# Measurement of Ultra-High Speed by Optical Multistage Cascade Frequency Reduction Technology
## 3 Discussion and Results
### Impact Loading Experiment of Three-Stage Light Gas Gun  
In order to further verify the dynamic test performance of multi-cascade superheterodyne laser interferometry, the impact loading experiment of a three-stage light gas gun was carried out. The principle, device, and experimental site of the three-stage light gas gun are shown in Figure 9. The flyer is composite gradient materials and the target sample is steel. Both of them are 1 mm thick, and the distance between them is 10 mm. The launching technology of the three-stage light gas gun is a high-speed launching technology based on the launching technology of a two-stage light gas gun [17; 18], which forms \"multi-stage pressurization\" by multiple reflections of shock waves between different materials in projectile and pushes the speed of target materials to more than 10 km/s. At the back end of the target material, an optical fiber velocimeter probe is installed to transmit and receive optical signals emitted by the velocimeter and reflected by the target material. The DPS probe is a probe with a return loss of 17 dB and is used for zero-differential velocimetry (DPS). The two-stage probe is a probe with a return loss of 60 dB, which is used in this paper for cascaded frequency reduction technology. The trigger probe is a full-return fiber optic probe that uses the change in light intensity to provide an external trigger signal after being impacted. In the test, a 5-GHz bandwidth oscilloscope is used as the signal recording equipment. In order to match the oscilloscope bandwidth, the wavelengths of the main laser module and the reference laser module are adjusted to 1550.120 nm, 1550.080 nm, and 1550.000 nm, respectively, and the frequency intervals are 5 GHz and 10 GHz in turn. In this way, the velocity measurement bandwidth of the velocimeter system reaches 20 GHz, and the corresponding maximum measured speed is 15.5 km/s. In order to verify the validity of the measured data of the velocimeter system, synchronous measurement is carried out by using the conventional non-frequency conversion velocimeter system (DPS) [19]. The spectrograms for the conventional DPS (Doppler Pins System) speeds and the two-stage downscaling speeds are shown in Figure 10. According to the principle of laser interferometric velocimetry, that is, \(u=1/2\cdot\lambda f\), the Doppler frequency \(f\) is obtained by using the short-time Fourier transform (STFT) from the interferometric signal, and the impact velocity is obtained by multiplying it with half the wavelength. Through data processing, a relatively complete velocity profile of the target material can be obtained, as shown in Figure 11. The red line is the velocity profile captured by the first stage of the prototype system, the blue line is the velocity profile captured by the second stage, and the black line is the velocity profile captured by the conventional velocity measurement system. The violet line is the displacement curve obtained by the time integration of the DPS velocity curve. Because two-stage downscaling uses a thermal expanded core probe, there is a test blind area when the measured surface is close to the probe, as shown by the dashed box in Figure 11. The maximum velocity profile of 11.47 km/s is measured by the two systems, the measuring time is about 2 \(\upmu\)s, and the measured displacement of target material is about 7.6 mm (depth of field). The first-stage signal is interrupted at 2.7 \(\upmu\)s after triggering, and the second-stage signal starts at 2 \(\upmu\)s after triggering, with a signal relay zone of 0.7 \(\upmu\)s between the two stages. In data processing, the window length  
Figure 9: Experimental principle and device of three-stage light gas gun. is 512 samples, the Fourier transform length is 4096 samples with the square window, and the product of velocity accuracy and time accuracy is 97 ns-m/s. When the time accuracy is 25.6 ns, the velocity accuracy is 3.8 m/s, and when the time accuracy is 50 ns, the corresponding velocity accuracy is 1.8 m/s, which meets the technical requirements.