<p>This paper presents the application of various artificial fractal-like background patterns and a digital image correlation algorithm, to enhance the accuracy of image displacement measurement within background-oriented schlieren technology. A novel method for generating new fractal-like patterns is proposed, allowing for the combination of different pattern strengths. A more robust image displacement estimation algorithm that considers the self-affine property inherent in fractal patterns is introduced. Various synthetic flow tests, as well as real supersonic flow and combustion tests, were conducted to demonstrate the advantages of the estimation algorithm and to gain a comprehensive understanding of the applicability of different fractal-like backgrounds.</p> Graphical abstract <p></p>