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The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the short-exposure optical transfer function.

We describe an adaptive optics (AO) system for correcting the aero-optical aberration of the supersonic mixing layer and test its performance with numerical simulations. The AO system is based on the measurement of distributed Strehl ratios and the stochastic parallel gradient descent (SPGD) algorithm. The aero-optical aberration is computed by the direct numerical simulation of a two-dimensional supersonic mixing layer. When the SPGD algorithm is applied directly, the AO cannot give effective corrections. This paper suggests two strategies to improve the performance of the SPGD algorithm for use in aero-optics. The first one is using an iteration process keeping finite memory, and the second is based on the frozen hypothesis. With these modifications, the performance of AO is improved and the aero-optical aberration can be corrected to some noticeable extent. The possibility of experimental implementation is also discussed.

The nano-particle-based planar laser scattering (NPLS) technique is used to measure the density distribution in the supersonic mixing layer of the convective Mach number 0.12, and the optical path difference (OPL), which is quite crucial for the study of aero-optics, is obtained by post processing. Based on the high spatiotemporal resolutions of the NPLS, the structure of the OPL is analysed using wavelet methods. The coherent structures of the OPL are extracted using three methods, including the methods of thresholding the coefficients of the orthogonal wavelet transform and the wavelet packet transform, and preserving a number of wavelet packet coefficients with the largest amplitudes determined by the entropy dimension. Their performances are compared, and the method using the wavelet packet is the best. Based on the viewpoint of multifractals, we study the OPL by the wavelet transform maxima method (WTMM), and the result indicates that its scaling behaviour is evident.