Petal-like Bessel beam based high-resolution optical ranging for hypersonic turbulence

For in-flight hypersonic vehicles, intense friction with the air and high-temperature ionization effects generate plasma sheath turbulence (PST) around the target, significantly impeding electromagnetic wave transmission and presenting challenges for target detection. Conventional time-domain ranging methods, such as the time-of-flight and pulse-based methods, exhibit limitations in PST. A spatial-domain ranging method is developed utilizing the unique propagation characteristics of petal-like Bessel beams. These beams, generated through the coherent superposition of vortex phases, exhibit high stability under PST conditions. By leveraging the relationship between the rotation angle of the petal-like Bessel beam and the propagation distance, high-precision ranging is achieved. Additionally, an angle recognition neural network (ARNN) is introduced to improve accuracy in turbulent environments, overcoming the limitations of traditional correlation intensity methods. The ARNN demonstrates high prediction accuracy and strong generalization capabilities. Our method achieves over 90% accuracy with a resolution of 1 mm across various plasma turbulence conditions characterized by refractive index fluctuation variance 〈Δ<i>n</i>²〉 and different distance resolutions. These findings indicate a viable approach for target detection in complex media such as PST.