Zhe Lv, Xiaojian Hao
The cat-eye effect provides strong retro-reflected echoes that are widely exploited for laser active detection, yet in long-range scenarios, the echo-field morphology can be jointly distorted by atmospheric turbulence and oblique incidence. In the present work, the experimental validation is carried out within a moderate off-axis range that is directly supported by the measurement system. Here, we develop an analytical-numerical unified framework to predict the three-dimensional (3D) echo field of a cat-eye target illuminated by a multiband Gaussian probe under turbulent propagation and oblique incidence. The analytical model combines a four-interval matrix-optics formulation with the Collins diffraction integral, incorporates turbulence statistics via the Rytov approximation, and maps oblique incidence to an equivalent transverse shift using a rotated coordinate system; hard-edge apertures are further treated by a complex-Gaussian expansion for efficient evaluation. In parallel, round-trip propagation is simulated using split-step Fourier propagation of the parabolic wave equation with a multi-phase-screen method, where phase screens are synthesized by FFT-based spectral inversion with subharmonic compensation. Angle-scan experiments in free space show consistent trends among measurements, analytical predictions, and numerical simulations in terms of echo-spot morphology, peak decay, and centroid drift. By varying the refractive-index structure constant Cn2, we further observe turbulence-induced speckle formation, spot broadening, and beam wander, and the analytical and numerical models agree in their overall trends. This framework enables echo-field prediction and supports pointing assessment and tracking of cat-eye targets in complex atmospheric environments.