Herbert Jahn 
  
STAGGERED LINE ARRAYS IN PUSHBROOM CAMERAS: THEORY AND APPLICATION 
Herbert Jahn, Ralf Reulke 
Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Weltraumsensorik und Planetenerkundung, 
Rutherfordstrasse 2, D-12484 Berlin, Germany, Tel.: (+49) 30 67055-518, Fax: (+49) 30 67055-529 
Herbert.Jahn G dlr.de, Ralf.Reulke Q dlr.de 
Working Group I/5 
KEY WORDS: Sensors, Camera, Performance Analysis, Simulation, Photogrammetry, Remote Sensing. 
ABSTRACT 
Using pushbroom sensors onboard aircrafts or satellites one needs - especially for photogrammetric applications - broad 
image swaths and high geometrical resolution together. To accomplish both demands staggered line arrays can be used. 
A staggered line array consists of two identical CCD lines with one shifted half a pixel with respect to the other. Today 
such sensors are available in the VIS/NIR spectral region with 2 x 12000 pixels (staggered CCD line arrays) and in the 
mid and thermal infrared with 2 x 512 pixels (staggered MCT line arrays). These sensors will be applied in spaceborne 
remote sensing missions (small satellite BIRD and International Space Station project FOCUS, both for hot spot 
detection and evaluation), in experimental airborne systems (with the Infrared Airborne Camera HSRS of the Institute 
of Space Sensor Technology and Planetary Exploration) and, most important, in the first commercial Airborne Digital 
Camera (ADC, new name: ADS40) of LH Systems. 
The paper presents the theory, some results of the simulation, examples with real imaging systems in the laboratory and 
on aircrafts. 
1 INTRODUCTION 
Spatial Resolution, Point Spread Function, and Sampling Theorem 
Spatial resolution depends on the PSF (point spread function) of the whole system. Above all the total PSF up to the 
sampling device (e.g. the CCD-line) compared to the sampling rate or the Nyquist frequency determines the resolution 
of the system. This can be illustrated with the example of the star sensor: In case of ideal imaging (with delta peak 
PSF) the location accuracy is not better then a pixel size. In the case of a wide spreading PSF the star image is smeared 
over much more then one pixel and can be detected also in the neighbouring pixel. Only under this condition the star 
position can be detected with subpixel accuracy using an interpolation algorithm. 
The investigation of the spatial resolution of an imaging system therefore must consider the PSF (at least from the 
optics) in relation to the sampling process. Moreover in this consideration the SNR (signal to noise ratio) of the whole 
system must be included, which can be shown on the following example: A smaller pixel size gives a better spatial 
resolution but a poorer signal to noise ratio at the same time and vice versa. 
In the following the spatial resolution of staggered arrays shall be investigated. To study the resolution the image of 
one or two delta signal peaks can be investigated. The resolution of the single 12k CCD-line (1), the staggered 212% 
line (2) and the linear 24k line (3) will be compared. For the same focal length the 24k line must have half of the pixel 
size as the 12k or 2-12k line. If the pixel size for the 24k line is the same as the 12k line, the focal length must be the 
twice of the 12k line camera. In both cases the radiometric characteristic for the 24k line is the same. 
For a single point we define the error of the location of the image as an accuracy measure. In the case of two point 
accuracy the resolution of these two points is defined by the minimal necessary contrast (according to the Rayleigh- 
criterion, Jahn, Reulke, 1998) 
_ MAX{I}- MINU} 
=0.25. (D) 
me MAX {I} 
  
164 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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