DOI: 10.1007/s00340-007-2759-7 Appl. Phys. B 89, 417–427 (2007) Lasers and Optics Applied Physics B e. therssen 1, ✉ y. bouvier 1 c. schoemaecker-moreau 1 x. mercier 1 p. desgroux 1 m. ziskind 2 c. focsa 2 Determination of the ratio of soot refractive index function E(m) at the two wavelengths 532 and 1064 nm by laser induced incandescence 1 UMR CNRS 8522/PC2A “Physico-Chimie des Processus de Combustion et de l’Atmosphère”, FR CERLA CNRS 2416 – Universit´ e des Sciences et Technologies de Lille, Bât C11, 59655 Villeneuve d’Ascq Cedex, France 2 UMR CNRS 8523/PhLAM “Physique des Lasers, Atomes et Mol´ ecules”, FR CERLA CNRS 2416 – Universit´ e des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France Received: 1 February 2007/Revised version: 3 July 2007 Published online: 19 September 2007 • © Springer-Verlag 2007 ABSTRACT A new method is proposed to measure the ratio of the refractive index function of soot particles E(m) at the two fixed wavelengths: 532 and 1064 nm. Using a non-intrusive, in-situ laser based technique, the ratio E(m, 1064 nm)/ E(m, 532 nm) can be determined by comparing laser induced incandescence (LII) intensities at 532 and 1064 nm excitation wavelengths. The method consists of selecting laser energies that insure the equality of the LII signals in the low fluence regime under given conditions. Such equality is consistent with the fact that the soot particle will have reached the same tem- perature independently of the laser wavelength, i.e. the soot particle has absorbed the same energy. As the absorbed energy is proportional to the laser irradiance times E(m), the measure- ment of the laser energies required to insure perfect concordance of the LII intensities (spatially and temporally) serves to deduce the ratio E(m, 1064 nm)/ E(m, 532 nm). The method is demon- strated in an acetylene/air flame, validated against extinction measurements performed by cavity ring-down spectroscopy (CRDS) by using laser radiations at 532 nm and 1064 nm and finally applied to different flame conditions. PACS 78.20.Ci; 78.90.+t; 81.05.Uw; 42.62.-b 1 Introduction The laser induced incandescence (LII) allows the measurement of soot volume fraction in flames or exhaust gases with high accuracy and sensitivity. The LII is based on fast heating of particles by a short laser pulse and on the observation of the subsequent thermal radiation whilst the particle cools in a constant pressure and temperature gaseous medium. The laser absorption, thermal conduction, radiative transfer, sublimation, photodesorption, oxidation and anneal- ing, which act competitively during this process, lead to the temporal evolution of the temperature T(t) and the diameter d p (t) of the primary soot particle [1–4]. The radiation emitted by one particle follows the Planck law and the LII signal can be expressed as follows at any time ✉ Fax: +33-320-436977, E-mail: eric.therssen@univ-lille1.fr during the laser pulse and during the cooling process: LII(t,λ i ) = C 8πc 2 h λ 5 i  exp  hc λ i k B T(t)  − 1  −1 × π 2 d p (t) 3 E(m,λ i ) λ i , (1) where λ i is the emission wavelength and E(m,λ i ) is the di- mensionless refractive index function (where m is the com- plex refractive index of soot considered at λ i [5]). The sym- bols h , c, k B are respectively the Planck constant, the speed of the light and the Boltzmann constant. C is a constant fac- tor related to the optical arrangement and to the gain of the detector. Experimentally and theoretically, the prompt LII signal has been shown to be proportional to the soot volume frac- tion [6, 7]. It also depends on the temperature reached by the particle during the laser process. The laser fluence, its temporal and spatial distribution, and the soot refractive in- dex function E(m) are sensitive parameters influencing the energy absorbed and then the temperature reached by the particle. The absolute soot volume fraction can be obtained through an “auto-compensating” procedure based on the determin- ation of each parameter of (1) [8] or using independent calibration based on gravimetric or light extinction tech- niques [9]. With optical methods, the knowledge of the refrac- tive index function E(m) or of the dimensionless absorption constant K e is necessary. K e is usually calculated using the Rayleigh-limit approximation with the complex refractive in- dex well documented in the literature [5]. A recent review paper [10] points out that references commonly used to deter- mine E(m) could be questionable. A particularly accurate knowledge of E(m) at 1064 nm is lacking although this wavelength is the most recommended to prevent any background fluorescence from being collected with the LII signal. Recently, by combining optical pyrom- etry and thermophoretic sampling/transmission electron mi- croscopy analysis, the E(m) at 1064 nm has been determined by using numerical calculations based on an improved LII model in the case of low laser fluences [11]. Assuming a con- stant value of E(m) versus wavelength, this work leads to