9 
Standard errors of the coefficients 
s xl = 0.411 
Sx 2 = 0.115 
s x 3 = 0.104 
s x4 = 0.008 
Confidence limits for the coefficients on the 5 % level are Az 2 S;. 
Thus, all the coefficients except x 2 in the regression analysis are significant on the 5 % level. The loca 
tion of the point of gravity as a function of the exposure time is shown in fig. 1:33.1 (Appendix). The total 
displacement is about 1 pm for a variation from one third normal exposure to three times normal exposure. 
The influence of the development variation was 0.5 pm. The influence of the filter corresponded to the 
reduced exposure. For the total number of observations (50) it was found that the point of gravity was 
situated 6.43 pm from the surface of the emulsion. An emulsion thickness of 15.8 pm was found 
obtained from about 500 settings. 
If the location of the point of gravity is considered as the point where the measurements are made 
in an instrument a radial displacement will occur. This can be obtained from fig. 1.33:2 (Appendix). 
_ sin V 
dr t — x 
n e 
where 
dr t — the radial displacement 
x = point of gravity from the emulsion surface 
v — angle of incidence 
n e — refraction index of the emulsion 
For a wideangle camera (c = 150 mm) and n e = 1.5 the radial distortion caused by the variation of 
1 pm in the location of the point of gravity (dr v ) due to variation in exposure is shown in fig. 1.33:3 
(Appendix). The total displacement (dr t ) caused by the fact that the picture is not located at the 
emulsion surface is shown in the same figure. 
Conclusions 
The radial distortion caused by variations in exposure and development has a small influence on the 
image coordinates. Most of this effect is eliminated with a scale factor. If it is assumed that the point of 
gravity is the location of the picture, then small errors are introduced when the picture is measured in 
an instrument with orthogonal observation. The errors increase with the radial distance and also contri 
bute to the weight variation within the photographic image. 
References: Geavert handbok: Recept och rad 
Hallert, B.: Investigations of the weights of image coordinates in aerial photographs. 
Phot. Eng. Sept. 1961. 
Mees, K.: The theory of the photographic process. New York 1954. 
Mutter, E.: Kompendium der Photographic, 1. Band. Berlin 1956. 
These investigations have been made by L. Andersson and J. Talts as diploma work. This report 
was written by J. Talts, MSE. (Master of Surveying Engineering). 
1.34 Flatness of Glass Plates 
Glass plates are used for many tasks in photogrammetry, such as supporting plates in cameras, glass 
plate negatives and diapositives, glass grids, supporting glass plates in plotting instruments and rectifiers. 
Ihe flatness of such plates is of great importance for the accuracy of image coordinates in central 
projection. Therefore, attention has been paid to the flatness of glass plates used in photogrammetry.