## 3 Results and Discussion  
The experiment based on the setup shown in Figure 1 was carried out. The low passband filter has a 3-dB bandwidth of 150 MHz and the suppression ratio of 20 dB. As a main component in the LFM signal generator, the InP-based (Indium phosphorus) laser array was designed and then fabricated in Fraunhofer HHI (Berlin, Germany) with the chip size of \(4\times 6\) mm. Four DFB lasers combine within an array waveguide grating, where four pair of electrodes are orderly arranged on the vertical direction of  
Figure 2: (**a**) The two-tone unknown signal from the received antenna, (**b**) the frequency-to-time relationship of the linear frequency modulation (LFM) signal by the heterodyning of two lasers, (**c**) a pair of pulses for two-tone signal can be recorded at the output of the low passband filter, (**d**) the principle based on the frequency information mapping to the time information. the device. The fabrication as well as the package is described in detail in our reported reference [12] and does not repeatedly demonstrate our previous work in the FTM-based frequency measurement system. Here, it focuses on the FTM-based frequency measurement method for measuring single-tone signal and two-tone signal with a high resolution over a large bandwidth. In the experiment, the optical module was kept at 25 \({}^{\circ}\)C controlled by thermoelectric cooler. The bias currents of DFB1 and DFB2 were fixed at 68 and 30 mA, respectively. The direct current from the controller (ILX Lightwave LDC-3724C, California, CA, USA) and an electrical signal from the pulse function arbitrary generator (Agilent Technologies 81150A, Woburn, MA, USA) was used to drive the DFB1 to achieve the precise wavelength tuning with a period of 18 KHz and a peak-to-peak voltage of 4 V. An erbium-doped optical fiber amplifier (JDS Uniphase, Santa Rosa, CA, USA) was used to amplify the light wave with a tunable gain and a noise figure of 3.3 dB. Double amplified light waves with an output power of 6.2 dBm is heterodyne detection at a photodiode (HP 11982A, Santa Rosa, CA, USA) with a 3-dB bandwidth of 15 GHz and a photoelectric conversion efficiency of 300 V/W. Thus, a frequency scanning microwave signal was generated at the output of photodiode. In the frequency measurement experiment, we assume that a microwave signal from a vector network analyzer (R&S ZVA40) acting as an unknown signal is down-conversion with the generated frequency-scanning microwave signal at the mixer. The beat-note pulse was selected after a low passband filter and observed in the oscilloscope. For the LFM signal generation, an 18 KHz saw-tooth driving signal was added to the DFB1 to realize wavelength scanning and a fast frequency scanning microwave signal can be generated by heterodyning of two lasers as demonstrated in our reported reference [12]. The frequency scanning performance in one period is shown in Figure 3a. The period approached 55 \(\mu\)s and the frequency scanning range is from 3.5 to 12.5 GHz by calculating the real-time frequency distribution of the generated LFM signal at the output of photodiode using STFT. As shown in Figure 3a, a saw-tooth signal is modulated on one laser, but the generated triangular-shape LFM consists of positive chirp rate region and negative chirp rate region which results from the relaxation oscillation of the laser. It is reported that the chirp-rate of the LFM signal rather than the waveform of the driving signal limits the measurement error [11]. Figure 3: (**a**) Measured frequency scanning property of the heterodyning with a scanning range from about 3.5 to 12.5 GHz. (**b**) The relationship between the frequency of the unknown signal and the time difference. The down-conversion microwave signal between the input microwave signal \(f_{i}\) and the generated frequency scanning signal by heterodyning of two lasers with the laser array, which includes two optical pulses with different pulse widths, was recorded by the oscilloscope.