A self-mixing (SM) dual-frequency (DF) laser Doppler velocimeter (LDV) (SM DF-LDV) is proposed and studied, which integrates the advantages of both the SM-LDV and the DF-LDV. An optically injected semiconductor laser operated in a dual-frequency period-one (P1) dynamical state is used as the light source. By probing the target with the light-carried microwave generated from the beat of the two optical frequency components, the spectral broadening in the Doppler signal due to the speckle noise can be significantly reduced. Together with an SM configuration, the SM DF-LDV has the advantages of direction discriminability, self-alignment, high sensitivity, and compact setup. In this study, speckle noise reduction and direction discriminability with an SM DF-LDV are demonstrated. The signal-to-noise ratios (SNRs) at different feedback powers are investigated. Benefiting from the high sensitivity of the SM configuration, an SNR of 23 dB is achieved without employing an avalanched photodetector or photomultiplier tube. The velocity resolution and the SNR under different speckle noise conditions are studied. Average velocity resolution of 0.42 mm/s and SNR of 22.1 dB are achieved when a piece of paper is rotating at a transverse velocity of 5 m/s. Compared with a conventional single-frequency LDV (SF-LDV), the SM DF-LDV shows improvements of 20-fold in the velocity resolution and 8 dB in the SNR.
© 2014 Optical Society of America
Self-mixing laser Doppler velocimeter (SM-LDV) is a well-established technique based on the dynamics of semiconductor lasers subject to optical feedback [1–4]. In a self-mixing (SM) configuration, the laser light is backscattered from a target and reenters into the laser cavity. The feedback light is amplified and mixed with the lasing field inside the cavity to generate the interferometric signal. With a built-in photodiode in the laser package, the semiconductor laser simultaneously plays the roles of a light source, an optical amplifier, an interferometer, and a detector. In general, the SM-LDV has the advantages of high sensitivity, self-alignment, and compact optical setup. In addition, the SM-LDV can discriminate the direction of a moving target. Unlike a conventional single-frequency LDV (SF-LDV) that generates sinusoidal interferometric signals from a Michelson interferometer, the signals of the SM scheme can be distorted from a sinusoidal waveform to an asymmetric saw-tooth waveform depending on the feedback parameters [4, 5]. The direction of a moving target can be determined from the orientation of the asymmetric waveform.
However, being a coherent detection scheme, the velocity resolution of the SM-LDV is inevitably affected by the inherent phase noise of the optical field and the speckle noise generated from diffused targets or targets with rough surfaces. Depending on the linewidth of the laser used, the phase noise in the SM signal increases when the distance to the target increases . Since the velocity resolution and the maximum detection distance are determined by the coherence of the laser, many studies are making efforts to develop lasers with narrow linewidths for high precision and long range measurements [7,8]. As for the speckle noise, on the other hand, it randomly modulates the amplitude and phase of the backscattered light. With the amplitude modulation, the laser can be unstable and hop between different dynamical states and regions. Due to the amplitude fading, the fringes will be lost so that displacement and velocity measurements become difficult. With the phase modulation, the spectral width of the Doppler signal will be broadened and the velocity resolution will be degraded. The direction discriminability can also no longer be preserved under severe phase modulation because of the pseudo-vibration generated by the speckle noise [9–11].
To overcome the problems caused by the amplitude modulation, a pair of piezo-actuators can be used to move the focusing lens for speckle tracking . Utilizing a voltage-controlled liquid lens, the focal length can be constantly changed to avoid the signal fading . A liquid crystal attenuator can be used to control the feedback power so that the laser can be kept in the same dynamical state and region . Based on the technique of sensor diversity that utilizes two laser diodes with different beam sizes and wavelengths, signals from two different positions on the target can complement with each other and mitigate the problem of amplitude fading. However, while the aforementioned techniques are all intended to solve the problems caused by the amplitude modulation, how to mitigate the problem from the phase modulation is of great interest.
Recently, nonlinear dynamics of semiconductor lasers subject to optical injection have been widely investigated and applied in various applications such as random bit generation, photonic microwave generation, chaotic lidar, and dual-frequency lidar [15–20]. In our previous study, a dual-frequency LDV (DF-LDV) based on an optically injected semiconductor laser operated in a period-one (P1) dynamical state has been proposed . Using a light-carried microwave to probe the target, coherence enhancement and speckle noise reduction have been demonstrated. To take the advantages from both the DF-LDV and the SM-LDV, in this paper, we study a self-mixing dual-frequency LDV (SM DF-LDV) based on the dynamics of a semiconductor laser subject to both the optical injection and the optical feedback. With a SM configuration, the SM DF-LDV has the advantages of high sensitivity, self-alignment, and compact setup. More particularly, by detecting the target with a light-carried microwave from a DF light source, the spectral broadening can be significantly reduced and the direction discriminability can be well preserved even under the strong influences of the speckle noise. To the best of our knowledge, the feasibility of an LDV employing both the dynamics of the optical injection and optical feedback have not been investigated. The capabilities of the speckle noise reduction and direction discriminability in an SM DF-LDV are demonstrated the first time.
2. Principles of the SM DF-LDV
For conventional SM-LDV, the emitted light of a semiconductor laser is reflected or backscattered from a target and reenters into the laser cavity to modulate the electromagnetic field. Depending on the phase of the backscattered field, the output power of the laser is then modulated to generate the interferometric signal. When detecting a target moving toward the laser with a constant longitudinal velocity vz, the corresponding Doppler signal can be written as4]. Because of the strong coupling between the optical gain and refractive index to the carrier density, the Doppler signal ISM(t) will not be an ideal sinusoidal function. When increasing the feedback power, the shape of the ISM(t) can gradually be distorted from a sinusoidal waveform into an asymmetric sawtooth-like waveform. Since the orientation of the asymmetric waveform ISM(t) is determined by the sign variation of the Φ, whether the target is moving toward or away from the laser can therefore be discriminated [1, 4, 5].
In practice, when detecting a moving target with a rough surface having both a longitudinal velocity vz and a transverse velocity vt, the Doppler signal has to be modified as22].
In the Doppler signal, the φ1(t) is determined by the intrinsic linewidth of the laser and the detection distance. When the detection distance increases, the root-mean-square noise caused by the variation of the φ1(t) increases. As the result, the range for effective detection is in general limited by the coherence length governed by the linewidth of the laser . The amplitude modulation caused by the speckle noise Aspeckle,1(t) results in amplitude fading, which makes the velocity measurements difficult due to the temporary loss of the interferometric fringes. The phase modulation caused by the speckle noise φspeckle,1(t) contributes to the broadening of the spectral width of the Doppler signal. Under strong phase modulation, the velocity resolution will be degraded and the direction discriminability may also be lost.
To suppress the effects of the speckle noise and enhance the coherence of the SM-LDV, an SM DF-LDV is proposed and studied in this paper. In the SM DF-LDV, the laser is subject to both the optical injection and optical feedback simultaneously. With the optical injection from a master laser (ML), the slave laser (SL) can be operated in a P1 dynamical state which has two optical frequency components f1 and f2 with a microwave beat frequency of fP1. The emitted light from this DF light source is sent to the target and the backscattered light with Doppler shift is injected into the cavity of the SL for self-mixing. Compared with Eq. (2) that uses light with only one frequency to probe the target, the Doppler signal obtained by the SM DF-LDV isEqs. (8) and (9) can be approximated as
Based on Eqs. (6) and (7), the velocity of the target vz can be deduced from the Doppler shift of the microwave beat frequency fP1. Here it can be viewed as detecting the target with a light-carried microwave, where the wavelength of the microwave c/fP1 is 4 order longer than the optical wavelengths of the optical components λ1 and λ2. By probing the target with a wavelength that is much longer than the surface roughness with an optical scale, the backscattered wavelets from different positions can be considered in-phase. As the result, both the speckle-induced amplitude modulation Aspeckle,P1(t) and phase modulation φspeckle,P1(t) in Eqs. (11) and (12) can be significantly reduced compared with the modulations found in Eqs. (3) and (4) for the SM-LDV case. Moreover, with the possibility of locking the phases of the two optical components φ1(t) and φ2(t) through a current modulation at fP1 [20, 23], variations of φP1(t) can be suppressed and a much better coherence can be obtained.
3. Experimental setup
The experimental setup of the SM DF-LDV is shown in Fig. 1. Both the ML and the SL are single-mode distributed-feedback (DFB) semiconductor lasers. The emitted light of the ML injects into the SL through a free-space circulator formed by a polarizing beamsplitter (PBS), a half-wave plate (HWP2), and a Faraday rotator (FR). By controlling the injection strength and the detuning frequency between the ML and the SL, the SL can be operated in the P1 state, which has two optical frequency components. To enhance the coherence of the microwave beat signal between the two, the SL is current modulated at the microwave beat frequency by using a microwave signal generator (MSG) (Anritsu MG3692B). The dual-frequency light from the SL is then coupled into a single-mode fiber and divided into the signal and the monitoring arms by a 20/80 fiber coupler (FC). For target detection, the light at the signal arm is amplified to about 20 mW by a semiconductor optical amplifier (SOA) (Covega BOA1130) and then collimated on the target with a spot size of about 3 mm in diameter. The monitoring arm is used to monitor the output of the SL, where the optical spectra are acquired by a 10 pm optical spectrum analyzer (OSA) (Advantest Q8384), the power spectra are detected by a 12 GHz high-speed photodetector (PD) (Newport 1544-A) and analyzed by a 30 GHz microwave spectrum analyzer (MSA) (R&S FSV30), and the Doppler waveforms are recorded with a 500 MHz oscilloscope (OSC) (Tektronix TDS7054). In the following measurements, a sampling rate of 250 kHz and a signal acquisition time of 10 s are used.
To demonstrate the ability of the speckle noise reduction of the SM DF-LDV, a piece of paper attached on a rotation table carried by a translating stage is used as the target. While the translating stage provides the longitudinal velocity, the transverse velocity generated by the rotation table determines the amount of the speckle noise added to the backscattered light. The backscattered light from the target is collected by a lens (L) and then fed back into the SL, where a polarization controller (PC) and a polarization-independent isolator (ISO3) are used to match the polarizations of the fiber and the SL. The feedback power is controlled by a variable attenuator (VA) and measured at the BS before coupling into the SL. The length of the feedback loop is about 45 m mainly determined by the fiber optic components used in the signal arm.
4. Results and discussions
The optical and power spectra of the SL operated in the P1 state are shown in Figs. 2(a) and 2(b), respectively. The normalized injection strength from the ML to the SL is 0.45 (the ratio between the strengths of the injection field and the emitted field) and the detuning frequency between the ML and the SL is 680 MHz. As can be seen, the output light from the SL contains two frequency components with equal amplitude. Their microwave beat frequency fP1 is 11.25 GHz, which has a 3 dB linewidth of 15 MHz measured with a resolution bandwidth of 100 kHz. By current modulating the SL at fP1 to phase-lock the two frequency components, as shown in Fig. 2(c), the 3 dB linewidth of the fP1 can be narrowed to less than 1 Hz (limited by the resolution bandwidth of the microwave spectrum analyzer). By enhancing the coherence of the microwave signal with the phase-locking, the coherent detection range is greatly extended.
To show the feasibility of the SM DF-LDV, Figs. 3(a)–3(b), 3(c)–3(d), and 3(e)–3(f) show the Doppler signals ISM,DF (t) (blue dashed curves), the mixed Doppler signals ISM,DF (t)2 (solid black curves), and their corresponding spectra for a plane mirror moving with vz = −2 cm/s and vz = +2 cm/s toward and away from the SL, respectively. As can be seen in Figs. 3(e) and 3(f), the Doppler-shifted frequency at 1.5 Hz corresponding to the velocity of the target is clearly shown in the spectra of the mixed Doppler signals. Note that similar results can also be obtained in the time domain by filtering the mixed Doppler signal with a low-pass filter (Here a third-order Chebyshev Type-II filter with a 7 Hz −3 dB bandwidth is used). As shown in Figs. 3(c) and 3(d) with the red dashed curves, sawtooth-like waveforms with a period of 0.67 s are obtained. From the orientations of these asymmetric sawtooth-like waveforms, the directions of the moving target can be determined.
Figure 4(a) shows the Doppler spectra of the SM DF-LDV for target moving at vz from 0.27 to 4 cm/s. From the frequency peaks of the Doppler spectra, the Doppler frequencies and their corresponding velocities measured under different vz are plotted in Fig. 4(b). As shown in Fig. 4(b), the velocity of the target is accurately measured by the proposed SM DF-LDV. The minimum detectable velocity is at 0.27 cm/s for the current setup, which is limited by the 10 s signal acquisition time. The maximum detectable velocity is at about 300 m/s, which is limited by the 500 MHz bandwidth of the oscilloscope used. However, limited by the length of the translating stage, a fastest velocity of 4 cm/s is demonstrated.
In the SM DF-LDV, amplitudes of the signal and noise in the detection are strongly depend on the level of the feedback power of the backscattered light. Figures 5(a)–5(c) show the amplitude of the signal, the noise level, and the signal-to-noise ratio (SNR) obtained under different feedback power (the power of the backscattered light). Here the signal amplitude is the amplitude of the frequency peak in the Doppler spectrum, the noise level is the average amplitudes in the Doppler spectrum from DC to 125 kHz, and the SNR is the ratio of the two. As can be seen in Fig. 5(a), the signal amplitude reaches its maximum at a feedback power of 7.5μW. Further increasing the feedback power reduces the signal amplitude. In contrast, the noise level shown in Fig. 5(b) increases as the feedback power increases. As can be seen in Fig. 5(c), a maximum SNR of 23 dB is achieved at a feedback power of 2.5μW. Note that, benefiting from the self-mixing scheme where the SL serves not only as the light source but also as the amplifier and the interferometer, signals at feedback power as low as 0.1μW can be detected without using an avalanched photodetector or photomultiplier tube.
The degradation of the SNR for feedback power larger than 2.5μW is mainly due to the coherence degradation of the P1 state. Figures 5(d)–5(f) show the power spectra of the SL with feedback power of 2.5μW, 32.5μW, and 102.5μW, respectively. As can be seen in Fig. 5(d), when the influence from the feedback is still weak, the P1 state generated from the optical injection has a very narrow linewidth. As the feedback power increases to 32.5μW, as shown in Fig. 5(e), the feedback light starts to destabilize the SL and the coherence of the P1 state begins to be deteriorated . As the result, the noise level increases and the signal amplitude decreases. Further increasing the feedback power may even change the dynamics of the SL where, as seen in Fig. 5(f), the SL evolves into a period-two state with a much wider linewidth. Therefore, to have the optimal SNR, the feedback power has to be adjusted in a range that the feedback light is sufficient but not destroying the coherence of the P1 state.
To demonstrate the capability of speckle noise reduction of the SM DF-LDV, a piece of paper is used as the target which generates different amounts of speckle noise when rotating at different transverse velocities. A SF-LDV using the same SL is also set up to serve as the benchmark, where the interferometric signals from an external Michelson interferometer has to be detected by an avalanched photodetector due to the poor SNR. With a coherence length limited by the 4.4 MHz linewidth, the path difference between the signal and the reference arms in the SF-LDV has to be less than 22 meters for successful coherent heterodyne detection.
The velocity resolution and the SNR obtained at different transverse velocities for the SF-LDV and the SM DF-LDV are shown in Fig. 6. Here the velocity resolution is calculated from the −3 dB bandwidth of the Doppler spectrum, where linear interpolation is used to estimate the full-width at half maximum (FWHM). For both configurations, the target has a longitudinal velocity of vz = 2 cm/s and the backscattered power is about 2 μW. As can be seen in Fig. 6(a), due to the spectral broadening caused by the speckle-induced phase modulation, the velocity resolution of the SF-LDV degrades linearly from 2.75 mm/s to 8.34 mm/s as the transverse velocity increases from 0 m/s to 5 m/s. At the same time, the SNR also drops from 20.9 dB to 13.8 dB as shown in Fig. 6(c).
On the contrary, by probing the target with a light-carried microwave that has a wavelength 4 orders longer than the optical light, the detection of the SM DF-LDV is not affected by the speckle noise provided. Figures 6(b) and 6(d) show the velocity resolution and the SNR of the SM DF-LDV obtained at different transverse velocities. As can be seen, the velocity resolution is at an average of 0.42 mm/s and the SNR remains at a level around 22.1 dB (blue dashed lines). When compared with the SF-LDV, at a transverse velocity of 5 m/s, the SM DF-LDV shows improvements of more than 20-fold on the velocity resolution and 8 dB on the SNR.
Note that, when the target moves in absence of the transverse velocity as seen in Figs. 6(a) and 6(b), the SM DF-LDV still shows a higher velocity resolution than the SF-LDV. This is due to the strong dependence of the Doppler bandwidth on the coherence property of the detection source when the speckle noise is not present. Although the SM DF-LDV has a lower sensing frequency (11.25 GHz) compared with the SF-LDV (228.48 THz), the better coherence of the SM DF-LDV (< 1 Hz in the SM DF-LDV compared with 4.4 MHz in the SF-LDV) yields a much narrower Doppler bandwidth for higher velocity resolution as long as enough signal time is acquired.
To show the direction discriminability under the influence of the speckle noise, Figs. 7(a) and 7(b) show the filtered mixed Doppler signals obtained with the SM DF-LDV when the target is moving toward and away from the SL with vz = −2 cm/s and vz = +2 cm/s, respectively. The target is rotated at a transverse velocity of vt = 5 m/s to generate the rapid phase modulation. As can be seen, under the condition where the transverse velocity is 250 times larger than the longitudinal velocity, the direction of the target can still be clearly determined from the orientation of the asymmetric saw-tooth waveform.
The SM DF-LDV integrating both the advantages of the SM-LDV and the DF-LDV is proposed and studied. Employing the nonlinear dynamics of both optical injection and optical feedback, the feasibility of SM DF-LDV is experimentally demonstrated. In the SM DF-LDV, the laser is operated in a P1 state as the DF light source. By detecting the target with the light-carried microwave under a SM configuration, the SM DF-LDV shows the advantages of speckle noise reduction, better coherence, high sensitivity, and direction discriminability. In the SM DF-LDV, the SNR is strongly dependent on the feedback power. To have the optimal SNR, the feedback power has to be controlled so that the backscattered light is sufficient but not destroying the coherence of the P1 state. With our setup, a maximum SNR of 23 dB is obtained at a feedback power of 2.5 μW without using any avalanched photodetector or photomultiplier tube. Under the influence of the speckle noise, average velocity resolution of 0.42 mm/s and SNR of 22.1 dB are achieved when the transverse velocity increases from 0 m/s to 5 m/s. With a transverse velocity that is 250 times faster than the longitudinal velocity, the direction discriminability is still shown to be preserved in the SM DF-LDV.
Compared with the previously proposed DF-LDV, the SM DF-LDV has a simpler setup where the external Michelson interferometer and avalanched photodetector are no longer required. Moreover, the SM DF-LDV is self-aligned and capable of discriminating the target directions. Compared with the conventional SM-LDV, the detection range of the SM DF-LDV will not be limited by the response time of the optical or electro-mechanical components used to control the problem of amplitude fading. Moreover, without spatial averaging or using the sensor diversity technique to mitigate the influences from the speckle noise, the spatial resolution is not sacrificed in the SM DF-LDV. In addition, unlike the conventional techniques employed in the SM-LDV that can solve only the problem of amplitude fading for a target moving in a longitudinal direction, the SM DF-LDV can suppress both the phase error accumulated when a target is traveling in a long distance and the random phase modulation generated with a transverse movement. Last but not least, with the possibility of locking the phases between the two optical frequency components from the DF light source, the coherence of the SM DF-LDV can be easily enhanced and the detection range can be significantly extended. While having all the above-mentioned advantages, it is worth noting that in order to have a higher velocity resolution, a longer acquisition time may be needed for the SM DF-LDV when compared with the conventional SF-LDV.
This work is supported by the National Science Council of Taiwan under contract NSC 100-2112-M-007-012-MY3 and the National Tsing Hua University under grant 102N2081E1.
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