# Phototheodolite Survey

## Phototheodolite Survey

a survey of localities, open pits, engineering structures, or other objects, made with the help of a phototheodolite and instruments for the photogrammetric analysis of photographs.

The photographs *P*_{1}, and *P*_{2} of an object are obtained from a phototheodolite stationed at the ends *S*_{1} and *S*_{2} of the base line (Figure 1). The coordinates of individual points are determined from the photographs with the aid of a stereocomparator or stereoautograph, and a numerical model or map of the object is then produced. The orientation of a photograph, for example, *P*_{1}, at the moment the photograph is made is determined by the elements of relative orientation (the focal length *f* of the camera and the coordinates *x*_{0}, *z*_{0} of the principal point *O*_{1}) as well as by the elements of absolute orientation (the coordinates *X*_{S1}, *Y*_{S1}, *Z*_{S1} of the center of projection *S*_{1} in the system *OXYZ* and the angles α_{1}, ω_{1}, κ_{1}).

In the general case, the orientation elements of the photographs have arbitrary values; in special cases, where the optical axis of the camera is horizontal, α = ω = κ = 0, *X*_{S1} = *Y*_{S1} = *Z*_{S1} = 0, and *x*_{0} = *z*_{0} = 0. Special cases are the convergent ψ_{1} ≠ ψ_{2}, Figure 2), parallel ψ_{1} = ψ_{2}), and normal (ψ_{1} = ψ_{2} = 90°) cases.

In the general case, the relationship between the coordinates of a point *M* of an object and the coordinates of the point’s images *m*_{1} and *m*_{2} on the stereopair *P*_{1}–*P*_{2} (Figure 1) is

where

*B _{X}*,

*B*, and

_{Y}*B*are the projections of the base line

_{Z}*B*on the coordinate axes;

*X*

_{1}’,

*Y*

_{1}’,

*Z*

_{2}’ and

*X*

_{2}’,

*Y*

_{2}’,

*Z*

_{2}’ are the coordinates of the points

*m*

_{1}and

*m*

_{2}in systems

*S*

_{1}

*XYZ*and

*S*

_{2}

*XYZ*parallel to

*OXYZ*, calculated from the formulas

Here, *x* and *z* are the plane coordinates of a point on the photograph in the system *O*_{1}’ *x*_{1}*z*_{1} or *O*_{2}’ *x*_{2}*z*_{2}; *a _{i}*,

*b*,

_{i}*c*

_{i}are direction cosines determined by the angles α, ω, and κ For the parallel case, the formulas in (1) assume the form

and for the normal case

Phototheodolite surveys are used in geodesy, topography, and astronomy to construct and condense geodetic datum bases and to compile maps of individual localities. A geodetic datum base has been created for the entire earth from tracking photographs of artificial earth satellites and from photographs of the heavens obtained with the help of satellite cameras.

Phototheodolite surveys are also widely used to solve problems in other fields of science and engineering: in geography, for studying glaciers and the process of snow accumulation on avalanche-prone slopes; in forest management and agriculture, for determining forest valuation characteristics and studying soil erosion;

in construction engineering, for surveying, designing, building, and operating various structures; and in architecture, for studying the features of structures and monitoring the condition of architectural ensembles, individual buildings, and ancient monuments. Such surveys are also used in industry to check the installation of turbine housings and rolling mills and to determine the condition of smokestacks, in the study of rivers, seas, and oceans to map the surfaces and floors of large bodies of water, and in space research to study the surface of the earth, moon, and other heavenly bodies from artificial earth satellites and spacecraft.

### REFERENCES

Lobanov, A. N.*Fototopografiia*, 3rd ed. Moscow, 1968.

Rapasov, P. N.

*Sostavlenie kart masshtaba 1:2000—1:25000 metodom kombinirovannoi nazemnoi i vozdushnoi stereofotogrammetricheskois”emki*. Moscow, 1958.

Kienko, Iu. P.

*Analiticheskie metody opredeleniia koordinat v nazemnoi stereofotogrammetrii*. Moscow, 1972.

Tiuflin, Iu. S.

*Sposoby stereofotogrammetricheskoi obrabotki snimkov, poluchennykh spodvizhnogo bazisa*. Moscow, 1971.

*Itogi nauki i tekhniki: Geodeziia i aeros”emka*, vol. 10. Moscow, 1975.

Rusinov, M. M.

*Inzhenernaia fotogrammetriia*. Moscow, 1966.

Serdiukov, V. M.

*Fotogrammetriia v inzhenerno-stroitel’-nom dele*. Moscow, 1970.

A. N. LOBANOV