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