Direct estimation of the standard error in phase-resolved luminescence measurements. Application to an oxygen measuring system

Abstract

Phase-resolved luminescence measurements provide accurate estimations under low illumination conditions and/or low signal-to-noise ratio. However, the accuracy of these measurements is limited by noise. In this article we propose a procedure, based on spectral analysis of noise, for the statistical characterization of the noise affecting the luminescent signal and the determination of the standard errors affecting the modulation-factor and the phase-shift estimates. This way, in addition to the phase-resolved luminescence measurements, we provide information about the uncertainty of these measurements. The standard errors are directly estimated from the recorded signal and the procedure only requires a FFT computation, which makes it fast and easy to be implemented. The proposed method was successfully applied to an oxygen measuring system based on phase-resolved luminescence. At each single measurement, it provides, in addition to the oxygen partial pressure, the corresponding standard error. Experiments show that the standard errors estimated from FFT using one signal are coherent with the standard deviations and the root mean square errors observed from a collection of measurements.