The optimum base distance 'B and the optimum 
object distance 'D at different values of 
convergence angle ( O ) are chosen to minimize 
the values of oy + and Spmt for 
Oxmt^9Dmt (i.e Gm" = Op =0)...... (13) 
Putting Gymis SD = 0 , we obtain one 
equation with two unknowns , B and D . The 
values of 'B and 'D at each value of convergence 
angle ( O ) are the values which satisfy the 
condition Oxmt ? 9pm: 8t the minimum values 
of Oxmt or ODmt : 
Table 1. gives the values of the convergence 
angle ( O ) in column 1 , the base distance (B) in 
column 2 , the corresponding object distance (D) 
which satisfies equation (13) in column 3 and 
the expected value op, in column 4 . 
Table 2. gives the values of the convergence 
angle ( © ) in column 1 , the optimum base 
distance (B) in column 2 , the corresponding 
optimum object distance ((D) in column 3 , and 
the optimum theodolite elevation (É,n) which 
satisfies equation ( 9 ) in column 4 . 
Figure 1. gives the ratios of ( 'D/W ) , ((B/W ) 
and (E;p/H) against the value of convergence(0) . 
Having the values of the object width (W) and 
the object height (H) , we can estimate the 
optimum object distance (D) , the optimum base 
distance ('B) and the optimum theodolite 
elevation (E;,) required to achieve the best 
accuracy in the case of using a phototheodolite 
at different values of camera convergence angle 
(9). 
1 mmen n R | 
1 The expected mean accuracy of all the object 
points (Sxmt’Ymt’°Dmt) for any 
phototheodolite positions can be obtained from 
equations (10,11 and 12) respectively . 
2 The accuracy can be maximized if B, D and Et} 
are taken according to each value of 
convergence angle (J) as mentioned in Table 2 or 
as shown in Figure 1. 
3 The accuracy of object points is a non-linear 
function of the base distance(B) , the object 
distance (D) , the convergence (©) and the 
theodolite elevation (Ey) - 
   
4. A COMPARISON BETWEEN, A 
PHOTOTHEODOLITE,A CAMERA AND A THEODOLITE 
In our comparison we chose a Wild P32 metric 
camera mounted on a T2 one second theodolite 
as a phototheodolite,a Wild P32 metric 
camera and a Wild T2 theodolite The 
comparison was between the mean positional 
error achieved from the theodolite (Grmtn)» the 
camera (GrRmç) and the phototheodolite (om )at 
different values of object and base distances . 
4.1. Normal Case of Photography 
In the normal case of photography the base 
distance (B) in both the camera and 
phototheodolite depends on the object distance 
(D) , but in the theodolite it does not . 
By assuming different values of D we can 
calculate the corresponding values of B from 
equation 8 . According to the values of B and D 
and by applying the equation developed by the 
author, we can obtain the mean positional error 
for the camera and the phototheodolite . In the 
case of the theodolite we can assume different 
values of B for each value of D, and by applying 
equation developed by Abdel - Aziz we can 
obtain the mean positional error of the 
theodolite . 
41.1. Comments and Analysis of Results 
  
From the results achieved it is clear that: 
1 in descending order ,the best accuracy of 
object points was obtained from the theodolite, 
then from the camera and  lastly from the 
phototheodolite . 
2 above the ratio D/W=0.3 the accuracy achieved 
from a theodolite is about 56% better than that 
obtained by camera and is about 62% better 
than that obtained by phototheodolite . 
3 above a certain ratio (D/W) the positional 
accuracy achieved from a camera mounted on a 
theodolite (phototheodolite) becomes nearly 
equal to the positional accuracy achieved from 
both a camera and theodolite separately . 
4.2 nvergen f Ph raph 
In this case the choice of B and D is independent 
, So we can assume different values of B for 
each value of D and by applying equation 4 we 
can obtain the best accuracy achieved at this 
object distance (D).