PRECISE DETERMINATION OF FISHEYE LENS RESOLUTION 
M. Kedzierski 
Dept, of Remote Sensing and Geoinformation, Military University of Technology, Kaliskiego 2, Str. 00-908 Warsaw, 
Poland - mkedzierski@wat.edu.pl 
Theme Session C2 
KEY WORDS: Close-Range, Resolution, Optical Systems, Accuracy, Camera, Non-Metric, Fisheye Lens 
ABSTRACT: 
Using fisheye lens in close range photogrammetry gives great possibilities in acquiring photogrammetric data of places, where access 
to the object is very difficult. But such lens have very specific optical and geometrical properties resulting from great value of radial 
distortion. In my approach before calibration, Siemens star test was used to determination of fisheye lens resolving power. I have 
proposed a resolution examination method that is founded on determination of Cassini ovals and computation of some coefficient. 
This coefficient modifies resolution calculations. Efficiency of my method was estimated by its comparison with classical way and 
statistical analysis. Proposed by me procedure of lens resolutions investigations can be used not only in case of fisheye lens, but also 
in case of another wide-angle lenses. What have to be mentioned is fact, that the smaller focal length of lens, the more accurate is the 
method. Paper presents brief description of method and results of investigations. 
1. INTRODUCTION 
Very important are: lens calibration and appropriately chosen 
test. Depending on gradient of resolution variations, the proper 
number of points (X, Y, Z) of the test, and their density 
(depending on radial radius) should be matched. Another 
possibility of using result of researches is creating map of 
fisheye lens resolution and determination of some difficult areas 
in the photo. In these areas (even after calibration) it is 
impossible using directly the content of the photo, because of its 
degradation. For these regions proper interpolation method of 
spectral response value for new complementary pixels has to be 
found. Such a process enables the full usage converted photos 
of fisheye lens camera. 
That is why investigations connected with lens resolution will 
have to be done. Additionally, selection of suitable 
photographing parameters is also depended on lens resolution. 
Conducted investigations of using fisheye lens, caused necessity 
of creating a map of fisheye lens resolution. One of possibilities 
of optical systems quality determination is evaluation of their 
resolution ability. It consists of determining the smallest 
structure that can be distinguishable in the image. Making 
investigations with fisheye lens, and taking into consideration 
its distortions, such a test has to be done in different way than in 
case of classical lenses. Strip test will not be proper in such 
investigations. In that case, test of Siemens is needed. In one 
photo, there is 192 identical Siemens stars, arranged in columns 
and rows in equal intervals. Error of such location is 0.01 mm. 
Current methods of optical systems quality estimation use 
image contrast in connection with information of transcribed 
details. These details are carried by the system and expressed by 
spatial frequencies (1/mm). The transfer function is the most 
universal tool of optical system quality assessment. 
The angular resolution criteria of Rayleigh are the basic 
measure of lens resolution. However, the quantity expressed by 
the Rayleigh criteria is the limiting resolution. More complete 
understanding of the system is expressed by the Optical 
Transfer Function (OTF), of which the limiting resolution is one 
point. The Optical Transfer Function describes the spatial 
(angular) variation as a function of spatial (angular) frequency. 
On the other side, I would like to propose different approach to 
determination of resolution, using Siemens star. All Siemens 
stars and their unrecognizable areas in the photo (broadening 
rings) derived from fisheye lens camera form not circles(ellipse), 
but Cassini ovals (a>b). Theoretically in fully symmetric lens, 
Bernoulli’s lemniscate (a=b) should appear on the diagonal of 
the image, but with assumption, that centers of some Siemens 
stars pass through this diagonal. Remaining stars, especially the 
main axis of Cassini oval, depending on quarter of the image, 
form with horizontal straight line characteristic angle. Because 
our image comes from fisheye lens, this are not straight lines, 
but arcs, so the angle includes between two arcs. Difference 
between value of theoretic angle (between straight line), and 
real angle (between straight lines) enables also determination of 
influence of distortion in particular point, on decrease of 
resolution. In my researches I have proofed, that according to 
proposed by me formula, it is possible to create resolution map 
of fisheye lens camera with much higher accuracy than in 
classic approach, what I proofed in my researches. What is more, 
probable lens errors being results of improper lens connection 
can be found. Resolution map is creating as a numeric model of 
lens resolution decrease. To this aim, best model is GRID. It 
enables average of noise, that can appear in our investigations. 
Very important criteria of such a model is its resolution, which 
should be in the range between 3-8% of difference between 
maximal and minimal value of lens resolution. Lower limit is a 
result of precision of used method, and using smaller values do 
not have any sense. Upper limit comes from possibility of 
presentation of the result. 
My researches I have made using Nikon lens with 10.5 mm 
focal length, mounted in digital camera Kodak DCS 14n pro (14 
min pixels). Measurement was made in Image Analyst and 
Microstation software. The only problem during measurements 
is chromatic aberration effect.