N À 
AT TE SO TS ET 
4.3 Averaging with respect to the image field 
This is an important parameter for aerial Survey lenses. For 
an image quality criterion, the MTF needs to be averaged with 
respect to the field angle w. The weights p(w) are similar to 
those used for the AWAR and are considered to take account of 
the appropriate area belonging to the chosen image point con- 
[ 
( 
sidered. Therefore averaging the areas of the MTF Q(w) with 
respect to the image field can be written: 
  
  
  
  
"max : Wmax 
Q = pw) Q (w) dw, with ( Pp (v) aw = 1 
vo 0 In 
Re : (0 
: S 1/2 
where Q (w) = ( (rs (R) T+ (R)) / dR 
0 
Tg - (Ts (R) Ty (RR = geometrical MTF from Tg(sag.MTF) 
and TX (tan.MTF) 
R = spatial frequency (Lp/mm) 
Rg - limiting spatial frequency (inter- 
Section of the threshold curve with 
the lower MTV. of T.-, TQ) 
For practical applications the integral is written as a sum, 
namely: 
m ces N (9 
Q = à Pk Qk , where = Pk = l1 and k = 152... 359.500 1 
k=1 k=1 
N = number of image points 
  
For the analysi 
the two images 
small variations of image quality with respect to image field 
are acceptable. To take into account Some information on the 
variation of image quality over the field we can write: 
AT 
N 
Qx = [2 
k=] 
Dk a] £02 | ila 50 
For a perfectly uniform image quality over the whole image 
field, Q for ali L