72 THREE-DIMENSIONAL PHOTOGRAPHYtwo points L-L’. The line wx passes through L and intersects the
picture plane xz. Draw yz parallel to wx, through E to the picture
plane. The intersection of the rays LA, LC and LB with xz are
repeated upon xz starting at point z. The significant ray paths are
then drawn from E through these repeated intersections, to form
the triangle A’B’C’.
It will be seen that this corresponds to the former description
of an object without perspective or parallax distortion, but which
appears to be nearer and smaller than the real object.
It is obvious that if E and E’ are assumed to be the lens posi-
tions, and L-L’ the eye positions, the same diagram will illustrate
the use of a less than normal base.
It should be said that the expression “appears to be smaller”
should be regarded as highly theoretical inasmuch as we have no
absolute size perception, size being always estimated by a system
of comparison. Therefore, as a matter of fact the abnormal size
factor is rarely observed unless the subject is so familiar that we
know its approximate size, or unless there is some external object
(as in trick stereograms) by which comparison may be made. On
the contrary, the differential distance perception by parallax is
surprisingly accurate.
Finally we have in Fig. 4-15 the explanation of the PePax
principle of maintained perspective-parallactic ratio. The lenses
F-F’ have twice normal focal length and are used at twice normal
separation. The viewer lenses E-E’ are normal. By the same rea-
soning used heretofore it will be seen that the original triangle
ABC will be seen in the apparent position A’, B’, C’. Here the
object appears to be at only half the distance, it appears to be
undistorted, and it appears to have natural size. This is the para-
stereoscopic image, and differs from the orthostereoscopic only in
the fact that a given space contains a greater amount of solids than
is physically possible, but because of the sequence system of hu-
man vision which prevents us from looking at the whole of a
scene simultaneously, we are unable to grasp the physical impos-
sibility in the form of any perceptible visible distortion. There-
fore the distortion of parastereoscopy is only that of knowing the
reproduction to be unnatural, not one of seeing that it is.
Hyperstereo.-No discussion of variable base would be complete
without the mention of hyperstereo. This is the making of stereo-