Detectability of strongly lensed gravitational waves using model-independent image parameters

Strong gravitational lensing of waves (GWs) occurs when the GWs from a compact binary system travel near massive object. The lensed waveform is given by product amplification factor $F$ and unlensed waveform. For many axisymmetric lens models such as point mass singular isothermal sphere that we consider, can be calculated in terms two parameters, ${M}_{L}$ source position $y$. In geometrical-optics approximation, these produces at most discrete images which parametrized image flux ratio $I$ time delay $\mathrm{\ensuremath{\Delta}}{t}_{d}$ between images. macrolensing regime for large compared to $T$ they spend within sensitivity band GW detectors, it natural parametrize searches parameters. functional dependence signal on parameters far simpler, facilitating data analysis events with modest signal-to-noise ratios, constraints inverted constrain $y$ any model. We propose this use extended microlensing ($\mathrm{\ensuremath{\Delta}}{t}_{d}<T$) interfering are observed single event. determine detectability find ratios $\ensuremath{\rho}$ total $M$, should principle identifiable $I\ensuremath{\gtrsim}2{\ensuremath{\rho}}^{\ensuremath{-}2}$ delays $\mathrm{\ensuremath{\Delta}}{t}_{d}\ensuremath{\gtrsim}{M}^{\ensuremath{-}1}$.