Based on the physical principle of the heterodyne laser Doppler vibration measurement process, we analyze the measurement process of high-frequency and low-speed movement in the presence of low-frequency and high-speed background movement. In the process, the measurement noise generated by the presence of stray light exhibits chirp characteristics, with the effects and patterns of chirp noise explained. In response to the chirp noise, we propose a derivative preprocessing method for demodulation. The theoretical analysis shows the method exerts a significant effect on suppressing chirp noise, which is verified by simulations and experiments. Meanwhile, we set a heterodyne laser Doppler vibration measurement system with stray light and measure the target vibration. The normal method and derivative preprocessing method are adopted respectively for demodulation. The experimental results verify the existence of chirp noise and the effectiveness of the derivative preprocessing method in suppressing chirp noise, which decreases the chirp noise power by about 81.8%. The method can effectively reduce the influence of stray light on vibration measurement.

Heterodyne laser Doppler vibration measurement technology is a widely adopted non-contact and non-destructive movement measurement method, with the advantages of fast response speed and high resolution. It has a strong detection ability for single frequency movement and can quickly identify the characteristic frequency of target movement. However, in the presence of low-frequency high-speed background movement, the measurement of high-frequency low-speed movement is severely affected by chirp noise, which is caused by stray light and closely related to low-frequency high-speed background movement. The chirp noise can seriously affect the measurement of high-frequency low-speed movement, with errors even reaching tens of times larger than those of real movement. There is a lack of research on the principle of chirp noise caused by stray light and suppression methods of chirp noise. We deeply analyze the principle of chirp noise caused by stray light and propose a novel demodulation method called the derivative preprocessing method (DPM). This demodulation method is easy to implement and exhibits a good effect for suppressing chirp noise. This demodulation method is expected to provide a reliable noise suppression method for measuring high-frequency low-speed movement in the presence of low-frequency high-speed background movement. This plays a significant role in analyzing high-frequency vibration modes of precision devices in some special measurement scenarios, such as in the presence of background movement.

Our study consists of theoretical analysis, simulation, and experimental verification. Firstly, the working principle and demodulation method of the heterodyne laser Doppler vibration measurement system, which is in the presence of stray light, are deeply analyzed. According to the analysis, the stray light would generate chirp noise in the process of normal demodulation method (ARCTAN). Based on the generation and characteristics of the chirp noise, a new demodulation method DPM is proposed. Then, the influence of chirp noise on the measurement of target movement velocity and the effect of DPM on chirp noise suppression are simulated. In the simulation, a low-frequency sinusoidal movement is utilized as the background movement, while a high-frequency sinusoidal movement is employed as the target movement. In the simulation, the background movement generates corresponding chirp noise to affect demodulation results severely. The normal demodulation method DPM is leveraged to restore the target movement by demodulating the overall movement and performing high-pass filtering. Finally, a heterodyne laser Doppler vibration measurement experiment is conducted to utilize a piezoelectric ceramic plate fixed on the pendulum device. In the experiment, the piezoelectric ceramic plate vibrates at a single and high frequency, which is regarded as the target movement, and the pendulum's movement is considered as the background movement. According to the experiment results, the existence of chirp noise is verified, and the DPM suppresses the chirp noise too.

In the process of the normal demodulation method (ARCTAN), the cause of chirp noise is the combination of stray light and background movement. The frequency of chirp noise changes in real time with the background movement speed, and specifically, it is proportional to the absolute speed of background movement and inversely proportional to the laser wavelength (Formula 11). When the background movement is low-frequency high-speed movement and the target movement is high-frequency low-speed movement, the chirp noise will seriously affect the measurement of high-frequency part movement [Fig. 2(b)]. Compared with the normal demodulation method, DPM can effectively restore target movement [Fig. 2(c)], but will generate erroneous velocity spikes in the positions that are near zero speed locations. Since adopting the normal demodulation method's results to partly replace the demodulation results of the DPM at the corresponding positions (near zero speed locations), the velocity spikes can be suppressed, and the demodulation results approach target movement more closely. In the experiment, the background movement of the pendulum indeed generates corresponding chirp noise [Figs. 4(a) and (b)], and DPM can effectively suppress the chirp noise [Fig. 4(c)]. DPM has a significant suppression effect on chirp noise, which reduces the power of chirp noise by about 81.8% at the peak of the chirp noise (Fig. 5).

The principle of heterodyne laser Doppler vibration measurement is deeply analyzed. It is pointed out that chirp noise is generated due to stray light and background movement. The frequency of the chirp noise changes in real time with the background movement speed, which is proportional to the absolute background movement speed and inversely proportional to the laser wavelength. Simulations and experiments have confirmed the existence of chirp noise and its frequency variation pattern. A novel demodulation method DPM has been proposed for this type of chirp noise. Simulations and experiments prove that DPM can effectively suppress chirp noise. Above the target movement frequency, the chirp noise power can be reduced by about 81.8%.