Optical constraints on rotating logarithmic- and exponential-entropy wormholes from strong-field lensing

The longstanding issue of whether horizonless compact objects can mimic black holes at horizon scales is addressed, a problem that persists because the shadow diameter alone is degenerate across a wide class of geometries. For slowly rotating traversable wormholes, we precisely formulate the optical appearance as a set of observables derived from equatorial null geodesics, yielding necessary and sufficient conditions for a multi-parameter fingerprint. Using a new lapse function that interpolates between exponential and rational redshift profiles, we obtain the photon-sphere condition, the strong-deflection lensing coefficients, and the Lyapunov exponent in closed form. The equations yield two families of wormhole solutions dependent on logarithmic and exponential entropy parameters. We compare the resulting quantum-modified spacetimes with Kerr and four regular black holes. The shadow diameter is shown to be tunable to within $5\mathrm{\%}$ to $11\mathrm{\%}$ of Kerr for all models considered, so that $\mathrm{\mid }{R}_{\mathrm{s}\mathrm{h}}^{\mathrm{W}\mathrm{H}}\mathrm{/}{R}_{\mathrm{s}\mathrm{h}}^{\mathrm{K}\mathrm{e}\mathrm{r}\mathrm{r}}-1\mathrm{\mid }\lesssim 0.11$ and the shadow alone cannot separate the models. The degeneracy is lifted when the rotational asymmetry, lensing coefficients, Lyapunov exponent, and orbital frequency are combined: for the $5$-component fingerprint $\mathbf{F}=(\text{Arot},\text{abar},\text{bbar},\text{Lya},\text{Oph})$, the fractional deviation ${\mathrm{\Delta }}_i=(F_i^{\mathrm{W}\mathrm{H}}-F_i^{\mathrm{K}\mathrm{e}\mathrm{r}\mathrm{r}})\mathrm{/}{F}_i^{\mathrm{K}\mathrm{e}\mathrm{r}\mathrm{r}}$ satisfies $\mathrm{\mid }{\mathrm{\Delta }}_i\mathrm{\mid }\gtrsim 0.05$ for every component, with the largest departures in the second lensing coefficient and the Lyapunov exponent. The combined discrimination signal reaches a signal-to-noise ratio of about $3.8$ to $3.9$ against Kerr and about $3.7$ against the Kazakov–Solodukhin benchmark, which is sufficient to break the shadow-diameter degeneracy at the $10\mathrm{\%}$ measurement level.