In this article essential principles of constructing geometry of contemporary space images with the purpose of definitions their common regularity and distinctions of generations’ inner photogrammetric relations and then – mathematical models, expedients for securing of strict processing are considered. It is significant, that scanning survey is the general case/way, but strip and panoramic surveys are particular cases. For the first time it was established, that under solving the problem of photogrammetric resection for scanner images on the basis of using dependences of well-known collinearity models the ambiguity of external orientation of images arises. The basic reason of its arising is discovered and established, by way of which it is determined poor domain the systems of initial equations’ corrections. A rigorous model of a push broom space image is introduced, which incorporates both a static a photogrammetric model and a dynamic one. The static model gives the only mean position and orientation of image, meanwhile the dynamic one makes them more exact. The table of condition numbers (cond A) of initial equations’ correction linear system is given and it confirms the fundamental idea of this article. A practical way of solving this problem is indicated for cases of using source data, both outboard measurements and control points.