Harmonic Angular Mapping Method for Binary Microlensing Grid Search

Searching for binary-lens microlensing solutions is computationally demanding because of the complex parameter space and the large number of trial models required. We present an algorithm that accelerates binary-lens grid searches by expanding the angular dependence of precomputed magnification maps in Fourier modes. By contracting the observation-dependent weighted sums in Fourier space, the $χ^2$ values for all trial source-trajectory angles can be evaluated efficiently using inverse fast Fourier transforms (FFTs), avoiding repeated calculations over individual observations. We tested the method on 200 Roman-like synthetic binary-lens events. For 166 events (83%), the recovered fits agreed with Levenberg--Marquardt fits initialized at the injected parameters to within $|Δχ^2|\leq1$. The FFT map scan required an average of 5.05~min per event. For the same discrete search volume, the Fourier angular evaluation was estimated to be approximately 900 times faster than conventional magnification-map sampling. These results demonstrate that the method can efficiently identify useful initial conditions for binary-lens light-curve modeling.