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formulas and partly by the fact that corrections to the orientation elements cannot be
with mathematical precision. As a result small but perceptible systematic paral]
often left. In analytical triangulation this is not the case: The relative or
established from observed co-ordinates can be achieved with
accuracy.
made
axes aye
: lentation
any required degree of
Furthermore in analytical triangulation a correct interior orientati
is automatically achieved. In an instrumental triangulation this
centering of the photograph in the plateholder only a limited ac
results in a distortion of the bundle of rays.
The higher accuracy of analytical triangulation makes it possible to reduce the Number
of ground control points and thus the cost of field surveys. The cost of bhotogrammeti,
operations will also be lower. A precise stereocomparator should be considerably Cheaper
than a first-order plotting machine. The operation of the machine is simpler, It therefore
requires less training and ability on the part of the operator.
On of the Camera
1S not the case: In the
curacy is reached, This
Method.
In the photogrammetric section of the National Research Council of Canada a method
of analytical triangulation has been developed and coded for Ferut, the Ferranti electronic
digital computer at the University of Toronto. This method Will now be described in some
detail.
The computations start from co-ordinate readings of corresponding points on a stereo
comparator. These readings are first referred to the principal point as the origin of a
rectangular co-ordinate system. They must be corrected for several types of errors,
Film distortion can be corrected for each single photograph. A grid plate is placed
in front of the film and photographed onto the negative at the time of exposure. The co-
ordinates of the required points are read with respect to one of the nearest grid inter-
sections. Plate co-ordinates are obtained by adding the calibrated co-ordinates of these
intersections.
The radial distortion is measured along a number of diagonals. The radial distortion
over the whole plate is then determined by interpolation and a correction for radial
distortion is applied to the co-ordinates. The tangential distortion can be measured and
corrected in a similar way.
Refraction in the atmosphere causes a symmetrical radial distortion if the photographs
are exactly vertical. Tables giving the refraction under certain assumptions may be found
in the photogrammetric literature, e.g. Leyonhufvud, Photogrammetria IX 1952—53 Nr. 3.
This distortion may amount to a few hundredths of a millimeter. It is eliminated by radial
corrections, also with a satisfactory degree of accuracy for nearly vertical photographs.
A radial correction may also be given for the effect of earth curvature:
h
dr = . 8
2f2R
in which:
r is the distance of an image point from the principal point;
h is the flying height above the terrain;
R is the mean radius of the earth in the area of the strip;
f is the calibrated focal length.
This correction reduces the reference sphere in the area of the strip to a plane. Fo
high altitude photography this correction may amount to as much as one tenth of à
millimeter.
From the corrected plate co-ordinates, that have now been obtained, the map c
ordinates of the required points must be computed. This computation is most convenient
performed with respect to a spatial rectangular co-ordinate system. An arbitrary initial
system n
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