ATION
nstruments, in
»rineiple. These
le reproduction
it des éléments
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irs qui peuvent
e des éléments
ireil de restiti-
ymétriques par
n). Des dévia-
nent facilement
ts de correction
nage aprés une
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ions of ground points
‚en by this record, so
e model.
se it is desirable to
duced into the record
as near as possible to
'e of all deviations is
ce. For this, the cause
be found. This would
ether the cause could
the result of the fault
gligible quantity. This
economy. If the cause
the question to be in-
he deviations can be
correction during pho-
the information is in-
he record, or during
it from the record.
errors we find first
tortion. This can be
secondly, asymmetrical
rected by alteration of
d asymmetrical errors
ted. Thirdly, irregular
'orrected.
error arises are first,
ive the lens distortion
r which gives a prism
ty and the emulsion
and non-uniform bend-
ier and film shrinkage.
era we have the errors
t glass, atmospheric re-
GEOMETRISCHE EIGENSCHAFTEN DES BILDES, AUTHOR'S PRESENTATION S3
fraction and earth curvature. Earth curvature
can be regarded as a deviation from the ideal
when a flat model is required.
The causes of the errors are first, deviations
from the ideal case depending on the design, for
instance distortion; deviations resulting from
manufacture, for instance eccentricity of the
lens, and deviations caused by the operation of
the camera.
Radial distortion in modern air survey lenses
is of the order of 5 microns to 20 microns only,
but radial distortion can be corrected for in the
mechanical plotter by simple means, that is op-
tically, using correction plates, or mechanically,
by the correction cam. The error remaining in
the correction plates is 2 microns; with cor-
rection plates made for the measured distortion
of a particular camera, a residual error of plus
or minus 2 microns is therefore to be expected
as a maximum error.
In practice correction plates are manufac-
tured for a certain lens type under the assump-
tion that the distortion is the same for all lenses
of the same type. However, small discrepancies
occur in manufacture which in general are up to
5 microns in the corner. The residual error in
correcting for symmetrical radial distortion can
thus generally be expected to be 4 to 7 microns.
These errors remaining after correction are
very small by comparison with those caused by
film shrinkage. Asymmetrical distortion is
caused by decentering errors in the lens system.
They originate during manufacture. When a lens
has a decentering error the resulting tangential
distortion cannot be corrected. One cannot speak
of the optical axis of a lens system which has
a decentering error. A new definition is needed
for the inner orientation and much work has
been done on this problem, and the residual er-
rors caused thereby are only mentioned in pu-
blications from Washer, Carman, Bertele, Meier
and others.
An attempt at improvement can be made by
a new definition of the principal points. This is
possible in that starting from the autocollimation
point, the principal point can be moved further
in the direction of the optical axis deflection.
Such a movement represents the correction of
a projecting error. However, the remaining non-
projective error, for instance the tangential
distortion, is now of the greatest importance.
This is the distortion component perpendicular
to the picture radius. Since it cannot be correct-
ed for, it remains as a defect in the photograph
and must therefore be kept down to the smal-
lest possible quantity. Computation of these
asymmetrical distortions and also measurement
of the lens show that the tangential distortion
is about one-third of the asymmetrical distortion
referred to the autocollimation point. This
relationship between the asymmetry in the di-
rection of deflection of the optical axis and the
tangential distortion is one reason why in spe-
cification for photogrammetric camera cali-
bration the autocollimation point is prescribed
as the reference point for the measurement of
radial distortion.
By extremely careful centering of the lens it
is at present possible to reduce a bend in the
optical axis to as little as 5 seconds. The maxi-
mum tangential distortion with this deflection is
3 microns.
The same observations concern the filter. A
filter might have manufacturing faults such as
a prism effect and spherical or irregular devia-
tions of the surfaces from the plane. This causes
asymmetry and tangential distortion like eccen-
tricity of the lens. Present-day filters have a
deflection of a few seconds so that the resulting
tangentia] distortion is smaller than the meas-
uring accuracy.
The emulsion carrying the record of the
image is in the ideal case a plane. This plane
should be stable so that the distances existing at
the moment of exposure between image points
and from the reference of fiducial marks are
maintained. If the emulsion carried by a glass
plate or by a film deviates from the plane the
result is a radial movement of the image points.
Whereas a few years ago it was hardly possible
to make plates with a maximum deviation from
the plane of 20 microns, the plates are available
today with a maximum deviation of 10 microns,
the irregular deviations being of the order of 1
micron. With the flexure of present-day plates
distortions of about 3 microns are to be ex-
pected.
Deformations of the film combined under
the name of film shrinkage are of very high im-
portance and even change in the film dimen-
sions has the same effect as a change in the
camera constants. On the other hand, a dif-
ference in shrinkage in the length and width of
the film and irregularities in shrinkage repre-
sent considerable sources of error. According to
data supplied by manufacturers, the difference
between longitudinal and transverse shrinkage
caused by development and ageing is about 0.01
per cent, that is 10 microns in 100 millimetres.
Little has been published concerning the irregu-
lar effects. Irregularities between 5 microns and
20 microns are spoken of. In unpublished in-
vestigations, I have determined from 200 se-
parate distance-measurements each 80 milli-
