Cauwerts C., Deneyer A., Bodart M., Vignetting effect of two identical fisheye lenses
VIGNETTING EFFECT OF TWO IDENTICAL FISHEYE LENSES
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2
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Cauwerts Coralie , Deneyer Arnaud , Bodart Magali
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2
Architecture et Climat, Université catholique de Louvain, Louvain-la-Neuve, Belgium
Belgian Building Research Institute, Department Acoustics, Energy & Climate, Belgium
ABSTRACT
This paper aims to determine and compare
the vignetting effect (luminance radial falloff)
of two identical SIGMA lenses mounted on
two identical cameras (same manufacturers,
models and references).
For the largest aperture (f/2.8), the
average luminance loss of the two devices is
66%, at the periphery of the fisheye, with a
difference of loss of 0.5%. For each
aperture, the difference between root mean
square errors (RMSE) of vignetting curve of
each device is always less than 0.7%.
Vignetting effect is thus similar for the two
devices.

180° field and thus variation of
illuminance is minimized;
the optical axis of the lens does not
match with the rotation axis of the
camera.
This device was placed under a mirror box
reproducing the CIE overcast sky [4]. Two
illuminance meters were placed in this mirror
box in order to record the variation of
horizontal illuminance.
Keywords: HDR imaging, fisheye, vignetting,
calibration
1. INTRODUCTION
Measuring real world luminances for the
entire field of view is possible with a fisheye
lens and HDR imaging techniques but
several calibrations are necessary to make
reliable luminance measurements [1].
Pictures taken with a fisheye lens present a
luminance falloff for pixels far from the
center of the picture. This phenomenon
called vignetting is proper to the lens and
should be corrected.
This paper determines vignetting effect of
two devices (lens + camera) of same
references to point out if vignetting differs
from one device to another one.
2. MATERIALS AND METHODS
Pictures were taken with two CANON EOS
40D on which two fisheye lenses SIGMA
4.5mm F2.8 EX DC HSM were mounted.
Measurements were realized for four
apertures (f/2.8, f/4, f/10 and f/22).
The device consists in a semi circle
presenting squares each 5 degrees (see
fig.1). 19 white squares (ρ=78%) alternate
with 18 grey ones (ρ=26%). This semi
circular device differs from the one used in
[1,2,3] and was preferred for several
reasons:

only one set of shots is necessary by
aperture to obtain luminances for the
Fig. 1: Device in the mirror box (plan)
The camera was placed in the centre of
the circle to capture the 180° field. Series of
Low Dynamic Range (LDR) pictures were
taken at different exposure time and then
combined to reconstitute an HDR picture
with the hdrgen application in Radiance. The
response curve needed for each camera
was determined from pictures taken with the
aperture of f/22.
Table 1: Settings of the camera
Parameters
Mode
White balance
Daylight
Picture quality
Medium/Normal
Sensibility
ISO 100
Number of f-stop
+/- 1EV
Number of shots
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Luminance of each square was
measured with a MINOLTA LS110
luminance meter, positioned at the centre of
the circle.
Vignetting effect was determined as the
ratio between measured luminances and
luminances from the calibrated HDR picture.
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Cauwerts C., Deneyer A., Bodart M., Vignetting effect of two identical fisheye lenses
Fig. 2: Luminances measurement
To verify that vignetting does not depend
on the color of the target, calibration factor
(CF) was calculated separately for white and
grey squares, for each set-up (camera +
lens + aperture). For the first device,
CFwhite_mean = 1.31 and CFgrey_mean = 1.21. For
the second device, CFwhite_mean = 1.35 and
CFgrey_mean = 1.29. For each aperture,
vignetting curves, determined from grey and
white squares separately, were then
compared by the difference between root
mean square errors (RMSE) of each curve,
calculated as
√∑
(
)
,
where is the value of the vignetting curve,
the value of the reference and N is the
number of data points.
The symmetry of the vignetting effect
was verified in the same way.
Finally, the difference of vignetting
between the two devices was evaluated by
this difference of RMSE too.
3. RESULTS
Difference of RMSE leads to the conclusions
that vignetting does not depend on the color
of the target (differences respectively < 1.5%
and 2.7% for each device) and was
observed to be symmetric (differences < 1%
for the two devices).
Vignetting effect of each device is
presented in fig.3. Luminance of the extreme
white squares was not taken into account
due to the geometrical imprecision of the
fisheye picture.
Vignetting effect increases with large
apertures. At the periphery of the picture
and for the largest aperture (f/2.8), the
average luminance falloff of the two devices
is maximal and reaches 66% (difference =
0.5%). For each aperture, difference
between RMSE of the curves of the two
devices is always less than 0.7%.
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Fig. 3: Vignetting curves
measured
points
(left
device#1, right part: device#2)
and
part:
For smallest apertures (f/10 and f/22),
vignetting effect disappeared and an
overestimation of the luminances was
observed.
4. DISCUSSION
The increase of vignetting effect with large
apertures was already mentioned in [2].
If, theoretically, the studied fisheye
lenses generate a 180° angle of view
through an equisolid angle projection,
measurements on the pictures showed an
inaccuracy of the borderline between the
circular image and its surrounding black
frame. This leads to difficulties to check the
adequate position of the camera to embrace
exactly and symmetrically the 180° field,
pointing on the central square.
Another difficulty consisted in matching
the luminance meter with the center of the
fisheye lens which is not precisely given by
the manufacturer.
The observed differences of RMSE can
be partially explained by these difficulties.
5. CONCLUSION AND FUTURE WORK
The comparison between the two identical
devices leads to the conclusion that their
vignetting effect is similar (difference of
RMSE < 0.7%) and is maximal at the
periphery of the picture for the largest
aperture (f/2.8) reaching a luminance loss
around 66%.
To improve the accuracy of the curves at
the lens periphery and confirm that
vignetting curves could be used for other
devices of same characteristics (SIGMA
4.5mm F2.8 EX DC HSM mounted on
CANON EOS 40D), measurements should
be reiterated with an increase of the
frequency of the targets at the periphery of
the fisheye.
Cauwerts C., Deneyer A., Bodart M., Vignetting effect of two identical fisheye lenses
REFERENCES
[1] D. Fan, B. Painter, J. Mardalvevic, A
data collection method for long-term field
studies of visual comfort in real-world daylit
office
environments,
Proceedings
of
PLEA2009, Quebec City, Canada (2009)
251-256.
[2] M. Inanici, Evaluation of high dynamic
range photography as a luminance data
acquisition system, Lighting Research and
Technology 38,2 (2006) 123-136.
[3] A. Jacobs, M. Wilson, Determining
lens vignetting with HDR techniques,
Bulgarian National Lighting Conference,
Varna, Bulgaria (2007).
[4] M. Bodart, A. Deneyer, A. De Herde,
P. Wouters, Design of a new single-patch
sky and sun simulator, Lighting Research
and Technology 38,1 (2006) 73-89.
ACKNOWLEDGEMENTS
Coralie Cauwerts and Magali Bodart were
supported by the Belgian Research National
Foundation (FNRS) and Arnaud Deneyer by
the Belgian Building Research Institute
(BBRI).
Cauwerts Coralie
FNRS research fellow
1, Place du Levant
1348 Louvain-la-Neuve (Belgium)
+3210/47.91.52
+3210/47.21.50
[email protected]
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