50 BALLISTIC PHOTOGRAMMETRY, AUTHOR'S PRESENTATION
able. *) Detail on the BC-4 instrument can be
obtained from the manufacturer, The Wild
Company, Heerbrugg, Switzerland.
Let me say a word in relation to an opti-
mum focal length for such an instrument,
because I believe that this problem may be-
come, aside from its significance for ballistic
application, of general interest in photogram-
metry.
Eventually a flashing light satellite will be
launched for geodetic purposes. The photo-
grammetric measuring method will be applied
as the most precise observation method avail-
able. Before photogrammetry sticks its neck
out too far, however, promises of absolute accu-
racy of 1 : 500,000 to 1 part in a million have
already been made — it is necessary to under-
stand that due to always present refraction
anomalies relatively close to the instrument, a
short duration flash of 1/1000—1/2000 sec, is to
at least — 2" uncertain, in so far as the geomet-
rical significance of its position is concerned.
In other words, the physics of the atmosphere
limits the method to about 1 part in 100,000. In
addition the Right Ascension — Declination
values of the star field must be assumed to be
accurate to == 0.5” for the northern portion of
the sky and for the southern portion, even
somewhat less.
A standard error of unit weight for an indi-
vidual plate coordinate measurement of + 3 u
has been assured by numerous routine meas-
urements. Consequently, a focal length of
about 300 mm seems to be optimum. A focal
length as short as feasible, not only enhances
the stability of the instrument and makes it
suitable for field use, but provides aside from
better image properties, a sufficiently large
angle of view for recording of numerous flash-
es, thus providing the possibility of compen-
sating statistically for the effect of the random
walk of a short duration flash image.
In my opinion, the data reduction methods
as applied in Ballistic Photogrammetry also
have something to offer to the whole field of
Photogrammetry, insofar as analytical evalu-
ation is of interest. The method developed is:
a. geometrically rigorous, incorporating for
each bundle all nine geometrical degrees of
freedom without any restriction, with respect
to geometrical arrangements;
b. flexible enough to absorb such physical
properties which act as disturbances on the
model, namely refraction and distortion;
c. based on a rigorous least squares treat-
*) BRL Report No. 1108, May 1960. Title: Ballistic
ment which handles all types of parameters
unrestricted with respect to quantity and
quality.
This generality could only be obtained, by
utilizing the simplest conceivable model, name-
ly the condition of colinearity of three points,
In other words, the individual ray is the basic
model on which the general solution is devel-
oped. This approach not only provides for a
potential evaluation method, but opens new
prospects for studying the error theoretical
condition in photogrammetry. We have grown
accustomed to identifying the problem of
relative orientation with the problem of deter-
mining five orientation parameters, based on 5
equations expressing the intersections of 5
pairs of corresponding rays, believing that such
an interpretation is in agreement with the
process of orienting a pair of photographs on
our restitution equipment. This is a fallacy.
Actually, we are determining the five orien-
tation parameters and the spatial positions of
five points of the model. In other words, we are
determining 20 unknowns. We could as well
have decided to eliminate the 5 orientation
elements and the problem would present itself
as a problem of determining 15 unknown coor-
dinates of the model.
Actually, the orientation problem in photo-
grammetry is to determine 12 orientation
parameters and 15 coordinates of the model,
altogether 27 parameters. Each ray gives rise
to 4 equations. Thus we obtain for 5 points, 20
equations and consequently 7 of the 27 para-
meters must be obtained independently. If we
assume that 7 orientation elements are given,
5 remain as unknowns, which together with 15
unknown coordinates of the model, add up to
a total of 20 unknowns. This situation cor-
responds to the problem of the so called
relative orientation. If we assume that 7 coor-
dinates of the model are given, then 8 remain
as unknowns, which together with the 12
unknown orientation elements again make a
total of 20 unknowns. This solution corre-
sponds to an absolute oriented model. Thus it
becomes evident that these two cases are only
two solutions of a far more general problem
and further, making it clear, that for a success-
ful error theoretical study, it does not suffice,
to study independently the condition of preci-
sion of the elements of orientation or the cor-
responding condition within the model, but the
answer must be sought in the condition of cor-
relation existing between the two groups of
Camera (BC-4) Synchronization System, by Ralph E. A.
Putnam, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, US A.
Archives 6
