Precise signal amplitude retrieval for a non-homogeneous diagnostic beam using complex interferometry approach

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Classical interferometry became widely used method of active optical diagnostics. Its more advanced version, allowing reconstruction of three sets of data from just one especially designed interferogram (so called complex interferogram) was developed in the past and became known as complex interferometry. Along with the phase shift, which can be also retrieved using classical interferometry, the amplitude modifications of the probing part of the diagnostic beam caused by the object under study (to be called the signal amplitude) as well as the contrast of the interference fringes can be retrieved using the complex interferometry approach. In order to partially compensate for errors in the reconstruction due to imperfections in the diagnostic beam intensity structure as well as for errors caused by a non-ideal optical setup of the interferometer itself (including the quality of its optical components), a reference interferogram can be put to a good use. This method of interferogram analysis of experimental data has been successfully implemented in practice. However, in majority of interferometer setups (especially in the case of the ones employing the wavefront division) the probe and the reference part of the diagnostic beam would feature different intensity distributions over their respective cross sections. This introduces additional error into the reconstruction of the signal amplitude and the fringe contrast, which cannot be resolved using the reference interferogram only. In order to deal with this error it was found that additional separately recorded images of the intensity distribution of the probe and the reference part of the diagnostic beam (with no signal present) are needed. For the best results a sufficient shot-to-shot stability of the whole diagnostic system is required. In this paper, efficiency of the complex interferometry approach for obtaining the highest possible accuracy of the signal amplitude reconstruction is verified using the computer generated complex and reference interferograms containing artificially introduced intensity variations in the probe and the reference part of the diagnostic beam. These sets of data are subsequently analyzed and the errors of the signal amplitude reconstruction are evaluated.