## 4 Experiment Results
To sum up, the TF diagram with periodicity can be obtained for the targets made of different materials. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Experimental Parameters of Laser Coherent Detection of Cube Targets**} \\ \hline Size & 5 mm \(\times\) 5 mm \(\times\) 5 mm & Wavelength & 1.064 μm \\ Window function & Hanning & Sampling Rate & 200 MHz \\ Window length & 2 \(\times\) 10\({}^{4}\) points & Frequency resolution & 2 kHz \\ Transmitting power & 100 mW & Time resolution & 5 ms \\ Detection range & 80 m & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental parameters of laser coherent detection of cube targets. Figure 8: Schematic diagram of laser micro-Doppler detection. The influence of spin rate is displayed in Figure 10, which illustrates the TF diagrams of the echo signals at different spin rates (1.4 Hz, 2.5 Hz, 3.8 Hz, 5.0 Hz, and 6.4 Hz, respectively) for attitude angle \(\alpha=45^{\circ}\). Equation (15) indicates that larger spin rate results in a more significant Doppler frequency shift. As Equation (15) predicts, it can be observed that when the spin is slow (control voltage equals 6 V, and the spin rate is about 1.4 Hz), the TF feature is insignificant (see Figure 10a). When the spin becomes faster, the periodicity can be clearly observed (see Figure 10b,c). The edge in the TF image is explicated and smoothed, which implies that the laser spot covers the whole target, while in Figure 10d,e, the appearance of the significant burs originates from the strong noise. The TF image becomes dim, which may be due to the reduction of the echo signal from each surface of the target. In our experiment, the spin rate of the target is controlled by the DC voltage. There exists a linear relation between spin rate and the control voltage. The estimation of spin rate according to our proposed approach is illustrated in Table 4. The maximum absolute error for the extraction of spin rate is less than 0.2 Hz, and the maximum relative error is less than 7.0%. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control Voltage** & **Rate Standard** & **Rate Estimated** & **Absolute Error** & **Relative Error** \\ (V) & **Value (Hz)** & **Value (Hz)** & **(Hz)** & **(\%)** \\ \hline
6 & 1.3895 & 1.3993 & 0.0098 & 0.71 \\
10 & 2.4487 & 2.6119 & 0.1632 & 6.67 \\
15 & 3.7325 & 3.8246 & 0.0921 & 2.47 \\
20 & 5.1306 & 5.0373 & 0.0933 & 1.82 \\
25 & 6.4132 & 6.4366 & 0.0234 & 0.36 \\ Mean & - & - & 0.0764 & 2.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cube target spin rate estimation results. Figure 9: TF diagrams of cube target with surface made of different materials. (**a**) Resin. (**b**) Aluminum alloy. (**c**) Fiber-reinforced polymer. In addition, the effect of the attitude angle is investigated. Here, the control voltage is set to 15 V. The attitude angles are given three values: 15\({}^{\circ}\), 30\({}^{\circ}\), and 45\({}^{\circ}\), respectively. Other parameters are shown in Table 3. Equation (15) shows that a larger attitude angle leads to a more significant micro-Doppler frequency shift. The TF diagrams obtained in the experiment are displayed in Figure 11. It can be seen that for a given spin rate, the micro-Doppler frequency shift \(f_{D}\) grows with the increase in attitude angle \(\alpha\), which agrees with the theoretical prediction. In addition, the time-frequency diagram also flattens out as the angle increases. The estimation of attitude angle is performed as well. Table 5 presents the measurement results of \(\alpha\). The maximum absolute error of the attitude angle estimate is not more than 3\({}^{\circ}\), and the relative error is less than 6%. For the case of the unknown target size with the attitude angle \(\alpha=15^{\circ}\) and \(\Delta=15^{\circ}\), one has \(f_{1}=0.042\) MHz and \(f_{2}=0.082\) MHz, respectively. Furthermore, the estimated result of the attitude angle is obtained as 14.7015\({}^{\circ}\) according to Equation (21) with a relative error of 1.99%.