Characteristics of the internal structure of the laser supported detonation (LSD) waves, such as the electron density n(e) and the electron temperature T(e) profiles behind the shock wave were measured using a two-wavelength Mach-Zehnder interferometer along with emission spectroscopy. A TEA CO(2) laser with energy of 10 J/pulse produced explosive laser heating in atmospheric air. Results show that the peak values of ne and Te were, respectively, about 2 x 10(24) m(-3) and 30 000 K, during the LSD regime. The temporal variation of the laser absorption coefficient profile estimated from the measured properties reveals that the laser energy was absorbed perfectly in a thin layer behind the shock wave during the LSD regime, as predicted by Raizer's LSD model. However, the absorption layer was much thinner than a plasma layer, the situation of which was not considered in Raizer's model. The measured n(e) at the shock front was not zero while the LSD was supported, which implies that the precursor electrons exist ahead of the shock wave. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3574922]