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Strong lensing of {gravitational-wave signals} can produce three types ofimages, denoted as Type-I, Type-II and Type-III, corresponding to the minima,saddle and maxima of the lensing potential of the lensed images. Type-IIimages, in particular, receive a non-trivial phase shift of $\pi/2$. This phaseshift can introduce additional distortions in the strains produced by theType-II image of the binary black hole signals depending on the morphology ofthe signals, e.g., when they have contributions from higher harmonics,precession, eccentricity, etc. {The probability of observing Type-II images isnearly the same as that of strong lensing itself, and thus these signals arelikely to be observed in the near future.} In this work, we investigate thepotential applicability of these distortions in helping identify Type-IIsignals from a single detection and the systematic biases that could arise inthe inference of parameters if they are recovered with gravitational-wavetemplates that do not take the distortion into account. We show that thelensing distortions will allow us to confidently identify the Type-II imagesfor highly inclined binaries: at network signal-to-noise ratio (SNR)$\rho=20(50)$, individual Type-II images should be identifiable with ln Bayesfactor $\ln \mathcal{B} > 2$ for inclinations $ \iota > 5 \pi/12 (\pi/3) $.Furthermore, based on the trends we observe in these results, we predict that,at high SNRs ($\gtrsim 100$), individual Type-II images would be identifiableeven when the inclination angle is much lower ($\sim \pi/6$). We then show thatneglecting physical effects arising from these identifiable Type-II images cansignificantly bias the estimates of source parameters. Thus, in the future,using templates that take into account the lensing deformation would benecessary to extract source parameters from Type-II lensed signals.

Detection and parameter estimation challenges of Type-II lensed binary black hole signals