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Image coordinates measured in comparators contain some systematic errors sourced from the 
photogrammetric system. Some corrections and reductions must be applied to these coordinates 
before they are used in the mathematical models. These corrections and reductions are 
comparator calibration effect and emulsion carrier, lens distorsion, atmospheric refraction, earth 
curvature and image motion (Gosh, 1979; Brown, 1980). These corrections, except lens distorsion 
correction , are independent from the orientation of exposue system of photographs. 
2.2 Corrections Related to Orientation Parameters 
Corrections related to the small errors of orientation parameters can be classified as following , 
with taking account of some applications: 
a. In some applications (Veress and Sun, 1978; Brandenberger and Erez, 1972), all of the 
exterior orientation elements or some of them are determined directly with measurements in 
field. A phototheodolite or a stereometric camera are used to exposure the photographs in 
these applications. 
b. Interior and exterior orientation elements are a priori known and can be assumed errorless in 
some photogrammetric applications (Bas, 1985). 
c. In some applications of analytical photogrammety ( Fuad, 1984; Abdel-Aziz, 1982), orientation 
of stereometric camera is fixed (such as Wild C40, C120, Zeiss SMK40, SMK120) . Namely 
orientation of two cameras remains constant for all of taken stereopairs in these applications. 
d. In some photogrammetric applications (Altan, 1983; Scott, 1978; Porter and Burns, 1978; 
Smidrkal, 1968), all photographs are taken from the same exposure station and under the 
same conditions, with the same interior and exterior orientations, at different times. The 
dimensional changes of objects are examined according to the principles of parallax 
photogrammetry, “False Parallax” method or “The Time-Parallax” method, in these 
applications. 
A stereometric camera consists of two identical metric cameras mounted rigidly at the ends of a 
fixed base so that their optical axes are parallel to one another. Angular orientation of a 
stereometric camera is set up by levels,and the accuracy of orientation depends on the sensitivity 
of used levels. This situation is valid for phototheotolites. 
Therefore the image coordinates measured in comparators can be corrected for small errors of 
orientation by using the approach introduced in this study. For applications in step d, image 
coordinates measured in the second photograph can be transformed onto the coordinates of first 
reference photograph by means of the offered approach. 
3 MATHEMATICAL FORMULATIONS 
The equations for the influence of small errors of orientation on the image coordinates can be 
found from literature (Gosh, 1979; Finsterwalder and Hoffman, 1968; Hallert, 1960) in different 
forms and for different aims. Figure 1 shows the used coordinate systems in this study. 
  
  
  
  
  
  
> X 
  
Figure 1. Object Space and Photographic Coordinate System 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 39