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A novel photonic instantaneous microwave frequency measurement system based on signal remodulation is proposed and experimentally demonstrated. Modulation and remodulation are achieved using a single electroabsorption modulator operating bidirectionally. The RF power and frequency are derived from the RF tone powers of the modulated and remodulated signals, respectively. The incoherent operation principle of the proposed system enables a high resolution measurement with reduced ambiguity over a large frequency range.