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Figure 2.
h' = hfv/Xv.
(6)
If a projection lens of focal length fp projects this image A' on a screen placed at a distance Xp, the image h" on the screen will have the dimension
h" = h'Xp/fp = hfvXp/fpXv. (7)
A spectator stationed at a distance Dr from the screen sees h" at an angle ft'
ft > = h "/D = hfvXp/fpXv -\/D'. (8)
The distance D at which one must be stationed to see h at the angle j8 = 0' in nature is given by
h/D = hfvXp/fpXv \/D', or D=fpXv/fvXp-D'. (9)
Consider a shot of the axial element a with a semibase bv (Fig. 2).
* = afvbv/Xv(Xv a}. (10)
Upon projection, we obtain an image k ' of k on the screen :
k' = kXp/fp, hence k' = afvbv/Xv(Xv a)-Xp/fp. (11)
The spectator sees k' at an angle a'
(12) We are to have a.' = a, or
fvXp/fpXv-\/D'.abv/(X, -a)
ab0/D(D a). (13)
The value of D is given by (9). Introducing this value of D into (13), we have
The condition (14) must be satisfied for any value of a whatsoever, and the ratio b0/bv cannot vary with a. It is therefore necessary that ()(6«/69)/(ta = 0 no matter what a is, or that
Xv = D'fpXv/fvXp = O. (15)
This relation (15) determines the value of/)7
D' = Xpfv/fp. (16)
Substituting this value of D' in (14),
b0/bv = 1, 60 = 6,; (17)
in (9), D = Xv; (18)
in (8), 0' = A/*.; (19)
and in (12) a' abv/Xv(Xv a). (20)
To summarize, the spectator receives the illusion of natural relief if the following two conditions are satisfied:
1. The camera base must be equal to the ocular base (relation 17);
2. The spectator must be stationed along the axis of projection at a distance from the screen which is to the projectorscreen distance as the focal length of the camera lens is to the focal length of the projection lens (relation 16).
Relations (18), (19) and (20) show us that when conditions 1 and 2 above are satisfied, the spectator will see all the dimensions of the image at the same angles as the photographer saw the corresponding dimensions of the object while shooting.
Condition 1 is readily satisfied by construction; the camera must have a base between 63 and 67mm.
As for condition 2, it is to be noted
Eugene Millet: Depth Effect in Motion Pictures
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