(two in line 
] in the four 
‚solution the 
ions (1), (2) 
le points the 
ar lines. This 
> resolution. 
e diffraction 
ional effects 
e motion (in 
e volume of 
th respect to 
1e optics and 
rranged in à 
x, y) with the 
(4) 
lirection. The 
Herbert Jahn 
  
1 o 0 
Lo df. I 
ken dio rptu (5) 
0 elsewhere 
The single or double point source &x,), &xo+a) generates in front of the focal plane an spatially dependent intensity 
distribution 
H(x —xo) or H(x — xo) + H(x — xo - a). (6) 
H(x) is the system PSF without the pixel PSF. 
The signal in the sampling point i-A is obtained by integrating the optical signal (6) over the pixel area (applying (4)) 
6/2 
I(ia)= [[H(x+iA=x,)+ H(x+iA-x, —a)lx. (7) 
-ó/2 
Assuming a Gaussian-PSF with a "width" (standard deviation) o in (7), the integration can be performed using GauB’s 
probability-integral 
  
7 X 2 
D(x)= Tax Jo 5) ; (8) 
am ? 2 
The result is a pixel dependent intensity distribution: 
fiue (ne 7 (8-28) (9) 
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(for single spot) and for double spot: 
  
(10) 
PL i ex 
The measured values Z(/A) (10) depend (for a given pixel distance A/o and a pixel size ó/o (related to the PSF width 
0)) also on the point position (phase) xp /0 and, for double point resolution, on the distance a/o of the light spots. That 
means that the accuracy definition or the contrast (1) depends on the displacement of the point source relative to the 
pixel. 
  
  
  
  
  
  
   
Figure 3. Double point resolution in relation to the optical PSF. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 167