5 02 180 
XIII Congress of the 
International Society for Photogrammetry 
Helsinki, 1976 
Commission V 
Working Group VII 
Invited Paper 
Pror. Dr. Inc. WOLFGANG FAIG 
University of New Brunswick 
Fredericton, N. B., Canada 
Calibration of Close-Range 
Photogrammetric Systems: 
Mathematical Formulation 
An analytical method for the self calibration of non-metric, 
close-range cameras, employing the coplanarity condition 
and minimum object space control, is described. 
INTRODUCTION 
ccording to Woodhead?? a system can be defined as a "collection of components 
which are connected together in a specific way described as the system structure so 
that collectively the components perform or satisfy the system purpose". In photogram- 
metric systems, components such as camera, film, compilation, and data processing 
equipment can be readily identified together with their structural—often sequential— 
arrangement such that they fulfill the purpose of obtaining quantitative (metric) informa- 
tion about an object via photography. The prefix “close range” merely indicates a short- 
er object distance. Such a system encompasses several subsystems, namely photo- 
graphic data acquisition, photographic processing, mensuration, data processing, and 
data presentation systems. 
Calibration, as far as photogrammetrists are concerned, applies to the data acquisition 
and mensuration systems or, more precisely, to the camera equipment and to the plotter 
or comparator. When performing a calibration, numerical values are extracted from a 
photograph and processed according to certain mathematical procedures. May I there- 
fore briefly consider analytical photogrammetric systems? As mentioned by Jaksic!?, a 
photograph is nothing but an analogue memory storage of the “read only” type. The 
processing unit is an electronic computer, while the reading device consists of a com- 
parator (or plotter with numerical read-out) which converts some of the analogue infor- 
mation of the photograph into digital form. In a simple one-way flow this constitutes 
what is commonly considered as analytical photogrammetry. If there is a feed back be- 
tween the computer and the comparator type unit, we have an analytical type plotter 
system capable of extracting additional analogue information. The digital computer can 
of course be replaced by an analogue instrument which is “programmed” for a certain 
configuration—central perspective, in our case—which satisfies the majority of photo- 
grammetric production purposes, is simple, and is less expensive in operation. In return, 
for accurate results it requires photography that is obtained with a close approximation 
of central perspective as is the case with metric cameras. 
In close-range applications, there are numerous cases where this condition cannot be 
fulfilled for various reasons, and non-metric cameras are used for data acquisition. 
Calibration provides the necessary data to process this general type of photography with 
PHOTOGRAMMETRIC ENGINEERING AND REMOTE SENSING, 1479 
Vol. 41, No. 12, December 1975, pp. 1479-1486