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A novel approach to implementing instantaneous frequency measurement (IFM) based on an amplified fiber-optic recirculating delay loop and a broadband incoherent light source (ILS) is proposed, analyzed, and experimentally demonstrated. Since the semiconductor optical amplifier-based fiber-optic delay loop has an infinite impulse response that varies from a large positive value to negative infinity on a log scale, a unique relationship between the output power, and the frequency of the input continuous-wave (CW) microwave signal is established. Meanwhile, it is experimentally shown that the use of the ILS can greatly improve the stability of the proposed IFM system. When the input power of CW microwave signal is within the range of -7 dBm to -16 dBm, the measured errors remain within ±400 KHz over a frequency range of 6.94-6.958 GHz. The measurement error, the complexity and cost of the proposed IFM system can be considerably reduced by only using one ILS, one modulator, and one photodetector. Since the proposed IFM system has a capability of optical integration, it is theoretically estimated that the measurement range can be extended to 20 GHz with a measurement resolution of 1.36 dB/GHz.