TESTS OF FUNDAMENTAL PHOTOGRAMMETRIC 
OPERATIONS* 
By Dr. BERTIL HALLERT 
Introduction 
Among the fundamental operations in the photogrammetric procedure 
we have: 
1. The reconstruction of the pencils of rays in the instrument. 
2. The correction of y-parallaxes. 
3. The correction of x-parallaxes. 
The accuracy of the performance of these operations is, of course, of the 
greatest interest for the photogrammetric procedure since the final data, the 
X, y- and z-co-ordinates on the ground are functions of the fundamental 
operations. 
For a comparison between methods, instruments and operators the 
accuracy of the fundamental operations can be used. The best way to express 
the accuracy is by using the principles of the method of the least squares. 
l. The accuracy of the reconstruction of the pencils of rays. See Fig. 1. 
An accurate grid is assumed to be projected through the projector and the 
co-ordinates of the projected grid points are measured in the projection plane. 
The grid and projection planes are assumed to be approximately parallel and the 
projector axis is approximately orthogonal to the planes. 
The origin of the grid co-ordinates x' y" is located near the principal 
point of the projector and the origin of the co-ordinates in the projection plane 
in the corresponding point of the projection plane. Furthermore, the co- 
ordinate axes of the grid system are approximately parallel to the co-ordinate 
axes of the projection plane. 
The scale ratio between the grid and the projection co-ordinates is approxi- 
C . . . 
mately known as 3, "here c and 7 are the projector constant and the projection 
*This paper is partly based on work performed at the Mapping and Charting Research 
Laboratory, Ohio State University, Columbus, Ohio, U.S.A., under contract with the 
Engineer Research and Development Laboratory, Fort Belvoir, Va., U.S.A. 
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