Herbert Jahn 
  
single point resolution two point resolution 
MRD = À MRD = 3-^*-2 |«———- 
Y 
| | | | | | | 
| | | | | | > =— linear array ad | | | | | | | 
O0  ..pixelsize 
flight direction A illuminated pixel 
X 
  
  
  
  
  
  
  
  
  
  
  
  
  
[77 -—- sampling points — —* 
$ aesie quer ee ete se 
e sie 9/9 & € » | 
L—-a4 ©, X 4 
A-0/2 ... sampling interval illuminated pixel 
Figure 2. Resolution of staggered arrays (neglectable PSF) 
Due to the point like image formation, in the case of staggered arrays each point influences four pixels (two in line 
direction and two in flight direction). The point can be shifted over a distance of 0/2 giving the same signal in the four 
pixels. 
For the single point resolution the accuracy of the point determination is A = 9/2, and for the two point resolution the 
MRD is 3A = 1.5-8. As a result, for the resolution of single point imaging we have for CCD-line configurations (1), (2) 
and (3) 
dd 
MRD(12K) > MRD(2-12Kstaggerea) = MRD(24K) or ô > = = S Q) 
and for the two point resolution 
MRD(12k) > MRD(2-12Kk;taggered) > MRD(24k) or 2-5>1.5-5>8. (3) 
For single point consideration the resolution of staggered 12k arrays is equal to 24k arrays. For the double points the 
resolution improvement due to the staggered arrays is between the both extreme cases of 12k and 24k linear lines.This 
consideration shows, that in the case of a vanishing PSF the application of a staggered array can improve the resolution. 
2.2 Real case - real PSF 
In this chapter the influence of the PSF on the resolution shall be investigated. The ideal PSF is given by the diffraction 
limit of the optics. Due to the lens aberration the PSF of a real optics in most cases is worse. Additional effects 
influencing the total system PSF are the geometry and sensitivity distribution of the detector elements, the motion (in 
flight direction), the atmosphere and, for higher wavelengths (greater then 700 nm), diffusion effects in the volume of 
the CCD-element. 
This consideration can not be done with a simple geometric illustration. Therefore the sampling process with respect to 
a special pixel size shall be described. We are looking for the sampling of the optical signal (x, y) behind the optics and 
in front of the focal plane. The sampling is done by rectangular or square detectors with pixel length 6 arranged in à 
regular line grid with sampling distance A. For the staggered arrays is A = 0/2. 
The signal values L;; 2 I(x,yj) (x; 5 iA, yj Xj A, ij — 0, +1, £2, ...) can be obtained by a convolution of /(x,y) with the 
geometrical pixel PSF 
(s. yj)» f 8G xy; y) Go. y)avay. 0 
For clarity the following calculation is done only in one dimension. But the same is valid for the other direction.The 
pixel PSF for the simplest case (constant sensitivity, no diffusion effects) is 
  
166 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 
The 
distr 
H(x) 
The 
Asst 
prob 
The 
(for 
The 
0)) € 
mea 
pixe