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Herbert Jahn 
  
1 
L' = 13 
2^ (13) 
is bigger than the spatial frequency of band limitation p (A is the sampling distance). In this case from the sampling 
values /;; the whole function /(x, y) can be reconstructed by application of Shannon's sampling theorem (see e.g. Jahn, 
Reulke, 1995) 
I(x, y) - Y,1, ; sin |x (x- ia) -sin jzo = js) (14) 
= A A 
For illustration the ADC camera of LH Systems (Eckardt et al., 2000) is considered now. The optics to be used has a f# 
= 4. This corresponds to a spatial frequency of band limitation k^^ of a diffraction limited optics of approximately 
500 Ip/mm (see Jahn, Reulke, 1998). Measurements show that the MTF at 130 Ip/mm drops to 1096. The characteristic 
width of the optical PSF therefore is O = 2.6jum (Schlienger, 1996). The Nyquist frequency K"^ for the linear array is 
77 Ip/mm and for the staggered array 154 1p/ mm (with respect to the pixel size 6.5um). In the case of linear array we 
have MTF(771p/mm)=45% and MTF(1541p/mm)=5%. 
The result of this consideration is that (in case of ADC) for staggered arrays the sampling theorem is valid and all 
geometrical structures which pass through the optics can be reconstructed. The MRD of staggered arrays in this case is 
the same as for linear 24k arrays. 
4 EXPERIMENTS 
41 Visual enhancement of ADC image quality using staggered CCD arrays 
To show the visual effects of using staggered and non-staggered arrays and to study the influence of various MTF's a 
simple image simulation program for ADC image simulation written in IDL was developed. First, a test image showing 
simple objects and patterns was generated (figure 5). Then the test image was Fourier transformed using an IDL FFT 
procedure. Various Optical Transfer Functions (OTF) (see Jahn, Reulke, 1995) have been taken into account, especially 
the geometrical OTF of a pixel, the measured (and approximated) OTF of the optics, and the OTF of pixel shift caused 
by motion. The total OTF obtained by multipying all single OTF's has substantial spatial frequency transmission above 
the Nyquist frequency but nearly zero transmission above the doubled Nyquist frequency. That means that with the non- 
staggered array substantial undersampling can occur whereas with the staggered array undersampling is negligible. 
After having multiplied the Fourier transformed test image with the total OTF the inverse Fourier transform is applied. 
Figure 6 shows the blurred i 
      
Figure 5. Test image. 
spatial frequency of stripe pattern: 100mm’, distance of dots and lines: 10pm 
Then the image is sampled. Two cases are considered: 
l. Non-staggered array: The sampling distance is A, — A, — 6.5pum. 
2. Staggered array: The sampling distance is 0.5-A; = 0.5-Ay = 3.25um. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 169