ained 
ziz in 
ain 
1 + 
2/4 + 
1246 
6) 
/3)/4 
ained 
lera 
W : the object width 
H : the object height 
Ein : the theodolite elevation 
Cth : the theodolite accuracy 
Oph :the accuracy in measuring the image 
co-ordinates 
The optimum theodolite positions as given by 
Abdel-Aziz (1982) are as follows : 
the optimum base distance ('B)= 1.4L or 0.7W ; 
the optimum object distance (/D) =0.26L or 
0.13W ; 
the optimum theodolite elevation (Ey) =0.5H 
The optimum camera positions may be achieved 
when the object distance (D) is a minimum and 
the base distance (B) is a maximum . 
In the normal case of photography B and D are 
related together by this formula 
BsD.F TIL... ierasectrs ren canter (8) 
where: 
B: the base distance 
D: the object distance 
F: the format size 
T: the overlap ratio 
f: the principal distance 
The optimum base distance 'B and the optimum 
object distance ‘D are chosen to minimize the 
value of om (equation 4 ) .Different values of 
D are assumed and the corresponding values of B 
are calculated from equation (8) . The optimum 
values of B and D which give the minimum value 
of on are B-0.31W and 'D-0.35W . 
The theodolite elevation E, affects only the 
value Oymt ( equation 6) , and it has no effect on 
the values of Gynt and Spmt - 
The optimum theodolite elevation Ein is chosen 
to give the minimum value of Oyqmt (i.e 
2Symt/Eth=0 ) 
3Symt/Etn =L W#/40 + ( 4D2/3 + B2/6 ).(W2/4 ) 
« 2D?^((2E,, Hy B?D?)] «(2Eg, H) «[ 
((H. Eg) ^ E, )/2HDW ] [ tan (0.5W40.5ByD.. 
tan 1(0.5W + 0.5B D] m0 ee (9) 
From equation (9) the estimated value of Ey, 
=0.50 H 
Analysis of | 
1 the expected mean accuracy of all the object 
points (Oxmt/oYmt?Dmti) for any 
phototheodolite positions can be obtained from 
equations (5,6 and 7) . 
. 2 the accuracy of object points obtained either 
from a camera mounted on a theodolite 
(phototheodolite) or from a special case of 
photography (i.e when we used the same 
stations and the same co-ordinate system for 
the camera and theodolite together ) can be 
maximized in the normal case of photography if 
the base distance (B) is taken as 0.31W , the 
object distance (D) is taken as 0.35W and the 
theodolite elevation E,n is taken as 0.5H . 
3 the accuracy of the object points is a 
non-linear function of the object distance (D) 
and theodolite elevation (Ej) . 
3. CONVERGENT CASE OF PHOTOGRAPHY 
From the equations developed by Abdel - Aziz in 
1982 and by the author in 1989, we can obtain 
Oxmt” = (0pn2/D22) [ (W410 + W2B2 4 BY/2 
).sin 49/8 + CUR B? ). pu D. Sine cosg/2 4. D? 
. sing . cos2g We +3B2 y242.B. QD 
cos?g.sing 4 (D^ Wî/6. Bé+D*/2 21.60 .cos^o ] * 
E EAM WÓ/224 + w4(8D2_B2)/160 + 
2(204/3_282D2/3_B%/24)/4 + B8/32 + 
cn 44 DB. den (10) 
Gvmi? - (0pp?/D?f?).[ D?W?sing?/t2 « 
D2B?sino?/4 + HW2sing*/36 « H?B?sino^/12 « 
D 3B sing cosg + H2 D B 
sinS0.cosg/3+D2.H2 sino2.coss2/3+(2.D*.H2/3.B2 
+D%2).c0582 1+( oq, (H2. 3HEq «Eqs 2)/2B?D?) 
[ W440 + W2(4D2/3+B2/6)/4 « 2D*) ] oq? [- 
W2/24 + B2/8 + D2/2 + (HZ_3HE,p+3E,p")/3 + 
(((H_Epn)°+E;n°/ 10WDH).(tan”*((0.5W+0.5B)/D 
— tan ! ((.0.5W40.5ByD )) ]....... n (11) 
Opmt> = (20 oh2/B22(1+tan@? )2).[D* « 203 B 
tanO 4 n (D^w?i2«3p^Bi2) +tan@“(D w2 
B/2 + DB3/2 ) 4 tanO *(W^780 + W2B2/8 + B*/16 
) ] + (044 2/B2).[W4/40 + (B2 + 4D2/3 ).(W2/4) + 
(B2/8 + B2D2 « 2D^) Jerem (12)