The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
i 
Figure 1. Photograph of Siemens star test, took with digital 
camera Kodak DCS 14nPro of 10.5mm lens. 
In case of fisheye lens we can notice that broadening ring is not 
an ellipse (like in case of lenses with focal length bigger than 20 
mm). This perturbation, presented in the figures 2 and 3 results 
from big geometrical aberrations, that means from distortion. 
Figure 2. Fragment of photo of Siemens star test took with 
digital camera Kodak DCS 14nPro (10.5 mm) with broadening 
rings 
In case of focal length 10.5 mm, after 3 measurements series, 
we can say (with confidence level 0.91), that shape of 
broadening ring complies with both Cassini oval and equation 
(11) in case a>b. 
These researches were made using 182 Siemens stars (test has 
192 stars). Discrepancies in Siemens stars numbers follows 
from vignetting shield in 10.5 mm lens. 
.... 
Figure 3. Broadening ring in shape of Cassini oval, digital 
camera Kodak DCS 14nPro (10.5mm lens) 
calculated according to formula (19). Nevertheless, such 
method do not take into consideration deformations of 
broadening ring caused by distortion (important in this type of 
lens). 
Therefore, in my opinion, there have to be taken into 
consideration a fitting factor, proposed by me. Assuming that 
ellipse area is: 
Р е1р=Я' аЬ 
Cassini oval area 
P = 
МЭнС 
(12) 
(13) 
Where: 
r* = a 1 -cos- cos 2 20-(a* -b 4 ) 
If not influence of distortion, shape of broadening ring wouldn’t 
be Cassini oval, but ellipse. Thus, we can assume that this 
ellipse would have the same shape as ellipse formed from 
Siemens star. In that case, their flattening would be equal. 
After reductions and excluding non-physical solutions we 
obtain: 
(17) 
thus, we could determine the value of semi-minor axis of 
broadening ring if not distortion influence. Having such data it 
is possible to define a coefficient enabling corrections in 
calculations of fisheye lens resolution. 
Coefficient is defined as a ratio of factual broadening area to 
hypothetical broadening area if not distortion influence. 
p 
p 
r Elipn (18) 
To formula (19) describing resolution (from Siemens star test), 
we insert coefficient W (computed according to formula (18)) 
and we replace d by 2rmax, what is a double broadening radius 
(such approach facilitates measurements). 
71-d (19) 
In classical approach, using Siemens star test, resolution is 
763 
where: 
Lpsek - is a number of sector pairs in Siemens star,