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通过激光外差干涉获得待解调语音信号表达式为:
$$I = A + B\;{\rm{cos}}[C\;{\rm{cos}}\;{\omega _c}\;t + D{\rm{cos}}({\omega _c}\;t) + \phi (t)]$$ (1) 式中:A为干涉场背景光强引起的直流信号,mW;B为干涉光强大小,mW,
$B = \sqrt {{I_s}{I_r}} $ ,其中${I_s}$ 为返回信号光光功率,mW;${I_r}$ 为参考光光功率,mW;C cos(ωct)为调制器(EOM)引起的相位差,其中C为调制幅度,rad;${\omega _{\rm{c}}}$ 为载波角频率,Hz;t为时间,s;D cos(ωst)为语音信号,其中D为语音引起目标物振动幅度,rad,${\omega _{\rm{s}}}$ 为语音引起目标物振动角频率,Hz;$\phi (t)$ 为初始相位差。为方便后续信号处理表述,令θ(t)=D cos(ωst)+ϕ(t),表述为待测语音信号和初始相位差的合成量,rad。鉴于激光语音获取系统的工作原理,根据漫反射大目标激光雷达作用距离方程可知,返回信号光功率
${I_s}$ [15]:$${I_s} = \frac{{{I_{\rm{i}}}T_A^2{\sigma _{pq}}{D^2}}}{{4{r^2}}}{\eta _t}{\eta _r}$$ (2) 式中:
${\sigma _{pq}}$ 为目标后向散射系数;$D$ 为接收口径;TA为单程大气传输系数;ηt为光学系统发射传输系数;ηr为光学系统接收传输系数;${{r}}$ 为工作距离;${I_i}$ 为入射光功率。$$B = \sqrt {{I_s}{I_r}} $$ (3) 由公式(2)和公式(3)可知,
$$B = \sqrt {\frac{{{I_{\rm{i}}}T_A^2{\sigma _{pq}}{D^2}}}{{4{r^2}}}{\eta _t}{\eta _r}{I_r}} $$ (4) 参考基尔霍夫驻留相位近似法,假定目标物粗糙表面随机起伏服从高斯分布,其后向散射系数表达式为:
$${\sigma _{pq}} = \dfrac{{{{\left| {\dfrac{{n - 1}}{{n + 1}}} \right|}^2}}}{{2{{\left(\sqrt 2 \dfrac{\delta }{T}\right)}^2}{{\cos }^4}\theta }}\exp \left[ - \dfrac{{{{\tan }^2}\theta }}{{2{{\left(\sqrt 2 \dfrac{\delta }{T}\right)}^2}}}\right]$$ (5) 式中:
$n$ 为目标物的折射率;$\theta $ 为探测激光入射角度;$\delta $ 为随机表面起伏的高度均方根;$T$ 为表面相关长度;$\delta $ 、$T$ 决定目标物的粗糙度。由公式(4)、公式(5)可知,干涉光强B为:
$$B = \sqrt {\dfrac{{{I_{\rm{i}}}T_A^2{D^2}}}{{4{r^2}}}{\eta _t}{\eta _r}{I_r}\dfrac{{{{\left| {\dfrac{{n - 1}}{{n + 1}}} \right|}^2}}}{{2{{\left(\sqrt 2 \dfrac{\delta }{T}\right)}^2}{{\cos }^4}\theta }}\exp \left[ - \dfrac{{{{\tan }^2}\theta }}{{2{{\left(\sqrt 2 \dfrac{\delta }{T}\right)}^2}}}\right]} $$ (6) 公式(6)说明B受后向散射系数
${\sigma _{pq}}$ 影响,存在着探测角度,目标物种类,目标物表面粗糙度的后向光散射特性影响。为此,文中将开展目标后向光散射特性抑制技术研究,通过归一化自相除PGC解调算法进行消光强扰动。其解调流程如图1所示。图1为归一化自相除的消光强扰动新算法流程图,包含乘法器、低通滤波器、微分器、减法器、平方器、加法器以及积分器。其中一倍频载波为
$G\cos ({\omega _c}t)$ ,二倍频载波为$H\cos (2{\omega _c}t)$ 。根据此解调方法,对公式(1)用Bessel函数展开后与一倍频载波$G\cos ({\omega _c}t)$ 及二倍频载波$H\cos (2{\omega _c}t)$ 相乘,经过低通滤波器,进行平方,其公式变为:$${I_{51}} = {B^2}{G^2}{J_1}^2(C){\sin ^2}\theta (t)$$ (7) $${I_{51}} = {B^2}{H^2}{J_2}^2(C){\rm{cos}}{^2}\theta (t)$$ (8) 系统中令C的调制度为2.63 rad[4],则
${J_1}(C) = $ $ {J_2}(C)$ ,且$G = H = 1$ ,将公式(7)与(8)相加后变为:$${I_{61}} = {B^2}{G^2}{J_1}^2(C)$$ (9) 对公式(1)分别与一倍频载波
$G\cos ({\omega _c}t)$ 及二倍频载波$H\cos (2{\omega _c}t)$ 相乘,得到:$$ \begin{split} {I_1}_1 =& GA\cos {\omega _c}t + GB{J_0}(C)\cos {\omega _c}t\cos \theta (t) + \\ & {\rm{ }}BG\cos \theta (t)\sum\limits_{k = 1}^\infty {{{( - 1)}^k}} {J_{2k}}(C)[\cos (2k + 1){\omega _c}t +\\ & \cos (2k - 1){\omega _c}t] - {\rm{ }}BG\sin \theta (t)\sum\limits_{k = 0}^\infty {{{( - 1)}^k}} {J_{2k + 1}}(C)\cdot \\ &[\cos (2k + 2){\omega _c}t + \cos 2k{\omega _c}t] \\ \end{split} $$ (10) $$ \begin{split} {I_{12}} =& HA\cos 2{\omega _c}t + HB{J_0}(C)\cos 2{\omega _c}t\cos \theta (t) + \\ & {\rm{ }}BH\cos \theta (t)\sum\limits_{k = 1}^\infty {{{( - 1)}^k}} {J_{2k}}(C)[\cos 2(k + 1){\omega _c}t + \\ & \cos 2(k - 1){\omega _c}t] - {\rm{ }}BH\sin \theta (t)\sum\limits_{k = 0}^\infty {{{( - 1)}^k}}\cdot\\ & {J_{2k + 1}}(C)[\cos (2k + 3){\omega _c}t + \cos (2k - 1){\omega _c}t] \\ \end{split} $$ (11) ${I_1}_1$ 和${I_{12}}$ 经过低通滤波器后变成:$$I_{21} = - {BGJ}_{1}(C)\sin \theta (t)$$ (12) $$I_{22} = - {BHJ}_{2}(C)\cos \theta (t)$$ (13) 对上述信号经过微分器后变为:
$${I_{31}} = - BG{J_1}(C)\theta '(t)\cos \theta (t)$$ (14) $${I_{32}} = BH{J_2}(C)\theta '(t){\rm{sin}}\theta (t)$$ (15) 将
${I_{22}}$ 与${I_{31}}$ 相乘,得到:$${I_{41}} = {B^2}GH{J_1}(C){J_2}(C)\theta '(t){\cos ^2}\theta (t)$$ (16) 将
${I_{21}}$ 与${I_{32}}$ 相乘,得到:$${I_{42}} = - {B^2}GH{J_1}(C){J_2}(C)\theta '(t){\sin ^2}\theta (t)$$ (17) 两式相减,得到:
$${{I'}_o} = {B^2}GH{J_1}(C){J_2}(C)\theta '(t) = {B^2}{G^2}J_1^2(C)\theta '(t)$$ (18) 公式(18)与公式(9)进行相除得:
$${{I'}_{o1}} = \theta '(t)$$ (19) 最后经过积分得到:
$${I_o} = \theta (t){\rm{ = }}D\cos {\omega _s}t{\rm{ + }}\varphi (t)$$ (20) 解调输出包含被测语音信号
$D\cos {\omega _s}t$ 及扰动信号$\varphi (t)$ ,经过高通滤波器后,滤掉低频噪声$\varphi (t)$ ,输出信号为:$${I_o} = D\cos {\omega _s}t$$ (21) 公式(21)为输出的语音信号,解调出的信号中没有干涉光强B、只与声音引起目标物振动幅度D及振动频率
${\omega _s}$ 有关。公式(21)成立限定条件为:当载波幅度C为2.63时,一倍频载波为$G\cos ({\omega _c}t)$ ,二倍频载波为$H\cos (2{\omega _c}t)$ 中的G与H相等。 -
综上,文中所提新的基于相位载波解调消光强扰动算法,通过理论分析与仿真可知,其频率响应范围为覆盖人耳可听频率范围,光强度变化所带来的扰动不会影响语音检测结果,基于该仿真前提,开展算法性能稳定性实验测试。具体实验设计方案如图6所示。
根据图6,信号发生器(AWG)输出单一频率,固定幅值的声音信号驱动扬声器(Speaker)发声,扬声器发出的声音驱动目标物产生振动,其振动频率与信号发生器一致。实验过程中保持目标物与扬声器的位置固定。系统发射一束激光照射到目标物(纸巾盒)上,目标物反射回的激光由系统接收后,进入新的解调方法中进行信号处理后,输出解调信号。为了验证该算法是否可以有效抑制光强变化而引起的解调信号幅度大小的变化,该方案采用一个光纤衰减器,利用光纤衰减器(Laser attenuator)对探测激光进行衰减,从而实现干涉光强的变化来进行新算法性能验证。其中光强变化趋势类似与2.2节中的光强逐渐变大,声音振动固定,均由3 V电压信号激励喇叭振动。
具体实验装置的实验测试场景如图7所示,系统测试装置包括激光语音获取系统、信号发生器、扬声器(喇叭)、纸巾盒、光纤衰减器,其中实验装置设计参数如表1所示。
表 1 实验系统参数
Table 1. Parameters of test system
Test system Value Laser voice acquisition/nm Laser: 1 550 AWG TEK AFG3102 Target object/mm3 Dimension: 230×120×80 Laser attenuator/dB 0.6-60 实验条件为:工作距离100 m,测试信号为扬声器引起纸巾盒的振动信息,基于该信号进行探测。具体方式为信号发生器发出的频率为1 kHz,幅度为3 V,该信号与扬声器相连,激励扬声器发声,声音信号传递到纸巾盒上,制使纸巾盒振动,激光语音获取系统针对该振动信号进行检测。为了获得新解调算法对光强度影响消除性能测试,通过光纤衰减器调节探测光强功率进行实验,具体为激光的初始功率为40 mW,调节光纤衰减器分别使发射激光器衰减到40、30、20、10 mW,针对上述4种光功率进行实验测试,解调结果如图8所示。
图 8 光强度对新算法解调影响测试。(a)光强度为10 mW; (b)光强度为20 mW; (c)光强度为30 mW; (d)光强度为40 mW
Figure 8. Performance of new method tested by different light intensity. (a) Light power is 10 mW; (b) Light power is 20 mW; (c) Light power is 30 mW; (d) Light power is 40 mW
图8(a)测试激光功率为10 mW,振动频率为1 kHz,通过新解调算法输出解调结果为,振动幅度为1 rad, 振动频率为1 kHz;图8(b)测试激光功率为20 mW,振动频率为1 kHz,通过新解调算法输出解调结果为,振动幅度为1rad, 振动频率为1 kHz;图8(c)测试激光功率为30 mW,振动频率为1 kHz,通过新解调算法输出解调结果为,振动幅度为1 rad, 振动频率为1 kHz;图8(d)测试激光功率为40 mW,振动频率为1 kHz,通过新解调算法输出解调结果为,振动幅度为1 rad, 振动频率为1 kHz。由解调结果对比可知,当探测光功率分别为10、20、30、40 mW条件下,系统解调输出语音信号幅度一致,消除了光强不同对信号探测的影响。
由实验结果可知,该实验测试结果与文中2.2小节中光强变化对解调信号影响的仿真结果一致,且频率响应一致。虽然发射的激光功率发生变化,导致干涉光强度B发生了变化,但利用新算法解调出来的信号,其信号幅度与频率均未发生变化,该实验结果说明了文中所研究的消光强扰动算法可以很好的消除光强对信号的影响。
Eliminating light intensity disturbance algorithm based on phase demodulation carrier
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摘要: 激光语音探测是一种非接触远距离信息获取技术,具有灵敏度高、探测距离远、抗干扰等优点被广泛应用。但是,在目标物的后向光散射特性的影响下,该技术探测性能受到机位角度、目标材料、表面粗糙度影响,严重者有效信号将湮灭到噪声里致使系统探测失效。针对此,结合传统的微分交叉相乘解调(PGC-DCM)算法,开展归一化自相除相位载波解调算法研究,解决目标物后向光散射特性差异所带来的光强扰动问题。首先,建立消光强扰动算法数学模型,利用LabView构建仿真模型,通过该模型进行新算法的频谱响应与消光强能力的仿真分析,发现该算法可实现对干涉信号中B值,一倍频G、二倍频H以及一阶贝塞尔函数J1和二阶贝塞尔函数J2影响的消除;其次,针对不同光强度B值,进行了PGC-DCM和新算法性能对比分析,结果表明新算法可以解调出语音信号,在弱光环境下,优势更加明显;而PGC-DCM解调方法在光强度较小情况下时(例如B=0.5 mW),语音信号湮灭,无法还原出信号;最后,建立了远距离光强扰动抑制实验系统,进行了光强扰动消除能力实验。实验结果表明:该算法在探测光功率为10、20、30、40 mW条件下,系统解调输出语音信号幅度一致,消除了光强不同对信号探测的影响。Abstract: Laser voice detection is a non-contact remote information acquisition technology, which has advantages of highly sensitivity, long work distance and anti-environment disturbance ability. However, under the influnece of backscattering characteristic, the performance of this technology was related to the angle of project laser beam, the kinds of object and surface roughness. At worst, the effective signal would be buried in oblivion, which made the system invalid. An eliminating light intensity disturbance phase generated carrier (PGC) demodulation algorithm based on the PGC-differential-cross-multiplying algorithm (PGC-DCM), which was used to solve the problem of light intensity disturbance caused by backscattering characteristics. Firstly, a new method mathematical model with LabView system design software was bulit. The frequency response and the performance of eliminating light intensity were analyzed. Through this algorithm, the influence of light intensity parameters B, G, H, J1 and J2 were eliminated; Secondly, for different light intensities, the performance of PGC-DCM algorithm and the new algorithm was compared. The experimental results showed that the new algorithm can demodulate the voice signal well, especially in the weak light environment. The PGC-DCM demodulation algorithm cannot demodulate the voice signal under the condition of weak light intensity (such as B=0.5 mW); Finally, a long-distance speech acquisition experimental system was established, and experiments on the influence of different light intensities were carried out. The experimental results show that under the conditions of 10, 20, 30, 40 mW detection optical power, the system demodulates the output voice signal with the same amplitude, which eliminates the influence of different light intensities on signal detection.
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图 2 不同频率的单频信号仿真。(a)频率为500 Hz;(b)频率为1 000 Hz;(c)频率为1 500 Hz;(d)频率为2 000 Hz;(e)频率为2 500 Hz;(f)频率为3 000 Hz
Figure 2. Single frequency signal simulation of different frequencies. (a) The frequency is 500 Hz; (b) The frequency is 1 000 Hz; (c) The frequency is 1 500 Hz; (d) The frequency is 2 000 Hz; (e) The frequency is 2 500 Hz; (f) The frequency is 3 000 Hz
表 1 实验系统参数
Table 1. Parameters of test system
Test system Value Laser voice acquisition/nm Laser: 1 550 AWG TEK AFG3102 Target object/mm3 Dimension: 230×120×80 Laser attenuator/dB 0.6-60 -
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