicular to the eye-base (this brings fig. II to mind).
179 We do not see the image covering F Let us not be mistaken, howeve r, that we do not see point F in the stereoscopic image, for the position of the mentally formed stereoscopic image is the psychical product of the retinal images and in the retinal images the point F was indeed covered. So the figure b seems to us to be the exact solution. Summing up we may say: 1. Stereoscopic vision is a function of normal binocular vision. 2. Looking with two eyes-normal binocular vision brings us to convergence and approximate accommodation beyond our will, as the object itself, by its rays touching our retinas, causes our mental reconstruction to be closely tied at the object sending the rays mentioned. 3. However it is not true that each single eye only views a direction and that difference in distance is only appreciated when looking with both eyes. 4. Looking with both eyes every point x that is nearer or further than our attention point F is mentally projected near the eye-axes, but keeps its normal distance. Bringing a complementary (stereoscopic) object on the same place where x appears, we get a three-dimensional combination. 5. That combination appearing on our eye-axes at a place nearer to or further from our attention point F originates from a place in the median plane. As the point x is projected on the eye-axis at about the same distance as the point is actually lying, it will be clear that the distance of the combination is slightly changing, the more our eye-axes converge or diverge:
INTERNATIONAL ARCHIVES OF P H O T O G R A M M E T R Y Proceedings of the 6 th International Congress of Photogrammetry The Hague (Netherlands), l~.t September .--lOth September 1948 V ' O L U M E X, 2 Parts Edited by the Netherlands Society of Photogrammetry Ir. B. Scherpbier, President Prof. R. Roelofs, Secretary A. Govers, Treasurer
2 Parts (complete volume) Dutch Guilders 4 0 . For U.S.A. and Canada . . . . . ~ 12.~ N.V.
UITGEVERIJ
Address your order t o : (ARGUS~ • AMSTERDAM Singel 26
(Holland)
The aim of the following study is to afford a deeper insight into the problems of stereoscopy. This cannot be attained without first considering how we "see" the m e n t a l image of the outside world when looking with one eye. Experience has taught us that when seeing binocularly, the rules of observations show a typical deviation with relation to the observation with one eye. The following considerations should therefore be taken into account, which in their turn, illustrate that when seeing binocularly, the mental images of each of our retinal images may occur separately. Let us examine this property more cl9sely, thus obtaining a clear insight into the ways and means of fusing these separated images. We then find that by one of these ways the so-called stereoscopic observation will become possible. At the same time the position as to where we subjectively "observe" the stereoscopic image may be approximately determined. This problem where we observe the stereo image has never, to our knowledge, been quite definitely solved, neither with regard to the distance of observation, nor with regard to its position. Monocular vision or vision with one eye.
When closing one eye and focusing the other upon an object, we get an image of the object on which the eye is focused. This lies for us unchangeable on one spot, viz. in the exact direction where the object is. Without special means we are not able to see the image anywhere else than in that place. By this we get the impression as if we see the object itself in its place in the olitside world. Yet this is only apparent. What is the case, however? We focus our eye on the object and we get on our retina a strongly reduced and at the same time an inverted image. Until this point the relation between us and the object is still merely of an optical nature. The retinal image itself is formed, after the rays coming from the object have passed our eye-lens, according to the normal optical rules (fig. I). After that, the retinal image we caught from "the outside world, comes to our consciousness by a neurological and psychological way by means of a process which has nothing to do and obviously cannot have anything to do with optics. We ourselves take possession of the retinal image and what we make of it need not be completely analogous to reality. Nobody exactly knows, at least with regard to the colour, how our outside world looks. We see'a red colour, but is that the very same colour the object reflects indeed? We do not know this; we only know that the average man experiences this colour as red; but at the same time we know that there are others, viz. the colourblind, who do not experience this colour as such. So becoming aware of the colour is already something subjective. But so is
169 dimension. W e can hardly prove this. The dimensions which an object apparently has. for us is again a matter of experience, for this cannot only b e derived from the dimensions of the retinal image. This is soon to be perceived when various people are asked how large they see the moon. The dimensions which they give differ fantastically. From experience we compare what we see as regards colour and size with what we know and then from this results our personal "observation". Besides these totally personal observations as to the form and the classification of the image, certain rules are to be recognised. We mean this: everyone who fixes his eye upon a ball does not see a square object. When a figure has been drawn on the ball we all see this in the same place on the whole if we turn the eye towards the same place of observing. This fact is very important. Of course little differences in observing the shape are possible as a consequence of variation of our eye-lens; it is also possible to have variations in the shape of the figure in the image, when we make recognition difficult by vague colours and contours or if we observe when it is more or less dark, but wheri the portrait of a cat is pictured on the ball we do not see a dog, as long as the portrait has been duly pictured. The relation between the object itself and the image which we get of that object is so closely tied down with mathematical rules, that we often make the mistake of thinking that the image we form of that object really is the object, that is to say that we really optically observe the object itself. The analogy is deceitful as well. We can aim at every point of the object if we want to shoot at it and hit the mark, supposing that we are good marksmen and have good rifles. We observe the movements of the object as well. This teaches us immediately that other persons, fully independent of us, see the movements in the same way. Yet, reality can already play us a trick now, because we switch on our speed of reaction, which is entirely subjective. It may happen that the one observes a movement in a somewhat different sense than another, even we can see a fact occur differently, if circumstances are too difficult for normal observation. If however we take people of normal psychical condition, who are normally sighted, and we have the observation taking place calmly and without involving difficulties, then the image observed will be the same for several observers, taking into consideration the restrictions mentioned before: variations in lens and colour sensibility. The fact that the relation between the object and the image which we make of it is so accurately tied down by rules, is also the cause of the error made by the unir~itiated, as if we project outside ourselves our image according to the rules of optics. Optics as such does not play a part at all in the creation of our mental image. Now it should be interesting to know whether that close connection between our image and the object (as we stated when viewing with one eye only) also holds good in the case of seeing binocularly. This we shall discuss later when treating binocular vision. Besides being able to fix our eye (that is our eye-axis) upon an object, we can also (once more
170 when we do not intentionally create a difficult case) view that object. That is not all the same. For we can also look aimlessly with one eye at something, without paying attention to it. If, however, we do the latter, then we usually make use of another property of our eye at the same time, viz. accommodation. By this we understand the adjusting of the form of the eyeball and o f the lens in such a manner, that we see the object "clearly", in other words the image is in sharp focus on the retina and especially in its yellow spot.
Binocular vision or vision with two eyes. If we open both eyes and look again at the object which we observed with one eye before, then we get the impression that each of our eyes exactly observes as we described before. When we look at a definite object it is evident that both eyes are directed at the same time at the same object and even at the same spot of the object. This is called the convergence of the eye-axes at that point. One supposes that convergence is at least partly acquired. Thus 'it is thought that a baby has to learn how to converge. In practice the trouble of the baby is that he is not as yet able to fix his attention upon an object. H e has to learn how to focus; consequently we observe that in his first days the baby is squinting or staring and does not really "see" us. However, that has nothing to do with inability to converge. The convergence follows automatically as soon as the baby knows how to focus and that he has to learn. An experiment may make this clear.
Experiment 1. Close one of the eyes and observe a given point. Although we think that with one eye no distance can be fixed and the observed point can only be determined as lying in the axis of the observing eye, it is evident that, if we close that eye and open the other at the same time, the latter, without having observed too, is directed to the same point, in other words, with the given eye-axes, if attention is paid to a given point, we cannot do anything else but converge, as our brain does so automatically. Afterwards we shall see why. A second wrong opinion is that the feeling of the convergence would be decisive for estimating distances. For the moment we know that beyond our will, purely by a psychical action, convergence always takes place faultlessly, notwithstanding closing one eye. Experiment 2. We now take another experiment and shut one of the eyes again. With the open eye we observe points at greater and smaller distances. This involves altering of convergence beyond our will. This altering of convergence we don't perceive; the eye that is closed does hardly move in our feeling. W h a t we feel in fact, is the pulling nearer or the gliding further away of the gaze of the observing eye. With training we can even attain this effect for different distances, without altering the direction of the eye-axes, by thus directing our attention respectively to the space behind the point, to the point itself or to the space before it; one will then clearly feel a kind of strain and relaxing as when breathing. But this feeling we evidently perceive in the viewing eye only.
J f/
- 0 "~'/
_ / t
~
/
-(
C~: ~
\
IC)'. , //
~::~:"
°Z~
~
~
171 From these various points we think we might deduct that convergence of the eyes is an inborn property, connected with "viewing" at something or "focusing" at something. But it is an error too if one thinks that with binocular vision each eye performs the same action as with monocular vision, that is to say, that a direct relation exists between the image that our right eye catches and the reflected image which our brain makes of it and which appears in our world of observation before our right eye. The next experiment serves to illustrate this.
Experiment 3 (fig. II). We take a ruler and put it straight before us against our nose, between both eyes. We now perceive two rulers in a position dependent on the point we focus. Both the rulers "in appearance" are directed towards our point of observation and moreover lie approximately in the line of our eye-axes 1). But if we blink in turn then the left ruler seems to disappear when closing the right eye, and the right ruler when closing the left eye. So it is obvious to assume that the right eye projects the ruler mentally near the left eye-axis and that the left eye does the same near the right eye-axis. The reciprocal relation we know of viewing with one eye appears not to exist with binocular vision, that is to say the image which is projected near our left eye in our field of observation originates from the right retinal image and reversely. This experiment itself is extremely important, for it is evident now that we see projected nearly~on both eye-axes an object which lies in the angle of our eye-axes. We shall show how this property again solves difficulties with stereoscopic vision. Perhaps one is inclined to doubt the existence of that relation between both eyes and therefore we make the following experiment.
Experiment 4 (fig. III). We take a stereoscope either with or without magnifying glasses and put a coin under one of the glasses. Soon we shall perceive that only one of the eyes can see that coin directly and that only one of the eyes receives a retinal image, Another person now can indicate the coin itself as well as the place in which the person looking through the stereoscope, sees t'.e coin, but he c a n indicate it also under the other glass, where there is nothing, and the observer "sees" it essentially and completely in the same shape and position as he observed it the first time under the other glass. So it is a fact that an action of our brain can cause the broadcasting of our mental image originating from the retina of the other eye. But this experiment teaches us something more, viz. when our right eye is better than the left one and we have put the coin under the good right eye, then i) We will speak in this article of the "eye-axis', whereas this is an optical definition. In reality the axes mentioned in this article and fig. II originate from points not far from the eyes and differ slightly for different persons.
172 the coin we observe under the bad left eye is o f the same quality as that which is observed by our good eye. When we do the reverse, then we observe before our right eye a more or less vague image, equal to that normally seen by the left eye. Evidently with binocular vision the one eye receives and the other eye observes this image; in more scientific terms, the perception of the one eye raises the apperception of the other one with binocular vision. As we saw before the point on which we concentrate is beyond our will the point of intersection of the eye-axes, the two mental images meet at this point of concentration and by that we get the "impression" that binocular vision is the combined function of the right and the left eye with monocular vision. That is not the case at all, e.g. exp. 3 shows that the image seen with the left eye, has been formed by the right one and reversed, while with monocular vision the image of the left eye is also formed by the left eye. When viewing an object with both eyes, the combination takes place near the object, but this combination must also be the image seen by the left eye but formed by the right one and the image seen by the right eye should be formed by the left one.
Fhe influence of binocular vision on the forming of a stereoscopic image. Human beings have the capability, when looking with both eyes, not only of evoking an impression of that part of the world that makes an image on the retinas of both our eyes, but also they have the capability of making that image move in a direction parallel to our eye base. So we can, when looking in the direction of a single object, bring this object in focus. Then we only see one sharp image of that object (fig. IVa). But we are also able to bring our eyes in the direction of that object and focus too far. The result is that in view of that object we stare with eye-axes that have a direction to a point that is too far away, so that the object lies within the angle formed by our eye-axes (fig. IVc). In this case we become aware that it is quite impossible to see only one object. An object near F may be seen as a single image, but O can only be seen as a double image, according to fig. II. When shutting the right eye suddenly, the left part of this double image will disappear; when shutting the left eye the right part disappears. If we devote our attention to what is happening, it is also observed that the left part of the image that disappeared when shutting the right eye, is seen in the direction of the left eye-axis; whereas the right part that disappeared when shutting the left eye, is seen in the direction of the right eye-axis. The more F is chosen at a greater distance, the more our eye-axes will have to diverge and so the more both parts of the double image will be separated. When looking to infinity, that is to say with F lying in infinity, both eyeaxes have to be parallel. Persons who practise a good deal can also make their eye-axes diverge. The writer can make his eyes diverge in such a way that the double objects are separated about 15 cm, that is about double the eye base. We discussed, however, that we can also look too short. Now again we see a double image. With relation to point F we are squinting. But now the object is
173 not lying in the angle, given in fig. IV c, but in the angle as is to be seen in fig. IV b. Again we see a double image. When shutting the right eye, the right part of that double image will disappear; when shutting the left eye, the left part will disappear. So, ~vithout solving the problem how we get a double image, we are sure that when looking at an object that is not lying near the intersection of the eye-axes, we always observe a double image of that object, whether we stare or squint. It is that ability of producing a double image that gives us the possibility of getting a stereoscopic image. The only thing we have to do is to choose a stereo-couple and to make from one of these a double image by staring or squinting. We only need to bring the other stereo-photo to the same place, where we see one of the parts of the double image of the first photograph and then we get a stereo-image. What is the solution of that problem? Well, normally each o f our eyes receives a flat reversed image of a given object (fig. V). The image on both retinas will be the same if the object is a flat one. But as soon as we take an object with three dimensions, both images on the retinas will be slightly different. We say that those images show different parallaxes. According to mathematical and physical laws we can know how great these parallaxes will b e . With the help of our brain we make a reconstruction of these two images and the result is that we "see" a three-dimensional object again. H o w these things can happen is beyond our knowledge. The only fact we really know is that the whole ability of men to "see" and "to see threedimensionally", is the possibility that out brain makes that reconstruction in any way. But at the very moment that we make a double image appear from one photograph and we bring an additional stereoscopic photograph in the same place of one of these double images, it is for us just the same as if an object itself were to bring images on our retinas and that our brain made the combination. Here we make that combination "free-handed'. Of course there is a law that we should not neglect, for we know already that staring or squinting has a different result. We know that when staring we see the image that we think is made by our right eye, ~ppear as the left one and when squinting we see it as the right one. So we can understand that in both cases the effect will be different, and so it is. But in both cases, staring or squinting, it is the person himself who has to do the work to make the images double in one way or another. There is still another solution of the same problem and that is that another person brings both images one upon the other. It is the printer of the stereo-photographs who can do this work (fig. VI). He can do this by applying vectographs, that is printing each of them in such a way that, when using eye glasses of polaroid material, the right eye only sees one of both photographs printed together, while the left eye only sees the other one. He can also establish the same effect by printing one of the photographs in blue and the other in r~d. When using a red and blue filter we see only the blue 1 2
174 photograph with the eye, before which the red filter is held and the other eye (blue filter) sees only the red one (fig. VII). So, since the combination has already been made by the printer, we have only to look with adapted eye glasses or filters to get the right stereoscopic image. It will always be necessary that the right eye only receives the image that normally is presented to the right eye when looking at the object as shown in fig. VIII. If we should change the photographs in a way that the left eye receives the image destined for the right and the right eye receives the image, destined for the left one, then all things are reversed. All intersections of rays that belong together, will give reconstructions which are opposite to normal; so we see points farther on that should be nearer and other points nearer, that should be at a greater distance. We call this pseudoscopic effect (fig. IX). With normal binocular vision we can never make any mistake, for it is the object itself that creates the right images in the right eye, and so at the right place. When looking without a stereoscope, it is not difficult to understand that we have the capacity of joining two stereo-photo's and getting a three-dimensional reconstruction, as if we looked normally. But we have to remember that in this case the convergence of our eye-axes has to be incorrect, i.e. nearly parallel. In case that the printer has brought both images together in such a way that we can separate them for the constru&ion of single retinal images, we know that he has created the same situation as when normally looking with two eyes and so the convergence is more or less normal. Still we see considerable difference between a normal binocular image and the three-dimensional image when seeing vectographs or anaglyphs. The difference is that when normally seeing, the object itself is in the place of the mental reconstruction that the brain makes of the object; it is as if the object hides in the image and does its work again and again by sending rays to our retina at the same time that our brain is giving the reconstruction. When seeing a vectograph or an anaglyph, We see the mental three-dimensional reconstruction, but now the object itself is not there; our image only consists of a veil of intersecting points of rays. In binocular vision that results in our mental reconstruction lying on the object itself and being unable to pass that object, while the mental three-dimensional reconstruction of the object by vectographs or anaglyphs is not brought to a standstill by the object itself and so we see it over and through tables, paper and other things. That is the difference. It is as if in the first case our reconstruction is materialized, whereas in the second case it is quite unmaterialized. But" what about the stereoscopic image we get when looking through a stereoscope? The stereoscope is nothing more than an instrument that helps to bring our eye-axes more or less parallel, but always in such a position that we have our object as in fig. 1V c. We already know what must be the result. All constructions of stereoscopes follow the same principle, whether they have magnifying glasses, mirrors to enlarge our eye base, or not. The only thing that is interesting is that the eye-axes have an intersection that does not lie on the combined objects themselves, but at a much larger distance (fig. IVc). So again double images have to appear and it is only the place where the
175 stereoscopic image is lying that we have to discuss now.
Place where we observe the stereoscopic, three-dimensional reconstruction. One of the figures which Wheatstone left us to explain clearly the problem of stereoscopic vision, is the figure with which the eye-axes of a persian have been converged at a fixed point F. He maintains that two points a and h, lying along the respective eye-axes (at practically equal distances from our eye), should raise a fused image in F (fig. X). This assertion is entirely wrong and though this principle was already put forward more than a century ago, the exactness of this seems to be so obvious that nearly everybody has simply accepted this and to-day one is still convinced that the thesis is right. Nevertheless it is completely wrong arid it is an indication of a lack of critical sense that no one has ever checked and rectified the facts. What is the case in reality? Let us take any given point in our field of observation and suppose that point is the point in question F. Now we take two matches and we put them upright before our eyes in such a way that the matches (thus the points a and b) cover the point F before each of our eyes. Far from seeing the Wheatstone phenomenon now and thus seeing in F a fused image of a and b (thus both matches), three images are formed of the two matches, that is to say two single images of one of the matches and one combined image which is in fact not lying in F but is hiding F. We can demonstrate that this fused image (essentially a stereoscopic image) cannot lie in F. For that purpose we have only to make the following experiment. We move the matches towards us in the same position. Undoubtedly we now see the following occur: The fused image comes nearer when moving the matches towards us and the single images do so too. Making the reversed motion with the two matches, that is to say moving them farther away from us, thus nearer to F, then the reverse happens. F being a fixed point, the fused image which is moving nearer or farther cannot lie in F. What is more, it only reaches F at the moment that we h a v e almost reached F with the matches. That last moment we can hardly observe. Too often do we experience how long wrong assertions can remain in currency if only a semblance of truth attaches to them. Let us hope, however, that this time the wrong figure of Wheatstone will be hushed up, once and for all. But we have not yet finished with it, for, of course, we want to know where the fused image is indeed situated. For that purpose let us make another experiment We take two smooth, round pencils, a red and a blue one, instead of the matches. We put them again in a and b, in other words along the lines of the converging eye-axes and we observe that the single images (the outer two) are respectively red and blue, red on the side we hold the red one and blue on the side we hold the blue pencil. The fused image has a combined colour and is evidently composed of red + blue, as we should expect.
176 Now however we let the red pencil make a small quick tumbling motion in the direction of the eye-axis, along which it is situated (if need be several times at a stretch) and after that we stop the red pencil just like the other one. The fused image is, obviously red now. After this we do the same with the blue pencil while keeping the red one still. The fused image now is a blue pencil 1). From this experiment it is obvious that the fused (stereoscopic) image is twofold. What did we do? By turns we compelled the eyes to devote our attention to one of the pencils (that which was moving), i.e. at first we especially observed the red pencil vcith the left eye. After xhis we especially observed the blue one with the other eye by attracting attention for that eye to the moving pencil. From this experiment it appears that we are able to compel ourselves to give priority to a certain eye. The other one then only plays a secondary role. When we move neither of the two pencils, then the fused image looks more red or blue, in accordance with the colour of the pencil which is brought along the eye-axis of our best eye and to which more attention is paid. But with our experiments the distance of a and b from our eye and from F was arbitrary. All the observed phenomena remain however the same, whether we keep the pencils nearer or farther, as long as we do not approach F too much. Thus the object can be put into an infinite number of places between our eye-axis and the point F we pay attention to. It follows that with normal binocular vision we are confronted with the special case, that we pay attention to the point F itself. We only observe a n o r m t l image as we observe this daily, if we have our eyes (at least approximately) converged at the point to which we are devoting attention. From the fact that we see the stereoscopic image lying near the moving pencil thus near the red as well as near the blue one, it should follow that in fact we have to do with two stereoscopic images, but we get the impression to see only one, for the situation of both is the same. Each of the stereoscopic images "appears" to consist of the object to which we pay our attention and a moved or a broadcasted image of the other one. So the explanation would be that we essentially observe four images of two objects but that the inner two, which both are fused images, can be observed by us as one image only (fig. XII A). To explain the things mentioned we revert to our experiment with the stereoscope, by which we put under one of the glasses, only the right one, an object e.g. a photo. We then see this photo lying under the left glass too. If we had brought under the left glass the accessory stereoscopic photo, then under each of the glasses a stereoscopic couple would have been seen. However, we see the whole only as one stereoscopic image and we now know that this phel~omenon has to do with the normal binocular vision, assuming that. we observe objects, which are not placed in the point of intersection or point of convergence of the eye-axes. l) Persons with strongly differing eyes will observe that one of the images is continually inclined to return.
177 From the fact that we observe a direct and a transmitted image covering each other and we then get a three-dimensional impression, we think we may deduce that man has a preferential eye which he uses normally. The second only plays a secondary role; it transmits its retinal image to the other eye. Now we understand why, when gazing at one object, we observe two, of which the left one disappears if we shut the right eye and the reverse. For we then take away the transmitted image, because the eye which should have to transmit does not receive an image and thus is not able to transmit anything. The consequence of this is very remarkable indeed. Between the optical part of forming the retinal image and the psychically observed image which is formed of it by the ego, there is a phase, which takes place in its entirety in our brain and which is of a neurological and psychological nature. For in the process of observation of this by our psycheformed image, the eye, as an optical instrument, no longer performs any duty at all. This implies that when observing with one eye only and shutting, the other one, we have to observe with the shut eye (thus not with the optical device of it, but with that organism which makes us observe the image projected o u t w a r d ) t h e same image indeed. We can only imagine the same with difficulty, but so it is. But because this eye al~o "observes" a mentally outward projected image, in case of normal vision the shut eye is directed at the same point which our viewing eye is directed at. An experiment teaches us that this is the very case. Things are not so, that we converge involuntarily from experience or by certain reactions of the body and focus an eye upon the point upon which the other eye does the same, but we focus both eyes upon that point because the optically non-viewing eye also "observes". Perhaps that is the very explanation of the disposition of our visual faculty, by which the nerve-bundles lie crosswise, but still have a direct connection, too (fig. XI). Presumably the single eye, which acts as perceptor, carries the image inward via the eye nerves and this image proceeds on its way in stimuli to both eyes. This should theri imply that the nerves do not represent both a percepting and appercepting action, but t h a t one- way traffic acts in our eye nerves. It is recommended that more competent persons than we might perhap~ investigate whether the nerve Connections to the cerebellum perform the sole duty of delivering motive p6wer in order to enable the nerves to let their transmitting function perform. The apparently senseless crossing of the eye nerves appears to be, when we make a diagram of it, the only possible solution of the problem of perception of one eye, combined with apperception for both eyes. One might reproach fis for neglecting to give a reconstruction diagram from which the eventual exactness of our solution should appear. In this connection we refer to the fact that the optical course of rays which causes the shaping of the retinal image, in itself, has nothing to do with our image which is mentally projected, so t¢ speak. After the foregoing one may understand in this way that the image has come to us optically on the retina, that it has been transmitted mentally in our brain and that we really "see" this mental image lying in our outside world. 12,
178 The connection of the pencil" of rays of o u r mental image with the optical course of'rays is only this, that the pencil of rays of the x number of points of the object which we observe, is to our eye congruent to the pencils of rays .from the instrument in our orbit to the image that we "observe" projected in the field of observation (except psychical aberrations and except for infirmities of our lenses). Both pencils of rays, that from the image, observed by our right "mental eye" and that from the image observed by our left ~mental eye", produce a system of intersections quite equal to those with normal vision, for in the two cases both the mental images cover each other, as we saw before. The difference with our binocular vision in our normal field of observation is only that in the last case the object itself lies in the place where our mental spatial image forms from the masses if intersections of corresponding rays, while when observing separated objects, placed within or outside our angle of convergence, the spatial intersection image floats near one of the flat stereoscopic photos. Our inborn and developed experience taught us in both cases, without fits and starts, to go fumbling along this whole mental image with our perception or with our "concentration". We want to call special attention to the fact that in our opinion the formed three-dimensional image lies nearly in the plane of the objects presented to our eyes, thus in the Wheatstone case nearly in the plane brought through a and b perpendicularly on our eye-axes. "Nearly", because one cannot speak of a fixed position, neither with normal vision nor with stereoscopic vision. This is not only due to the action of parallaxes, through which part of all the points of the image is nearer to our eyes and another part further away (therefore we cannot speak only of a plane), but also because the ego is brought into action. And this complex of psychical and neurological reactions has raised properties in the mental image which were not present in the original object nor in the perceived retinal image. Here we have discussed, however, the case of normally reacting persons with normally functioning eyes and nerves. Finally we want to point out that in our opinion nothing indicates that amalgamation into a fused image should take place in the brain, but we think that fusion takes place in our field of observation of two images not yet fused. What, among other things, points to this is the fact that we are able to observe the fusion of two images but that the stereoscopic effect, especially for the unskilled, is brought about almost simultaneously and then, as it were, with a shock. Had fusion happened before in the brain, this would not be the case. Now we want to solve from the constructional point of view, too, the position of the stereoscopic image (fig. XII). In figs. a and b we tried to show how observation works. It is certain that fig. a must represent the matter welt in so far as we indeed observe the stereoscopic image in two places and well along both the eye-axes so far they are focussed upon F. It is certain too that we observe the outer by-images with interspaces, which entirely harmonize with the space between the points a and b. Yet it is certain that we d o not observe four images and so we have to believe that fig. b is more correct and consequently the stereoscopic image, psychical and physical disturbances excepted, must lie in the median plane, the plane through our nose perpendicular to the eye-base (this brings fig. II to mind).
179 We do not see the image covering F Let us not be mistaken, howeve r, that we do not see point F in the stereoscopic image, for the position of the mentally formed stereoscopic image is the psychical product of the retinal images and in the retinal images the point F was indeed covered. So the figure b seems to us to be the exact solution. Summing up we may say: 1. Stereoscopic vision is a function of normal binocular vision. 2. Looking with two eyes-normal binocular vision brings us to convergence and approximate accommodation beyond our will, as the object itself, by its rays touching our retinas, causes our mental reconstruction to be closely tied at the object sending the rays mentioned. 3. However it is not true that each single eye only views a direction and that difference in distance is only appreciated when looking with both eyes. 4. Looking with both eyes every point x that is nearer or further than our attention point F is mentally projected near the eye-axes, but keeps its normal distance. Bringing a complementary (stereoscopic) object on the same place where x appears, we get a three-dimensional combination. 5. That combination appearing on our eye-axes at a place nearer to or further from our attention point F originates from a place in the median plane. As the point x is projected on the eye-axis at about the same distance as the point is actually lying, it will be clear that the distance of the combination is slightly changing, the more our eye-axes converge or diverge:
INTERNATIONAL ARCHIVES OF P H O T O G R A M M E T R Y Proceedings of the 6 th International Congress of Photogrammetry The Hague (Netherlands), l~.t September .--lOth September 1948 V ' O L U M E X, 2 Parts Edited by the Netherlands Society of Photogrammetry Ir. B. Scherpbier, President Prof. R. Roelofs, Secretary A. Govers, Treasurer
2 Parts (complete volume) Dutch Guilders 4 0 . For U.S.A. and Canada . . . . . ~ 12.~ N.V.
UITGEVERIJ
Address your order t o : (ARGUS~ • AMSTERDAM Singel 26
(Holland)