A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

No abstract

This Letter proposes a robust processing of phase dislocations to recover continuous phase maps. The approach is based on combined unwrapping and inpainting methods. Phase dislocations are determined using an estimator based on the second order phase gradient. The algorithm is validated using a realistic simulation of phase dislocations, and the phase restoration exhibits only weak errors. A comparison with other inpainting algorithms is also provided, demonstrating the suitability of the approach. The approach is applied to experimental data from off-axis digital holographic interferometry. The phase dislocation from phase data from a wake flow at Mach 0.73 are identified and processed. Excellent phase restoration can be appreciated.

This paper proposes quantitative phase imaging by using a high resolution holographic grating for generating a four-wave shearing interferogram. The high-resolution holographic grating is designed in a "kite" configuration so as to avoid parasitic mixing of diffraction orders. The selection of six diffraction orders in the Fourier spectrum of the interferogram allows reconstructing phase gradients along specific directions. The spectral analysis yields the useful parameters of the reconstruction process. The derivative axes are exactly determined whatever the experimental configurations of the holographic grating. The integration of the derivative yields the phase and the optical thickness. Demonstration of the proposed approach is carried out for the case of the analysis of the supersonic flow of a small vertical jet, 5.56mm in diameter. The experimental results compared with those obtained with digital holography exhibit a very good agreement.