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Using magnetic field data from under aerial power transmission lines, tomographic reconstruction techniques have been applied to determine the magnitudes and phases of currents in each power conductor. Phasor current values at fundamental (60 Hz) and harmonic frequencies are produced. This measurement technique requires no physical contact with power lines (even by clamp-around transformers) and hence should be convenient for monitoring and trouble-shooting cases of excessive harmonic currents on transmission and distribution facilities. The method has been implemented experimentally, and laboratory and initial field tests have demonstrated its basic validity.