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Fig. 3. Convergence and stereoscopic depth of field.
that this condition cannot be satisfied strictly for any spectator; for it is impossible to have the spectator's head on the axis of projection without casting a shadow on the screen. Still, it must be remembered that the closer the spectator is to the axis, the more closely the observed depth effect will approach natural relief. Again, if the spectator is not stationed at the distance D' from the screen as defined by (16), he will see a somewhat distorted relief. In particular, if the spectator is farther from the screen the image of an axial element a, or the segment transversely projected into k', will suffer an apparent enlargement Eaf equal to the apparent enlargement Et' suffered by the image h" of h. Upon projection, therefore, we have Ea' = Etf — 1. In nature, if the observer had withdrawn from the object so that the transverse dimensions would suffer an enlargement Et = Etr, the axial element would have suffered an apparent enlargement.
= Et'
D
D/Et' a
given by (5).
Ea/Ea' =
Comparing Ea and Ea ', D a
DlEt' a
Having assumed D/Et' D and
Et' — 1,
have
Ea.
We can therefore conclude that if the spectator is farther from the screen, the depth of objects will be exaggerated,
while if he is closer to the screen, the picture flattens.
The choice of focal lengths of cameras and projectors must be such that the largest possible number of spectators can be placed near the position of natural relief; this position should not be too close to the screen, since the spectators at optimum distance would then necessarily be fairly far away from the projector-screen axis.
Stereoscopic Depth of Field
Comfortable stereoscopic vision is impossible unless the extreme frontal planes of the object lie within two definite limits.
Let A\ and A2 be the intersections of the two extreme frontal planes of the object with the ocular axis of the eyes 0, semibase b0. The convergence is 71 = 2b0/Dl at Ai and y2 = 2b0/D2 at A2 (Fig. 3). For comfortable observation of the object, it is necessary that the maximum increment of convergence of visual rays, i.e. the difference 71 — 72, should not exceed a certain limiting value. This limiting value, unfortunately, varies from one observer to another; some people find a convergence differential of as little as 1° slightly troublesome, while others tolerate much higher differentials without fatigue. Since a stereoscopic film is to be viewed by numerous spectators, we must adopt a maximum value of 71 — 72 sufficiently small so that anyone may witness the performance without fatigue. At the same time, the limit must not be too
520
December 1952 Journal of the SMPTE Vol. 59