Light deflection and gravitational lensing effects in acoustic black-bounce spacetime

In the present work, we analyze the gravitational deflection for a light beam in the weak and strong field regimes for the gravitational analog geometry of an acoustic black hole and acoustic black bounce. Motivationally, the first spacetime arises as an exact solution of the field equations for gravitational black holes in Einstein-scalar-Gauss-Bonnet theory [P. Ca\~nate, J. Sultana, and D. Kazanas, Classical Quantum Gravity 38, 125002 (2021)]. In contrast, the second model arises from the combination of phantom scalar field and nonlinear electrodynamics in general relativity [P. Ca\~nate, [Phys. Rev. D 106, 024031 (2022)]. We construct analytical expressions for the angular deflection of light in both limits and, from them, analyze the construction of the observables, which allow us to relate theoretical models to observational data. We compare these observables and show how much they differ from those obtained in the Schwarzschild solution.