On photogrammetric distortion 
By Horst Schüler, Jena, G.D.R. 
Introduction 
With the advance of photogrammetric methods with respect to 
measuring accuracy,systematic model deformations are gaining 
closer interest as a subject of discussion. In relevant 
publications, frequent use is made of the word'"distortion" 
as a component of various terms such as "asymmetrical dis 
tortion", "tangential distortion" etc. In photogrammetrie 
instrument engineering, however, the term "photogrammetrie 
distortion" in a narrower sense describes certain properties 
of an optical system used in photogrammetry, so that from the 
instrument design aspect it is undesirable to ascribe the 
term to a sum of ill-defined residual systematic errors in the 
photogrammetrie measuring system. Some deeper exploration 
seems to be imperative and should help to find possibilities 
of eliminating systematic errors in the restitution process. 
Distortion in optical imaging systems 
Normally, image formation by an optical-photographical system 
is, to a first approximation, based on the mathematical-geo 
metrical model of perspective projection. In any physical im 
plementation of optical imaging by glass elements of (mostly) 
spherical curvature, deviations from this model will occur 
due to the laws of geometric optics. Such deviations are 
defined as "distortion". 
In a photolens, the mathematical projection centre is replaced 
by the centres of the entrance and exit pupils, which are the 
vertices of an object-side and an image-side cone of rays. If 
in a mathematical perspective projection we know the spacing 
c of the projection centre 0 from an image plane and the ang 
le of incidence of an imaging ray emerging from the object 
point P relative to the projection axis, then the image dis-