The radial distortion of a Multiplex projector has been determined, in the manner 
recently described by Professor Bertil Hallert in Photogrammetria.* The grid con- 
sisted of thirty-five points symmetrically plotted on an aluminium sheet (Fig. 1). 
The size of the grid was 40 cm. x 60 cm. 
The projector was placed vertically above the central point of the grid and was 
carefully levelled with a spirit-level. The projection distance was around 40 cm. A 
diapositive plate was placed in the projector and exposed through the lens. Each 
point of the grid had been marked with a circle, the diameter of which was given such 
a size as to appear a little larger than the measuring mark when observed in a stereo- 
comparator. This gives a very high accuracy in the setting of the mark. 
The co-ordinates of the grid were determined by measurements in a co-ordinato- 
graph. The image co-ordinates were measured in a stereocomparator. Due to the 
small size of the image, these measurements could be performed with the parallax- 
screws. 
The radial distortion was determined and plotted and the distortion curve was 
drawn by estimation (Fig. 2a). The standard error of the measurements according to 
the adjustment was found to be around 5 microns. The standard error of the dis- 
tortion was determined to be around 2-5 microns. 
The Hypergon lens used in Multiplex projectors is supposed to be free from 
distortion. However, the investigation shows that this projector lens is impaired by 
quite a large radial distortion. 
The experiment was repeated and this independent determination of the dis- 
tortion is shown in Fig. 2b. The two curves agree very well with each other. 
If the grid is exposed at two different heights, if the height difference is accurately 
determined and if the projection plane is moved accurately parallel to itself, the 
projector constant can be obtained. The principal point may be determined, if the 
projection centre is placed vertically above the central point of the grid 
Determination of the Radial Distortion of the Multiplex Projector Zeiss No. 201199 
The grid shown in Fig. 1 was used in the experiment. The radial distortion is 
assumed to be symmetrical around the principal point. Thus the distortion can be 
determined for groups of points with the same distance from the central point of the 
grid. We obtain eight groups of such points. 
33, 42, 43, 44, 53 
32, 34, 43, 52, 54 
23, 41, 43, 45, 63 
22, 24, 31, 35, 43, 51, 55, 62, 64 
21, 25, 43, 61, 65 
13, 43, 73 
12, 14, 43, 72, 74 
11, 15, 43, 71, 75 
By ” A new method for the Determination of the Distortion and Inner Orientation in Cameras and Projectors. 
Y B. Hallert, Photogrammetria, Vol. XI, 1954/55, No. 3. 
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