25 
1.82 X-Ray Instruments 
L. Hollender, Dentist, has determined the interior orientation of X-ray instruments for medical 
purposes with the grid method. He has used films and glass plates and some of his results are shown in 
figures 1.82:1 through 7 in the Appendix. 
Reference. Hollender, L.: Determining the interior orientation of roentenography. Diss. Malmo 1964. 
1.83 Calibration of Underwater Cameras 
Obviously a camera which will be used for measuring purposes under water must be calibrated under 
operational conditions. J. Talts, MSE, has conducted a series of calibrations and tests with two under 
water cameras and some of the results are summarized below. 
The grid method was used throughout. See references 1.342:1 and 1.8:1. Test fields were constructed 
on a wall and on the bottom of a swimming pool to supplement existing test fields within the Division 
of Photogrammetry of the R. Institute of Technology in Stockholm. The cameras were tested by 
photography in air with and without underwater housings as well as under water. Only negative film 
was used. All measurement of image coordinates were made in the Wild StK 824 stereocomparator and 
the calculations in the FACIT electronic computer. 
A theoretical derivation was calculated of the radial distortion to be expected. From fig. 1.83:1 
in the Appendix the following formula for the radial distortion was found: 
sin v 
* = DTdTk i {D+d),gv ~ D ^ 
sin V 
V n 2 2 
Variations in temperature, salinity and pressure—deformations of the glass window of the underwater 
housing included—may have considerable influence upon the radial distortion. 
The most important results of the tests are shown in figs. 1.83:3 through 14 in the Appendix. 
The underwater radial distortion effects observed agree well with the theoretical derivation (hgs. 
1.83:3 and 9 in the Appendix). The standard error of unit weight is rather large and indicates a low 
basic accuracy. Pronounced weight variations with the radii were also found. Closer investigations 
indicated that there were considerable image coordinate errors, probably caused by lack of film flatness. 
Correlation tests between photographs taken with the same camera also indicate that there are significant 
correlations between the residual coordinate errors. Tests of the distribution of residuals show that 
generally they are not normal on the 5 per cent level. See hgs. 1.83:12 and 13 in the Appendix. It should 
be noted that variable class intervals were chosen in these tests. 
In fig. 1.83:14 an underwater image of a grid is shown, and the strong radial distortion is clearly 
visible. 
The accuracy (expressed as standard error) which can be expected in the final coordinates from a 
stereopair taken under water can be calculated according to the law of error propagation, provided that 
the regular errors are known and corrected and that the residuals are normally distributed. (Ref. 
1.342:1). 
For the Hasselblad camera and for the neat model area (60% overlap and five complete control points 
in the corners and in the middle of the model) this gives: 
= S y = 1.2 — So 
c 
S z = 2.7 -s 0 
c 
and for the Rolleiflex camera: 
S* - Sy = 1.2 - So 
c 
S z = 5.1 
D 
So 
c