The three deformations which we have con sidered can be understood by imagining the visual rays to be replaced by elastic thread, so that in registering the elementary perspectives and in viewing the pair these threads are all the time attached to every point of the per spectives, and follow the eyes of the observer in all positions.
It is obvious that several conditions of viewing a stereoscopic pair may be violated at once ; the resulting deformation is the sum of the elemen tary deformations.
823. Consider a stereoscopic pair viewed under the correct conditions, and suppose each image turned through the same angle about its principal point. If the reliefs of the recon structed objects are feeble relative to the distance of the object itself, stereoscopic vision remains possible, but the relief diminishes more and more until it vanishes at a rotation of 90°. After this, it gives a pseudoscopic effect of increasing intensity until a rotation of 180° is obtained ; the same phenomena then repeat themselves in inverse order.
Such anomalies obviously cannot occur in subjects where vertical lines appear, but every precaution must be taken to avoid it in the case where there is nothing to give a sense of depth in one of the pictures by itself ; this is often the case in various scientific or technical applications (aerial photographs taken vertically, astronom ical subjects, photographs of fossils, anatom ical preparations, photo-micrography, etc.).
824. Range of Stereoscopic Vision. By reason of the aberrations of the lens and the grain of the photographic image, the values previously calculated 814) for the range of direct bino cular vision cannot be used in the case of stereoscopic photographs taken from a base equal to the separation of the eyes. The values calculated for the extent of the effective zones are the maxima, whilst those for the extent of the neutral zone are the minima.
In the most favourable circumstances the range of stereoscopic photography is not as much as 8o yd. When using objectives of short focal length and rapid emulsions with pro nounced grain, the stereoscopic range sometimes does not exceed 16 yd. This is why it is usual, in stereoscopic photography of landscapes, to include in the field a near object serving to enhance the sensation of relief, in the manner of a material foreground in a diorama.
These ranges are obviously very different when the base is smaller or larger than the separation of the eyes. If, for example, a pair taken from the two extremities of a base of length B with a principal distance F is examined at a distance f from the pair (or with eyepieces of focal lengthf), variation of separation between the pairs of corresponding points of two objects situated respectively at distances d and d' is e el - ) d d' so that, for corresponding points of the structed solid to appear at different distances, it is sufficient that the variation (e - e') is greater or equal to the limit of separation f/2,000, then I \ f d d' 2000BF BF or d j BF 2000 Taking, for example, the values f = 10 cm. F = 50 cm. B = 200 in.
we find as range 2,000 kilometres and as depth of the neutral zone 2 metres to 2,000 metres, or o-5 metres to 1,000 metres.' It will be noticed that if the distance from the background remains the same, the extent of the neutral zone is constant if, all other conditions remaining the same, the product BF of the base and the principal distance is a constant. To obtain at different distances d' stereograms of the same power (same extent of neutral zone) the product BF must be varied proportionally to the square of the distance d'.
825. Normal and Exaggerated Relief. The relief perceived in the viewing of the stereogram of a very distant object or an object of micro scopic size is often said to be exaggerated. But without this exaggeration it would be our eyes would not be able to perceive the relief of a distant range of mountains, or of the ground as seen from an aeroplane, or of a microscopic preparation.
An object a, m times as small as an object A, and situated m times as near, gives a sensation of relief m times as great, and it is here that the large bases become useful in stereoscopy.
If it is correct to say that, under certain condi tions, the sensation of relief is much more pro nounced, it is not correct to speak of exaggerated relief when the reconstructed object is similar to the object itself, the stereogram being viewed under normal conditions.
One should avoid as far as possible the use of the expression exact relief. If under certain conditions we can obtain a stereograin which, correctly viewed, suggests perfect similarity between a relatively thin object and its image, objects situated nearer or farther from the observer will not give this sensation of similarity ; the relief will be increased for near objects, and weakened for distant objects. We know, besides this, that the stereoscopic sensation varies from one individual to another.