ON THE DEFINITION OF LENS DISTORTION REFERENCE DATA 
WITH ODD-POWER POLYNOMIALS 
  
Hartmut Ziemann 
Sabry El-Hakim 
Photogrammetric Research ! 
National Research Council of Canada | 
Ottawa, Canada 
K1A OR6 
ABSTRACT 
Odd-power polynomials were determined for all lens distortion reference data ever included into the 
various editions of the Canadian Specification for Aerial Survey Photography. The degree of the 
polynomials as well as the number of valid digits of the polynomial coefficients were varied in an 
attempt to best fit the given data. For fifteen of the nineteen lens types included into the 
investigation, the maximum deviation between best-fitting polynomial and given data was smaller than or 
equal to the resolution with which the original data were given. The values for the other four lens 
type were 1.1, 1.5, 1.3 and 1.7 times that resolution; the last two values apply to lenses no longer in 
service in Canada. 
INTRODUCTION 
Odd-power polynomials appear well suited to define average radial lens distortion from both, 
theoretical considerations as well as published data. We attempted to find best-fitting odd- power 
polynomials for all lens distortion reference data ever included into the various editions of the 
Canadian Specification for Aerial Survey Photography using, whenever available, the data provided by 
the manufacturers to either the National Research Council or the Interdepartmental Committee on Air 
Survey as base for defining the reference data. The degree of polynomial as well as the number of 
non-zero decimal digits of the coefficients were varied. 
We shall first introduce the used lens distortion reference data, then discuss the determination of 
the polynomials and give results. These will be followed by a description of an averaging process and 
of the results thus derived. 
LENS DISTORTION REFERENCE DATA 
  
Table 1 lists all lens types included into the investigation and indicates in which of the editions 
of the Specification they were included. The data used for most lens types were those submitted by 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Table 1: Lens types, their inclusion in editions of the Specification BE 
for Aerial Survey Photography, and dates of fixed | 
references, if those could be located. | 
i 
i i BIS Dis Md 
No. Lens Type eajoloisijojesigsioi 91[.9 | Date on Reference fe 
Document | 
* * 
1 Ross 153/5.5 lens G| G| G | 
2 Bausch & Lomb Metrogon 153/6.3 G| G| G 
3 Wild Aviogon 153/5.6 and c| ci c G| T | 
Wild Universal-Aviogon 153/5.6 G G| T | 
4 Zeiss-Oberkochen Pleogon 153/5.6 T| G G| T 
5 Zeiss-Oberkochen Pleogon-A 153/5.6 6 G| T 
6 Wild Super-Aviogon 88/5.6 (lens only) Tl el T 
7 Galileo-Santoni Ortogon 154/5.6 G| T 1969-01-31 
8 Zeiss-Oberkochen Pleogon-A2 153/5.6 T 1971-06-29 
9 Zeiss-Jena Lamegon 152/4.5 T 1971-06-11 
10 Wild Super-Aviogon-II 88/5.6 T 1974-03-05 
11 Wild Universal-Aviogon-I 153/5.6 T 1976-01-09 
12 Wild Universal-Aviogon-II 153/4 T 1976-01-09 
13 Wild Aviotar-II 303/5.6 1976-01-09 
14 Zeiss-Jena Super-Lamegon-II 90/5.6 1979-10-15 
15 Zeiss-Jena Lamegon-PI/B 152/4.5 1981-06-13 
16 Zeiss-Oberkochen S-Plegon-A2 85/4 1981-08-28 
17 Zeiss-Oberkochen Pleogon-A2 153/4 1981-08-28 
18 Zeiss-Oberkochen Topar-Al 305/5.6 1981-08-29 
19 Zeiss-Jena Lamegor-PI 300/5.6 1981-11-20 
G .. lens distortion is given graphically 
T .. lens distortion is given in tabular form 
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