Long range polarimetric imaging through fog
Julien Fade,
1, ∗
Swapnesh Panigrahi,
1
Anthony Carr´e,
1
Ludovic Frein,
1
Cyril
Hamel,
1
Fabien Bretenaker,
2
Hema Ramachandran,
3
and Mehdi Alouini
1
1
Institut de Physique de Rennes, CNRS, Universit´e de Rennes 1,
Campus de Beaulieu, 35 042 Rennes, France
2
Laboratoire Aim´e Cotton, CNRS, Universit´e Paris-Sud 11, 91 405 Orsay, France
3
Raman Research Institute, CV Raman Avenue, Sadashivanagar, 560 080, Bangalore, India
compiled: March 16, 2015
We report an experimental implementation of long-range polarimetric imaging through fog over kilo-
metric distance in real field atmospheric cond itions. An incoherent polarized light source settled on a
telecommunication tower is imaged at a 1.3 km distance with a snapsh ot polarimetric camera includ-
ing a b irefringent Wollaston prism, allowing simultaneous acquisition of two images along orthogonal
polarization directions. From a large number of acquisitions datasets and under various environmental
conditions (clear sky/fog/haze, day/night), we compare the efficiency of u sing p olarized light for source
contrast increase with different signal representations (intensity, polarimetric difference, polarimetric
contrast,...). With the limited-dynamics detector used, a maximum fourfold increase in contrast was
demonstrated under bright background illumination using polarimetric difference image.
OCIS codes: (110.0113) Imaging through turbid media; (110.5405) Polarimetric imaging;
(010.7295) V isibility and imaging; (110.4280 Noise in imaging systems).
http://dx.doi.org/10.1364/XX.99.099999
1. Introduction
Imaging of objects and light sources hidden behind
a turbid medium has wide applications in areas per-
taining to medical diagnostics [1, 2], remote sensing
[3] and transport and navigation [4 ]. More specifi-
cally, imaging through nebulous media encountered
in nature, like fog, rain and light haze is still a
topical issue that attracts a lot of attention. En-
hanced vision in such weather conditions has indeed
tremendous applications for assistance in naviga-
tion of all modes of vehicular transport. Vision sys -
tems th at can offer enhanced visibility during such
weather conditions can be used to provide visual
assistance by means of augmented reality displays
that can efficiently detect and isolate light sources
hidden beyond foggy intervening media. Besides,
with the advent of autonomous vehicles, both air-
borne and terrestrial, this problem becomes increas-
ingly important in the field of machine vision and
vehicular safety as well.
In general, the photons travelling through any
∗
Corresponding author: julien.fade@univ-rennes1.fr
random medium can be classified into ballistic,
snake and diffused photons. The diffused photons
undergo maximum scattering as they travel through
the m edium, wh er eas ballistic and snake photons
undergo predominantly forward scattering. As a
result, the diffused photons randomly take longer
paths and times to reach the detector. Conse-
quently, in th e process, they are received as noise
over the ballistic p hotons that retain the spatial and
temporal information of the source (signal). Vari-
ous app roaches have been studied to d iscr im inate
and record only the ballistic and snake photons in
order to attain a better contrast of signal over the
noise. For instance, time-gated imaging, using a
gated camera synchronized to a pulsed illumination
source is shown to be an efficient way to recover
the information carried by ballistic photons [1, 5].
Other approaches have also been studied such as
spatial filtering techniques [6 , 7], intens ity modula-
tion schemes [8, 9] or laser optical feedback imaging
[10, 11].
An alternative approach, such as polarization-
gated imaging [12–16], involves this time light po-
larization. It is based on the preservation of the
2
state of polarization of light (linear or circular)
during propagation th rough thick scattering media,
such as heavy fog conditions, with m inor depolar-
ization. This so-called polarization memory effec t
has been analyzed in numerous references, both for
linearly polarized [17] and circularly polarized light
[18, 19]. As a result, such effect can be exploited
using a polarization-sensitive imaging device to en-
hance the visibility of a source provided this latter
emits polarized light. T hese approaches have al-
ready proved efficient and been reported in a num-
ber of in laboratory experiments [12–16], with sim-
ulated turbidity conditions on very short distances
using artificial scatterers like aerosols.
In case of light travelling through fog, photons
undergo scattering by a cloud of randomly dis-
tributed particles with sizes in the order of 5-50
µm and varying number density [20]. Moreover, de-
pending on the environm ental conditions, the scat-
terers in the intervening medium may not retain a
perfect spheroid shape due to drag (as in case of
large rain drops) or may have ice crystals with pre-
ferred orientations [21].
Although th ese overall studies on polarized light
propagation bring very useful elements of under-
standing, they remain quite difficult to exploit for
sizing an outd oor imaging sy stem because they are
carried out in well-established and well-controlled
conditions. Indeed, the combined effects of sun il-
lumination, surrounding artificial illumination, vis-
ibility evolution, change of scatterers density and
size, varying atmospheric conditions are extremely
difficult to mimic or anticipate in a laboratory.
In addition, unless resorting to numerical scatter-
ing simulations, long range pr op agation is a phe-
nomenon that cannot be easily simulated by a lab-
oratory experiment, even with a scaling approach.
Keeping in mind the aforementioned applications
and requirement of study of such vision sys tems in
real atmospheric cond itions, we report in this pa-
per the design, implementation and operation of an
imaging experim ent we developped to investigate
the polarimetric contrasts of a scene including a po-
larized light source in real foggy environment over
a kilometric distance. Such distance corresponds to
a r easonable range requirement for transport safety
applications. We also analyze the efficiency of sev-
eral representations of the polarimetric inf orma-
tion obtained with our imaging installation in var-
ious environmental conditions (clear sky/fog/haze,
day/night).
This article is organized as follows: in the next
section, we recall some basics of polarimetric imag-
ing an d the corresponding experimental techniques.
Then, in Section 3, we detail the long-range polari-
metric imaging setup u sed in this experiment, as
well as calibration procedures in Section 4. Two
representative datasets are then extensively ana-
lyzed in Section 5, among numerous datasets ac-
quired during experimental campaigns. The effi-
ciency of different polarimetric signal representa-
tions to increase visual contrast of a polarized light
source in fog over long distance is discussed for vary-
ing environ mental conditions. Then, a general dis-
cussion and conclusion on the experiment is even-
tually provid ed in Section 6.
2. Polarimetr ic contrast imaging
Polarization sensitive imaging h as proved efficient
in the context of enhanced vision through turbid
media [22], indus trial quality control [23, 24] and
machine vision [25]. To pr obe the complete polari-
metric properties of a light source, one needs to
measure the Stokes vector S given by
S =
S
0
S
1
S
2
S
3
=
I
x
+ I
y
I
x
− I
y
I
+45
◦
− I
−45
◦
I
R
− I
L
(1)
from which the degree of polarization (DOP) of
the source can be obtained using the relation,
DOP =
p
S
2
1
+ S
2
2
+ S
2
3
/S
0
. Hitherto, various
techniques have been employed to fully or partially
measure the Stokes vectors of an image and obtain
the polarimetric information of the scene of inter-
est. Most often, rotating polarizers and/or mov-
ing birefringent plates are used. Other schemes in-
cluding prisms [26], Savart plates [27], polarization
gratings [28], liquid crystal modulators [29] or mi-
crogrid division-of-focal-plane polarimetric imagers
[30] have been used with varying degrees of com-
promise towards mechanical reliability and real-
time acquisition and processing. Measuring the full
Stokes vector at each pixel can be a slow and storage
heavy task and hence not very suitable for imaging
moving objects, thus, limiting their application in
real-time scenarios. In the experiment p resented
here, we consider a highly polarized source with
a priori known linear polarization state with the
intervening medium being non-birefringent. There-
fore, it is not necessary to measure the full Stokes
vector but only the first two compon ents of the
Stokes vector to define the so-called Orthogonal
States Contrast given by Eq. (2)
OSC =
S
1
S
0
=
I
k
− I
⊥
I
k
+ I
⊥
, (2)
3
Map data © 2014 Google, INEGI
N
Reception site
TDF Tower
1.27 km
Fig. 1. Long range polarimetric imaging experimental setup. The source and the camera are separated by 1.27 km
with the camera placed in the University of Rennes 1 campus and the source located on a telecommunication tower
of the TDF company. The photograph shows the polarized light source settled on the telecommunication tower.
where I
k
and I
⊥
are the intensities obtained
through orthogonally aligned analyzers or through
a polarization splitting Wollaston prism. In the
case considered here of a linearly polarized light
propagating through non-birefringent medium, the
OSC is equal to the DOP of the source after pass-
ing through the atmosphere and fog. The inten-
sity measures recorded by a p ixel of a camera are
of course affected by various noise sources, for in -
stance, (a) the Gaussian electronic n oise induced
by the electronic read-out circuit of the CCD array
sensor ; and (b) optical noise due to photon noise,
atmospheric turbulence and fluctuations introduced
by spatial/temporal evolutions of the intermediate
foggy medium. As will be seen later, the com-
putation of the OSC may be strongly affected by
this noise, especially in low illumination conditions,
since the division by total intensity (I
T
= I
k
+ I
⊥
)
may lead to unbou nded values.
3. Long range Experimental Setup
The experiment presented here is designed to imple-
ment a long-range polarimetric imaging system over
kilometric distance, and in real-field outdoor condi-
tions. Such experiment allows u s to assess th e bene-
fits of using polarized light for improved detectabil-
ity of a light-mark through turbid atmosphere over
long distances. Such a system can have practical
applications in aviation or navigation at sea in poor
visibility conditions. The setup mainly consists of
a polarized light emitter and a polarimetric imag-
ing system that s imultaneously acquires two images
of a scene corresponding to the two orthogonal di-
rections of polarization. These elements, which are
extensively described in this section, are located on
the Beaulieu campus of University of Rennes 1, and
are separated by 1.27 km. The source is located on
the top of a telecommunication tower own ed by the
TDF company. The detection setup is located in
a laboratory building as illustrated in Fig. 1. The
various parts of the setup are d escribed in detail in
the following subsections.
3.A. Polarized Source
The source used is a 300 W halogen incandescent
lamp with a linear polarizer, both p laced inside a
weatherproof steel h ou sing as shown in Fig. 1. The
light from the incandescent lamp is polarized us-
ing an adhesive dichroic polymer polarizing sheet
glued to a glass plate and oriented such that the
polarization axis is vertical. Half the optical power
provided by the lamp being absorbed by the polar-
izer, it turned out that standard polaroid sheets are
subject to deterioration after a few minutes of illu-
mination. For this reason, we use polarizing sheets
specifically designed for LCD projector industry,
thus ensuring high durability under high power op-
eration conditions. Before installing the source, we
conducted durab ility tests in indoor conditions with
a 300 W lamp. The lamp was allowed to run con-
tinuously during day times. In these conditions, it
was noticed that the polarimetric contrast of the
sheet was reduced by 57.4% in a period of 5 days
with continuous daytime usage. In light of this, a
weather-proof steel housing was d esigned, such that
the polarizing sheet glu ed on a glass plate is placed
sufficiently far (20 cm) from the lamp. Moreover,
holes have been drilled in the bottom and top of
the housing to enable air-flow in-b etween the lamp
and the glass plate. This air flow is stimulated by
convection when the temperature of the glass-plate
increases allowing the hot air in-between to be re-
moved, and thus providing an efficient heat dissipa-
tion. Such mechanical design ensures a reasonable
lifetime of almost one year in outdoor conditions
4
before requiring replacement.
The telecommunication tower is about 80 m in
height and provid es a suitable location for the
source. The distance of the tower from the labo-
ratory site in the University of Rennes 1 is optimal
for various applications where a long-range imaging
through fog may be crucial. The tower is also the
tallest structure in the surr ou nding area and is in
line-of-sight from laboratory buildings. The polar-
ized source is connected to a GSM switch enablin g
easy remote control of the emission part of the ex-
periment.
3.B. Snapshot polarimetric camera
The detection system consists of a snapshot po-
larimetric imaging setup and a computer dedicated
for control and image acquisition. Th e detection
system is housed on a m ezzanine floor of a labo-
ratory building in the line-of-sight of the emitter.
The schematic of the imaging setup is shown in
Fig. 2.(a) and 2.(b). T he imaging setup consists of a
telescopic arrangement of lenses L1 (50 mm, F/2.8
camera objective) and L2 (25 mm, F/2.1 camera
objective) which creates a collimated beam of light
that is incident on a Wollaston prism (WP). The
WP is a calcite birefringent prism with a 5
◦
splitting
angle which intro duces an angular separation be-
tween the vertical and horizontal polarization com-
ponents of the incident beam. These ordinary and
extraordinary beams are then focused onto the cam-
era using a third lens L3 (25 mm, F/2.1 camera
objective), thus creating two images I
k
and I
⊥
on
the CCD. This setup allows us to simultaneously
record a scene along orthogon al polarization direc-
tions using a single camera. T his has huge ad van-
tage in real-time processing of moving objects and
has proved to be efficient in the presence of tur bu-
lence and relative motion of the scene [26], such as
fog in our case. It has been demonstrated that this
configuration suffers from lower geometrical aber -
ration as well [26]. In order to avoid chromatic
aberrations due to th e WP, we use a selective red
filter (F) with a central wavelength of 612 nm and
a linewidth of 12 nm. The two images produced
on the CCD have considerab le overlap because of
the small splitting angle of the WP. To prevent this
overlap, a stainless-steel slit painted with dark matt
paint of dimension 3 mm × 18 mm is used as a field
mask (FM) and is placed in the intermediate image
plane existing between lenses L1 and L2. The CCD
camera is a 12 bits, 782 × 582 pixels resolution
camera (Basler A312f) with pixel size of 8 µm and
average dark count of 23 e
−
/s with standard devi-
ation of 0.6 e
−
/s. The camera was selected for its
low n oise properties in low light conditions, w hich
as we will see, is preferable while performing arith-
metic on the acquired polarimetric im ages.
Fig. 2. Polarimetric imaging setup: The Wollaston
prism (WP) angularly separates the incident beam into
two orthogonal polarization components forming two im-
ages I
k
and I
⊥
on the CCD. The illustration in (a) shows
a orthographic view of the polarimetric imager while
the schematic in (b) g e ometrically indicates the working
principle of the imaging setup. A top vie w photograph
of the imaging setup is shown in (c).
3.C. Control program
The camera is controlled through an IEEE 1394a
interface by a custom acquisition program devel-
oped using LabVIEW. A number of features are
implemented in the program that suit the experi-
ment and provide automation of acquisition using
a user-friendly interface. One of the features im-
plemented is what we will refer to as auto-exposu re
mode (AEM). We had to implement such AEM be-
cause the imaging system is by essence operated
for long time periods under varying weather con-
ditions. Under th is mode, the exposure time of
the camera is automatically changed depending on
the illumination of a given pre-defined pixel. This
pixel can be chosen to be the pixel representing the
source on the camera (we will refer to this pixel
as ”source pixel” for brevity in further s ections),
thereby avoiding saturation or un derexposure of the
source pixel with respect to the surrounding scene.
It is also possible to feed this control loop with the
average brightn ess of a region of interest, or of the
5
overall scene. The advantage of this mode is most
apparent d uring twilight and in foggy conditions
when the illumination of the scene varies strongly
in time. Using dynamically controlled exposure
time, one obtains a time series of frames, wh ich can
be normalized to their respective exposure times
(which are stored in a data-file by the program) so
as to continually exploit the full dynamic r an ge of
the camera. We also implement a so-called cu mula-
tive grab mode (CGM) to avoid recording the 100
Hz intensity fluctuations due to the 50 Hz modula-
tion of the electrical supply network. This mode is
automatically activated for exposures smaller than
10 ms, that is when the source blinking becomes
apparent. Under CGM mode, a frame hav ing max-
imum gray-level value of the source pixel is chosen
from a sample of N
CGM
frames where N
CGM
de-
pends on the exposure time T
exp
in milliseconds as
N
CGM
= 20(ms)/T
exp
. The program also displays
the calculated OSC of the source pixel in real-time
and allows for compensation of the ambient light
contribution, in which case the OSC reads
OSC
A
=
(I
s
k
− I
a
k
) − (I
s
⊥
− I
a
⊥
)
(I
s
k
− I
a
k
) + (I
s
⊥
− I
a
⊥
)
. (3)
In the above equation, I
s
k
(respectively I
s
⊥
) denotes
the average intensity over a 3 × 3 p ixels area enclos-
ing the pixel corresponding to the source location
(source pixel) in I
k
(respectively I
⊥
). On the other
hand, I
a
k
(respectively I
a
⊥
) estimates th e ambient
illumination by averaging a 3 × 3 pixels area in
the vicinity of the source pixel, but strictly distinct
from the source spatial extent. With such defin i-
tion, the OS C is computed taking into account in-
tensity measures I
a
k
and I
a
⊥
of a reference area close
to the source representing the ambient illumination.
Using such control s oftware with AEM allows us
to acquir e images at predefined intervals over long
periods of time with strongly varying illumination
conditions (i.e., clear sky, obstructed vision, day-
time/night-time and twilight).
4. Experiment calibration
In this section, we first describe the camera cal-
ibration and im age registration procedures which
have to be implemented so as to provide reliable
polarimetric images and measurements. Then, we
report some experimental results which allowed us
to validate the experimental system (emission and
acquisition) and laboratory calibration on real field
conditions.
4.A. Imaging setup calibration
The frames obtained in th e experiment described
above are bin ary values obtained f rom the cam-
era. Processing of the frames to extract the im-
ages is at this step carried out in a post-acquisition
stage. The post-pro cessing includes fixed pattern
dark frame subtraction, pixel non-uniformity cor-
rection, image registration and optical distortion
correction. The latter pro cessing steps are orga-
nized in the following manner.
Detector calibration: For a camera sensor
there are mainly three calibrations to be performed
in order to record an image that closely corresponds
to the scene being imaged, namely dark pattern cal-
ibration, non-uniformity of pixel gain and removal
of hot and dead pixels. Each pixel has different
dark noise properties at a particular temperature
and exposure time. After averagin g over a number
of dark frames acquired in total darkness, one ob-
tains the fixed pattern dark frame (I
F P D
) that can
be subtracted from the images of interest. It must
be noted that this correction depends on the expo-
sure time. We thus averaged 500 dark frames to
obtain the I
F P D
for different exposure times. An-
other important correction to be made is the non-
uniformity in pixel gain. Owing to the fabrication
process, each pixel in the sensor may not have the
same sensitivity/gain. This n on -uniformity is es-
timated by illuminating the sensor with spatially
uniform white light and recording the resulting pat-
tern. This image is normalized by dividing by the
mean gray level to create a gain non-uniformity im-
age I
GNU
. Using the above two calibration images,
a raw image recorded is systematically corrected
using I
corr
= (I
raw
- I
F P D
)/I
GNU
.
Image registration and distortion calibra-
tion: Once performed the above calibrations and
corrections on the bare detector itself (without
any image forming optics), the polarimetric optical
imaging system is mounted. When the system is
assembled and images are recorded, one has to ex-
tract the two images corresponding to orthogonal
polarization directions from a single fr ame. It is re-
quired that the two extracted images have a one to
one correspondence between pixels su ch that they
map the same scene. This process is straightfor-
ward if there is no geometrical distortion or if both
the images share the same geometrical distortion.
However, the WP used in the polarimetric imaging
setup does introduce astigmatism and anamorphic
distortion in the resulting images [31]. The distor-
tion is non-symmetrical with resp ect to the two im-
age channels and hence a per fect image registration
