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A modified power spectrum of biological tissues involving upper length-scale and bottom length-scale was introduced. In addition, the analytical expression of Hermite–Gaussian rectangular vortex beam with the parameter () in free space was derived. By this modified power spectrum, we established the normalized probability model of orbital angular momentum (OAM) states for Hermite–Gaussian rectangular vortex beams propagation in biological tissues. The results revealed that Hermite–Gaussian rectangular vortex beam exhibits a better anti-interference performance than Laguerre–Gaussian beam under the same conditions. The Hermite–Gaussian rectangular vortex beam propagates through a biological tissue with large bottom length-scale, small upper length-scale, small characteristic length of heterogeneity, low the fractal dimensions, and weak fluctuation strength, which produces a large normalized probability of signal OAM states. These results are fundamental to improving light propagation in tissue and provide a quantitative guidance for medical imaging and diagnosis.

Influence of structural length-scale sensitivities on Hermite–Gaussian rectangular vortex beam propagation in biological tissues