Estimation of lightning channel-base current from far electromagnetic field in the case of inclined channel

•Expressions to estimate the current peak from the far-field peak considering channel tilt are derived.•Expressions to reconstruct the entire current waveform from the field waveform are derived.•The expressions are derived for three most widely used engineering return-stroke models.•This is the first attempt to solve the inverse problem (infer sources from fields) for inclined channels.