I
*
16
where
dx = [pi(r 2 + 2 (x—Xq) 2 ) + 2p 2 (x—x 0 ) (y—yo)] [1 + ¿V 2 -f /V 4 4- . .]
5.3.1
dy = [2pi (x—Xq) (y—y 0 ) + p 2 (r 2 + 2 (y—yo) 2 )] [1 + P+ T 4 r 4 + . .]
5.3.2
— Ji sin a 0
— /i cos a 0
JJJi
h/Ji
Pn Jn-1 / J1
The tangential distortion is maximum in direction a 0 and varies according to
the following formula:
dt = cos (a—a 0 ) (J\r 2 + / 2 ^ 4 "h J^r 6 + . . .) 5.3.3
If we want to introduce tangential distortion in our mathematical model the
terms 5.3.1 and 5.3.2 are added to the basic expressions 5.1.1 and 5.1.2.
5.4. AFFINE FILM SHRINKAGE
When the emulsion base is made of acetate we very often get an affine film
shrinkage. This means that we have unit scale in direction a of the image co
ordinate system, (x, y), and scale 1 + d in direction a + —. See Fig. 5. These
directions define the axes s and t, and we obtain the relations
x—x 0 — s cos a — t sin a 5.4.1
y—yo —S sin a + t cos a 5.4.2
or
s = [x—xo) cos a + (y—y 0 ) sin a 5.4.3
t — — (x—x 0 ) sin a + (y—y 0 ) cos a 5.4.4
A scale error 3 in the quantity t in formulas 5.4.1 and 5.4.2 causes the co-ordi
nate errors
Ax = — t d sin a 5.4.5
Ay = t S cos a 5.4.6