Algorithm for supersonic gas jet density profile retrieval from interferometric measurement

A novel algorithm developed for supersonic gas jet profile retrieval from interferometric measurement is presented. The algorithm uses the Fourier transform method for the phase map restoration and method based on radial profile approximation by a set of hyper-Gaussian functions and their forward Abel transform for 3D gas density profile restoration. The numerical algorithm of the 3D gas density profile restoration based on expansion of the density radial distribution by a basis of hyper-Gaussian functions is compared with algorithms of the inverse Abel transform. Examining accuracy of the algorithms shows that the developed approach is more stable than the inverse Abel transform, and, in the case of axisymmetric objects like supersonic gas jets, it provides higher accuracy. The developed technique was applied for studying the density profile of the pulsed nitrogen supersonic jet produced using a de’Laval nozzle with an exit diameter of 1.5 mm. It is shown that the radial density distributions at distances of 10–700 μm behind the nozzle exit have a hyper-Gaussian-like form with sharp boundaries and a jet top of ∼0.8  mm length, where gas density is about 5.5·1018  cm−3 and varies by no more than 10%.