Harvard Psychological Studies, Volume 2

by Unknown

STEREOSCOPIC VISION AND THE DIFFERENCE OF RETINAL IMAGES

BY G. V. HAMILTON

The question which the Laboratory proposed to me for experimental enquiry was one which demanded a definite reply of yes or no. The positive answer seemed a necessary consequence of the traditional psycho-physiological theories, while a certain practical consideration seemed to suggest the negative solution. The question which seems to have been overlooked so far was this: According to the theory of stereoscopic vision two points of light which are seen by each of the two eyes under the same angle appear to lie in the same plane; as soon as the angle for the right eye is larger than that for the left, that is, as soon as the two stimulated retinal points in the right eye are more distant than the two retinal points stimulated in the left eye, the right light-point seems to be farther away than the left one. If we relate them to planes vertical on the ideal binocular fixation-line, the right point lies in a more distant plane. This principle, which, of course, controls all arrangements for stereoscopic effect, is deduced from experiences in which the fixation-line is vertical to the line that connects the nodal points of the two eyes; the plane in which the equally distant points lie is then parallel to the forehead. If, on the other hand, the eyes are turned to the side, that is, if the ideal fixation-line forms an acute angle with the line connecting the eyeballs, the two fixated light-points, which lie in a plane perpendicular to the fixation-line, cannot be seen by the two eyes under the same angle. Any object on my right side is somewhat nearer to my right eye than to my left, and therefore must throw a larger image on my right retina. The two light-points of a plane vertical to the fixation-line give thus with the eyes turned to the right two unequal pairs of retinal stimuli; and the difference of the retinal stimulations is evidently just the same as if the eyes were looking straight forward but the two lights were at different distances. If difference of retinal images really produces the conscious experience of seeing the lights in differently distant planes, vertical to the fixation-line, it follows that with the eyes turned to the right, lights which objectively lie in the same plane must appear subjectively to lie in different distances. The question arises whether the facts correspond to this conclusion. If we look with eyes turned sidewise towards a plane vertical to the direction of seeing, do the points of that plane remain in it for consciousness or do we see them in different planes? We see that practical considerations suggest a "No" to this question, because it would mean that everything which does not lie exactly in front of us must change its plastic form, and this the more strongly the more we see it on our right or our left, and this of course again the more strongly the nearer it is to the eyes, inasmuch as the relative difference of the retinal images must increase with the nearness of the object. If a short-sighted person fixates an object a few centimetres from the eyes strongly turned to the side, the distances in the retinal image of the one eye may be almost the double of those in the other. Under normal conditions the differences would be smaller, but yet everything would be necessarily distorted in its three-dimension shape as soon as it is seen in indirect vision or with sidewise fixation. On the other hand, if the objects keep their three-dimensional relations in spite of sidewise movements, it is evident that the accepted psycho-physiological theory of stereoscopic vision is incomplete and must be revised in a very essential way. The experiment had to decide. Of course the question might be approached experimentally in different ways. It would have been possible, for instance, to study the stereoscopic synthesis of two separate flat pictures seen with the eyeballs in different positions. But we preferred the simplest possible way, seeking the threshold of distance for two parallel vertical edges with eyes turned forward and to the side. We chose edges instead of hanging threads for the purpose of avoiding the possible influence of the apparent thickness of the threads on the judgment of distance. Of course, distance is here never distance from the one or the other eye, but from the centre of the line which connects the two nodal points of the eyes; the two vertical planes whose edges were to be compared stood always vertical on the ideal line of fixation which starts from that central point between the two eyeballs.

The apparatus used in these experiments consists of three parts, viz.:

(1) A plank 2.5 metres x 9.5 centimetres x 4 centimetres, set on edge and screwed to a table at either end.

(2) A head-rest 45 centimetres high, 35 centimetres broad and 15 centimetres deep. Attached to the centre of the lower strip of the frame is a concave trough for the chin. Another trough, shaped to fit over the vertex and with a strip of wood fastened to the front of it for the forehead, slides up or down within the frame. The attachment for the forehead can be moved and fixed at various positions antero-posteriorly. By means of these devices the head can be securely fixed in any position desired without discomfort to the subject.

In order to have the eyes always in the same plane and at a known distance from the apparatus at the other end of the plank, a hole was made in either side of the frame with its centre at a level of the eyes. Extending through the vertical diameter of each hole is a fine wire. Fitted into the inner portion of each hole is a cardboard tube 10 centimetres long: the inner end of each tube contains a vertical wire so arranged that the four wires all fall into a plane at right angles to the long direction of the plank. A mirror at the outer exit of either hole enables the experimenter to align the tips of the subject's corneæ with the wires.

Two parallel strips of wood are so attached to the "head-rest" end of the plank—one below and the other above it—that they can be rotated laterally upon the plank, with the bolt which secures them to it for a centre of rotation. Opposite this centre, and attached to the anterior surface of the upper parallel strip is a wire needle 25 centimetres long. By means of a quadricircular piece of cardboard attached to the plank at the end of the needle, the extent of rotation to the right or left can be read off in degrees. (The point midway between the two corneal tips when they are aligned with the wires is in the same axis of rotation as the head-rest.)

A vertical iron rod 50 centimetres long extends upwards from either end of the parallel strips, and upon these rods the frame of the head-rest can be moved up or down by means of thumb-screws upon which it rests.