the system varies with spatial frequency. The function is normalized 
to 100 7 at zero frequency. Modulation is defined as 
M: ( E max - E min ) / ( E max * E min ) { 3.2) 
E max and E min are the maximum and minimum amplitude of the signal 
and M 1s computed for all spatial frequencies k. The advantage of 
using the MTF lies in the multiplicative property. MTF:s can be cas- 
aded 1.e. multiplied frequency by ‘frequency. Thus if the transfer 
functions for the system components can be determined the system MTF 
is known. There also exists a relation between contrast ratio and mo- 
dulation 
C = (1 + M ) / t 4 - M ) (3.3) 
This relation is important because resolution is dependent on object 
contrast. 
The use of MTF curves makes it possible to predict system resolution 
by cascading MTF:s for different steps in the image formation process. 
MTF:s for lenses, image motion and emulsion can be computed 
theoretically, or measured ( 8rock, 1970 ). System MTF:s can be 
computed from measurements on operational imagery ( Welch, 1971 ). 
We have at least two different methods for predicting system 
resolution. The first is based on the use of a system MTF excluding 
the contribution of the emulsion. A threshold modulation curve (TM 
curve) or aerial image modulation curve ( AIM curve ) is used with the 
system MTF ( Brock, 1970 ). Both curves are plotted in the same 
diagram and the spatial frequency at the intersection of the two is 
accepted as system resolution. The TM or AIM curves are produced for 
different emulsions and object contrasts. TM curves are measured under 
laboratory conditions and show target modulation as a function of 
spatial frequency. The curve represents the optimum resolution for a 
given film/observer combination. 
  
  
    
  
  
  
  
  
  
  
  
100 i99 
sor; t ue 
F 2 L WucwLens + image motion 20 um 
60 sc N 
ë - 
~ 4g. E ao 
T @& 
: x pe 
: - 
x ac 
* 20H 
10 LLLI À 1 1 i4 4 1a 10 ibid x i 1 i tt 114 
i 105 18020 5 30,0, 5060, 100 5 6 10, i$. 20. 30. 40.50 60 100 
Spatial frequency (cycles/mm) Spatial frequency (cycles/m) 
Fig. 3.41 
3.1 a : MTF's for lens, emulsion, 20 Um image motion and the corre- 
sponding system MTF ( After Manual of Photogrammetry ). 
3.1 b : Prediction of system resolution from NTF's for lens and image 
motion and threshold modulation estimated according to (3.4). 
142