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The resolution concept uses the notation “image resolution” or “image quality”. This can lead sometimes to 
misunderstandings for describing the resolution of small structures defined by a distance (e.g. the distance between two 
peaks). In this case an increasing resolution is related to a decreasing distance. Therefore we introduce as a measure for 
the resolution the a Minimum Resolvable Distance (MRD). In the context of a Rayleigh-criterion (equation (1)) based 
resolution concept, the MRD is the minimum distance of two radiating points to be resolved. 
The investigation of the attainable resolution for staggered and non-staggered arrays is the main topic of this paper. 
1.1 Staggered Arrays 
To validate the usefulness of staggered arrays theoretical investigations of the ultimate spatial resolution taking into 
account the total point spread function (PSF) and Shannon's sampling theorem have been carried through. Staggering 
means that because of using two shifted sensor lines twice as much sampling points are used as without staggering, i. e. 
the sampling distance A of the non-staggered array is divided by two. This often guarantees that the sampling condition 
can be fulfilled which means that no spatial spectral components above the spatial frequency limit 2/A are present and 
which often is not fulfilled in the non-staggered case (here no spatial spectral components above 1/A are allowed). 
Therefore, better spatial resolution is obtained even in the case where the pixel size equals the sampling distance A. 
Theoretically, the resolution is as good as for a non-staggered line with half pixel size A/2 if the pixels of the staggered 
line array have size A/2 too (with pixel distance A). Of course, in practice the slightly different viewing angle of both 
lines of a staggered array can lead to a deterioration because of aircraft motion and attitude fluctuations and a non-flat 
terrain. Fulfilling the sampling condition further means that no aliasing occurs. This is essential for the image quality in 
quasi - periodical (textured) image areas. Because the sampling theorem can be applied errorless interpolation between 
pixels (sub - pixel resolution) is possible. That way precise positions of points, lines, edges and corners can be 
determined. Furthermore, image restoration methods for enhancing the image quality can be applied more efficiently. 
Image simulation with imaging sensor simulation software for staggered and non - staggered sensors developed at the 
Institute of Space Sensor Technology and Planetary Exploration and experiments in the laboratory confirmed the results 
of the theory. Airborne experiments with the infrared HSRS sensor system also showed considerable enhancements of 
the image quality using the staggered mode of operation. It is planned to carry through corresponding investigations 
also with an prototype of the Airborne Digital Camera using the first time the staggered 2 x 12000 pixels line array in 
an airborne experiment. 
2 RESOLUTION AND PSF 
2.1 Ideal case - neglectable PSF 
In the ideal case there is a neglectable influence of the optics compared to the sampling. That means that the width of 
the PSF is very small (or neglectable) compared with the pixel size. In this case the resolution can be derived by simple 
geometrically consideration (see Figure 1). 
single point resolution two point resolution 
  
  
  
es MRD=6 MRD - 2-àxz. |-a—————»- 
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Figure 1. Resolution of linear arrays (neglectable PSF) 
In the case of a linear array with neglectable PSF the single point resolution is not better than 0, where 9 is the pixel 
size. For the two point resolution the criterion (1) can only be fulfilled if the distance between the two points is greater 
than 25+e (8 is a very small value) . The same consideration can be carried out for staggered arrays (see Figure 2). 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part Bl. Amsterdam 2000. 165