## 3 Results and Discussion
The fluctuation of operating temperature would result in the wavelength change of the laser array and then the frequency of beat-note signals subsequently changing after the heterodyning detection of two lasers. Besides, the overheated laser chip is vulnerable to burn out in the case of nonuse of the thermal control. As we all know, the wavelength of laser varies with the temperature approximately 0.2 nm/\({}^{\circ}\)C and then the thermal control accuracy reaches to \(4\times 10^{-5}\)\({}^{\circ}\)C/MHz. When the home-made temperature control circuit is about \(10^{-4}\)\({}^{\circ}\)C in our laboratory, the wavelength stability is theoretically 2.5 MHz. Figure 5: Frequency measurement results for single-frequency microwave signal at 4, 6, 8, 10, and 12 GHz. (**a**–**e**) Measured waveform on the oscilloscope. (**f**–**j**) Corresponding instantaneous frequency and time relationship using STFT. Figure 6: Frequency measurement results (**a**) and errors (**b**) for different frequency microwave signals. Multifrequency measurement based on the proposed microwave frequency measurement system was also verified. Two-tone signal at 5 and 5.3 GHz from two signal generators are combined using an electrical power combiner and then injected into the electrical mixer. The pulses from the output of the low passband filter are shown in Figure 7a and its real-time frequency distribution is calculated using STFT as the result shown in Figure 7b. The frequencies of unknown signals were mapped using the FTM relationship with the time differences \(\approx\)\(\Delta T_{1}\) and \(\Delta T_{2}\). The frequency measurement accuracy for multiple frequencies based on the proposed frequency measurement system was also demonstrated. The fixed frequency was set as 5 GHz and the other frequency was changed from 5.1 to 5.3 GHz with a frequency step of 0.05 GHz, where the measured results are shown in Figure 8a-e. The time differences with different frequency spaces are calculated in Figure 8f-j after the STFT. From the results in Figure 8f-j, we can know that the frequencies of two-tone cannot be clearly distinguished when the frequency space less than 100 MHz. From Figure 7b, we can find that two peaks are close to each other and the 3-dB bandwidth of the recorded two-tone signal is approximately double the 3-dB bandwidth of the single-frequency signal. As the frequency space increases, the measured microwave signal is obviously separated into two lines. Hence, the resolution of the proposed frequency measurement system for two-tone microwave signal is about 150 MHz. The measurement accuracy for two-tone is determined by the bandwidth of the electrical filter as well as the chirp-rate of the generated frequency-scanning microwave signal [11]. A higher chirp-rate by increasing the microwave frequency bandwidth can lead into a lower measurement error. Besides, a narrower electrical filter, which is 150 MHz in our experiment, can be expected to improve the measurement accuracy. Figure 7: Measured result for two-tone microwave signal at 5 and 5.3 GHz. (**a**) Measured waveform for two-tone signal in the oscilloscope. (**b**) Corresponding instantaneous frequency and the time relationship.