Measurement of the Group Velocity of Light in Sea Water at the ANTARES Site
ABSTRACT The group velocity of light has been measured at eight different wavelengths
between 385 nm and 532 nm in the Mediterranean Sea at a depth of about 2.2 km
with the ANTARES optical beacon systems. A parametrisation of the dependence of
the refractive index on wavelength based on the salinity, pressure and
temperature of the sea water at the ANTARES site is in good agreement with
- SourceAvailable from: Ray Smith[Show abstract] [Hide abstract]
ABSTRACT: A new UV submersible spectroradiometer has been employed to determine the diffuse attenuation coefficient for irradiance in the clearest natural waters [K(w)(lambda)] with emphasis on the spectral region from 300 to 400 nm. K(w)(lambda) can be related to the inherent optical properties of pure water, in particular the total absorption coefficient a(w)(lambda) and the molecular scattering coefficient b(m)(lambda), by means of equations derived from radiative transfer theory. We present an analysis showing that limiting values of K(w)(lambda) can be estimated from a(w)(lambda) and vice versa. Published a(w)(lambda) data, which show discrepancies much larger than their estimated accuracies, are briefly reviewed and then compared, via our analysis, with K(w)(lambda) data (our own new and previously published data as well as relevant data of others). This comparative analysis and new data allow a consistent and accurate set of optical properties for the clearest natural waters and for pure fresh water and saltwater to be estimated from 300 to 800 nm.Applied Optics 01/1981; 20(2):177-84. · 1.69 Impact Factor
Article: The ANTARES Optical Module[Show abstract] [Hide abstract]
ABSTRACT: The ANTARES collaboration is building a deep sea neutrino telescope in the Mediterranean Sea. This detector will cover a sensitive area of typically 0.1 km-squared and will be equipped with about 1000 optical modules. Each of these optical modules consists of a large area photomultiplier and its associated electronics housed in a pressure resistant glass sphere. The design of the ANTARES optical module, which is a key element of the detector, has been finalized following extensive R & D studies and is reviewed here in detail.
- Astroparticle Physics. 04/2011; 34(9):652–662.
arXiv:1110.5184v1 [hep-ex] 24 Oct 2011
Measurement of the Group Velocity of Light
in Sea Water at the ANTARES Site
S. Adri´ an-Mart´ ıneza, I. Al Samaraib, A. Albertc, M. Andr´ ed,
M. Anghinolfie, G. Antonf, S. Anvarg, M. Ardida,
A.C. Assis Jesush, T. Astraatmadjah,1, J-J. Aubertb,
B. Bareti, S. Basaj, V. Bertinb, S. Biagik,ℓ, A. Bigim,
C. Bigongiarin, C. Bogazzih, M. Bou-Caboa, B. Bouhoui,
M.C. Bouwhuish, J. Brunnerb,2, J. Bustob, F. Camarenaa,
A. Caponeo,p, C. Cˆ arloganuq, G. Carminatik,ℓ,3, J. Carrb,
S. Cecchinik, Z. Charifb, Ph. Charvisr, T. Chiarusik,
M. Circellas, H. Costantinie,b, P. Coyleb, C. Curtilb,
G. De Boniso,p, M.P. Decowskih, I. Dekeysert, A. Deschampsr,
C. Distefanou, C. Donzaudi,v, D. Dornicn, Q. Dorostiw,
D. Drouhinc, T. Eberlf, U. Emanuelen, A. Enzenh¨ oferf,
J-P. Ernenweinb, S. Escoffierb, P. Fermanio,p, M. Ferria,
V. Flaminiom,x, F. Folgerf, U. Fritschf, J-L. Fudat, S. Galat` ab,
P. Gayq, K. Geyerf, G. Giacomellik,ℓ, V. Giordanou,
J.P. G´ omez-Gonz´ alezn, K. Graff, G. Guillardq, G. Halladjianb,
G. Hallewellb, H. van Hareny, J. Hartmanh, A.J. Heijboerh,
Y. Hellor, J.J. Hern´ andez-Reyn, B. Heroldf, J. H¨ oßlf,
C.C. Hsuh, M. de Jongh,1, M. Kadlerz, O. Kalekinf,
A. Kappesf, U. Katzf, O. Kavatsyukw, P. Kooijmanh,aa,ab,
C. Kopperh,f, A. Kouchneri, I. Kreykenbohmz,
V. Kulikovskiyac,e, R. Lahmannf, P. Lamareg, G. Larosaa,
D. Lattuadau, D. Lef` evret, G. Limh,ab, D. Lo Prestiad,ae,
H. Loehnerw, S. Loucatosaf, S. Manganon, M. Marcelinj,
A. Margiottak,ℓ, J.A. Mart´ ınez-Moraa, A. Melif,
T. Montarulis,ag, L. Moscosoi,af,4, H. Motzf, M. Nefff,
E. Nezrij, D. Palioselitish, G.E. P˘ av˘ ala¸ sah, K. Payetaf,
P. Payreb,4, J. Petrovich, P. Piattelliu, N. Picot-Clementeb,
V. Popaah, T. Pradierai, E. Presanih, C. Raccac, C. Reedh,
G. Riccobeneu, C. Richardtf, R. Richterf, C. Rivi` ereb,
Preprint submitted to Astroparticle Physics 25 October 2011
A. Robertt, K. Roenschf, A. Rostovtsevaj, J. Ruiz-Rivasn,
M. Rujoiuah, G.V. Russoad,ae, F. Salesan, D.F.E. Samtlebenh,
P. Sapienzau, F. Sch¨ ockf, J-P. Schulleraf, F. Sch¨ ussleraf,
T. Seitzf, R. Shanidzef, F. Simeoneo,p, A. Spiesf, M. Spuriok,ℓ,
J.J.M. Steijgerh, Th. Stolarczykaf, A. S´ anchez-Losan,
M. Taiutie,ak, C. Tamburinit, S. Toscanon, B. Vallageaf,
V. Van Elewycki, G. Vannoniaf, M. Vecchib, P. Verninaf,
S. Wagnerf, G. Wijnkerh, J. Wilmsz, E. de Wolfh,ab,
H. Yepesn, D. Zaborovaj, J.D. Zornozan, J. Z´ u˜ nigan
aInstitut d’Investigaci´ o per a la Gesti´ o Integrada de les Zones Costaneres (IGIC) - Universitat
Polit` ecnica de Val` encia. C/ Paranimf 1 , 46730 Gandia, Spain.
bCPPM, Aix-Marseille Universit´ e, CNRS/IN2P3, Marseille, France
cGRPHE - Institut universitaire de technologie de Colmar, 34 rue du Grillenbreit BP 50568 - 68008
dTechnical University of Catalonia, Laboratory of Applied Bioacoustics, Rambla Exposici´ o,08800
Vilanova i la Geltr´ u,Barcelona, Spain
eINFN - Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
fFriedrich-Alexander-Universit¨ at Erlangen-N¨ urnberg, Erlangen Centre for Astroparticle Physics,
Erwin-Rommel-Str. 1, 91058 Erlangen, Germany
gDirection des Sciences de la Mati` ere - Institut de recherche sur les lois fondamentales de l’Univers -
Service d’Electronique des D´ etecteurs et d’Informatique, CEA Saclay, 91191 Gif-sur-Yvette Cedex,
hNikhef, Science Park, Amsterdam, The Netherlands
iAPC - Laboratoire AstroParticule et Cosmologie, UMR 7164 (CNRS, Universit´ e Paris 7 Diderot, CEA,
Observatoire de Paris) 10, rue Alice Domon et L´ eonie Duquet 75205 Paris Cedex 13, France
jLAM - Laboratoire d’Astrophysique de Marseille, Pˆ ole de l’´Etoile Site de Chˆ ateau-Gombert, rue Fr´ ed´ eric
Joliot-Curie 38, 13388 Marseille Cedex 13, France
kINFN - Sezione di Bologna, Viale Berti-Pichat 6/2, 40127 Bologna, Italy
ℓDipartimento di Fisica dell’Universit` a, Viale Berti Pichat 6/2, 40127 Bologna, Italy
mINFN - Sezione di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
nIFIC - Instituto de F´ ısica Corpuscular, Edificios Investigaci´ on de Paterna, CSIC - Universitat de
Val` encia, Apdo. de Correos 22085, 46071 Valencia, Spain
oINFN -Sezione di Roma, P.le Aldo Moro 2, 00185 Roma, Italy
pDipartimento di Fisica dell’Universit` a La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy
qClermont Universit´ e, Universit´ e Blaise Pascal, CNRS/IN2P3, Laboratoire de Physique Corpusculaire,
BP 10448, 63000 Clermont-Ferrand, France
rG´ eoazur - Universit´ e de Nice Sophia-Antipolis, CNRS/INSU, IRD, Observatoire de la Cˆ ote d’Azur and
Universit´ e Pierre et Marie Curie, BP 48, 06235 Villefranche-sur-mer, France
sINFN - Sezione di Bari, Via E. Orabona 4, 70126 Bari, Italy
tCOM - Centre d’Oc´ eanologie de Marseille, CNRS/INSU et Universit´ e de la M´ editerran´ ee, 163 Avenue
de Luminy, Case 901, 13288 Marseille Cedex 9, France
uINFN - Laboratori Nazionali del Sud (LNS), Via S. Sofia 62, 95123 Catania, Italy
vUniv Paris-Sud , 91405 Orsay Cedex, France
wKernfysisch Versneller Instituut (KVI), University of Groningen, Zernikelaan 25, 9747 AA Groningen,
xDipartimento di Fisica dell’Universit` a, Largo B. Pontecorvo 3, 56127 Pisa, Italy
yRoyal Netherlands Institute for Sea Research (NIOZ), Landsdiep 4,1797 SZ ’t Horntje (Texel), The
zDr. Remeis-Sternwarte and ECAP, Universit¨ at Erlangen-N¨ urnberg, Sternwartstr. 7, 96049 Bamberg,
aaUniversiteit Utrecht, Faculteit Betawetenschappen, Princetonplein 5, 3584 CC Utrecht, The
abUniversiteit van Amsterdam, Instituut voor Hoge-Energie Fysika, Science Park 105, 1098 XG
Amsterdam, The Netherlands
acMoscow State University,Skobeltsyn Institute of Nuclear Physics,Leninskie gory, 119991 Moscow,
adINFN - Sezione di Catania, Viale Andrea Doria 6, 95125 Catania, Italy
aeDipartimento di Fisica ed Astronomia dell’Universit` a, Viale Andrea Doria 6, 95125 Catania, Italy
afDirection des Sciences de la Mati` ere - Institut de recherche sur les lois fondamentales de l’Univers -
Service de Physique des Particules, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
agDPNC, Universit´ e de Gen` eve, Quai Ernest-Ansermet 24, 1211 Gen` eve, Switzerland
ahInstitute for Space Sciences, R-77125 Bucharest, M˘ agurele, Romania
aiIPHC-Institut Pluridisciplinaire Hubert Curien - Universit´ e de Strasbourg et CNRS/IN2P3 23 rue du
Loess, BP 28, 67037 Strasbourg Cedex 2, France
ajITEP - Institute for Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117218 Moscow,
akDipartimento di Fisica dell’Universit` a, Via Dodecaneso 33, 16146 Genova, Italy
The group velocity of light has been measured at eight different wavelengths between
385 nm and 532 nm in the Mediterranean Sea at a depth of about 2.2 km with the
ANTARES optical beacon systems. A parametrisation of the dependence of the
refractive index on wavelength based on the salinity, pressure and temperature of
the sea water at the ANTARES site is in good agreement with these measurements.
Key words: ANTARES, neutrino telescope, optical beacon system, velocity of
light, refractive index
Also at University of Leiden, the Netherlands.
On leave at DESY, Platanenallee 6, D-15738 Zeuthen, Germany.
Now at University of California - Irvine, 92697, CA, USA.
The ANTARES neutrino telescope is located on the bottom of the Mediter-
ranean Sea (42o50′N, 6o10′E) at a depth of 2475 m, roughly 40 km offshore
from Toulon in France. The main objective of the experiment is the observa-
tion of neutrinos of cosmic origin in the southern hemisphere sky. Sea water
is used as the detection medium of the Cherenkov light induced by relativis-
tic charged particles resulting from the interaction of neutrinos. The particle
trajectory is reconstructed from the measured arrival times of the detected
photons. The detector consists of 885 photomultiplier tubes (PMTs) mounted
on twelve vertical lines with a length of about 450 m. The horizontal separation
between lines is about 70 m. Further details can be found elsewhere [1,2,3].
Charged particles traveling through sea water produce the emission of Cherenkov
light whenever the velocity of the particle exceeds that of light in water. The
Cherenkov photons are emitted at a characteristic angle, θc, with respect to
the particle direction. This angle is related to the index of refraction of the
medium as cosθc=
the speed of light in vacuum. The index of refraction, np, corresponds to the
ratio between the speed of light in vacuum and the phase velocity of light
in water. The individual photons then travel through the water at the group
velocity. Both the phase and the group velocity depend on the wavelength of
the photons. This is usually referred to as chromatic dispersion. The group
velocity is related to its phase velocity in the following way:
βnp. In this, β is the velocity of the particle relative to
where λ is the wavelength of light. The index of refraction, ng, corresponds to
the ratio between the speed of light in vacuum and the group velocity of light
Since the PMTs cannot distinguish the photon wavelength, the variation of
the photon emission angle and the group velocity due to chromatic dispersion
cannot be accounted for on the individual photon level. Nevertheless, the av-
erage effect of the wavelength dependencies are accounted for in the algorithm
used to reconstruct the particle trajectory [4,5].
A measurement of the group velocity of light has been made using the optical
beacon system of ANTARES. This system consists of a set of pulsed light
sources (LEDs and lasers) which are distributed throughout the detector and
illuminate the PMTs with short duration flashes of light. The refractive index
is deduced from the recorded time of flight distributions of photons at different
distances from the sources for eight different wavelengths between 385 nm and
Fig. 1. Picture of a standard LED optical beacon (left), the modified LED optical
beacon (middle) and a laser beacon (right).
The PMTs of ANTARES are sensitive to photons in the wavelength range
between 300 nm and 600 nm. The maximum quantum efficiency is about
22 % between 350 nm and 450 nm. The arrival time and integrated charge of
the analogue pulse from the PMT are measured by the readout electronics .
The transit time spread of single photo-electrons of the PMT is around 3.5 ns
The group velocity of light has been measured using the ANTARES optical
beacon system. This system was primarily designed to perform time calibra-
tion in situ [7,8]. There are two types of optical beacons, the LED optical bea-
cons and the laser beacons. There are four LED optical beacons distributed
along each detector line and two laser beacons at the bottom of two central
lines. The in situ measurement of the temperature and salinity is provided by
some Conductivity/Temperature/Depth sensors5.
A standard LED optical beacon contains 36 individual LEDs distributed over
six vertical faces forming a hexagonal cylinder housed in a pressure resistant
glass enclosure (Figure 1, left). On each face, five LEDs point radially outwards
and one upwards. All LEDs emit light at an average wavelength of 469 nm,
except the two LEDs located on the lowest LED optical beacon of Line 12
which emit light at an average wavelength of 400 nm. A modified LED optical
beacon was installed in 2010 on Line 6. This LED optical beacon has three
LEDs per face instead of six, all of them pointing upwards (Figure 1, centre).
The three LEDs of each face emit light of the same colour. The average wave-
length of the light from the six faces are 385, 400, 447, 458, 494 and 518 nm.
The LEDs emit light with a maximum intensity of about 160 pJ and a pulse
width of about 4 ns FWHM. The intensity of the emitted light can be varied
changing the voltage feeding the LEDs.
The laser beacon consists of a Nd-YAG solid state laser (Figure 1, right). It
5SEABIRD CTD (SBE37-SMP), http://www.seabird.com/.
350 400450500 550600
385 400447 458 469494518532
Fig. 2. (a) Wavelength spectra of the light sources used in this work as measured
with a calibrated spectrometer. The spectrometer measurements are made in air.
The data points have been smoothed and the highest value of each spectrum is set
equal to one. On the top of the Figure the peak wavelengths are indicated in units
of nm. (b) Simulated light spectra at a distance of 120 m in sea water with the
highest value renormalized to one. The differences between the spectra are due to
the variation of the absorption length as a function of the wavelength.
can emit pulses of light with an intensity of about 1 µJ and pulse width of
about 0.8 ns FWHM. The average wavelength is 532 nm. This light is spread
out by an optical diffuser, so that the light can reach the surrounding lines.
During calibration runs, the LEDs and lasers flash at a frequency of 330 Hz.
Further details about the optical beacon system can be found elsewhere [7,8,9].
The wavelength spectra of the light sources used for this analysis were mea-
sured using a calibrated spectrometer6(see Figure 2a). The typical width of
each spectrum is around 10 nm except for the green LED (518 nm), which is
larger, and the laser (532 nm), which is much smaller.
Due to the wavelength dependence of the absorption of light in water, the
spectra change as a function of the distance travelled by the light. The ex-
pected wavelength distributions as a function of distance have been estimated
by Monte Carlo simulations using the dependence of absorption length on
wavelength given by Smith and Baker . In Figure 2b the spectra at a dis-
tance of 120 m are shown for the different light sources. The evolution of the
spectra is taken into account in the final results (Section 4), in particular the
uncertainty assigned to the wavelengths has been taken to be the root mean
square (RMS) of the wavelength distribution given by the simulation.
6Ocean Optics HR4000CG-UV-NIR, http://www.oceanoptics.com/.
0100 200300 400500600 700800900
Number of entries
Fig. 3. Example of a distribution of arrival times observed at a distance of 100 m
from an LED. The inset shows a zoom around the signal region. The solid curve
corresponds to a fit function as described in the text and given in Equation 2.
3Data Acquisition and Analysis
In order to measure the optical properties of the deep sea water, designated
data taking runs were performed using the optical beacon system. During
these runs, one single LED located in the lowest optical beacon of a line and
pointing upward was flashed. Only the signals recorded by the PMTs along
the same line are used in the analysis. As a result, the line movements due to
the sea currents can safely be ignored.
The runs used in this analysis were taken between May 2008 and April 2011.
Each run contains typically more than 100,000 light flashes. Each flash is
detected by a small PMT inside the optical beacon. The time of the flash and
the arrival times of the photons on the PMTs were recorded within a time
window from 1500 ns before to 1500 ns after the flash. The integrated charge
of the analogue pulses of the PMTs were also recorded. Only runs were used
when the average rate of background light was below 100 kHz.
In Figure 3, the distribution of the arrival times of photons on a PMT located
100 m above the LED optical beacon (λ = 469 nm) is shown. The time,
t = 0 ns, corresponds to the time of the flash. A clear peak at t = 470 ns can be
seen which corresponds to the shortest propagation time of the light. The tail
with late photons can be attributed to light scattering. The flat background
arises from the optical background due to40K decays and bioluminescence.
A convolution of a Gaussian and an exponential distribution on top of a flat
background is fitted to the data. The Gaussian distribution reproduces the
transit time spread of the PMTs, the duration of the light flash and the effect
0 50 100150200250 300 350
Light velocity = 0.2171
Index of refraction
Number of runs
Mean = 1.3825
RMS = 0.0015
Fig. 4. (a) Arrival time as a function of the distance between the LED (λ = 469 nm)
and the PMT. The solid line corresponds to a fit of a linear function to the data
(see text). (b) Distribution of the measured refractive index for a total of 42 runs.
of the chromatic dispersion in water. The exponential distribution takes into
account the effect of the scattering of photons in water. The fit function can
be formulated as:
f(t) = B + S · e−t − µ
τ−t − µ
where t is the arrival time of the photons. The fit parameters are the optical
background, B, the signal strength, S, the mean, µ, and width, σ, of the
Gaussian distribution and the exponential decay constant, τ. In Equation 2,
erfc(t) is the complementary error function distribution. An example of the
fit is shown in the inset of Figure 3. The fit is determined in the range from
200 ns before the most populated bin and 20 ns after. The arrival time of the
light flash at each PMT is estimated by the fitted mean value of the Gaussian
An example of the measured arrival times as a function of the distance between
the optical beacon and the PMT is shown in Figure 4a. A linear function
has been fitted to the data to extract the group velocity of the light. In the
fitting procedure, the distance between the light source and the PMT has been
restricted to the range between 50 m and 250 m in order to limit the effects
of time slewing  and optical background on the measurement.
A Monte Carlo simulation of the response of the detector to LED flashes has
been made. The analysis method was performed to validate the analysis pro-
cedure and to study the systematic effects due to the assumed light absorption
and scattering parameters. The largest contribution to the systematic uncer-
tainty was found to originate from the assumed scattering length; varying the
scattering length between 20 m and 50 m , the measured refractive index
changes by 0.3 %.
4Determination of the Refractive Index
Between May 2008 and March 2010, a total of 42 runs were taken using an
LED with an average wavelength of 469 nm. Three different LED intensities
were used. For a high, middle or low intensity run the range of distances
between the optical beacon and the PMT used in the fit were 50 – 250 m,
40 – 220 m and 10 – 130 m, respectively. The measured refractive index values
of these runs are shown in Figure 4b. In addition to these runs, 14 runs using
an LED with an average wavelength of 400 nm and 13 runs using an LED with
an average wavelength of 532 nm were taken. Between November 2010 and
April 2011 eight runs with a modified optical beacon were taken, extending
the measurements with six additional wavelengths. The index of refraction is
estimated at each wavelength by the mean of the distribution. The measured
refractive indices with the systematic uncertainty are shown in Figure 5 and
tabulated in Table 1. As mentioned in Section 2, the uncertainties in the
wavelengths have been taken to be the RMS of the corresponding distribution
at the middle of the distance ranges. The variation of the RMS values in this
range with respect to the middle is ± 2 nm.
The velocity of light in sea water at a given wavelength depends on the temper-
ature, the salinity and the pressure of the water. A parametrisation of the light
velocity proposed by Quan and Fry  is based on data from Austin and Ha-
likas . This parametrisation was modified to incorporate a correction for
pressure . During the data taking period, the temperature and salinity
were measured in situ at a depth of 2250 m. At an ambient temperature of
T = 13.2oC and salinity of S = 38.44 ?, the refractive index corresponding
to the phase velocity as a function of wavelength is expressed as:
np(λ,p) = 1.32292 + (1.32394 − 1.32292) ×
p − 200
240 − 200+
+1.1455 × 106
where λ is the wavelength (in units of nm) and p is the pressure (in units of
atm). Using Equation 1, the result of this parametrisation can be compared
to the measurements (see Figure 5).
Data 2010 - 2011 This paper
Data 2008 - 2010 This paper
Data 2000 Ref. 
Parametrisation of n
Fig. 5. Index of refraction corresponding to the group velocity of light as a function
of the wavelength. Also shown are results from measurements made in . The
grey band shows the systematic uncertainty. The two solid lines correspond to a
parametrisation of the index of refraction evaluated at a pressure of 200 atm (lower
line) and 240 atm (upper line) (see text).
From the known variations of temperature, salinity and pressure, the refractive
index for a particular wavelength and at a given depth can be determined with
an accuracy of better than 4×10−5. The parametrisation is in good agreement
with the measurements.
As mentioned in Section 1, the PMTs are unable to distinguish the wavelength
of the incoming photons, so the effect of this chromatic dependence can only
be taken into account on average. The spread of the arrival time residuals with
respect to the expected arrival time of a 460 nm photon have been computed
by means of a standalone Monte Carlo simulation using the phase velocity
for the emission angle and the group velocity (as given by the Equations 3
and 1) for the arrival time. This simulation indicates that the spread of the
time residual is 0.6 ns at 10 m, 1.6 ns at 40 m, 2.7 ns at 100 m and 3.6 ns at
200 m. The time uncertainty introduced by this spread is unavoidable and is
taken into account in the ANTARES official simulation program [14,15]. Even
though the exact influence of the medium depends on the particular Cherenkov
photon (wavelength, distance to the hit PMT) and therefore requires a full
simulation, a rough estimate of the average effect can be obtained assuming
that a majority of hits are between 40 m and 100 m from the track, which gives
a value of ∼2 ns for the uncertainty introduced by the transmission of light in
Wavelength (nm)Refractive indexNumber of runs Time period
403 ± 10
469 ± 12
532 ± 1.4
387 ± 11
403 ± 10
449 ± 13
460 ± 15
489 ± 11
491 ± 11
532 ± 1.4
1.3916 ± 0.0007
1.3825 ± 0.0002
1.3702 ± 0.0007
1.3960 ± 0.0007
1.3930 ± 0.0007
1.3854 ± 0.0003
1.3817 ± 0.0003
1.3785 ± 0.0003
1.3794 ± 0.0006
1.3666 ± 0.0006
Summary of the refractive index results for the 2008 - 2011 data shown in Figure 5.
For the refractive index only the statistical uncertainties are shown. In addition,
there is a total systematic uncertainty of ± 0.004.
sea water, including chromatic dispersion. This value is to be compared with
∼1.3 ns coming from the PMTs transit time spread and to ∼1 ns from time
Using pulsed light sources with wavelengths between 385 nm and 532 nm the
group velocity of light in sea water at the ANTARES site has been measured
as a function of wavelength. The emission spectra determined in the labora-
tory for the different pulsed sources have been used as input to a Monte Carlo
simulation in order to correct for the effect of absorption on the corresponding
velocity measurement. Except for two sources these corrections are in general
small. Likewise, a Monte Carlo simulation has been used to evaluate the sys-
tematic uncertainties and to check, that the procedure to obtain the speed of
light is robust and unbiased. The results obtained for the dependence of the
group refractive index on wavelength are in agreement with the parametrisa-
tion as a function of salinity, pressure and temperature of sea water at the
The authors acknowledge the financial support of the funding agencies: Centre
National de la Recherche Scientifique (CNRS), Commissariat ´ a l’´ enegie atom-
ique et aux ´ energies alternatives (CEA), Agence National de la Recherche
(ANR), Commission Europ´ eenne (FEDER fund and Marie Curie Program),
R´ egion Alsace (contrat CPER), R´ egion Provence-Alpes-Cˆ ote d’Azur, D´ epar-
tement du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium
f¨ ur Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica
Nucleare (INFN), Italy; Stichting voor Fundamenteel Onderzoek der Materie
(FOM), Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO),
the Netherlands; Council of the President of the Russian Federation for young
scientists and leading scientific schools supporting grants and Rosatom, Rus-
sia; National Authority for Scientific Research (ANCS), Romania; Ministerio
de Ciencia e Innovaci´ on (MICINN), Prometeo of Generalitat Valenciana and
MultiDark, Spain. We also acknowledge the technical support of Ifremer, AIM
and Foselev Marine for the sea operation and the CC-IN2P3 for the computing
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