Analyzing laser-plasma interferograms with a Continuous Wavelet Transform Ridge Extraction technique: the method

Laser-plasma interferograms are currently analyzed by extracting the phase-shift map with FFT techniques (K.A.Nugent, Applied Optics {\bf 18}, 3101 (1985)). This methodology works well when interferograms are only marginally affected by noise and reduction of fringe visibility, but it can fail in producing accurate phase-shifts maps when dealing with low-quality images. In this paper we will present a novel procedure for the phase-shift map computation which makes an extensive use of the Ridge Extraction in the Continuous Wavelet Transform (CWT) framework. The CWT tool is {\it flexible} because of the wide adaptability of the analyzing basis and it can be very {\it accurate} because of the intrinsic noise reduction in the Ridge Extraction. A comparative analysis of the accuracy performances of the new tool and the FFT-based one shows that the CWT-based tool phase maps are considerably less noisy and it can better resolve local inhomogeneties.