White light Fourier spectrometer: Monte-Carlo noise analysis and test measurements

This work reports on investigation of the sensitivity of a Fourier-transform spectrometer to noise sources based on Monte-Carlo simulation of measurement of a single spectrum. Flexibility of this approach permits easily to imitate various noise contaminations of the interferograms and to obtain statistically reliable results for widely varying noise characteristics. More specifically, we evaluate the accuracy of restoration of a single absorption peak for the cases of an additive detection noise and the noise which adds a fluctuating component to the carrier frequency in the source and the measurement channel of the interferometer. Comparison of spectra of an etalon He-Ne source calculated from more than 200 measured interferograms with the true spectrum supports a hypothesis that the latter fluctuations have characteristics of a coloured noise. Taking into account that the signal-to-noise ratio in the Fourier spectroscopy is constantly increasing, we focus on limitations on the achievable accuracy of spectrum restoration that are set by thi~ type of noise which modifies the shape of the recorded interferograms. We present also results of the test measurements of the spectrum of a laser diode chosen as a test source using a three-channel Fourier spectroscopic system based on a white­ sourced Michelson interferometer realized with the Twyman-Green scheme. The obtained results exhibit that fluctuations in the current displacement of the movable mirror of the interferometer should remain below 20 urn to restore the absorption spectrum with acceptable accuracy, especially at higher frequency bandwidth of the fluctuations.