The tilt of the aero-optical aberration caused by the supersonic turbulent boundary layer is obtained by analyzing the center wandering of the far-field optical pattern, and its characteristics are examined from the viewpoint of statistics. When the diameter of the beam propagating through the flow is small compared with the boundary layer thickness, the probability density function (PDF) of the tilt coefficient is centered and can be approximated with a Gaussian distribution. For a larger beam diameter, the PDF of the tilt in the spanwise direction can still be regarded as centered and Gaussian, but the tilt in the streamwise direction clearly deviates from a Gaussian distribution. The correlation of the tilts in the two directions is investigated by computing the correlation coefficient, and the results indicate that the correlation is negative and strong for a small beam diameter and becomes positive and weak for a large beam diameter. These characteristics are explained by the hairpin vortex structures in the boundary layer, which prevail and meander for a very long distance streamwise.
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