Distance and Velocity Measurement of Coherent Lidar Based on Chirp Pulse Compression

sensors

Article Distance and Velocity Measurement of Coherent Lidar Based on Chirp Pulse Compression

Jing Yang 1,2, Bin Zhao 2 and Bo Liu 2,* 1 University of Chinese Academy of Sciences, Beijing 100049, China; [email protected] 2 Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China; [email protected] * Correspondence: [email protected]

Received: 11 March 2019; Accepted: 13 May 2019; Published: 20 May 2019

Abstract: To explore lidar, which can simultaneously measure the distance and velocity of long-distance targets at high resolution, a coherent lidar system based on chirp pulse compression has been studied. Instead of a conventional acousto-optic modulator (AOM), we used an electro-optic modulator (EOM) to modulate a continuous 1550 nm laser. Using EOM, the resolution of the lidar is higher and the system simpler. The electrical waveform used to modulate the laser is a chirp pulse, which has a sweeping bandwidth of 98 MHz, a duration of 10 µs, and a pulse repetition rate of 20 kHz. The result of 100 measurements shows that the system may yield accurate information in range, 22 cm, and radial velocity, 1.066 cm/s. ± ± Keywords: lidar; coherent; distance; velocity; pulse compression

1. Introduction Compared with microwave radar, lidar uses near-infrared or visible light as a carrier, which provide higher transverse resolution and better directivity because of the shorter wavelength. Traditional lidar uses the time-of-flight (TOF) of unmodulated narrow light pulse echoes that are reflected from a target to measure distance, and uses the time difference between pulses to measure velocity. In order to achieve high precision and sensitivity when making long-distance measurements, many TOF lidar systems use short-pulse lasers with a low pulse repetition rate and extremely high peak power [1,2]. This results in the problem of photon damage, since laser pulses of megawatt-level peak power will gradually damage optical devices and shorten system life, and high-power lasers are both expensive and cumbersome. Furthermore, this system can only measure the average velocity during the differential time. Compared with the unmodulated narrow light pulse technique, the modulated wide light pulse technique based on chirp compression is a better solution [3]. In this technique, a low-power laser, modulated by a long-pulsed RF up-sweep chirp wave, is used as the emitted light signal. The RF chirp wave also acts as a local RF wave. The modulated light signal is emitted by the beam expander collimator into free space, then reflected by the target and received by the same collimator. The received light signal is detected by a photodetector, and the RF chirp wave is demodulated and then convolves with the local RF wave. After convolution, this long chirp wave is compressed into a narrow pulse with a high peak whose position represents the speed and distance of the target. Since the energy of the signal is concentrated into a short period of time, the distance resolution and signal-to-noise (SNR) are greatly improved. The compression ratio is equal to the time bandwidth product (TBP), namely Bτ where B is the frequency sweep bandwidth and τ is the duration of the pulse. The local wave convolves with the echo wave, such that the anti-interference of the system is improved. For velocity measurement, traditional pulse compression lidar uses AOM to modulate the phase of laser [4,5]. Thus, it requires modulating the up-sweep and down-sweep chirp wave to measure both distance and velocity, thus making the system more complicated. The bandwidth of the AOM is narrow and

Sensors 2019, 19, 2313; doi:10.3390/s19102313 www.mdpi.com/journal/sensors Sensors 2019, 19, 2313 2 of 10 the response speed is slow, such that the compressed pulse is not narrow enough. In this paper, we have used EOM instead of AOM to modulate the amplitude of laser. After coherent detection, the RF chirp wave will split in frequency domain due to the Doppler shift, causing splitting of the compressed narrow pulse in the time domain. As a result, two narrow pulses will be obtained, allowing simultaneous calculation of the distance and velocity. With EOM, ﬁrst, the compressed pulse is greatly narrowed so the resolution is greatly improved and, second, we only need to modulate an up-sweep chirp signal to achieve simultaneous measurement of distance and velocity. Furthermore, we can measure the speed and distance of multiple points of the target and then use the measurement information to achieve recognition of the targets [6,7]. As for frequency-modulated continuous wave (FMCW) lidar, it can only utilize the part where the local oscillator light and echo light coincide in one sweeping period. The farther the target, the larger the time delay, and the shorter the coincidence time [8–11]. As pulse compression lidar is not aﬀected by time delays, and all echo light can be utilized, a pulse compression solution is therefore more advantageous for long-distance detection. Moreover, the FMCW system is susceptible to frequency modulating (FM) nonlinearity and requires additional auxiliary paths to compensate for nonlinearity.

2. Materials and Methods

2.1. Principle

The frequency of the RF chirp wave increases linearly from f 1 to f 2 over pulse duration τ as shown in Equation (1), and is modulated onto a laser. Through transmission, reﬂection, receiving, and detection of the modulated laser pulse, the RF chirp wave is demodulated, and the RF chirp wave is

f f t j2 f t+j 2− 1 t2 t jw t+j kt2 s(t) = rect( )e π 1 π τ = rect( )e 1 π (1) τ τ where w = 2πf , k = B , and B = f f , so the received RF wave is 1 1 τ 2 − 1

t t0 j(w +w )(t t )+jπk(t t )2 sr(t) = Arrect( − )e 1 d − 0 − 0 (2) τ where t0 is the time delay, wd is the Doppler angular shift caused by a moving target, and Ar characterizes the amplitude of the echo. Here, for the convenience of derivation, we assumed Ar = 1, and we have 2ν t = 2d/c, wd = 2π f d, f d = (3) 0 λ where d is the distance of the target, c is the speed of light, λ is the wavelength of the laser, and ν is the velocity of the target. The conjugation of the inversion of the transmitted RF chirp wave over time also works as a local chirp wave, namely s (t) = s( t)∗ (4) l − The output signal is the convolution of the local and received delayed RF chirp wave. Then, the output wave is

Z + Z + ∞ ∞ u t0 j(w +w )(u t )+jπk(u t )2 u t j[w (u t)+πk(u t)2] sout = sr(t) s (t) = sr(u)s (t u)du = rect( − )e 1 d − 0 − 0 rect( − )e− 1 − − (5) ⊗ l l − τ τ −∞ −∞ + We set u t t0 = y and t t = t . If w > 0, then t t < 0, so − 2 − 0 0 d − 0

τ+t Z 0 wd τ+t0 w 2 w w 2 sin[2 k(t + )( )] i(w t+ d )t j2πk(t + d ) i(w + d )t π 0 2πk 2 sout = e 1 2 0 e 0 2πk ydy = e 1 2 0 (6) τ+t wd 0 2πk(t0 + ) − 2 2πk Sensors 2019, 19, x FOR PEER REVIEW 3 of 10

w   t w  t w w d i(w t d )t j2k(t d ) i(w  d )t 2sin[2k(t  )( )] 1 2 2 2k 1 2 2k 2 sout  e  t e ydy  e (5)  wd 2 2k(t  ) 2k It is a Sinc function, and can be thought of as a narrow pulse. When s has its maximum value, out namely,Sensors 2019 the, 19 peak, 2313 of the narrow pulse, we derive 3 of 10

w   t 2k(t  d )( )  0 (6) It is a Sinc function, and can be thought of2 ask a narrow2 pulse. When sout has its maximum value, namely, the peak of the narrow pulse, we derive Near the narrow pulse peak, t can be neglected because it is much less than , so we derive wd τ + t0 2πk(t0 + )( ) = 0 (7) w  2πk 2 w 2k(t  d )( )  0  t  t  t  d 2k 2 peak 0 2k Near the narrow pulse peak, t0 can be neglected because it is much less than τ, so we derive wd  wd 2[2k(t  )( )] (7) i(w1  )t wd τ 2 2k 2 wd 2πks(outmaxt +  e )( ) = 0 t = t = t   0 peakwd 0 2π k 2 ⇒2k(t  w ) − 2πk wd 2kd τ 2[2πk(t0+ )( )] i(w1+ )t0 (8) s = e 2 2πk 2 = τ outmax wd The sout max is only related| to the| pulse duration 2 πandk(t + magnitude) of the echo signal (we set it to 0 2πk 1), so, in order to increase SNR to detect farther targets, we can increase the pulse duration  and amplifyThe thesoutmax magnitudeis only relatedof the detected to the pulse signal duration Ar. Theτ andposition magnitude of the peak of the represents echo signal the (we time set itdelay to 1), so, in order to increase SNR to detect farther targets,wd we can increase the pulse duration τ and amplify of the transmitted signal: t0 denotes distance and denotes velocity, so the distance and velocity the magnitude of the detected signal Ar. The position2k of the peak represents the time delay of the w cantransmitted be calculated. signal: Whent denotes s first distancely becomes and zerod denotes, we can velocity, derive so the distance and velocity can be 0 out 2πk calculated. When sout ﬁrstly becomes zero, we can derive

wd  1 wd 2k(t wd )(τ )    tzero  t0  1 wd (8) 2πk(t0 + 2k)( 2) = π tzero = t k+ 2k (9) 2πk 2 ⇒ 0 kτ − 2πk The difference between t peak and tzero is 1/ k 1/ B seconds, so the wide pulse with a duration of  The diﬀerence between t peak and tzero is 1/kτ = 1/B seconds, so the wide pulse with a duration of isτ compressedis compressed to to1/B 1 /secondsB seconds by by convolution. convolution.

2.2.2.2. System System Description Description FigureFigure 1 shows the block diagram of the proposed lidar system. A coupler divides the power of thethe laser laser souce souce into into a a 99% 99% part part and and 1% 1% part. part. T Thehe 99% 99% part part is is modulated modulated by by EOM EOM and and then then amplified amplified by by opticaloptical amplifier amplifier.. The The amplified amplified modulated modulated light light is is injected injected into into port port 1 1 of of the the optical optical circulator circulator and and then then injectedinjected into into the the telescope telescope through through port port 2. 2. The The echo echo light light is is obtained obtained by by the the same same telescope telescope and and sent sent to to 33 dB dB coupler coupler through through port port 3 3.. Since Since the the circulator circulator is is not not perfect perfect,, parts parts of of the the modulated modulated light light will will leak leak fromfrom port port 1 1 to to 3. 3. This This is is useful useful and and important important because because it it can can be be used used as as a a zero zero-time-time base. base. The The 1% 1% part part worksworks as as local local light, light, and and mixes mixes with with the the echo echo and and leakage leakage light light.. The The mixed mixed light light is is detected detected by by balance balance detectordetector so so as as to to get get both both the the delayed delayed leakage leakage and and echo echo RF RFchirp chirp signal, signal, which which will will partly partly coincide coincide if the if targetthe target is not is far not enough far enough.. Then, Then, they convolve they convolve with the with local the RF local chirp RF wave. chirp wave.

99% circulator telescope Optical 1 2 Laser 1:99 EOM amplifier 3 Balance 3dBcoupler 1% detector Data Optic signal Analys Signal is Rf signal Source

FigureFigure 1 1.. BlockBlock diagram diagram of of the the system. system.

First, we can only analyze the echo light because convolution is a linear process. The voltage waveform used to drive the modulator is

f2 f1 2 Vs(t) = V cos(2π f t + π − t ) = V cos[V(t)] (10) D 1 τ D where the VD is the amplitude of the driving voltage signal. When the modulator is based at null point, the output optical ﬁeld of the modulator is Sensors 2019, 19, 2313 4 of 10

πVs(t) Eo = Es sin( ) cos(2π f0t) (11) Vπ where Es is the amplitude of the constant input optical ﬁeld, Vπ is the half-wave voltage of the EOM, and f 0 is the center frequency of the laser source. For small-signal modulation, Equation (11) can be approximated as EsπVD Eo m cos[V(t)] cos(2π f0t), m = (12) ≈ Vπ The received echo and local optical ﬁelds are

ER = a cos[V(t0)] cos[2π( f0 + fd)(t0)], EL = b cos[2π f (t)] (13) where a and b are the amplitude of echo and local optical ﬁelds, respectively. Usually, a is much smaller than b because of the propagation loss. They mix in the 3 dB coupler, so the two output optical ﬁelds of the 3 dB coupler are

a b π E1 = cos[V(t0)] cos[2π( f0 + fd)t0] + cos(2π f0t + ) √2 √2 2 a π b (14) E2 = cos[V(t0)] cos[2π( f0 + fd)t0 + ] + cos(2π f0t) √2 2 √2

Photocurrents of the two photodetectors of the balance detector are n o = = + ab [ ( )] ( + ) Iarm1 R E1 2 R iD 2 cos V t0 cos 2π fdt0 θ π n − o (15) = = + ab [ ( )] ( + ) Iarm2 R E2 2 R iD 2 cos V t0 cos 2π fdt0 θ

a2 b2 π iD = R( 1 + cos[2V(t0)] + ), θ = f (t0 t) + (16) 8 { } 4 0 − 2 where R is the responsivity of the photodetectors. The output voltage of the balance detector [12,13] is proportional to the diﬀerence between the two photocurrents: Iarm1 and Iarm2. Then, the output voltage of the balance detector is Gab V = Gab cos[V(t0)] cos(2π f t + θ) = cos[V(t0) + 2π f t0 + θ)] + cos[V(t0) 2π f t0 θ)] (17) 0 d 2 { d − d − } where G is the conversion gain of the balance detector. As can be seen from Equation (17), two chirp waves emerge. Hence, after compression, the two narrow pulses will emerge. According to Equation (8), the time delays of the two peaks are

fd fd t = t , t = t + (18) peak1 0 − k peak2 0 k The distances represented by these two peaks are

tpeak1 c tpeak2 c d = ∗ , d = ∗ (19) 1 2 2 2 In particular, when the target is stationary, the two pulses will completely coincide, that is, only one narrow pulse will emerge. The actual distance is given by

d + d d = 1 2 (20) real 2 and the velocity is given by (d1 d2)B v = − (21) 2τ f0 Sensors 2019,, 19,, xx FORFOR PEERPEER REVIEWREVIEW 5 of 10

The distances represented by these two peaks are

ttpeak1 c ttpeak2 c d  peak1 ，d  peak2 (18) 1 2 2 2 In particular, when the target is stationary, the two pulses will completely coincide, that is, only one narrow pulse will emerge. The actual distance isis givengiven byby

d1  d2 drealreal  (19) 2 and the velocity is given by Sensors 2019, 19, 2313 5 of 10 (d1  d2 )B v  (20) 2ff0

In order to improve the performance of of the system, we we need need to to do do extra two kinds of data processing. First, First, we we multiply multiply the the local local RF RF wave wave by bythe the Hamming Hamming window window to suppress to suppress the high the highside lobessidelobes lobes ofof thethe of SincSinc the waveform,waveform, Sinc waveform, soso asas toto so reducereduce as to reduce thethe probabilityprobability the probability of false of alarm. false alarm.Second, Second, the phase the term phase θ,, describedterm θ, described by Equation by Equation (16), will (16), affect will a ﬀ theect phase the phase of the of the Sinc Sinc waveform, waveform, so so we we perform perform Hilbert transformation on the compressed narrow pulse to obtain its envelopes envelopes,,, which would not be affected aﬀected by θ.. After After these these two two steps of data processing, the the output signal will will be a narrow positive pulse as shown in Figure 22,, ratherrather thanthan anan oscillatingoscillating Sinc Sinc waveform. waveform.

Figure 2 2... TheThe principle principle of distance distance and velocity measurement measurement...

The graphs in the first ﬁrst row show th thee frequency over time of the echo and its envelopes after compression for a stationary target, and the second second row row shows shows those those of of a a moving moving target. target. In In this this way, way, we can accurately measure distance and velocity. The direction of the velocity can be determined by the two successive measurements.

3. R Resultsesults

3.1. Distance Distance and and Velocity Velocity Measurement As shown shown in in Figure Figure 3,3, the the verification veriﬁcation experiment experiment was was performed performed using using a spinning a spinning disk disk as the as target.the target.

Figure 3 3... Spinning disc target.

The laser frequency was set at 193.4 THz. The RF chirp had a duration of 10 µs, a repetition rate of 20 kHz and sweeps from 1 MHz to 99 MHz. The fiber amplifier was set at 50 mW. The delayed RF chirp wave detected by the balance detector was sampled using a real-time oscilloscope. One of the detected chirp waves is shown in Figure4. The signal on all screens is a full cycle (50 µs). The middle part is two almost coincident chirp pulses which consist of the leakage signal of the circulator and echo signal reflected by the target. It is worth noting that the amplitude of the latter is much smaller than that of the former due to the strong loss of echo light after propagation through free space. Beyond that, the target is not far enough, and the time delay is so short that most part of them overlap. Sensors 2019, 19, x FOR PEER REVIEW 6 of 10

The frequency of the laser was set at 193.4 THz. The RF chirp had a duration of 10 µs, a repetition rate of 20 kHz and sweeps from 1 MHz to 99 MHz. The fiber amplifier was set at 50 mW. The crosstalk of the circulator is approximately −55 to −50 dB, namely 0.15 µW to 0.5 µW modulated light will leak directly from port 1 to 3. The delayed RF chirp wave detected by the balance detector was sampled using a real-time oscilloscope. One of the detected chirp waves is shown in Figure 4. The signal on all screens is a full cycle (50 µs). The middle part is two almost coincident chirp pulses which consist of the leakage signal of the circulator and echo signal reflected by the target. It is worth noting that the amplitude of the latter is much smaller than that of the former due to the strong loss of echo light Sensorsafter propagation2019, 19, 2313 through free space. Beyond that, the target is not far enough, and the time delay6 of 10is so short that most part of them overlap.

Figure 4.4. The output RF signa signall of the balance detector.

After convolution, the middle two 10 µµss-long-long chirp pulses were compressed to two 11//B secondsecond narrow pulses, whose width were doubled when the local chirp was multiplied by the HammingHamming window, andand werewere halvedhalved becausebecause ofof thethe two-waytwo-way propagation,propagation,so sothe thedistance distanceresolution resolution is is

1 = 1 drd  cc  3m m (21 (22)) r BB· ≈ ToTo achieve higher higher resolution, resolution, we we can can use use an an RF RF chirp chirp signal signal generator generator of wider of wider bandwidth. bandwidth. The The sampling frequency f was 1 GHz, so the distance precision is sampling frequency fs wass 1 GHz, so the distance precision is

dp = c/2 fs = 15 cm (23) dp  c / 2 f s  15cm (22)

To achieveachieve higherhigher precision,precision, wewe cancan useuse anan instrumentinstrument withwith higherhigher samplingsampling speed.speed. Based on EquationsEquations (20)(20) and (21),(21), the velocity precisionprecision isis d B = c = vp dc B 0.7448 cm/s (24) v τ f0  0.7448cm / s p f (23) Sensors 2019, 19, x FOR PEER REVIEW 0 7 of 10 We sampled and processed the detected signal 100 times. One of these results is shown in Figure5. We sampled and processed the detected signal 100 times. One of these results is shown in Figure 5.

FigureFigure 5. 5.One One ofof thethe 100100 measurements.measurements.

TheThe greengreen lineline is the compressed compressed signal, signal, the the blue blue line line is isthe the envelopes envelopes of ofthe the green green line, line, and and the thered red line line is the is the noise noise threshold. threshold. The The abscissa abscissa represents represents the thedistance distance and and the theordinate ordinate represents represents the theamplitude amplitude of the of thesignal signal.. The Thehigh high peak peak at 0 cm at 0 came cm came from fromthe leakage the leakage of light of of light the ofcirculator, the circulator, while while the two small peaks on both sides came from the echo light. The left peak is 2805 cm and the the two small peaks on both sides came from the echo light. The left peak is −2805− cm and the right rightpeak peakis 5685 is 5685cm, so cm, the so actual the actual distance distance is 1440 is 1440 cm and cm andthe theactual actual velocity velocity is 214.95 is 214.95 cm/s. cm For/s. Forthe the100 100measu measurements,rements, we we eliminated eliminated unreasonable unreasonable datasets datasets because because of of instability instability of coherent coherent detection detection causedcaused byby thethe randomrandom phasephase didifferenceﬀerence betweenbetween thethe echoecho andand thethe locallocal lightlight inin thethe opticaloptical domain.domain. ThisThis problemproblem cancan bebe solvedsolved byby phasephase diversitydiversity homodynehomodyne techniquetechnique [14[14,15,15]] oror phase-lockedphase-locked looploop technique [16]. Measurement can be done with just one pulse, so we do not have to accumulate several pulses [17]. Thus, the data rate can be as high as 20 kHz. The remaining datasets has a distance within 1000–1800 cm and velocity within 180–240 cm/s. It turns out that there were 71 valid results, as shown in Figure 6.

(a) (b)

Figure 6. (a) The distance measurements; (b) The velocity measurements.

The blue circles are the 71 valid measurement results, and the green line is the average. The mean value of distance is 1440 cm, and the standard deviation is 22 cm, which is close to the theoretical value of 15 cm. The mean value of velocity is 215.65 cm/s with a standard deviance of 1.066 cm/s, which is approximately the same as the theoretical value of 0.7448 cm/s.

Sensors 2019, 19, x FOR PEER REVIEW 7 of 10

Figure 5. One of the 100 measurements.

The green line is the compressed signal, the blue line is the envelopes of the green line, and the red line is the noise threshold. The abscissa represents the distance and the ordinate represents the amplitude of the signal. The high peak at 0 cm came from the leakage of light of the circulator, while the two small peaks on both sides came from the echo light. The left peak is −2805 cm and the right peak is 5685 cm, so the actual distance is 1440 cm and the actual velocity is 214.95 cm/s. For the 100

Sensorsmeasu2019rements,, 19, 2313 we eliminated unreasonable datasets because of instability of coherent detection7 of 10 caused by the random phase difference between the echo and the local light in the optical domain. This problem can be solved by phase diversity homodyne technique [14,15] or phase-locked loop techniquetechnique [ 16 [1].6]. Measurement Measurement can can be be done done with with just just one pulse,one pulse, so we so do we not do have not to have accumulate to accumulate several pulsesseveral [17 pulses]. Thus, [17]. the Thus, data the rate data can rate be as can high be as 20high kHz. as 20 The kHz. remaining The remaining datasets datasets has a distance has a distance within 1000–1800within 100 cm0–180 and0 velocitycm and withinvelocity 180–240 within cm180/s.–240 It turns cm/s. out It turns that there out that were there 71 valid were results, 71 valid as results, shown inas Figureshown6 .in Figure 6.

(a) (b)

FigureFigure 6.6. ((aa)) TheThe distancedistance measurements;measurements; ((bb)) TheThe velocityvelocity measurements.measurements.

TheThe blueblue circlescircles areare thethe 7171 validvalid measurementmeasurement results,results, and and the the greengreen line line isis thethe average.average. TheThe meanmean valuevalue ofof distance distance is is 1440 144 cm,0 cm, and and the the standard standard deviation deviation is 22 is cm, 22 whichcm, which is close is close to the to theoretical the theoretical value ofvalue 15 cm. of 15 The cm. mean The value mean of value velocity of velocity is 215.65 is cm 215.65/s with cm/s a standard with a standard deviance deviance of 1.066 cmof /1.066s, which cm/s, is Sensors 2019, 19, x FOR PEER REVIEW 8 of 10 approximatelywhich is approximately the same asthe the same theoretical as the theoretical value of 0.7448 value cmof /0.7s. 448 cm/s. 3.2. Computational Burden 3.2. Computational Burden The pulse duration of the signal is , and the sampling rate is fs . Then, the detected digital signal The pulse duration of the signal is τ, and the sampling rate is fs. Then, the detected digital signal is a sequence of length N where N =  fs. Hence, the local oscillator is also a sequence of length N. The is a sequence of length N where N = τ f s. Hence, the local oscillator is also a sequence of length N. signal processing operation is a circular convolution of two sequences of length N used to obtain a The signal processing operation is a circular convolution of two sequences of length N used to obtain a sequence of length 2N, and the sequence is then Hilbert-transformed and, finally, the modulus value of sequence of length 2N, and the sequence is then Hilbert-transformed and, ﬁnally, the modulus value the sequence is calculated to determine the peak position. Although the calculated amount of pulse of the sequence is calculated to determine the peak position. Although the calculated amount of compression is larger than that of MFCW, this is no longer a limiting factor due to the rapid pulse compression is larger than that of MFCW, this is no longer a limiting factor due to the rapid development of digital signal processor (DSP) chip technology. development of digital signal processor (DSP) chip technology.

3.33.3.. Sensitivity Sensitivity Test Test In Inorder order to evaluate to evaluate the the performance performance of the of the system, system, Simplified Simpliﬁed experiments experiments have have been been conducted conducted to totest test the the sensitivity sensitivity of ofthe the system system.. The The sensitivity sensitivity (minimum (minimum input input power power of ofsignal signal light light when when SNR SNR is nois no smaller smaller than than 13 13dB) dB) is, is,namely, namely, the the minimum minimum output output optical optical power power of ofthe the adjustable adjustable optical optical attenuator.attenuator. Usually, Usually, the the sensitivity sensitivity is at is atnW nW or orpW pW magnitude, magnitude, which which cannot cannot be bedirectly directly detected detected and and mustmust therefore therefore be betested tested indirectly. indirectly. The The co correspondingrresponding block block diagram diagram is isshown shown in inFigure Figure 7.7 .

99% Optical Laser 1:99 modulator attenuator

1% Balance 3dBcoupler detector Data Optic signal Signal Analysis Rf signal Source

Figure 7. The block diagram of the sensitivity test. Figure 7. The block diagram of the sensitivity test.

We start up the MATLAB program to detect the target in real time, and slowly rotate the knob of the attenuator to gradually reduce the output optical power until SNR drops to about 13 dB. The SNR was calculated by dividing the peak value of the compressed narrow pulse by the standard deviance of the noise. Dividing the peak value by 2700 was the amplitude of the chirp pulse before compression, namely, V0. The ratio 2700 was given by simulation. Then, we could calculate the power of the echo light through the RF output conversion gain (30 × 103 V/W) of the balance detector. This optical power was characterized by ab in Equation (25). The local optical power characterized by b2/2 was detected using an optical power meter. Finally, we obtained the optical power indicated by a2/2, namely, the sensitivity. In our experiments, when the SNR dropped to 13 dB, the high peak value was about 15 V, as shown in Figure 8.

Figure 8. Sensitivity test result.

Sensors 2019, 19, x FOR PEER REVIEW 8 of 10

3.2. Computational Burden

The pulse duration of the signal is , and the sampling rate is fs . Then, the detected digital signal is a sequence of length N where N =  fs. Hence, the local oscillator is also a sequence of length N. The signal processing operation is a circular convolution of two sequences of length N used to obtain a sequence of length 2N, and the sequence is then Hilbert-transformed and, finally, the modulus value of the sequence is calculated to determine the peak position. Although the calculated amount of pulse compression is larger than that of MFCW, this is no longer a limiting factor due to the rapid development of digital signal processor (DSP) chip technology.

3.3. Sensitivity Test In order to evaluate the performance of the system, Simplified experiments have been conducted to test the sensitivity of the system. The sensitivity (minimum input power of signal light when SNR is no smaller than 13 dB) is, namely, the minimum output optical power of the adjustable optical attenuator. Usually, the sensitivity is at nW or pW magnitude, which cannot be directly detected and must therefore be tested indirectly. The corresponding block diagram is shown in Figure 7.

99% Optical Laser 1:99 modulator attenuator

1% Balance 3dBcoupler detector Data Optic signal Signal Analysis Rf signal Source

Sensors 2019, 19, 2313 Figure 7. The block diagram of the sensitivity test. 8 of 10

We start up the MATLAB program to detect the target in real time, and slowly rotate the knob We start up the MATLAB program to detect the target in real time, and slowly rotate the knob of of the attenuator to gradually reduce the output optical power until SNR drops to about 13 dB. The the attenuator to gradually reduce the output optical power until SNR drops to about 13 dB. The SNR SNR was calculated by dividing the peak value of the compressed narrow pulse by the standard was calculated by dividing the peak value of the compressed narrow pulse by the standard deviance deviance of the noise. Dividing the peak value by 2700 was the amplitude of the chirp pulse before of the noise. Dividing the peak value by 2700 was the amplitude of the chirp pulse before compression, compression, namely, V0. The ratio 2700 was given by simulation. Then, we could calculate the power namely, V . The ratio 2700 was given by simulation. Then, we could calculate the power of the echo of the echo0 light through the RF output conversion gain (30 × 103 V/W) of the balance detector. This light through the RF output conversion gain (30 103 V/W) of the balance detector. This optical power optical power was characterized by ab in Equation× (25). The local optical power characterized by b2/2 was characterized by ab in Equation (25). The local optical power characterized by b2/2 was detected was detected using an optical power meter. Finally, we obtained the optical power indicated by a2/2, using an optical power meter. Finally, we obtained the optical power indicated by a2/2, namely, the namely, the sensitivity. In our experiments, when the SNR dropped to 13 dB, the high peak value sensitivity. In our experiments, when the SNR dropped to 13 dB, the high peak value was about 15 V, was about 15 V, as shown in Figure 8. as shown in Figure8.

FigureFigure 8 8.. SensitivitySensitivity test test result. result.

Then, we calculated that the V0 was about 11.11 mV,and converted it to output optical power, obtaining 0.37 µW as characterized by ab. The local optical power after coupling loss was 0.4 mW, characterized by b2/2, which is directly detected by an optical power meter. According to the proportional relationship

 2  b 0.4 mW a2  2 → 86 pW (25)  ab 0.37 µW ⇒ 2 → → The sensitivity was determined to be approximately 86 pW.

4. Discussion Next, we will discuss the coupling effects of speed and distance. The Doppler shift makes it possible to measure velocity. At the same time, it introduces peak gain loss caused by frequency mismatch, since only the convolution of matching bandwidth between the echo and local chirp wave contributes to the high peak. We simulated the effects of the frequency mismatch. Figure9 shows the relationship between soutmax and fd. The abscissa represents Doppler shift, and the ordinate represents the compressed amplitude. Here, we set the amplitude of the chirp wave to be 1, and the maximum amplitude of peak of envelopes is 2700. As the velocity increases, the Doppler shift increases. The frequency of the inflection point is about half of the modulation bandwidth, at which point the peak drops to half of the maximum. As the Doppler shift increases, it accelerates to decrease before the inflection point and, after the inflection point, it decelerates to decrease. This relationship was computed under the condition that we multiplied the local RF chirp wave by the Hamming window and performed Hilbert transform to the Sinc pulse to obtain its envelopes. When the target moves faster, the Doppler shift is larger and the peak will decrease. When fd exceeds the bandwidth B, the frequency of the transmitted and received RF signals will not match at all. The peak will decrease to zero. For a slow-moving target, the Doppler shift introduces few effects, but for faster targets, these effects have to be considered. Sensors 2019, 19, x FOR PEER REVIEW 9 of 10

Then, we calculated that the V0 was about 11.11 mV, and converted it to output optical power, obtaining 0.37 µW as characterized by ab. The local optical power after coupling loss was 0.4 mW, characterized by b2/2, which is directly detected by an optical power meter. According to the proportional relationship

b2   0.4mW a2  2   86 pW (24)  2 ab  0.37uW

The sensitivity was determined to be approximately 86 pW.

4. Discussion Next, we will discuss the coupling effects of speed and distance. The Doppler shift makes it possible to measure velocity. At the same time, it introduces peak gain loss caused by frequency mismatch, since only the convolution of matching bandwidth between the echo and local chirp wave contributes to the high peak. We simulated the effects of the frequency mismatch. Figure 9 shows the relationshipSensors 2019, between19, 2313 s and f . 9 of 10 out max d

FigureFigure 9.9. The eeffectﬀect of of frequency frequency mismatch. mismatch.

5. Conclusions The abscissa represents Doppler shift, and the ordinate represents the compressed amplitude. Here, weIn this set paper,the amplitude we have demonstrated of the chirp a wave coherent to lidar be 1, system and the based maximum on chirp pulse amplitude compression of peak of envelopesthat measures is 2700. both As distance the velocity and velocity. increases, This the lidar Doppler can realize shift the increases. simultaneous The high-precision frequency of the inflectionmeasurement point is of about both distance half of andthe modulation velocity. The bandwidth, ranging accuracy at which is 22 cm,point and the the peak speed drops accuracy to half of is 1.066 cm/s. By optimizing the system, we have recently realized the distance measurement of a the maximum. As the Doppler shift increases, it accelerates to decrease before the inflection point white painted wall at 65 m, while the transmitted peak power was only 7 mW. This solution is still in and, after the inflection point, it decelerates to decrease. the experimental stage. We will then further optimize the system to detect farther targets and, after that,This this relationship solution could was be com usedputed in equipment under the working condition in real that conditions. we multiplied The effects the oflocal the frequencyRF chirp wave by themismatch Hamming have beenwindow discussed. and performed For fast-moving Hilbert targets, transform this impact to the must Sinc be pulse taken to into obtain consideration. its envelopes. When the target moves faster, the Doppler shift is larger and the peak will decrease. When Author Contributions: Conceptualization, J.Y., B.Z. and B.L.; methodology, J.Y.; software, J.Y.; formal analysis, J.Y.; exceedsinvestigation, the bandwidth J.Y., B.Z.; writing—original B, the frequency draft of preparation, the transmitted J.Y.; writing—review and received and RF editing, signals J.Y., will B.Z. andnot B.L. match at all. Funding:The peakThis will research decrease received to zero. no external For a funding.slow-moving target, the Doppler shift introduces few effects, but for faster targets, these effects have to be considered. Conflicts of Interest: The authors declare no conflict of interest.

5. ConclusionsReferences

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