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internal precision at the expense of causing a deterioration in
object point accuracy due to over-parameterisation was clearly
demonstrated.
Donnelly (1988) examined film unflatness in 35 mm cameras,
the Canon AE-1 Program camera in particular. He found the
film to bulge away from the image plane by approximately
0.6 mm in the centre and assume a shape which was
reasonably constant frame to frame throughout the length of the
film.
For most 35 mm cameras, the film transport mechanism is
similar and uses a system of guide and support rails to constrain
the film longitudinally. There are no specific lateral constraints
at either end of the frame, although one end is held by the slot in
the film cassette and the other by the wind-on transport
sprocket.
Donnelly removed the camera back and took comparative
photographs on glass plates of a computer drafted grid of
19 vertical and 13 horizontal lines. Comparisons were made
between the positions of the grid intersections on the film with
those on the glass plates. The vectors of difference in position
were approximately radial from the principal point and up to
60 um at the edges. In other words, the extent of the film
which was exposed was approximately 100 pm longer, and
70 um wider, than the area of the image format.
A further study by Fryer, Kniest and Donnelly (1990) explored
the hypothesis “are the radial effects of film unflatness absorbed
by the parameters for radial distortion?”. The plumb-line
method was used to extract radial distortion profiles from both
the glass plates and the unflattened film frames. Up tor = 18
mm, the difference between the profiles did not exceed 1.5 um,
well within the error budget, and to the initial surprise of the
researchers. (Atr = 18 mm, ôr was —183 um).
Two reasons have been proposed for the closeness of the radial
distortion profiles. Firstly, the radial distortion formula,
equation (3), is quite insensitive to small changes in radial
distance. Even towards the edge of the format area, dr was
only changing by 1.5 um for every 50 [um of radial distance r.
Secondly, in the setting up phase, or the interior orientation, the
edges of the frame were used as pseudo fiducial marks and an
affine transformation performed. Since the vectors showing the
difference in position between the unflattened film and glass
plates were basically radial, the affine transformation removed
the majority of the effect as it would apply in the determination
of radial lens distortion. Quite clearly, the hypothesis was
refuted and the effects of film unflatness and the parameters of
radial lens distortion must be viewed as independent in terms of
camera calibration parameters.
4.2 Film Unflatness and AP's
The model for AP's in equation (7) and (8) have been used by
Fraser (1982) and also this author to attempt to improve the
internal precision of a self-calibrating bundle adjustment and
also the accuracy of object point co-ordinates. Fraser found
that the coefficients b, and b» in equation (8) were the most
significant in improving the reliability of the adjustment and the
object co—-ordinates. These AP's are linear terms in x and y
which refer to non-orthogonality and affinity. He found that
the other AP's were either not statistically significant (that is,
did not effectively remove any systematic error signal) or did
reduce overall accuracy. Fraser's model was only minimally
provided with control points, a situation which is common in
many non-metric close-range situations.
In addition to the AP terms used by Fraser, this author has
found the term a, in equation (7) to be most useful in a variety
of adjustments. This is a second order term, hyperbolic in
nature, and it is not difficult to visualise. its relevance to
unflattened film.
4.3 Attempts at Film Flattening
A wide variety of attempts to flatten film in close-range cameras
have been made over the last decade. These have ranged from
the professional and demonstrably very successful vacuum
systems in Geodetic Services Inc’s CRC-1 camera (Brown,
1984) to commercially available backs for 35 mm to 70 mm
cameras such as the Pentax 645 or the Contax RTS III (Fryer,
Kniest and Donnelly, 1992) to experimental vacuum systems
such as that described by Donnelly (1988). The alternative to
vacuum back systems is the addition of a reseau grid, with or
without a pressure plate. One difficulty with reseau systems is
the focussing problem caused by the addition of the glass pane
between the lens and the image plane. A thin reseau pane is
essential, but its location adjacent to the focal plane camera
shutter system can pose engineering problems.
The commercial pricing of film flattening devices for small
format cameras probably reflects the low level of acceptance and
use of these devices by the “amateur” photogrammetric
community. The cost of vacuum backs, or reseau plates, seems
exorbitant to this author, often more than doubling the price of
the original camera and lens combination. Surely this is a
reflection of the numbers of units sold on a worldwide basis,
each unit representing an almost individual order.
There can be no doubting the improvement in overall accuracy
provided by a film flattening device. The references noted
earlier in this section show improvements two—fold or better,
with the ultra-specific flat vacuum back of the CRC-1 camera
coupled with automatic image co-ordinate measurements
achieving accuracies up to one part in a million (Fraser, 1992).
Vacuum back system have demonstrated a capability to produce
more accurate results than reseau systems. Apart from the
difficulties which were noted earlier, another difficulty which
has been observed with reseau systems includes lack of contact
between the film and the glass plate, probably caused by
trapped air. This is identifiable in gross cases since not all
reseau crosses will appear sharp (Chandler, Cooper and
Robson, 1989). Another problem can arise in the case of
backing paper with 120 roll film when air becomes trapped
between the paper and film. Lack of flatness of both the reseau
plate and the pressure plate has also been identified as a source
of error, along with a lack of parallelism between those
surfaces.
There is some evidence that film unflatness can cause "larger
than expected" errors in object point co-ordinates in
configurations with weak geometry, especially in
stereophotogrammetric situations (Robson, 1992). In other
situations, often where the majority of control and object points
lie near the centre of the frame, the effect of out-of-plane
deformation is not large. Attempts to model the shape of the
deformed film surface, and correct all observed image co—
ordinates accordingly, have not yet proved to be successful.
5. PRINCIPAL DISTANCE
In close-range photogrammetric situations, the distinction
between focal length and principal distance becomes an
important consideration. The convention is that principal
distance is the perpendicular distance from the perspective
centre of the lens system to the image plane. Focal length is that
value of the principal distance which corresponds with infinity
focus. The constant c is used in the earlier equations to describe
the principal distance at any setting.
The principal distance may be evaluated in a number of ways,
with an accuracy of 10 um to 20 um being attainable without
too much difficulty. A very simple method is to photograph
two points spaced equi-distant either side of the camera's axis
and distant from camera at the required focus setting. Two
targets on a straight fence when the whole set-up is on level
ground are ideal. The targets and the fiducial centre must lie on
a straight line if no corrections for camera axis tilt is to be
