Differential optical-path approach to improve signal-to-noise ratio of pulsed-laser range finding

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1 Diffeential optical-path appoach to impove signal-to-noise atio of pulsed-lase ange finding Qun Hao, * Jie Cao, Yao Hu, Yunyi Yang, Kun Li, and Tengfei Li School of Optoelectonics, Beijing Institute of Technology, Beijing, , China * qhao@bit.edu.cn Abstact: A pulsed-lase ange finding based on diffeential optical-path is poposed, and the mathematical models ae developed and veified. Based on the method, some simulations ae caied out and impotant conclusions ae deduced. (1) Backgound powe is suppessed effectively. () Compaed with signal-to-noise atio (SNR) of taditional method, SNR of the poposed method is moe suitable than taditional method in long-ange finding and lage tilt angle of taget. (3) No matte what the tilt angle of taget is, it always has optimal sensitivity of zeo coss as long as the diffeential distance is equal to the light speed multiplied by the eceived pulse length and thee is an ovelap between two echoes. 014 Optical Society of Ameica OCIS codes: ( ) Lase ange finde; ( ) Range finding; ( ) Lases, pulsed; ( ) Avalanche photodiodes (APDs). Refeences and links 1. R. D. Richmond and S. C. Cain, in Diect-detection LADAR Systems (SPIE, 010).. G. Bekovic and E. Shafi, Optical methods fo distance and displacement measuements, Adv. Opt. Photonics 4(4), (01). 3. B. Schwaz, Mapping the wold in 3D, Nat. Photonics 4(7), (010). 4. P. F. McManamon, Eata: Review of lada: a histoic, yet emeging, senso technology with ich phenomenology, Opt. Eng. 51(6), (01). 5. M. Fidlund, Futue space missions to seach fo teestial planets, Space Sci. Rev. 135(1-4), (008). 6. B. Kaldvee, A. Ehn, J. Bood, and M. Aldén, Development of a picosecond lida system fo lage-scale combustion diagnostics, Appl. Opt. 48(4), B65 B7 (009). 7. J. Yun, C. Gao, S. Zhu, C. Sun, H. He, L. Feng, L. Dong, and L. Niu, High-peak-powe, single-mode, nanosecond pulsed, all-fibe lase fo high esolution 3D imaging LIDAR system, Chin. Opt. Lett. 10(1), 1140 (01). 8. A. McCathy, R. J. Collins, N. J. Kichel, V. Fenández, A. M. Wallace, and G. S. Bulle, Long-ange time-offlight scanning senso based on high-speed time-coelated single-photon counting, Appl. Opt. 48(3), (009). 9. S. Pellegini, G. S. Bulle, J. M. Smith, A. M. Wallace, and S. Cova, Lase-based distance measuement using picosecond esolution time-coelated single-photon counting, Meas. Sci. Technol. 11(6), (000). 10. S. Kutti and J. Kostamovaaa, An integated eceive channel fo a lase scanne, in Poceedings of IEEE Confeence on Instumentation and Measuement Technology (Congess Gaz, Gaz, Austia, 01), pp H. Lim, Compaison of time coections using chage amounts, peak values, slew ates, and signal widths in leading-edge disciminatos, Rev. Sci. Instum. 74, (003). 1. M. Lee and S. Baeg, Advanced compact 3D lida using a high speed fibe coupled pulsed lase diode and a high accuacy timing discimination eadout cicuit, Poc. SPIE 8379, 83790Z (01). 13. S. Mitchell, J. P. Thaye, and M. Hayman, Polaization lida fo shallow wate depth measuement, Appl. Opt. 49(36), (010). 14. T. R. Chevalie and O. K. Steinvall, Lase ada modeling fo simulation and pefomance evaluation, Poc. SPIE 748, (009). 15. H. J. Kong, T. H. Kim, S. E. Jo, and M. S. Oh, Smat thee-dimensional imaging LADAR using two Geigemode avalanche photodiodes, Opt. Expess 19(0), (011). 16. Y. Qin, T. T. Vu, Y. Ban, and Z. Niu, Range detemination fo geneating point clouds fom aibone small footpint LiDAR wavefoms, Opt. Expess 0(3), (01). 17. F. Wang, Y. Zhao, Y. Zhang, and X. Sun, Range accuacy limitation of pulse anging systems based on Geige mode single-photon detectos, Appl. Opt. 49(9), (010). # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 563

2 18. R. Agishev, B. Goss, F. Moshay, A. Gileson, and S. Ahmed, Simple appoach to pedict APD/PMT lida detecto pefomance unde sky backgound using dimensionless paametization, Opt. Lases Eng. 44(8), (006). 19. Z. Zhang, Y. Zhao, Y. Zhang, L. Wu, and J. Su, A eal-time noise filteing stategy fo photon counting 3D imaging lida, Opt. Expess 1(8), (013). 0. J. Yang, L. Qiu, W. Zhao, and H. Wu, Lase diffeential eflection-confocal focal-length measuement, Opt. Expess 0(3), (01). 1. S. De, B. Redman, and R. Chellappa, Simulation of eo in optical ada ange measuements, Appl. Opt. 36(7), (1997).. S. E. Johnson, Effect of taget suface oientation on the ange pecision of lase detection and anging systems, J. Appl. Remote Sens. 3(1), (009). 3. T. Ishii, K. Otani, T. Takashima, and Y. Xue, Sola spectal influence on the pefomance of photovoltaic (PV) modules unde fine weathe and cloudy weathe conditions, Pog. Photovolt. Res. Appl. 1, (011). 4. M. Jack, J. Wehne, J. Edwads, G. Chapman, D. N. Hall, and S. M. Jacobson, HgCdTe APD-based lineamode photon counting components and Lada eceives, Poc. SPIE 8033, 80330M (011). 1. Intoduction Pulsed-lase ange finding is an active emote sensing technique. The taget is illuminated by shot pulse emitted fom a pulsed-lase souce, and the distance is obtained by calculating time of flight (TOF) of echo fom taget. Supposing the light speed is c, and the ound-tip time is t, the distance can be obtained with R = ct/ [1, ]. Since this method has advantages of simplicity, high accuacy and utility, it is widely used in the fields of both militay and civilian [3 5]. Lase souce with shot pulse duation of nanosecond, picosecond o even femtosecond incease the ange finding accuacy geatly [6 9]. The key of acquiing TOF is disciminating the exact aival time of the echo pulse. Some methods have been used in acquiing TOF. Leading edge disciminato (LED) is a simple appoach, and the leading edge of the eceived pulse is detected as the signal cosses a cetain theshold. LED is easy to cay out because of its simple electical stuctue, but it poduces lage walk eo of a few of nanosecond [10]. Hansang Lim et al used fou kinds of amplitude paametes, including slew ates, peak values, signal widths, as well as chage amounts [11], to coect time eo in the leading edge disciminato espectively. Constant faction disciminato (CFD) is used to enhance timing accuacy, and it educes the walk eo to less than picosecond [1, 13]. Peak disciminato is an appoach to decease walk eo, but the disadvantage of this method is that echo is easily affected by both backgound powe and tagets tilt angle, which esults into poo pefomance in the condition of low SNR [14]. Recently, Hong Jin Kong et al poposed a method using two Geige-mode avalanche photodiodes (GmAPD) to ealize acquisition of TOF. The echo was divided into two beams by splitte and aival time of the electical signals fom the GmAPDs wee compaed. Though intensity of echo is deceased by half, the false alam was deceased and detection pobability was inceased because the noise was filteed out [15]. Actually, the souces of noise of ange finding include speckle, themal and backgound, etc. Among of them, backgound powe is pime noise fo long ang detecting and exists in most of optical system [16 18]. Meanwhile, it is constant and does not change with time. Othe noises distibute andomly [19]. In geneal, the method of diffeential optical-path has the ability to suppess backgound powe. The method uses two eceiving channels, of which one is efeence channel, and the othe is signal channel. Backgound powe is suppessed by subtacting them. Fo example, the stuctue of diffeential optical-path suppesses commonmode noise and impoves measuement accuacy of the confocal micoscopy [0]. In ode to suppess backgound powe and incease SNR of pulsed-lase ange finding, a method based on diffeential optical-path is poposed. The pinciple and theoetical analysis ae illustated in Section. Simulations based on the method ae caied out in section 3. Conclusions ae listed in the last section, which suggest the poposed pulsed-lase ange finding can suppess backgound powe and gain high SNR at long ange. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 564

3 . Methods and mateials.1 Pinciple The system based on diffeential optical-path is shown as Fig. 1. A shot pulse is tiggeed by field pogammable gate aay (FPGA) and collimated by TL. Then, the pulse is divided into two pats by beam splitte BS1. One is focused by CL and detected by PD, which geneates the electical stat signal. The othe is used to illuminate the taget. The scatteed o eflected light fom the taget is eflected by BS1 and divided into two beams by BS. Thee ae two same eceives consisting of an APD and the coesponding lens RL, espectively. APD A is illuminated by eflected light fom BS and RL1, and geneates echo signal P. Similaly, APD B geneates echo signal P 1. The diffeential echo signal P -P 1 is obtained by subtaction in FPGA. The diffeential echo signal has a point of zeo powe, i.e. zeo coss, and it is set as the stop signal. TOF is detemined between the stat and stop signal. The tempoal change ate of the powe at the zeo coss in the diffeential echo signal is defined as the sensitivity of zeo coss. It can be changed by adjusting diffeential distance between optical-path OA and OB. FPGA contols the stage using SC to change diffeential distance until the system acquie highest sensitivity of zeo coss. Supposing the distance between BS1 and CL is l 0, the distance between BS1 and BS is l 1, the distance between BS and RLA is l, the distance between BS and RLB is l 3, diffeential distance between OA and OB is d. The positions of two eceives can be descibed as l1 l l0 d. l1 l3 l0 d (1) PD CL Tigge Lase TL BS1 Ai FPGA Position B APD B B O BS Taget - + P 1 P SC1 RL B A RL A Position A APD A SC Fig. 1. Pulsed-lase ange finding system stuctue based on diffeential optical path. BS-beam splitte, TL-tansmitting lens, RL-eceiving lens, PD-photo detecto, APD-avalanche photo diode, CL-convegent lens, SC- stage contolle. Figue shows the diffeence of echo signal between poposed method based on diffeential optical path and peak disciminato. On the left side is the stat signal fom PD. The peak is easy to detect because of the high intensity and low backgound powe, so it is set as the stat timing moment. Taditional system includes only a single APD. In the long-ange measuement, peak position of the echo is difficult to disciminate because of the backgound powe and echo boadening. Meanwhile, the tempoal change ate of echo powe nea the peak is vey small, i.e. the sensitivity nea peak is vey low, which inceases the difficulty of disciminating peak position. Diffeent fom peak disciminato, diffeential optical-path # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 565

4 method uses two APDs. Two eceives ae moved by a distance of d symmetically nea o fa fom BS. Compaed with taditional method, although echo powe is educed by half in each detecto, the backgound powe can be suppessed by subtacting between two echo signals, Meanwhile, thee is a zeo coss in the diffeential echo signal and the sensitivity of zeo coss is obviously highe than that of the peak in the oiginal echo signal. I Stat t 0 =R/c Stop taditional method poposed method P (APD A) P P 1 (APD B) 0 Stop t P d =P -P 1. Echo analysis Fig.. Diffeence between diffeential echo and echo of peak disciminato. Schematic diagam of lase ange finding is shown in Fig. 3, left side is an system of tansmitte and eceive, and ight side is a taget plane, which has a tilt angle of θ. R is the ange between the system and the taget. Lase pulse is with a tempoal function of Gaussian model, which is witten as [1] t P t E t exp, t whee E t is the oiginal pulse enegy, τ is tansmitting pulse width. Taditional eceive includes a single detecto and echo signal powe expession is witten as [1, 0] X () Tansmitte /Receive O Z R Y Fig. 3. Schematic diagam of pulsed-lase ange finding. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 566

5 EtTa ToD 1 R P t exp t c tan w z, c z wz w0 1 w0 whee P (t) is the eceived powe on the detecto, T a is the one way atmospheic tansmission, T o is the eceive optics tansmission efficiency, η D is quantum efficiency, ρ is the eflectance of the taget, τ is the eceived pulse width, w 0 is the waist adius of the lase, w(z) is the beam adius, and λ is the wavelength. Accoding to Fig. 1, Eqs. (1) and (3), the echo signal powe expessions of APD A and APD B ae witten as EtTa ToD 1 R d P 1 t exp t c. (4) EtTa ToD 1 R d P t exp t c Equation (3) is unde the ideal condition with no effects of backgound powe. In fact, the backgound powe should be concened in the system, especially in the long-ange measuement. The backgound powe is witten as [1, 1] B sun o P h T A sin /, (5) whee ρ is the eflectance of taget, hsun is the backgound sola iadiance, A is the aea of the eceive, α is the field of view, and λ is the optical bandwidth. Accoding to Eq. (5), P B is constant and does not change with time. The echo signal powe fom APD A and APD B with backgound powe ae descibed as following. EtTa ToD 1 R d B1 exp c P t t PB, EtTa ToD 1 R d PB t exp t P B c The diffeential echo powe is obtained by subtaction and is witten as P t P t P t d B B1 EtTa ToD 1 R d 1 R d exp t exp t, c c Equation (7) shows that the backgound powe can be suppessed by using the stuctue of diffeential optical-path. Futhemoe, at the zeo cossing tempoal point when P d = 0, we can obtain Eq. (8), which demonstates that the TOF of zeo coss is the same as peak disciminato. (3) (6) (7) # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 567

6 .3 Sensitivity of zeo coss R d R d R t t t. c c c Sensitivity of zeo coss k d = dp d (t)/dt is defined as the tempoal change ate of echo powe at zeo coss, and it is witten as k d EtTa ToD u u u 1 u 1 exp exp, whee k d is sensitivity of zeo coss, u 1 = t-[(r-d)/c], u = t-[(r + d)/c] and othe symbols ae descibed above. In ode to obtain the cossing point of the tailing edge and the leading edge of echo signals, the diffeential distance should be less than 8log() c [0], i.e. thee is an ovelap between two echoes. When t = R/c, the sensitivity of zeo coss is d 1 d EtTa ToD kd exp. t R/ c (10) c c Denoting f = k d t = R/c, we can obtain Eq. (11) fo the deivative tem d fom Eq. (10). EtTa ToD 1 1 d d 1 d d 1 f ' d exp exp. (11) c c c c c c The highest sensitivity of zeo coss is deduced by f d = 0, yielding d c. (1) The highest sensitivity of zeo coss is acquied when d = cτ, and the diffeential distance should be changed with τ which esults fom tilt angle of taget []. Theefoe, stage is used to adjust the position of the eceives to meet Eq. (1) in diffeent conditions. Accoding to analysis above, the method based on diffeential optical-path has two notable advantages. (1) Backgound powe is suppessed because of the subtaction of two echo signals. () The sensitivity of zeo coss is much highe than that of the peak. The poposed method tansfoms disciminating time of peak into detecting zeo coss...4 SNR analysis SNR is one of most impotant paametes since it affects the measuement ange and accuacy. Unde the same conditions of tansmitting system and taget, the ange and accuacy of system incease with impovement of SNR. SNR of taditional method is witten as [4] SNR D P D P eb D P DPB eb idk 4 ktb / R n TH D P h f B hf P PB e i DK e D 4kT R whee ρ D is the detecto cuent esponsivity, ρ D = η D e/hf, <P > is effective value, i.e. oot mean squae (RMS) of the echo powe at the detecto, <σ n > is RMS of total noise, B is the eceive bandwidth, h is the Planck s constant, f = c/λ is the fequency of the eceived signal, e is the electon chage, <i DK > is RMS of the dak cuent of detecto, k is the Boltzmann s TH, (8) (9) (13) # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 568

7 constant, T is the tempeatue in Kelvin, and <R TH > is RMS of the effective load esistance that ceates the same themal noise spectal density as the eceive electonics. The backgound powe P B is constant and suppessed by subtacting the two echoes. Theefoe, the total noise of system based on diffeential optical-path can be witten as 1 1 eb P eb i i 4kTB R R nd D d DK1 DK TH1 TH 1 1 B ed Pd e idk1 idk kt, RTH 1 R TH Accoding to the definition of SNR, the method based on diffeential optical-path can be witten as SNR 3. Simulations and esults d 3.1 System model veification D Pd h f 1 1 B hf P e i i kt d DK1 DK e D RTH 1 RTH (14). (15) Accoding to echo analysis discussed above, in long-ange finding system, echo of taditional method is mainly affected by backgound powe. Accoding to paametes of typical anging finding and taget, simulation paametes ae set as following: E t = 0.4nJ, ρ = 0.5, T o = 0.8, η D = 0.6, τ = ps, d = 50mm, θ = 10, 0, 30, 40, d = 50mm, h sun = 500W/m /μm (λ = 905nm) [3], α = 5, λ = 10nm, R = 18km, 19km, 0km, 1km. T a is difficult to detemine because of the complex envionment conditions. In ode to simple the question, the appoximate elation among γ(λ), visibility and λ is used in the simulation, shown in Eq. (16), whee R v is visibility, q is coection facto which is depended on diffeent visibility, shown in Table 1. R v = 10km is chosen in the simulation q R v (16) Table 1. Coection Facto unde Diffeent Visibility visibility (R v) coection facto (q) R v>50km q = 1.6 R v = 10km q = 1.3 R v<6km 1 3 q 0.085R v In ode to illustate conditions that echo signal is affected by backgound powe and veify model, accoding to the conditions set above, the esults ae shown in Fig. 4. Figue 4 shows the echo powe and backgound powe at diffeent ange diectly. In the conditions of 18km and 19km, shown in Fig. 4(a) and 4(b), the echo signal powe is highe than backgound powe. Theefoe, signal may be distinguished and peak position can be detected with peak disciminato coectly. Howeve, when echo signal powe is lowe than backgound powe, shown in Fig. 4(c) and 4(d), it is had to detect peak of echo signal. Fo such situations, the method of diffeential optic-path is vey useful because backgound powe is suppessed, as shown in Fig. 5. Figue 5(a) and 5(b), coesponding to Fig. 4(c) and 4(d) espectively, ae diffeential echo signals obtained by subtacting echo signal of APD A and APD B. Backgound powe is suppessed and peak detection is tansfom into zeo coss. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 569

8 (a) (b) (c) (d) Fig. 4. Compaison between backgound powe and echo signal powe. (a) is unde the condition that ange is 18km. (b) is unde the condition that ange is 19km. (c) is unde the condition that ange is 0km. (d) is unde the condition that ange is 1km. (a) (b) Fig. 5. Diffeential echo signal at diffeent anges. (a) Range between system and taget is 0km. (b) Range between system and taget is 1km. Figue 6 shows compaison between echo signal fom single detecto and diffeential echo signal at diffeent ange, unde the conditions that the ange is 0km and tilt angle of taget ae θ = 10, 0, 30, 40. In the taditional method, as shown in the Fig. 6(a), echo is boadened because of the tilt angle of taget. Echo boadening inceases with the gowth of tilt angle. Fo instance, with tilt angle of taget changing fom 10 to 40, eceiving echo width is boadened fom 3ns to 16ns. Echo boadening and low peak sensitivity may lead to geate eo in peak position detection. Compaed with taditional method, diffeential echo signal unde the same condition is shown in the Fig. 6(b). It is clea that no matte what the angle of taget is, the position of zeo coss is not affected by pulse boadening. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 570

9 (a) (b) Fig. 6. Compaision of echo signal unde diffeent tilt angle of taget. (a) The echo pulse is boadened with gowth of tilt angle. (b) The position of the zeo coss is not affected by pulse boadening. 3. Zeo cossing sensitivity affected by diffeential distance Based on analysis on sensitivity of zeo coss and diffeential distance, some simulations ae caied out unde the condition that taget is R = 0km, θ = 10 and othe paametes unchanged. The esults is shown in Fig. 7, fom 7(a) to 7(d) ae the diffeential echo signals fom APD A and APD B unde the condition of d = cτ /3, cτ /, cτ, 3cτ. Accoding to Fig. 7, we can find: (1) Thee is a zeo coss in diffeential echo signal; () The elative positions of echo signal fom APD A and APD B ae changed with diffeent diffeential distances, which esults in diffeent sensitivity of zeo coss. (a) (b) 1 d c 3 (c) 1 d c (d) d c d 3c Fig. 7. Echo signals fom APD A, APD B and diffeential echo signal unde the diffeent diffeential distance. (a) Diffeential distance is cτ /3. (b) Diffeential distance is cτ /. (c) Diffeential distance is cτ. (d) Diffeential distance is 3cτ. In ode to quantify the sensitivity of zeo coss k d affected by diffeential distance d, the elation between sensitivity and diffeential distance is simulated. Unde the conditions of d = cτ /3, cτ /, cτ, 8log() c, and 3cτ, the coesponding diffeential distance ae 0.34m, 0.51m, 1.0m,.4m, and 3.06m, espectively. The esults ae shown in Fig. 8 in which five diffeential echo signals ae acquied. It is clea that sensitivity of zeo cossing is diffeent because of diffeent diffeential distance. Fo example, k d is 410.5W/s unde the # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 571

10 condition that d is cτ /, and k d is 564.3W/s unde the condition that d = cτ. Accoding to analysis above, the diffeential distance should be less than 8log() c to ealize the cossing point of the tailing edge and the leading edge of echo signals. If d is lage than that value, the slop of zeo coss decease quickly. Fo instance, unde the condition of d = 3cτ, shown in Fig. 8, sensitivity of zeo coss k d is low and is only 31W/s. d c d c d c d d /3 / 8log 3c c Time/ μs Fig. 8. Diffeential echoes at diffeent diffeential distance. Figue 9 shows the elation between sensitivity of zeo coss and diffeential distance. We can find: (1) with the incease of diffeential distance, the tend of sensitivity of zeo coss fist inceases and then deceases. Meanwhile, keeping the diffeential distance unchanged, zeo cossing sensitivity deceases as the tilt angle of taget inceases. Fo example, holding d = cτ, k d is 564.3W/s unde the condition of θ = 10. As θ is 30, k d deceases to 5.6W/s. () Thee is an optimal diffeential distance, i.e. d = cτ. No matte what the tilt angle of taget is, the optimal diffeential distance is still satisfying d = cτ. As shown in Fig. 9, unde diffeent tilt angle (10, 0, 30, 40 ), cτ is 1.0m,.1m, 3.33m, 4.83m, espectively. Although the sensitivity of zeo coss is diffeent, the position of highest sensitivity is always cτ, which help to keep the system obtain highest sensitivity of zeo coss. (1.0,564.3) / (W / s) k d (.1,13.4) (3.33,5.6) (4.83,5) d /m Fig. 9. Relation between sensitivity of zeo cossing and diffeential distance. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 57

11 3.3 SNR compaison Many factos affect SNR, including the featues of detectos, tansmitting o eceiving lens and noise souce. Meanwhile, the intensity of echo signal is elated to the ange, tilt angle and eflectance of taget. Theefoe, it is difficult to conside so many conditions at the same time. Usually, fo a ange finding system, the paametes of taget ae unknown, and paametes of system ae given. Theefoe, unknown paametes can be seen as vaiant, such as ange and angle of taget, and designed systematic paametes ae kept as constant, such as the optical o electical paametes of tansmitting o eceiving system. The typical paametes ae set as following: R = 1km~5km, θ = 0 ~50, <i DK > = <i DK1 > = <i DK > = 10pA [4], <R TH > = <R TH1 > = <R TH > = 10kΩ, h = Js, e = C, B = 1GHz. The esults of SNR of taditional and poposed method ae shown in the Fig. 10(a) and 10(b) espectively. The data can be analyzed fom two aspects: fixing ange and changing angle, fixing angle and changing ange. Fist, setting ange unchanged (R = 10km) and θ inceasing fom 10 to 50, shown in Fig. 10(a), SNR deceases fom 185.4dB to 15.9dB. Unde the same situation, SNR of poposed method, shown in the Fig. 10(b), deceases fom 19.dB to 7.6dB. Second, setting angle unchanged (θ = 40 ), SNR of taditional method deceases fom 187dB to 6.7dB with the incease of ange fom 0.1km to 4km, while SNR of the poposed method deceases fom 198dB to 39.7dB. SNR / db SNR d / db R /m (a) / degee R /m (b) / degee Fig. 10. Compaison of SNR between the taditional method and the poposed method. (a) Relation between SNR, ange and tilt angle in the taditional method. (b) Relation between SNR, ange and tilt angle in the poposed method. In ode to compae the SNR of two methods clealy, elative incement pecentage of SNR is used, i.e. SNR = [(SNR d -SNR)/SNR] 100%. The esult is shown in Fig. 11, in which SNR is gowing with the incease of ange and angle of taget, especially in the conditions of long ange o lage tilted angle of taget. Taking θ = 50 as an example, the ange of the taget is fom 0.1km to 4km, and SNR inceases fom 3.6% to 317.1%. Unde the condition that R is 4km, SNR inceases fom.3% to 317.1% as θ changes fom 0 to 50. Accoding to analysis above, although SNR of two methods decease with the incease of the ange and angle, the SNR of diffeential optical-path is bette than that of the taditional method, especially in long ange finding. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 573

12 SNR /% R /m / degee 4. Discussion Fig. 11. Relationship between SNR and R, θ. The system based on diffeential optical-path tansfoms peak position into zeo-cossing. Howeve, the position of zeo-cossing can t coespond to peak position pecisely due to inconsistent beam of splitting atio, diffeence of photo detectos, and diffeence of optical alignment in the two paths. An example is shown in Fig. 1, the echo of P is stonge than P 1, so the zeo-cossing position deviates fom t 1 to t, and t is the amount of deviation. Actually, the system should be calibated both of the inconsistence of the two eceives and system eos befoe use. P P P 1 P -P 1 t 1 t t t 4.1 Calibating consistence of two eceives Fig. 1. Deviation of zeo-cossing fom peak position. The key of deviation is the diffeent amplitude of echo signals fom two eceives. Theefoe, gain contol cicuit (GCC) is used in the system, shown in Fig. 13. Fist, a unifom diffuse eflecto is placed in font of the system as the taget. Second, diffeential distance is located pecisely by pecision stage. Meanwhile, amplitude of the echo signals fom two eceives can be obtained. Thid, the gain of detectos ae adjusted by GCC until the two echo signals ae the same. The calibation of two eceives is finished. Accoding to the pocess, the eo esulting fom diffeent echo signal amplitude is avoided. # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 574

13 Lase TL BS1 Position B APD B P 1 Gain contol cicuit B O A BS RL A Unifom diffuse eflecto Position A Gain contol cicuit APD A P 4. Calibating systematic eo Fig. 13. Pincipal of calibating inconsistence of two eceives. Systematic eos include delay of inne optical-path, delayed-esponse of stat signal and stop signal, etc., should be calibated. Fistly, put a taget plane in font of the system and the ange R 0 is measued by anothe ange finde with highe accuacy than the system based on diffeential optical-path. Secondly, accoding to the nominal ange of taget R 0, the time-offlight (TOF) is obtain by t = R 0 /c. Meanwhile, the system based on diffeential optical-path acquies the TOF t. Finally, the system eo can be calculated by t - t, and calibation of system eo is finished. In egula wok condition, the system eo should be subtacted fom the TOF acquied by the system based on diffeential optical-path. 5. Conclusion In this pape, a novel pulsed-lase ange finding system based on diffeential optical-path is poposed, and the mathematical models ae developed and veified. Two eceives ae used to fom diffeential optical-path, and backgound powe is suppessed effectively by subtacting both echo signals. Meanwhile, the position of zeo coss is not affected by pulse boadening. Based on the poposed system, some simulations ae caied out, including modeling veification, factos affecting sensitivity of zeo coss, compaison of SNR between two methods. Some conclusions ae achieved. (1) The model based on diffeential optical-path is veified, in which peak discimination tansfom into detecting zeo coss. () Effects fom backgound powe can be suppessed. (3) Zeo coss is not affected by echo boadening. (4) Compaed with the SNR of two methods, poposed method is moe suitable than taditional method in long-ange finding and lage tilt angle of taget. (5) No matte what the tilt angle of taget is, it always has optimal sensitivity of zeo coss as long as d = cτ and thee is an ovelap between two echoes. Acknowledgments This eseach was suppoted by the gant fom the National Natual Science Foundation of China (No and No ), Reseach Fund fo the Doctoal Pogam of Highe Education of China ( ). # $15.00 USD Received 11 Nov 013; evised 13 Dec 013; accepted 16 Dec 013; published 3 Jan 014 (C) 014 OSA 13 Januay 014 Vol., No. 1 DOI: /OE OPTICS EXPRESS 575