one assumes that there is not the distortion around the
central part of lens generally(Fig. 5). If one knows the
equivalent focal length, one may calculate the theoretical
radial distance that the collimator image illuminated from
collimator. So, one may obtain the radial lens distortion
by comparing with the practically photographed radial
distance(Kang, 1992).
Lens
Collimator
Negative surface
Fig. 5. Principal of calculation of equivalent focal length
As for the CFL(calibrated focal length) of lens, this
researcher obtained 36.079mm, by averaging all the
focal length of radial direction(Karren,1967, Wolf,1983).
In case of applying the equivalent focal length, the
distortion of lens of horizontal appeared as 9um~-144um,
But, in case of applying the calibrated focal length, 4um
-—-51um that about 64% was reduced appeared by
being distributed evenly. In case of vertical direction
also, the reduction of about 76% appeared from 5um~
53um to 64m- 194m. So, in the photogrammetry, it is
considered desirable to apply the calibrated focal length.
If one knows the radial lens distortion, one may
obtain the coefficient of radial lens distortion from
correction polynomial(Kang, 1992).
3. APPLICATION
After choosing the small-size stone lantern(tower to
light a candle or to keep sarira in Buddhist temple)
which is suitable for very close-range photogrammetry
as the object, this researcher arranged 28 unknown
points on the surface of object equally. After attaching
the calibrated square, so that it may be the axis of X,
Y of coordinate system, this researcher utilized the scale
of this square as the self-control point. This researcher
took total 60 sheets of photographs by 15 sheets
respectively, by changing the rotation angle with 10
interal at the object distance, 0.45m, 0.67m, 1.0m and
1.4m by means of NIKON F-801 non-metric camera
(f=36mm) in this study. At this time, this researcher
made f-stop as 22 by considering the circle of
confusion, and photographed with indirect illumination so
as to prevent the halation. About the triangulation, we
executed with Kern DKM 2-A(1" reading) theodolite.
And, about the observation of baseline, we corrected
the systematic error after observing with the calibrated
steel tape over several times repeatedly. And about the
comparator coordinate, we used the photo densitometer
that the observation to 1um is possible. This
researcher decided the exterior orientation parameter
and the 3-D coordinates | of unknown point
simultaneously, by executing space resection and space
intersection with the bundle adjustment based on
collinearity condition (Kang,1989, Kang,1990).
In the photogrammetry science to calculate 3-D
coordinates of object from the projection relation of
object and camera, the geometrical conditions such as
photographing position, direction and arrangement of
control point etc. are Important. Therefore, this
researcher examined as to which influence the change
of object distance, convergent angle, numbers of control
point, and number of photographs etc. has on 3-D
coordinates of object.
3.1 Self-Control Point System
Table 1. Comparison of calculation of results by
theodolite and self-control point (m)
# of To Toe, Ti Tia) So Sos Sto. Si
photos
46 74.115 164 45 66 99 137
34 55 82 115 93 "48 M 99
25 38 53 80 25-31 1 50 À
18 28. 43 58 18 23 .37 50
C105 RIS
Table 1 is what showed the r.m.s.e calculated by
using the result of control surveying based on theodolite
and the self-control point. T means the result of control
surveying by theodolite, S is the result of self-control
point, and the subscript is object distance(meter). In
case that the number of photographs changes into 2
sheets, 4 sheets, 8 sheets and 15 sheets at the object
distance, 0.45m, the r.m.s.e based on the result of
self-control point is 45 um, 33um, 25um, and 184m,
and the r.m.s.e based on the result of control surveying
by theodolite is 46 um, 34 um, 25um and 184m. So,
it can be known that the case to have calculated by
using the result of control surveying based on theodolite
and the result to have calculated by using the result of
self-control point are very similar. Thus, it is expected
that one will be able to solve the difficult problem about
the manufacture and installation of control point,
observation of angle and baseline which is raised at
the time of control surveying of small size object
efficiently, if one uses the self-control point.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
3.2 Object
Photo:
Eig 6 i:
change of
which was
point. Accc
14m io. 1
28%, 50%
number of
sheets, 8 S
Average standard error(um)
Fig. 6 R.m
and numb:
3096, 5096
seen that |
are very
measuremel
3.3 Conver
œ
©
eo
e
e
e
A
©
©
300
Standard error (um)
vs
©
o
100
Fig. 7 Rn
