1504 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 17, NO. 7, JULY 2005 Criterion for Subpulse-Length Resolution and Minimum Frequency Shift in Distributed Brillouin Sensors Fabien Ravet, Student Member, IEEE, Xiaoyi Bao, Senior Member, IEEE, Qinrong Yu, and Liang Chen, Member, IEEE Abstract—We introduce a Rayleigh equivalent criterion to mea- sure stressed section shorter than the spatial resolution of a dis- tributed Brillouin sensor. Under this criterion for the worst-case of any given sensing length, the minimum resolvable strain length is 1/2 of the pulse length with Brillouin frequency uncertainty of 5% or with 2% frequency uncertainty. This is smaller than the pulse length. Index Terms—Distributed Brillouin sensor, measurement accu- racy, spatial resolution. I. INTRODUCTION D ISTRIBUTED Brillouin scattering-based sensors have proven to be powerful candidates to measure temperature and strain profiles [1], [2] in structural health monitoring, for instance, fire detection, aerospace, and other applications where degradation must be identified and localized. Temperature and strain are derived from the analysis of the Brillouin loss (or gain) by peak detection, known as the Brillouin frequency , which has a linear relationship to temperature and strain. Pulsewidth determines minimum length the measuring system is able to resolve, the so-called spatial resolution . To bring Brillouin sensors to the field, we must handle particu- larly multipeak distributions. In theory, it would be possible to reduce the size of the pulse in order to resolve smaller defects. Unfortunately, this approach induces low signal-to-noise ratio and higher cost for the sensor system. We propose to use broad pulse ( 10 ns) and develop the signal-processing scheme to deal with multipeak distributions caused by the use of pulses broader than stressed regions. In this letter, we discuss the impact of stress sections shorter than spatial resolution on measurement error and unwanted peak discrimination. The innovative aspect of our approach lies in the establishment of a minimum resolvable frequency shift defini- tion based on a Rayleigh equivalent criterion (REC) for Bril- louin loss profiles, which allows unambiguous peak identifica- tion. Errors associated with the use of the REC are eventually discussed. Our REC is complementary to Horigushi’s relation [3], where the smallest detectable frequency shift applies to one Manuscript received November 30, 2004; revised April 2, 2005. This work was supported by Intelligent Sensing for Innovative Structures (ISIS) Canada, and by Natural Science and Engineering Research Council of Canada. The authors are with the Fiber Optic Group, Department of Physics, Univer- sity of Ottawa, Ottawa, ON K1N6N5, Canada (e-mail: fabien.ravet@ieee.org). Digital Object Identifier 10.1109/LPT.2005.849246 peak, and the only noise source is the laser frequency fluctua- tion over time, while our criterion deals with two peaks condi- tion and allows the searching for the minimum detectable strain section. II. MODEL AND PARAMETERS OF THE ANALYSIS The model we use is based on the steady state coupled in- tensity equations [4] to describe interaction between two coun- terpropagating laser beams, being a pulse, and being a continuous-wave (CW) signal. The steady state approximation applies to pulses larger than the phonon lifetime ( 10 ns). It is equivalent to a spatial resolution . We consider a uniform strain profile over the whole fiber length except on a short section at distance and whose extension is smaller than spatial resolution . Within the pulse length at around the stress point, the Brillouin frequency shift is constant over , while the rest of the pulse covers a section of that has a Brillouin frequency shift of . We solved the coupled intensity equations following a perturbation approach initially used in [2]. The difference lies in the construction of the integration interval. At position , the pulse interacts with the CW signal over the distance . We complete the integration by subdividing this interval into with a gain coeffi- cient spectrum characterized by a Brillouin frequency shift , and with a gain coefficient character- ized by a Brillouin frequency shift . We assume that the two Brillouin coefficients have the same full-width at half-maximum (FWHM) . The variation of intensity of the CW signal due to the interaction with the pulse at position is then given by the Brillouin loss spectrum whose mathematical expres- sion is (1) where is the exponential integral, , , , and , , 1041-1135/$20.00 © 2005 IEEE