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A scheme of pulse compression lidar with enhanced modulated bandwidth for detection through scattering media
Optics Communications 381 (2016) 205–209
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A scheme of pulse compression lidar with enhanced modulated bandwidth for detection through scattering media Cheng-hua Yang, Yong Zhang n, Chen-fei Jin, Lu Xu, Xu Yang, Qiang Wang, Yue-hao Liu, Yuan Zhao n Department of physics, Harbin Institute of Technology, Harbin, Heilongjiang province 150001, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 January 2016 Received in revised form 26 May 2016 Accepted 30 May 2016 Available online 18 July 2016
This paper presents a scheme of pulse compression lidar with enhanced electrical modulated bandwidth. An ultra-wideband linear frequency modulated signal with a bandwidth of 50 GHz is generated using femtosecond laser and superimposed linear chirp fiber Bragg gratings in the transmitter, which separates the echo of the target from the backward scattered noise with low modulated frequency. An optical pulse compression system based on a negative dispersion fiber Bragg grating is used to compress the ultrawideband linear frequency modulated signal in the receiver. SNR and range resolution of the proposed scheme are numerically simulated to prove its feasibility. The simulation results indicate that an enhancement of SNR by 15.8 dB can be achieved using the scheme, and the range resolution of the scheme increases from 0.68 m to 0.0027 m. It is therefore concluded that the proposed scheme is suitable for detection through scattering media. & 2016 Published by Elsevier B.V.
Keywords: Scattering Pulse compression Lidar
1. Introduction Lidar systems are widely used for such applications as estimation of atmospheric parameters [1,2], identification of target [3], measurements of velocity and vibrations [4], remote sensing [5], and imaging [6]. When applied in detecting targets in fog, faze, smoke and other scattering media, modulated lidars are commonly restrained by the influence of rapid attenuation of the laser pulse scattered along the transmission path. In these modulated lidar systems, high frequency modulated signal is utilized in order to separate target echo from the backward scattering noise of the scattering media with low frequency [7–9]. Up to now, the performance of reported pulse compression lidars cannot yet satisfy the practical application requirements because of the limitation of the electronical modulation bandwidth of drive signal for modulators [10,11]. It has been demonstrated in recent reports that photonic technologies can be applied for generation and detection of microwave radar signals [12,13], which supposes the possibility of an architecture of wideband modulated lidar by employing photonic technologies. In this paper, a scheme of pulse compression lidar with ultrawideband modulated signal is proposed using photonics technologies. And the structure of the proposed lidar is shown in Fig. 1, a femtosecond laser of 1550 nm is utilized as laser source, and a pair n
Corresponding authors. E-mail addresses: [email protected] (Y. Zhang), [email protected] (Y. Zhao).
of superimposed linear chirp fiber Bragg gratings (SLCFBG) are utilized to generate ultra-wideband modulated pulses in the transmitter [14]. In addition, single mode fiber (SMF) and a gain flatten filter (GFF) are used as a frequency-to-time mapping system. SMF is used to map the modulation waveform form frequency domain to time domain through broadening the femtosecond laser pulse according to the difference of dispersion between wavelengths, and GFF is employed to pick out linear frequency modulated(LFM) signal without distortion by band-pass filtering on the spectrum. By properly setting the parameters of SLCFBG and frequency-to-time mapping system, ultra-wideband LFM signals can be generated with an intended bandwidth of 50 GHz. The modulated pulse echo can then be picked out by the optical pulse compression using a negative dispersion fiber Bragg gratings (NDFBG), which is a LCFBG with a negative dispersion coefficient [15]. The compressed pluses are collected by a high speed photodetector and transmitted to the data processing system where the distance information of target is calculated. Therefore, both highspeed processing and compact solutions can be achieved using the laser modulation and optical pulse compression in full optical fiber components with excellent performance.
2. System description and theory analysis The structure of the proposed pulse compression lidar is shown in Fig. 1, the pulses from femtosecond laser are modulated using a
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Fig. 1. The structure of proposed pulse compression lidar with ultra-wideband modulated signal: A: modulation system; B: frequency-to-time mapping system; C: optical pulse compression system.
modulation system in dashed box A. The modulation system consists of a pair of superimposed linear chirp fiber Bragg gratings with lengths L1 and L2, chirp coefficients F1 and F2, and spacing h. In addition, a fiber circulator is utilized to route the modulated pulses to the following optical fiber components. SLCFBG is equivalent to a series of Mach–Zehnder cavities with different cavity lengths which correspond to different wavelengths. The reflection spectrum of SLCFBG can be expressed as [16]:
RF − P =
r1 + r2 − 2 ρ1 ρ2 cos(2βh − ϕ1 − ϕ2) 1 + r1r2 − 2 ρ1 ρ2 cos(2βh − ϕ1 − ϕ2)
,
(1)
where β = 2nπ /λ , n is the refractive index of fiber, and λ is the wavelength of input laser. ρ1 and ρ2 are the reflection coefficient, r1 and r2 are the reflectivity of cascaded SLCFBG. The transmitting procedure of each LCFBG can be analyzed using transmission matrix method. For a single LCFBG with length L and chirp rate F, the transmission matrix can be expressed as [17]: N
F=
∏ Fj,
(2)
j=1
where N is the number of LCFBG sections. Each section can be calculated as a uniform fiber grating. According to Ref. [18], the transmission feature of a real LCFBG normally requires N 450. Fj is the transmission matrix of j-th section:
⎡ σ^ κ ⎢ cosh(γBΔL ) − i sinh(γBΔL ) −i sinh(γBΔL ) γB γB ⎢ ⎢ Fj = ⎢ κ σ^ i sinh(γBΔL ) cosh(γBΔL ) + i γB γB ⎢ ⎢ sinh(γBΔL ) ⎣
⎤ ⎥ ⎥ ⎥ ⎥, ⎥ ⎥ ⎦j
ρS = −
F21 , F22 2
r S = ρS .
(3)
(4)
where RN and SN represent the forward and reverse mode of laser pulses. Reflection coefficient ρS and reflectivity rS of SLCFBG can be derived as below:
(5)
(6)
Combining (1), (5) and (6), the simulated reflection spectrum of SLCFBG is shown in Fig. 2. It can be found that the output of SLCFBG is a linear chirp modulated signal which varies with wavelength. In other words, the output signal is a linear amplitude modulated signal in frequency domain. Considering that the output of SLCFBG is still a narrow laser pulse in time domain, a frequency-to-time mapping system is placed after the fiber circulator. A piece of SMF is utilized in this section for dispersion, and a GFF consisting of long-period fiber gratings is adopted to pick out the laser pulse with intended bandwidth by band-pass filtering on the spectrum [19]. In this system, the modulated bandwidth of LFM will change with the total dispersion of the standard SMF G652 whose dispersion coefficient is about 17 ps/nm/km. For example, to generate a modulated bandwidth of 50 GHz of the LFM signal corresponds to a dispersion of 5 ns, 36.7 km G652 fiber is required in frequencyto-time mapping system. As the modulated bandwidth decreases, longer SMF is required. After frequency-to-time mapping system, the intensity of laser pulse is then mapped into LFM signal, which can be approximated as:
⎡ ⎛ ⎞⎤ ⎛t⎞ 1 P (t ) = P0rect ⎜ ⎟exp⎢ j2π ⎜ f0 t + Kt 2⎟⎥, ⎣ ⎝ ⎠⎦ ⎝ τ⎠ 2
2 where ΔL is the length of each section, and γB = κ 2 − σ^ is the coupling coefficient related to ac coupling coefficient κ and dc selfcoupling coefficient σ^ . Depending upon the boundary conditions, the output of femtosecond laser pulses modulated by LCFBG can be given by:
⎡ RN ⎤ ⎡ R0⎤ ⎡ 1⎤ ⎢ ⎥ = F⎢ ⎥ = F⎢ ⎥ , ⎣ 0⎦ ⎣ SN ⎦ ⎣ S0 ⎦
Fig. 2. Simulated reflection spectrum of SLCFBG: Chirp rate F1 ¼ -F2 ¼ 2.8 nm/cm; L1 ¼ L2 ¼1.5 cm; h ¼ 0.
(7)
where τ is the width of LFM pulse, K = B/τ is the modulation slope, and P0 is the peak power of LFM pulse. The waveform of output signal is shown in Fig. 3. Thus, stable LFM pluses with high bandwidths can be generated by setting appropriate SLCFBG parameters. It should be pointed out that the time-bandwidth product of a signal is determined by SLCFBG which enhances the SNR of a compression lidar, while the SMF and GFF can be used to adjust pulse width T and bandwidth B of LFM signal only. The echo signal collected by the receiving optics consists of the reflected echo from the target with an ultra-high bandwidth, and the low-frequency backward scattering noise from the scattering media after multiple scatterings, which can be derived from the lidar equation as shown below [20]:
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C.-h. Yang et al. / Optics Communications 381 (2016) 205–209
Fig. 3. LFM signal obtained with frequency-to-time mapping system in time domain, the filtering passband of GFF is 1550 7 4 nm.
Fig. 4. Simulated dispersion delay of NDFBG with a center wavelength of 1550 nm, and linear dispersion bandwidth of 8 nm; D ¼ 625 ps/nm; L ¼1.5 cm. N
N
r ΓΓ A Pb(t ) = 1 22 r ρb ∑ e−2γvtiP (t − ti ), R i
sb(t ) = k ∑ δi(t−tbi )⋅ i=1
(8)
st (t ) = kδ(t−tt )⋅ Pt (t ) =
ΓΓ 1 2A r ρ e−2γvtt P (t − tt ), R2 t
(9)
where Γ1 and Γ2 are the efficiencies of the transmitting and receiving optics in a lidar system; Ar is the receiving area; ρb is the backward scattering ratio of scattering media; ρt is the reflectivity of target; R is the distance of the target; Nr is the scattering number which represents the refractive index, density, glutinousness and other characteristics of scattering media; ti is the timing of i-th scattering in the medium, and tt is the timing of reflection from the target. γ and v are the average of attenuation and velocity of laser pulse during the whole detection procedure respectively. Considering the technical difficulties and expenses for a traditional pulse compression to process LFM signal with a bandwidth of more than 5 GHz due to electronic response rate, optical pulse compression is utilized as a solution on the basis of the outstanding linear negative dispersion ability of NDFBG. According to the transmission matrix method mentioned above, phase angle ϕ and dispersion delay τ of NDFBG can be expressed as:
ϕ = arctan( ρN ),
τ (λ ) =
(10)
λ2
dϕ dϕ =− , dω 2π c dλ
(11)
where ρN is the reflection coefficient of NDFBG. Fig. 4 shows the dispersion delay of a NDFBG designed for 1550 nm femtosecond laser, which demonstrates the optical pulse compression capability of NDFBG by adjusting dispersion coefficient D = dτ (λ ) /dλ and length L of NDFBG. It is shown in Fig. 4 that the total dispersion compensation of the designed NDFBG is round 5 ns during the linear dispersion spectra sections from 1546 nm to 1554 nm. By the help of NDFBG, the LFM signals will be reshaped to narrow pulses. This procedure can be ideally considered as matched filtering. Thus, the compression function of NDFBG can be given by:
H (t ) = P *( − t ).
(12)
The echo signals of scattering media and target after compression can be expressed as:
207
1 −2γvtt e ⋅ρbi + C , (vti )2
(13)
1 −2γR e ⋅ρt + C . R2
(14)
It is indicated in (13) and (14) that the compressed echo signal is hidden in the scattered noise, while the high-frequency component of scattered noise Pb(t ) will be rapidly consumed by multiple scattering, thereby getting the scattered noise filtered by the compression process. As a result, a higher SNR can be obtained using the proposed lidar scheme. Considering that when matched filtering is provided, the width of the LFM pulses after compression τ′ will reach its minimum [21]:
τ′MIN =
1 , B
(15)
which suggests that the photodetector will be unresponsive to the compressed narrow pulses when the modulated bandwidth B is too high. As a result, a modulated bandwidth of 50 GHz is conceivable based on the researches on high speed photodetectors [22].
3. Numerical simulations The proposed scheme is numerically simulated with MATLAB to prove its feasibility to detect through scattering media. The simulated target is a planar object placed in water mist. The parameters used for simulation are displayed in Table 1 and the simulation result is shown in Fig. 5(a). In addition, the detection Table 1 Parameters used for simulation. Parameter
Value
Attenuation factors of air Attenuation factors of water mist Back reflections of target Back reflections of water mist Distance of the water mist from lidar Distance of target from lidar Pulse width of LFM signal Frequency band range of LFM signal Scattering number in water mist Refractive index of water mist Sampling rate
0.7 km 1 0.05 m 1 0.2 0.0006 810 m 835 m 5 ns 0.7–50.8 GHz 500 1.10 100 GHz
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with optical pulse compression is provided by NDFBG, which proves the suitability of the scheme for detection through scattering media. Firstly SNR of the scheme is discussed. The SNRs of target echo are simulated with different modulated bandwidths. According to Fig. 5(a), the SNR of the proposed lidar can be shown as:
SNR = 10 lg
( max(IΣ ) − IΣ )2 , 2 ∑ ( IΣ − IΣ )
(16)
where IΣ is the stable sum of signal and noise around the echo of target. The simulation SNRs by averaging to 1000 repeated measurements with different modulated bandwidth are shown in Fig. 6. It can be seen from Fig. 6 that the average of SNR increases as the modulated bandwidth of LFM signal. So it can be concluded the performance of the lidar improves as the modulated bandwidth of LFM signal increases. According to the variation curve shown in Fig. 6, the SNR of LFM signal with a bandwidth 50 GHz shows a superiority of 15.8 dB than that of 1 GHz which demonstrated the feasibility of the proposed pulse compression lidar in detection through scattering media. Besides, range resolution of the scheme is estimated according to FWHM of the target echo marked by red boxes in Fig. 5. In Fig. 5 (a), FWHM of compressed target echo of the proposed scheme is τ FWHM1 = 2Δt = 0.02 ns, and the corresponding range resolution is:
ΔR1 =
c τ FWHM1 = 0.0027 m, n
(17)
where n is refractive index of water mist as shown in Table 1. While in Fig. 5(b), FWHM of target echo without pulse compression is τFWHM2 = 496Δt = 4.96 ns, and the corresponding range resolution is:
ΔR2 =
Fig. 5. Simulated target echo of the proposed pulse compression lidar, the target is placed in water mist 810 m away from the lidar, the distance between the target and lidar is 835 m: (a) with optical pulse compression; (b) without optical pulse compression. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
c tFWHM2 = 0.68 m. 2n
(18)
It is shown that the range resolution of the proposed scheme increases from 0.68 m to 0.0027 m. The result also indicates the advantage of the proposed pulse compression lidar scheme when detecting through scattering media.
4. Conclusion
Fig. 6. Variation of SNR with modulated bandwidth of LFM signal by averaging to 1000 repeated measurements.
result without optical pulse compression is given in Fig. 5(b) as a reference. It can be seen from Fig. 5 that without compression the target echo is lost in the noise and it becomes remarkable at t = 5.58 μs
It can be seen from the presentation above that an ultrawideband linear frequency modulated signal with a bandwidth of 50 GHz is generated using femtosecond laser and superimposed linear chirp fiber Bragg gratings to separate the echo of the target from the backward scattered noise in the transmitter. An optical pulse compression system based on a negative dispersion fiber Bragg grating is used to compress the ultra-wideband linear frequency modulated signal in the receiver. The SNR and range resolution of the scheme are numerically simulated to prove its feasibility. The simulation results indicate that an enhancement of SNR by 15.8 dB can be achieved using the scheme. Meanwhile, the simulation range resolution of the scheme improves from 0.68 m to 0.0027 m. It is therefore concluded that the proposed pulse compression lidar is suitable for detection through scattering media.
Funding Young Scientist Fund of the National Natural Science Foundation of China (Grant No. 61108072).
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Please cite this article as: C.-h. Yang, et al., Optics Communications (2016), http://dx.doi.org/10.1016/j.optcom.2016.05.084i
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
A scheme of pulse compression lidar with enhanced modulated bandwidth for detection through scattering media Cheng-hua Yang, Yong Zhang n, Chen-fei Jin, Lu Xu, Xu Yang, Qiang Wang, Yue-hao Liu, Yuan Zhao n Department of physics, Harbin Institute of Technology, Harbin, Heilongjiang province 150001, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 January 2016 Received in revised form 26 May 2016 Accepted 30 May 2016 Available online 18 July 2016
This paper presents a scheme of pulse compression lidar with enhanced electrical modulated bandwidth. An ultra-wideband linear frequency modulated signal with a bandwidth of 50 GHz is generated using femtosecond laser and superimposed linear chirp fiber Bragg gratings in the transmitter, which separates the echo of the target from the backward scattered noise with low modulated frequency. An optical pulse compression system based on a negative dispersion fiber Bragg grating is used to compress the ultrawideband linear frequency modulated signal in the receiver. SNR and range resolution of the proposed scheme are numerically simulated to prove its feasibility. The simulation results indicate that an enhancement of SNR by 15.8 dB can be achieved using the scheme, and the range resolution of the scheme increases from 0.68 m to 0.0027 m. It is therefore concluded that the proposed scheme is suitable for detection through scattering media. & 2016 Published by Elsevier B.V.
Keywords: Scattering Pulse compression Lidar
1. Introduction Lidar systems are widely used for such applications as estimation of atmospheric parameters [1,2], identification of target [3], measurements of velocity and vibrations [4], remote sensing [5], and imaging [6]. When applied in detecting targets in fog, faze, smoke and other scattering media, modulated lidars are commonly restrained by the influence of rapid attenuation of the laser pulse scattered along the transmission path. In these modulated lidar systems, high frequency modulated signal is utilized in order to separate target echo from the backward scattering noise of the scattering media with low frequency [7–9]. Up to now, the performance of reported pulse compression lidars cannot yet satisfy the practical application requirements because of the limitation of the electronical modulation bandwidth of drive signal for modulators [10,11]. It has been demonstrated in recent reports that photonic technologies can be applied for generation and detection of microwave radar signals [12,13], which supposes the possibility of an architecture of wideband modulated lidar by employing photonic technologies. In this paper, a scheme of pulse compression lidar with ultrawideband modulated signal is proposed using photonics technologies. And the structure of the proposed lidar is shown in Fig. 1, a femtosecond laser of 1550 nm is utilized as laser source, and a pair n
Corresponding authors. E-mail addresses: [email protected] (Y. Zhang), [email protected] (Y. Zhao).
of superimposed linear chirp fiber Bragg gratings (SLCFBG) are utilized to generate ultra-wideband modulated pulses in the transmitter [14]. In addition, single mode fiber (SMF) and a gain flatten filter (GFF) are used as a frequency-to-time mapping system. SMF is used to map the modulation waveform form frequency domain to time domain through broadening the femtosecond laser pulse according to the difference of dispersion between wavelengths, and GFF is employed to pick out linear frequency modulated(LFM) signal without distortion by band-pass filtering on the spectrum. By properly setting the parameters of SLCFBG and frequency-to-time mapping system, ultra-wideband LFM signals can be generated with an intended bandwidth of 50 GHz. The modulated pulse echo can then be picked out by the optical pulse compression using a negative dispersion fiber Bragg gratings (NDFBG), which is a LCFBG with a negative dispersion coefficient [15]. The compressed pluses are collected by a high speed photodetector and transmitted to the data processing system where the distance information of target is calculated. Therefore, both highspeed processing and compact solutions can be achieved using the laser modulation and optical pulse compression in full optical fiber components with excellent performance.
2. System description and theory analysis The structure of the proposed pulse compression lidar is shown in Fig. 1, the pulses from femtosecond laser are modulated using a
http://dx.doi.org/10.1016/j.optcom.2016.05.084 0030-4018/& 2016 Published by Elsevier B.V.
Please cite this article as: C.-h. Yang, et al., Optics Communications (2016), http://dx.doi.org/10.1016/j.optcom.2016.05.084i
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Fig. 1. The structure of proposed pulse compression lidar with ultra-wideband modulated signal: A: modulation system; B: frequency-to-time mapping system; C: optical pulse compression system.
modulation system in dashed box A. The modulation system consists of a pair of superimposed linear chirp fiber Bragg gratings with lengths L1 and L2, chirp coefficients F1 and F2, and spacing h. In addition, a fiber circulator is utilized to route the modulated pulses to the following optical fiber components. SLCFBG is equivalent to a series of Mach–Zehnder cavities with different cavity lengths which correspond to different wavelengths. The reflection spectrum of SLCFBG can be expressed as [16]:
RF − P =
r1 + r2 − 2 ρ1 ρ2 cos(2βh − ϕ1 − ϕ2) 1 + r1r2 − 2 ρ1 ρ2 cos(2βh − ϕ1 − ϕ2)
,
(1)
where β = 2nπ /λ , n is the refractive index of fiber, and λ is the wavelength of input laser. ρ1 and ρ2 are the reflection coefficient, r1 and r2 are the reflectivity of cascaded SLCFBG. The transmitting procedure of each LCFBG can be analyzed using transmission matrix method. For a single LCFBG with length L and chirp rate F, the transmission matrix can be expressed as [17]: N
F=
∏ Fj,
(2)
j=1
where N is the number of LCFBG sections. Each section can be calculated as a uniform fiber grating. According to Ref. [18], the transmission feature of a real LCFBG normally requires N 450. Fj is the transmission matrix of j-th section:
⎡ σ^ κ ⎢ cosh(γBΔL ) − i sinh(γBΔL ) −i sinh(γBΔL ) γB γB ⎢ ⎢ Fj = ⎢ κ σ^ i sinh(γBΔL ) cosh(γBΔL ) + i γB γB ⎢ ⎢ sinh(γBΔL ) ⎣
⎤ ⎥ ⎥ ⎥ ⎥, ⎥ ⎥ ⎦j
ρS = −
F21 , F22 2
r S = ρS .
(3)
(4)
where RN and SN represent the forward and reverse mode of laser pulses. Reflection coefficient ρS and reflectivity rS of SLCFBG can be derived as below:
(5)
(6)
Combining (1), (5) and (6), the simulated reflection spectrum of SLCFBG is shown in Fig. 2. It can be found that the output of SLCFBG is a linear chirp modulated signal which varies with wavelength. In other words, the output signal is a linear amplitude modulated signal in frequency domain. Considering that the output of SLCFBG is still a narrow laser pulse in time domain, a frequency-to-time mapping system is placed after the fiber circulator. A piece of SMF is utilized in this section for dispersion, and a GFF consisting of long-period fiber gratings is adopted to pick out the laser pulse with intended bandwidth by band-pass filtering on the spectrum [19]. In this system, the modulated bandwidth of LFM will change with the total dispersion of the standard SMF G652 whose dispersion coefficient is about 17 ps/nm/km. For example, to generate a modulated bandwidth of 50 GHz of the LFM signal corresponds to a dispersion of 5 ns, 36.7 km G652 fiber is required in frequencyto-time mapping system. As the modulated bandwidth decreases, longer SMF is required. After frequency-to-time mapping system, the intensity of laser pulse is then mapped into LFM signal, which can be approximated as:
⎡ ⎛ ⎞⎤ ⎛t⎞ 1 P (t ) = P0rect ⎜ ⎟exp⎢ j2π ⎜ f0 t + Kt 2⎟⎥, ⎣ ⎝ ⎠⎦ ⎝ τ⎠ 2
2 where ΔL is the length of each section, and γB = κ 2 − σ^ is the coupling coefficient related to ac coupling coefficient κ and dc selfcoupling coefficient σ^ . Depending upon the boundary conditions, the output of femtosecond laser pulses modulated by LCFBG can be given by:
⎡ RN ⎤ ⎡ R0⎤ ⎡ 1⎤ ⎢ ⎥ = F⎢ ⎥ = F⎢ ⎥ , ⎣ 0⎦ ⎣ SN ⎦ ⎣ S0 ⎦
Fig. 2. Simulated reflection spectrum of SLCFBG: Chirp rate F1 ¼ -F2 ¼ 2.8 nm/cm; L1 ¼ L2 ¼1.5 cm; h ¼ 0.
(7)
where τ is the width of LFM pulse, K = B/τ is the modulation slope, and P0 is the peak power of LFM pulse. The waveform of output signal is shown in Fig. 3. Thus, stable LFM pluses with high bandwidths can be generated by setting appropriate SLCFBG parameters. It should be pointed out that the time-bandwidth product of a signal is determined by SLCFBG which enhances the SNR of a compression lidar, while the SMF and GFF can be used to adjust pulse width T and bandwidth B of LFM signal only. The echo signal collected by the receiving optics consists of the reflected echo from the target with an ultra-high bandwidth, and the low-frequency backward scattering noise from the scattering media after multiple scatterings, which can be derived from the lidar equation as shown below [20]:
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Fig. 3. LFM signal obtained with frequency-to-time mapping system in time domain, the filtering passband of GFF is 1550 7 4 nm.
Fig. 4. Simulated dispersion delay of NDFBG with a center wavelength of 1550 nm, and linear dispersion bandwidth of 8 nm; D ¼ 625 ps/nm; L ¼1.5 cm. N
N
r ΓΓ A Pb(t ) = 1 22 r ρb ∑ e−2γvtiP (t − ti ), R i
sb(t ) = k ∑ δi(t−tbi )⋅ i=1
(8)
st (t ) = kδ(t−tt )⋅ Pt (t ) =
ΓΓ 1 2A r ρ e−2γvtt P (t − tt ), R2 t
(9)
where Γ1 and Γ2 are the efficiencies of the transmitting and receiving optics in a lidar system; Ar is the receiving area; ρb is the backward scattering ratio of scattering media; ρt is the reflectivity of target; R is the distance of the target; Nr is the scattering number which represents the refractive index, density, glutinousness and other characteristics of scattering media; ti is the timing of i-th scattering in the medium, and tt is the timing of reflection from the target. γ and v are the average of attenuation and velocity of laser pulse during the whole detection procedure respectively. Considering the technical difficulties and expenses for a traditional pulse compression to process LFM signal with a bandwidth of more than 5 GHz due to electronic response rate, optical pulse compression is utilized as a solution on the basis of the outstanding linear negative dispersion ability of NDFBG. According to the transmission matrix method mentioned above, phase angle ϕ and dispersion delay τ of NDFBG can be expressed as:
ϕ = arctan( ρN ),
τ (λ ) =
(10)
λ2
dϕ dϕ =− , dω 2π c dλ
(11)
where ρN is the reflection coefficient of NDFBG. Fig. 4 shows the dispersion delay of a NDFBG designed for 1550 nm femtosecond laser, which demonstrates the optical pulse compression capability of NDFBG by adjusting dispersion coefficient D = dτ (λ ) /dλ and length L of NDFBG. It is shown in Fig. 4 that the total dispersion compensation of the designed NDFBG is round 5 ns during the linear dispersion spectra sections from 1546 nm to 1554 nm. By the help of NDFBG, the LFM signals will be reshaped to narrow pulses. This procedure can be ideally considered as matched filtering. Thus, the compression function of NDFBG can be given by:
H (t ) = P *( − t ).
(12)
The echo signals of scattering media and target after compression can be expressed as:
207
1 −2γvtt e ⋅ρbi + C , (vti )2
(13)
1 −2γR e ⋅ρt + C . R2
(14)
It is indicated in (13) and (14) that the compressed echo signal is hidden in the scattered noise, while the high-frequency component of scattered noise Pb(t ) will be rapidly consumed by multiple scattering, thereby getting the scattered noise filtered by the compression process. As a result, a higher SNR can be obtained using the proposed lidar scheme. Considering that when matched filtering is provided, the width of the LFM pulses after compression τ′ will reach its minimum [21]:
τ′MIN =
1 , B
(15)
which suggests that the photodetector will be unresponsive to the compressed narrow pulses when the modulated bandwidth B is too high. As a result, a modulated bandwidth of 50 GHz is conceivable based on the researches on high speed photodetectors [22].
3. Numerical simulations The proposed scheme is numerically simulated with MATLAB to prove its feasibility to detect through scattering media. The simulated target is a planar object placed in water mist. The parameters used for simulation are displayed in Table 1 and the simulation result is shown in Fig. 5(a). In addition, the detection Table 1 Parameters used for simulation. Parameter
Value
Attenuation factors of air Attenuation factors of water mist Back reflections of target Back reflections of water mist Distance of the water mist from lidar Distance of target from lidar Pulse width of LFM signal Frequency band range of LFM signal Scattering number in water mist Refractive index of water mist Sampling rate
0.7 km 1 0.05 m 1 0.2 0.0006 810 m 835 m 5 ns 0.7–50.8 GHz 500 1.10 100 GHz
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C.-h. Yang et al. / Optics Communications 381 (2016) 205–209
with optical pulse compression is provided by NDFBG, which proves the suitability of the scheme for detection through scattering media. Firstly SNR of the scheme is discussed. The SNRs of target echo are simulated with different modulated bandwidths. According to Fig. 5(a), the SNR of the proposed lidar can be shown as:
SNR = 10 lg
( max(IΣ ) − IΣ )2 , 2 ∑ ( IΣ − IΣ )
(16)
where IΣ is the stable sum of signal and noise around the echo of target. The simulation SNRs by averaging to 1000 repeated measurements with different modulated bandwidth are shown in Fig. 6. It can be seen from Fig. 6 that the average of SNR increases as the modulated bandwidth of LFM signal. So it can be concluded the performance of the lidar improves as the modulated bandwidth of LFM signal increases. According to the variation curve shown in Fig. 6, the SNR of LFM signal with a bandwidth 50 GHz shows a superiority of 15.8 dB than that of 1 GHz which demonstrated the feasibility of the proposed pulse compression lidar in detection through scattering media. Besides, range resolution of the scheme is estimated according to FWHM of the target echo marked by red boxes in Fig. 5. In Fig. 5 (a), FWHM of compressed target echo of the proposed scheme is τ FWHM1 = 2Δt = 0.02 ns, and the corresponding range resolution is:
ΔR1 =
c τ FWHM1 = 0.0027 m, n
(17)
where n is refractive index of water mist as shown in Table 1. While in Fig. 5(b), FWHM of target echo without pulse compression is τFWHM2 = 496Δt = 4.96 ns, and the corresponding range resolution is:
ΔR2 =
Fig. 5. Simulated target echo of the proposed pulse compression lidar, the target is placed in water mist 810 m away from the lidar, the distance between the target and lidar is 835 m: (a) with optical pulse compression; (b) without optical pulse compression. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
c tFWHM2 = 0.68 m. 2n
(18)
It is shown that the range resolution of the proposed scheme increases from 0.68 m to 0.0027 m. The result also indicates the advantage of the proposed pulse compression lidar scheme when detecting through scattering media.
4. Conclusion
Fig. 6. Variation of SNR with modulated bandwidth of LFM signal by averaging to 1000 repeated measurements.
result without optical pulse compression is given in Fig. 5(b) as a reference. It can be seen from Fig. 5 that without compression the target echo is lost in the noise and it becomes remarkable at t = 5.58 μs
It can be seen from the presentation above that an ultrawideband linear frequency modulated signal with a bandwidth of 50 GHz is generated using femtosecond laser and superimposed linear chirp fiber Bragg gratings to separate the echo of the target from the backward scattered noise in the transmitter. An optical pulse compression system based on a negative dispersion fiber Bragg grating is used to compress the ultra-wideband linear frequency modulated signal in the receiver. The SNR and range resolution of the scheme are numerically simulated to prove its feasibility. The simulation results indicate that an enhancement of SNR by 15.8 dB can be achieved using the scheme. Meanwhile, the simulation range resolution of the scheme improves from 0.68 m to 0.0027 m. It is therefore concluded that the proposed pulse compression lidar is suitable for detection through scattering media.
Funding Young Scientist Fund of the National Natural Science Foundation of China (Grant No. 61108072).
Please cite this article as: C.-h. Yang, et al., Optics Communications (2016), http://dx.doi.org/10.1016/j.optcom.2016.05.084i
C.-h. Yang et al. / Optics Communications 381 (2016) 205–209
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