Integrable solution for light shaping based on a Fourier-pair mapping

Abstract In far-field light shaping, one of the design methods is based on a one-to-one map between irradiance source and target. However, an integrability issue may occur in this kind algorithms, either ray mapping method for designing freeform surface or those geometric-optics-based achieving required output phase. We introduce another mapping-type algorithm to tackle problem, which instead establishing both target space domain, assumed electric fields Fourier pair domain spatial-frequency domain. By solving from pair, gradient phase achieved, that equivalent obtained function. Moreover, existence characterization guarantees so smooth can be directly integrated. Based phase, then designed light-shaping task. Numerical examples are demonstrated comparison approaches with different assumptions.