THE OPTIMUM PHOTOTHEODOLITE POSITIONS THAT MAXIMIZE THE 
    
ACCURACY OF THE OBJECT POINTS 
Dr. Adel Ahmed Esmat Mahmoud 
Lecturer , Department of Civil Engineering , 
Al - Azhar University , Cairo , Egypt. 
Commission V. 
Abstract 
Ground points are necessary in close range photogrammetry , especially for 
camera calibration and for orientation of the object stereomodel.New 
mathematical formulae for estimating the required accuracy of object point 
co - ordinates achieved from using a phototheodolite were developed 
. The 
optimum phototheodolite positions that maximize the accuracy of these 
object points were obtained 
A comparative study 
involving the 
phototheodolite , the camera and the theodolite was undertaken in order to 
achieve the required accuracy of the object points. 
A set of analysis of results, concluding remarks and recommendations was 
achieved. 
1. INTRODUCTION 
The phototheodolite is a terrestrial survey 
instrument combining a camera and theodolite 
in which the relationship between the camera 
axis and the line of collimation of the 
theodolite can be measured The accuracy 
achieved from using a phototheodolite is equal 
to the accuracy achieved when we used a camera 
and theodolite together at the same stations and 
with the same co-ordinate system . To achieve 
the best accuracy a combination of the formulae 
developed by the author in 1989 and the 
formulae developed by Abdel-Aziz (1982 ) for 
estimating the optimum theodolite positions 
that maximize the accuracy of the object points 
has been used to obtain the optimum positions 
of the phototheodolite in two cases of 
photography : (1) normal, and (2) convergent . 
The total mean accuracy of the target 
co-ordinates achieved from both the camera and 
the theodolite together ( phototheodolite ) can 
be obtained as follows : 
*Oymth "vvv (1) 
+ Ovmth ett (2) 
* opin? Sh Ae (3) 
+ ORmth* isssaebss e ein E (4) 
Oxmt = °Xmc 
Ovmt = ©Yme 
Dmt = 9Dmc 
°Rmt = °Rme 
where : 
SXmc'SYmc’°Dme 
object points obtained from the camera . 
Oxmth:/OYmth/ODmtn : the mean accuracy of 
obtained from the theodolite . 
NN N N 
mo "m N N 
N N 
: the mean accuracy of the 
object points 
SxmtSyYmtSDmt : the mean accuracy obtained 
from both camera and theodolite 
together ( phototheodolite ). 
SRmt: 
and theodolite together 
the positional error of the camera 
2. NORMAL CASE OF PHOTOGRAPHY 
From the equations developed by Abdel - Aziz in 
1982 and by the author in 1989, we can obtain 
Gxmi-s = Caen /B2D2) p W°/224 + 
(8D2_B2)W4/160 _ (2B2D2/3 + B%/24 )W2/4 + 
B6/32 + B4D%/4 ] + 
( Opp 2/2 + 64,2 ).(D2W2/6B2 « p2/2 ). ........ ( 5) 
Ov mi? -((H?. SHE, 43E,,2).0,,2)/38?D?). 
[W4/40+(4D2/3+B2/6).W2/4 J+ 64, 2[W2/24 + 
B2/8 + (H2_3HE{p+E4{n“)/3 + ((( H _ Eyp)° 
+E,,°)/10WDH).(tan”*((0.5W+0.5B)/D)_tan”! 
((_0.5W+0.5B)/D ))]+ 
(D2/2).(0 pp 2/12+ 042) +(2D?/3B2) [0p 2 H?/f^ «c 
mettant didn, (6) 
Spmt“ = (6142/82) [ w4/40 + W2 (B2+4D2/3)/4 
«ques. 20%) +2 0,,%0% / 
Digne e te ates (7) 
where : 
Oxmt:9 Y mt/'9 Dmt : the mean accuracy obtained 
from the phototheodolite 
f :the principal distance of the camera 
F : the format size 
T : the overlap ratio 
B : the base distance 
D 
: the object distance