  In this paper, we describe an experiment performed at the Laboratoire de
Physique des Lasers and dedicated to an optical measurement of the Boltzmann
constant. With the proposed innovative technique, determining comes down to an
ordinary frequency measurement. The method consists in measuring as accurately
as possible the Doppler absorption profile of a rovibrational line of ammonia
in thermal equilibrium. This profile is related to the Maxwell-Boltzmann
molecular velocity distribution along the laser beam. A fit of the absorption
line shape leads to a determination of the Doppler width proportional to
sqrt(kT) and thus to a determination of the Boltzmann constant. The laser
source is an ultra-stable CO2 laser with a wavelength . The absorption cell is
placed in a thermostat keeping the temperature at 273.15 K within 1.4 mK. We
were able to measure with a relative uncertainty as small as 3.8x10-5, which
represents an improvement of an order of magnitude for an integration time
comparable to our previous measurement published in 2007 [1]
