4 
1. THE IMAGING PROCEDURE 
FACTORS AFFECTING THE GEOMETRICAL QUALITY 
OF IMAGE COORDINATES 
1.1 Atmospheric Refraction and Curvature of the Earth 
In reference (1.1:1) A. Leijonhufvud has calculated the influence of atmospheric refraction and the 
curvature of the earth upon the image coordinates of wide angle photographs at specific flying altitudes. 
The ICAN-atmosphere was used in his calculations. 
In this research he has extended the formulas to superwide angle photographs and for flying altitudes 
of 1 000, 4 000 and 10 000 meters. Some minor defects in the original formula systems have been corrected 
and some better determinations of basic constants have been used. The radial distortion effects are 
graphically presented for wide angle cameras in fig. 1.1:1 and for superwide angle cameras in fig. 1.1:2. 
Dr. Leijonhufvud has also estimated possible deviations between the basic data of the ICAN-atmos 
phere (temperature, pressure, humidity etc.) and corresponding data under operational conditions, 
primarily affecting Northern Europe. The deviations have been estimated in statistical terms. The 
influence of differences between the ellipsoid and the sphere and the influence of elevation differences on 
the ground have also been considered. The combined standard error of the radial distortion effects as 
shown in fig. 1.1:1 — 2 is presented graphically in fig. 1.1:3 (centesimal seconds cc of the angles of the 
rays) and in fig. 1.1:4—6 («m in the images from wide angle and superwide angle cameras). The detailed 
procedure for the determination of the results presented here will be published later by Dr. Leijonhufvud. 1 
According to these investigations the standard errors of the radial distortion effects resulting from 
atmospheric refraction and curvature of the earth are comparatively small under assumed conditions, 
but extreme deviations from the normal values according to the ICAN-atmosphere caused by unfavour 
able combinations of the errors of basic data cannot be excluded. Practical tests of the atmospheric 
refraction under operational conditions for aerial photography are desirable. 
All illustrations are shown in the Appendix. 
Reference. 1.1:1. Leijonhufvud, A.: On Astronomic, Photogrammetric and Trigonometric Refraction. 
Diss. Stockholm 1950. 
1.2 The Influ ence of Refraction and Curvature upon Horizon Images 
The influence of refraction and curvature upon the location of the horizon is of special interest for 
the Finnish horizon image method of determining inclinations of the aerial camera at the moments of 
exposure. Some results of detailed investigations of this problem by Dr. A. Leijonhufvud will be presented 
here 2 . The principles of the problem are shown in fig. 1.2:1. Table 1.2:1 (the Appendix) contains numerical 
results of the investigations. Note the explanations to the right of the table, g and c are centesimal 
grades and minutes respectively. The deviations (dev) are referred to O m horizon. 
1.3 Flatness Defects of the Image 
In general, the photographic image should be a plane 3 , but the physical realization of this mathemati 
cal concept will always be approximate. Because the image is a central projection, image coordinates 
measured orthogonally to the image will be influenced if the image deviates from a plane in the moment 
1 Fotogrammetriska Meddelanden. Division of Photogrammetry, Stockholm 70. 
2 The investigations will be presented later in more detail in Fotogrammetriska Meddelanden. Division of Photogrammetry, 
Stockholm 70. 
3 There are cases when surfaces other than planes are used intentionally for recording the photographic image in photo 
grammetry. An example is the Wild superwide angle camera where the supporting back of the magazine is curved.