Emission noise spectra from premixed sheathed C 2H 2-air flames and the detection limit

Abstract

Noise spectra in the frequency range 0.02 Hz < f < 20 kHz are reported for the thermal emission of the Na- D doublet and the background from premixed, sheathed, quasi-laminar C 2H 2-air flames at 1 atm under various experimental conditions. Below 1.5 Hz noise spectra were obtained by numerical Fourier transformation of a digitized noise signal; above 1.5 Hz a frequency-analyzer and a lock-in analyzer were used. The measuring procedure is theoretically explained and its experimental testing is described. The role of statistical cross-correlation is emphasized. The flame-emission noise proper was obtained by subtracting the shot-noise power, measured with the aid of an incandescent lamp, from the total noise power. The shot noise level exceeded the theoretical value as a consequence of the reduction in the number of amplifying stages of the photomultiplier used. Below 1 Hz the noise spectra showed roughly a 1/ f γ-dependence with γ values above and below unity for the Na emission and the background, respectively. Between 5 and 50 Hz pronounced peaked structures were observed for both emissions. At higher frequencies a steep roll-off with γ > 2 was seen. A dip in the noise spectrum was not found; but the flame-emission noise was already drowned in the shot noise above 500 Hz as a result of the low photocathode currents used. Some tentative explanations of the noise observations are given. A standardized figure-of-merit for the effect of flame-emission noise in FES, FAAS and FAFS is introduced and conclusions are drawn for the optimum choice of modulation frequency. The general theory of the analytical detection limit for paired readings, given in a previous paper, is worked out for the present case. Allowance is made for the presence of a high-pass filter (blocking any drifting d.c. component) and for the deviation of the background noise spectrum from a strict 1/ f-dependence. The application of the theory is illustrated by calculating the optimized detection limit for Na in FES with the simple flame equipment described in this paper.