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光學工程

光學工程

用于測速測距的全光纖外差激光雷達系統

Development of an all-f iber heterodyne lidar for range and velocity measurements

A 1550-nm all-fiber monostatic lidar system based on linear chirp amplitude modulation and heterodyne detection for the measurements of range and velocity is presented. The signal processing method is given, after which the relationship between the peak frequency values in the final signal spectrum, the target’s range, and the line-of-sight velocity is obtained in the presence of the fiber end-face-reflected signal plaguing many monostatic lidar systems. The range of an electric fan as well as the line-of-sight fan speed of different levels is tested. This proposed system has a potential application for the space-borne landing system.

OCIS codes: 280.3640, 280.3340, 280.3400, 040.2840.

doi: 10.3788/COL20100807.0713.

The coherent lidar system plays a key role in planetary exploration and autonomous safe soft landing by providing precise range and velocity information. In fact, the space missions on the Moon and Mars launched by the NASA at locations with scientific values adopted this kind of system. Both the main oscillator and the local oscillator (LO) are frequency-modulated through a triangular frequency. By calculating the up-ramp and the down-ramp beat frequencies, the target distance and the relative line-of-sight velocity can be obtained[1]. In many frequency-modulated continuous wave (FMCW) laser radars[2], the transmitted waveform is often produced by linearly expanding or contracting the length of a laser resonator through a piezoelectric transducer (PZT). However, varying the length of a laser cavity is often undesirable since it can cause many problems, such as large phase noise and increased sensitivity to the environment[3]. In this letter, we propose a monostatic eye-safe 1550-nm laser lidar system combining the external linear positive chirp amplitude modulation through an electro-optical modulator (EOM) and the heterodyne detection[4,5]. All of the devices used in the system are of f-the-shelf commercial products, guaranteeing stability while reducing research costs. Target range and velocity measurements are made using low peak laser power, long laser pulse, and a small telescope aperture.The schematic of the system is shown in Fig. 1. The laser adopts a communication band of 1550 nm, which is safe for the eyes; it also adopts a single-mode continuouswave (CW) fiber laser with a linewidth of 6 kHz[6]. The 50:50 beam coupler divides the laser into two equal parts. One part serves as the LO, while the other part serves as the main oscillator. The LO is frequency-shifted by 55 MHz through an acousto-optic modulator (AOM), whose drive signal is of fered by a signal generator. The main oscillator is amplitude-modulated with a linear chirp signal by an EOM, whose drive signal is of fered by a linear chirp signal generator. This signal generator can determine the bandwidth and pulse length of the linear chirp signal, which is the laser pulse length. The output of the EOM is entered into a circulator through port 1. An electric fan (San Jiao brand, Model No. Kyt25-802) was used as a target, to which the laser was transmitted through a telescope which used aspherical lens with an aperture of 3 cm. The return signal from the fan was collected by the same telescope and mixed with the LO in a 3-dB coupler. The optic devices of this system were connected by optical fibers, which, along with the monostatic setup, significantly simplified the optical adjustment. The mixed signal was then detected by a balanced photo detector, which had a common mode rejection ratio of 25 dB. The output of the photo detector was amplified and then sampled by a dual-channel 1-GHz 8-bit resolution analogto-digital (A/D) converter. This signal is a broadband chirp signal modulated at 55 MHz. The other channel of the A/D converter sampled the chirp signals driving the EOM. The A/D converter and the chirp signal generator were triggered by the same electric circuit to ensure the time synchronization. All of the signal processing was carried out in a computer. The signal processing comprised the dechirp process, the in-phase and quadrature detection, filtering, and the combination of the in-phase and quadrature signals.

The chirp signal m(t) can be expressed as

where f1 and ?0 are the chirp signal start frequency and the chirp signal initial phase, respectively, B is the bandwidth of the linear chirp signal, and T is the length of the laser pulse. The output of the circular port 3 signal in Fig. 1 can be formulated as

where A1 and A2 are the amplitudes of the fiber end-facereflected signal and the target-reflected signal, τ1 and τ2 are the time delays caused by the fiber end face and the target, ws and fd are the main oscillator optical frequency and the Doppler frequency generated by the lineof-sight velocity of the target, ?1 and ?2 are the phases of the fiber end-face-reflected signal and the target-reflected signal, respectively.

The LO signal can be expressed as

where f1 = B T τ1, f2 = B T τ2, and ?6 and ?7 are the phase signals.

The signal processing after the dechirp process comprises the in-phase (I) and quadrature (Q) detection; it is carried out by mixing s2(t) with the AOM drive signal. The I and Q signals are almost the same, except for the phase dif ference of 90? . The I and Q signals after the low-pass filtering with a bandwidth of fAOM can be formulated as

The fast Fourier transforms (FFTs) of the I and Q signals are expressed as

The combination of I and Q signals is derived by summing up the square of the IFFT and QFFT. The combination signal is

There are five items in Eq. (11). As cos(2πf1t + ?6), cos(2πfdt + ?9), and cos(2πf2t + ?7) have dif ferent peak values in the FFT, the product of F[cos(2πf1t+?6)] and F[cos(2πfdt + ?9) cos(2πf2t + ?7)] can be ignored along with the fifth item. As a result, the last two items in Eq. (11) can also be ignored. Considering the three previous items, three peak values could be derived, namely, F1, F2, and F3, which are expressed as

If f2 ?f1 is the frequency in proportion to the true target distance, then the line-of-sight target velocity v and the target distance dt can be calculated as

The system parameters are shown in Table 1. The system distance resolution and velocity resolution can be expressed as

where c is the speed of light. According to the values in Table 1, ?dt and ?v are 3.75 m and 1.2 cm/s, respectively.

The laser transmits to the target, and the incident angle is almost vertical. Thus, the line-of-sight velocity is small. The electric fan has three speed levels, wherein level 1 is the slowest and level 3 is the fastest. We tested the system performance with varying fan speed levels while keeping the position of the fan constant. Using the above processing method, the final spectra with variable fan speed levels are shown in Fig. 2. Each spectrum is a single-shot measurement result, there are indeed three peaks in the final spectrum. According to the frequency values, the peaks are F1, F2, and F3 as shown in Eq. (12). The value of F1 is constant in the three figures because F1 corresponds to the fiber end-face-reflected signal. The values of F2 and F3 increase along with the rise in fan speed level. The space between F2 and F3 is almost the same regardless of the fan speed level since the space represents the target distance. Owing to the frequency resolution, the true peak frequency lies between neighboring quantization points. Taking the fiber end-face-reflected signal as an example, the true signal frequency lies between the second and the third quantization points, corresponding to the frequencies of 15.2625 and 30.525 kHz, respectively, the true peak frequency can be extracted[7] .

After extracting the true peak frequency and by using Eq. (14), the respective line-of-sight target velocities and the true target distances corresponding to dif ferent levels are derived as follows: level 1, 1.008 m/s and 10.496 m; level 2, 1.433 m/s and 10.57 m; and level 3, 1.799 m/s and 10.453 m, respectively.

In conclusion, a 1550-nm all-fiber monostatic lidar system based on linear chirp amplitude modulation and heterodyne detection for the measurements of range and velocity is demonstrated. The derivation of the target range and the target line-of-sight velocity is given. The performance test shows that the system can detect the target distance and the target line-of-sight velocity accurately using low-transmitting power and small telescope aperture. Since the wavelength of the system is 1550 nm, the system is not only safe for the eyes, but also easy to be built from communication band commercial devices, ensuring robustness and stability of system. This system has great potential value in the future landing system, which requires both accurate relative range and velocity information.

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