Homodyne laser radar system for surface displacement monitoring

Homodyne laser radar system for surface displacement monitoring Alejandro Rodriguez, MEMBER SPIE Adolfo Comeron, MEMBER SPIE David Garcia Universitat Polite `cnica de Catalunya (UPC) Electromagnetics and Photonics Engineering Group Departament de Teoria del Senyal i Comunicacions Campus Nord UPC, Edifici D-4 C/Jordi Girona, 1-3 08034 Barcelona, Spain Abstract. A prototype of a homodyne laser radar system for surface displacement monitoring using the reference beam technique is presented. The prototype is very simple, is easy to align and focus, and is able to measure the velocity of the surface displacement at distances up to 16 m. We present an optical analysis of the prototype, a power budget, a criterion on tolerance in distance and laboratory measurements. © 2001 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.1347031] Subject terms: laser radar; homodyne; optical mixing; velocity measurement; surface displacement measurement; HeNe laser; avalanche photodiode; Doppler shift; coherence. Paper 200058 received Feb. 21, 2000; revised manuscript received Sep. 11, 2000; accepted for publication Sep. 25, 2000. 1 Introduction Coherent laser radar systems can be used to monitor the speed of moving surfaces. Although systems based on a differential technique 共namely, laser Doppler velocimeters1兲can measure components of the velocity vector, they do not provide good performance figures at distances over a few centimeters. Some homodyne systems have been proposed in the literature. Rudd2presented a homodyne prototype that used a single HeNe laser source as transmitter, a local oscillator 共reference beam兲and a mixer, but this system 共as shown formally by Potter3兲cannot measure Doppler shifts greater than 1 MHz for targets located at distances farther than about 1 m. Churnside proposed a similar system 共meticulously studied in his papers4,5兲based on a CO2laser. Some authors 共see, for instance, Refs. 6 and 7兲have reported systems based on laser diodes that perform the mixing on the same source. The results presented are promising, but the short coherence length of the light produced by actual laser diodes still limits their performance. In this paper, we present a homodyne coherent laser radar system, based on a HeNe laser, that measures Doppler shifts up to ⬃93MHz when a laboratory target is placed at distances ranging from 1 to 16 m. In this system, the mixing takes place on the active surface of an avalanche photodiode 共APD兲, so it does not have the limitations of the system proposed by Rudd.2In Section 2 the prototype built is described and the theory of operation is explained. Section 3 is devoted to the optical analysis of the prototype. Section 4 presents a power budget and proposes a criterion concerning the tolerance in the distance adjustment of such a system. Section 5 describes some experimental results. 2 Prototype Description and Theory of Operation The prototype developed is shown in Fig. 1 共Refs. 8 and 9兲. A Siemens LGK7627 HeNe laser is employed as the transmitter and local oscillator source and an Analog Modules 713-4 APD/transimpedance amplifier set is used as the photoreceiver. A homemade beamsplitter and two general purpose lenses 共with focal lengths 1 and 15 cm兲are used as the transmitting/receiving/mixing 共Tx/Rx/Mx兲optics. The components are fixed on an optical board. The transmitted beam is expanded and then focused on the target, using the telescope formed by the two lenses. The distance d3, where the beam waist lays, can be controlled by changing the separation d1between the laser and lens 1, with the overall distance Dbetween the laser and lens 2 a constant. The target scatters some of the incident light, which has been frequency-shifted by the Doppler effect. The frequency shift can be written: ⌬fD⫽2vr ␭,共1兲 where ␭is the wavelength of the light produced by the laser 共633 nm兲. Part of the scattered light is collected by the Tx/Rx/Mx optics and directed to the laser output mirror, where it is reflected. Approximately 5% of both the received signal and transmitted beam 共which plays the role of the local oscillator, LO兲powers are reflected by the beamsplitter and impinge on the APD active area. In this way, the interference between the LO beam and the received light can be detected and amplified. The resulting voltage vDopp(t), called the Doppler signal from here on, has a dc component due to the average incident light power and an ac component due to the interference between the LO and the received light. It can be written as1 vDopp共t兲⫽ ␳ v2共 ␩ hetPLOPRx兲1/2 cos共2 ␲ ⌬fDt⫹ ␹ 兲,共2兲 where ␳ vis the voltage responsivity 共in volts per watt兲of the photoreceiver; ␩ het is the so-called heterodyne efficiency,10,11 PLO and PRx are the local-oscillator and received-signal powers, respectively; and ␹ is an unknown phase. 398 Opt. Eng. 40(3) 398–405 (March 2001) 0091-3286/2001/$15.00 © 2001 Society of Photo-Optical Instrumentation Engineers This mixing mechanism is different from the modulation of the laser proposed by Rudd2and Churnside,4,5 but was suggested by the latter in his paper. It overcomes the limitation in bandwidth for a HeNe laser interferometer described by Potter,3because the mixing takes place outside the laser, on the active surface of the photodetector. The prototype also presents a self-aligned configuration that makes the backpropagated local oscillator12 beam to coincide with the transmitted beam, for mixing process optimization. 3 Optical Analysis 3.1 Transmitted Beam and Backpropagated Local Oscillator As the transmitted beam and the backpropagated local oscillator12 beam coincide, both can be modeled by the same equations. The optical analysis presented here is based on the Gaussian beam formalism.13,14 As shown in Fig. 2, the laser output beam can be characterized by its q-parameter q1, which depends on distance z1. The output beam of the Tx/Rx/Mx optics is characterized also by its parameter q3(z3). The value of q3at the output of the optics q3(0) can be related to the q1parameter at the input of the optics q1(d1) by the following expression: q3共0兲⫽Aq1共d1兲⫹B Cq1共d1兲⫹D,共3兲 where A,B,Cand Dare the ABCD parameters of the Tx/Rx/Mx optics.13,14 These parameters can be calculated in a matrix notation: 冋 AB CD 册 ⫽ 冋 A2B2 C2D2 册 ⫻ 冋 1d2 01 册 ⫻ 冋 A1B1 C1D1 册 ,共4兲 where d2is the distance between the two lenses, and 冋 AiBi CiDi 册 is the ABCD matrix of lens i. In order to achieve a good spatial coherence of the light scattered by the target, the size of the transmitted beam at its position must be minimum. The condition that the output beam has a waist at the target position d3is imposed as follows: Re 兵 q3共0兲 其 ⫽⫺d3.共5兲 As the Ddistance is a constant 共only distance d1is changed兲we can also add another equation: d1⫹d2⫽D.共6兲 The result of combining Eqs. 共5兲and 共6兲is a fourth-order polynomial in d1as a function of d3. The values of d1to have the waist of the transmitted beam at a distance d3of lens 2 in a range between 0 and 30 m vary from 8 to 24 cm. In Figs. 3共a兲and 3共b兲we present two derived magnitudes of the Tx/Rx/Mx optics output beam, the spot diameter at the target surface and the convergence angle, which is used in the following study. 3.2 Temporal Coherence Considerations: Transmitted Signal Two possible causes of temporal coherence loss can be identified in the laser source: the presence of multiple longitudinal modes and the spectral width of any of these modes. The presence of multiple longitudinal modes usually limits the temporal coherence in other interference based techniques 共such as laser Doppler velocimetry1or holography15兲to approximately twice the length of the laser cavity. Nevertheless, in systems that perform a spectral analysis of the detected signal this limitation can be overcome. Figure 4 shows the resulting spectrum of the electrical signal obtained. A spectral peak appears at the Doppler frequency ⌬fD, but some more peaks can be seen at n⌬fM⫾k⌬fD, where ⌬fMis the frequency difference between longitudinal modes, and nand kare positive integers. Assuming a uniform power distribution among the NM different longitudinal modes in the laser, and considering that the different contributions to the peak at ⌬fDare uncorrelated,9a power loss of NMmust be considered, so Eq. 共2兲changes to: vDopp共t兲⫽ ␳ v 冑 NM 2共 ␩ hetPLOPRx兲1/2 cos共2 ␲ ⌬fDt⫹ ␹ 兲共7兲 Fig. 1 Prototype layout. Fig. 2 Prototype layout for optical analysis. Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 399Optical Engineering, Vol. 40 No. 3, March 2001 3.3 Temporal Coherence Considerations: Loss of Coherence of the Received Signal by Target Scattering The light incoherently scattered by the target is collected by the Tx/Rx/Mx optics. This light has been partially decorrelated by different mechanisms related to the scattering process. These mechanisms introduce a spectral broadening in the Doppler signal. They are identified in Figs. 5共a兲,5共b兲 and 5共c兲. Teich16 presented the first mechanism, loss due to the spatial decorrelation of the scatterers present on the target surface, and it is sketched in Fig. 5共a兲. According to Fig. 5共a兲, the maximum coherence time ␶ cof the light scattered by the target is: ␶ c⬇ ␦ v,共8兲 Fig. 4 Received Doppler signal spectrum. Fig. 3 (a) Diameter 2 w 0of the transmitted-beam waist as a function of distance d 3to target on which it is assumed to lie, and (b) convergence angle of transmitted beam 2 q 0as a function of distance d 3to the target on which the beam waist is assumed to lie. Fig. 5 (a) Spectral broadening due to loss of temporal coherence (loss due to the spatial decorrelation of the scatterers), (b) spectral broadening due to loss of temporal coherence (loss due to nonzero convergence angle), and (c) spectral broadening due to loss of temporal coherence (loss by spread of the scatterer linear velocities). Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 400 Optical Engineering, Vol. 40 No. 3, March 2001 where ␦ is the diameter of the laser spot on the target, and vis the target lineal speed. Considering that ␦ ⫽2w0/cos ␸ , the spectral broadening ⌬fscan be calculated as: ⌬fs⫽1 ␶ c⬇ vcos ␸ 2w0,共9兲 where vis the linear speed of the target in the incidence point, ␸ is the nominal incidence angle, and w0is the incident beam waist radius at 1/e2of its maximum illumination value. A second spectral broadening mechanism is due to the convergence angle of the transmitted beam, which makes the value of the incident angle ␸ not unique. This situation is presented in Fig. 5共b兲. The corresponding spectral broadening ⌬f ␪ 0, due to the incident angle range, can be written9 as: ⌬f ␪ 0⫽4v ␭cos ␸ sin ␪ 0⬇4v ␭ ␪ 0cos ␸ ⬇4v ␲ w0cos ␸ ,共10兲 where ␭is the laser wavelength, and ␪ 0is the beam convergence half angle that must be very small for the paraxial approximation applied to be valid.13,14 The third mechanism appears only when the illuminated spot on the target rotates with instantaneous angular speed Wand radius vector r. The nonnegligible size of the transmitted beam waist on the target encompasses a range of values of the longitudinal component of linear velocity, as presented in Fig. 5共c兲; which produces a spectral broadening in the Doppler signal. This rotating-target broadening ⌬frcan be calculated9as: ⌬fr⫽4⍀w0 ␭.共11兲 The three effects can be combined in a root mean square 共rms兲manner to obtain an overall spectral broadening9 ⌬frot : ⌬frot⫽共⌬fs 2⫹⌬f ␪ 0 2⫹⌬fr 2兲1/2 ⫽ 冋 cos2 ␸ 共 ␲ 2⫹64兲 4 ␲ 2w0 2v2⫹16w0 2 ␭2⍀2 册 1/2 .共12兲 3.4 Considerations on the Spatial Coherence of the Received Signal To mix efficiently with the local oscillator the received signal must show spatial coherence over a significant part of the receiving aperture. Due to the roughness of the target surface 共of the order of the carrier wavelength兲, the scattering must be considered as spatially incoherent. Nevertheless, the Van Cittert-Zernike theorem17 predicts a gain in coherence due to propagation. Let us consider the situation described in Fig. 6, in which the lidar system focuses the transmitted beam on the target surface. The illuminated spot on the target shows an intensity Gaussian distribution of radius w0at 1/e2from the maximum: I共r兲⫽I0exp关共2r2/w0 2兲兴,共13兲 where I0is the maximum intensity and ris the distance to the center of the spot. According to the Van Cittert-Zernike theorem, the modulus of the complex coherence factor at a distance z from the target can be calculated9as: 兩 ␮ 12共 ␳ 兲 兩 ⫽exp 再 ⫺ 冋 w0 2 8(␭z)2 ␳ 2 册 冎 .共14兲 This function falls to 1/e2for a value ␳ ⫽ ␳ c⫽4(␭z)/w0. We call ␳ cthe coherence radius of the backscattered light. It can be compared to the radius of the transmitted beam at the Tx/Rx/Mx optics output, W3(0): W3共0兲⫽␭z ␲ w0.共15兲 Thus, the coherence radius of the backscattered light at the optics output is 4 ␲ times greater than the transmitted beam radius. According to Ref. 11, we calculate the average receiving area as: 具 AR 典 ⫽共 兵 ␲ 关W3共0兲兴2 其 ⫺1⫹共 ␲␳ c 2兲⫺1兲⫺1.共16兲 Thus, in a focused system, according to the previous results concluding that ␳ cⰇW3(0), the receiving area is nearly equal to the transmitted beam section area at the Tx/Rx/Mx optics output. This means that we can assume very little loss due to loss of spatial coherence. Atmospheric turbulence must be considered as an additional mechanism of reducing effective receiving area. According to Hufnagel,18 for propagation through a homogeneously turbulent atmosphere the atmospheric coherence diameter r0can be calculated, for a spherical wave: r0⫽0.332 冉 ␭2 Cn 2R 冊 3/5 ,共17兲 Fig. 6 Illustration for the computation of the coherence area of the received signal. Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 401Optical Engineering, Vol. 40 No. 3, March 2001 where Cn 2is the so-called structure constant of the index of refraction,18 and Ris the propagation length. For a standard turbulence in open space, much stronger than that expected in a laboratory environment, we can consider Cn 2 ⬇10⫺15 m⫺2/3. For a propagation length R⬃20m, r0is greater than 1 m, much greater than any aperture considered on the system, specially the effective receiving aperture 具 AR 典 , whose diameter is around 1 cm. Thus, no reduction due to atmospheric turbulence is considered. 4 Power Budget and Tolerance in the Distance Adjustment 4.1 Signal and Noise Power Budget According to Eq. 共7兲, the average power of the Doppler signal depends on the voltage responsivity of the photoreceiver ␳ vthe number of longitudinal modes present in the laser light NM, the power of the local oscillator beam PLO and the average received light power 具 PRx 典 . In our experimental setup we used a beamsplitter with two reflecting sides, characterized by an average reflection coefficient rBS⫽0.05. So the local oscillator power can be calculated as: PLO⫽rBSPTLD,共18兲 where PTis the optical power transmitted by the laser, and LDis the power loss due to spilling of the local oscillator power over the APD active area when the latter is smaller than the local oscillator beam cross section. This loss can be calculated as: LD⫽dAPD 2 dLASER 2,共19兲 where dAPD is the APD diameter and dLASER the local oscillator beam diameter, equal to that of the laser output beam. The average power 具 PRx 典 of light backscattered by the target collected by the Tx/Rx/Mx optics and directed onto the active surface can be calculated through the expression: 具 PRx 典 ⫽ 具 AR 典 LD共1⫺2rBS兲2rBS ␴ 0PT ␲ R2,共20兲 where ␴ 0is the backscattering coefficient of the surface of the target and Ris the distance to the target. Expression 共7兲also includes a heterodyne efficiency term ␩ het . According to the earlier considerations, and based on the definition by Rye and Frehlich,11 this term is calculated as ␩ het⫽LD 2 具 AR 典 Lpol ARL ,共21兲 where ARL is the geometrical area of the receiving aperture, and Lpol is the loss due to the depolarization of the backscattered light 共not considered in Ref. 11兲; adopting a pessimistic criterion, we will consider Lpol⫽0.5. With this definition ␩ het varies with the distance to the target, with a typical value of ␩ het⫽0.4% being obtained. The main reason for this low value is the fact that the lens diameter is much larger than the BPLO diameter at the lens plane, which was deliberately chosen to avoid the truncation of the transmitted beam. This low value for ␩ het is compensated in the total power budget by an accordingly increased value of the received power PRx , according to Eq. 共7兲. We can consider that our photoreceiver works in a shotnoise limited regime, due to the high value of light arriving to the APD active surface. So we can calculate the rms noise voltage 具 vn 2 典 at the photoreceiver output through the expression19: 具 vn 2 典 ⫽2eGAPDFGZ ␳ vPLOBW, 共22兲 where eis the electron charge, GAPD is the avalanche gain of the APD, Fis the excess noise factor of the APD, GZis the transimpedance gain of the photoreceiver electronics, and BW is the electric bandwidth of the photoreceiver. 4.2 Criterion on Tolerance in the Distance Adjustment The system presented employs a beam focused onto the target surface, as shown in Fig. 6. If the distance to target is known within a certain tolerance, the performance of optical mixing can be reduced. In this subsection, we present a criterion9that enables us to calculate a maximum tolerance in distance for every situation. According to the Van Cittert-Zernike theorem, the coherence area of the light backscattered by an incoherent surface with Gaussian distributed illumination Acoh 共see Subsection 3.4兲is given by Acoh共w0,d3兲⫽ ␲␳ c 2⫽16 ␲ 冉 ␭d3 w0 冊 2 .共23兲 For our system, the value of w0is related to the characteristics of the transmitted Gaussian beam, and is given by: W3共d3,⌬z兲⫽w03共d3兲 再 1⫹ 冋 ⌬z z03共d3兲 册 2 冎 1/2 ,共24兲 where ⌬zis the distance from the beam waist, W3(d3,⌬z) is the radius of the transmitted beam at 1/e2of the maximum intensity, w03(d3) is the transmitted beam waist radius for a beam focused at a distance d3, and z03(d3) is the Rayleigh distance of the transmitted beam, which is the imaginary part of the q3parameter. The parameters z03 and w03 are related by the expression: z03共d3兲⫽ ␲ w03 2共d3兲 ␭.共25兲 According to the Van Cittert-Zernike17 theorem, as the distance ⌬zgrows, the target gets out of focus and the size of the light spot increases, which makes the coherence area smaller at a given distance of the scattering spot. A loss of detected signal can be associated to this loss in spatial coherence by means of the reduction of effective receiving Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 402 Optical Engineering, Vol. 40 No. 3, March 2001 area. To assess a maximum tolerance in the distance adjustment a loss in the detected Doppler signal equal to the loss in coherence area is assumed. The criterion of maximum tolerance in distance considers that the system must work with a minimum signal to noise ratio SNR⫽10dB, and can be written in the following way: Acoh共⌬z⫽0,d3兲 Acoh共⌬z,d3兲⭐SNR共d3兲 10 ,共26兲 where SNR(d3) is the SNR for a target that is situated at a known distance d3when the transmitted beam is perfectly focused on its surface. According to this criterion, the maximum tolerance in distance 兩 ⌬ztol 兩 for such a system can be calculated with the following expression9 兩 ⌬ztol 兩 ⭐z03共d3兲 冋 SNR共d3兲 10 ⫺1 册 1/2 ,共27兲 which will be valid only for those values of d3that allow a SNR(d3) equal to or greater than 10 dB. Of course, this is a pessimistic criterion because it considers that a reduction of the coherence area of the backscattered light results in a proportional reduction of Doppler signal. Nevertheless, it has proven to be very simple and describes quite reasonably the actual behavior of our experimental prototype. 5 Experimental Results To test the homodyne coherent laser radar system, a prototype has been built and tested. The following elements were used: 1. a Siemens model LGK 7627 laser transmitter with a wavelength of 632.8 nm, a typical output power of 10 mW, a spatial mode of TEM00, a beam size at 1/e2 intensity of 0.8 mm, and a longitudinal beam spacing of 438 MHz. 共Number of longitudinal modes was estimated to be 4.兲 2. an Analog Modules model 713-4 photoreceiver with a EG&G C30902E photodiode, a nominal responsivity at 632.8 nm of 60 A/W, a responsivity at 632.8 nm and 125 V of 7 A/W, and active area diameter of 0.5 mm, an electrical bandwidth of 200 to 250 MHz, and a transimpedance gain of 20 k⍀. The APD included in the photoreceiver has been biased at ⬃125V, thus reducing the avalanche gain, instead of its nominal value 230 V due to the high local oscillator power level. In fact, at its nominal bias, the high avalanche gain made that the C30902E could not dissipate the heat produced by the dc current induced by the local oscillator. The value of the rest of the parameters are as follows: Distance D⫽40cm, Lens1: focallength⫽1 cm, diameter⫽0.9cm, Lens2: focallength⫽15cm, diameter⫽5 cm. The laboratory target was a 25-cm-radius rotating disk made of PVC. Its cylindrical surface was enhanced using an aluminum plate covered in paper. We performed some measurements on the backscattering characteristics of the paper employed, which showed that it can be considered as a Lambertian scatterer, with a backscattering coefficient ␴ 0⫽0.775. The Doppler signal was observed in a general-purpose spectrum analyzer with a resolution bandwidth RBW ⫽100kHz. This adjustment proved to be the most adequate for the obtained electrical signal. Nevertheless, due to the spectrum broadening effects presented in Subsection 3.4, the spectral width of the observed signal is larger than the indicated RBW, and so the height of the spectral peak observed in the spectrum analyzer is slightly diminished. This reduction was considered in the calculations presented in Figs. 7共a兲and 8共a兲. Two series of measurements were performed, the first one with the disk rotating at approximately 400 rpm and the second one with an angular velocity of approximately 1300 rpm. In both series, we measured the Doppler signal power, its spectral width, and the noise level at the photoreceiver output. In the low-speed series, we also measured the tolerance in the distance adjustment of the system. When the target rotates at 400 rpm, the detected Doppler shift is 16 MHz for ␸ ⫽30deg, 23 MHz for ␸ ⫽45deg and 29 MHz for ␸ ⫽60deg, which coincide with the expected values. Figure 7共a兲shows the Doppler signal power and noise versus distance for the three different values of the incidence angle ␸ ; the Doppler signal power measurements show power values slightly lower than the calculations. The maximum working distance, defined with a criterion of a minimum SNR⫽10dB, when the spectrum analyser resolution bandwidth is RBW⫽100kHz, is 16 m for ␸ ⫽30 and 45 deg and 12 m for ␸ ⫽60deg. Figure 7共b兲shows the Doppler signal spectral width at ⫺10dB. The election of this definition of spectral width was made for practical measurement reasons 共specifically, good signal shape visibility兲and because the theoretical calculations were made on a 1/e2basis, which is approximately ⫺8.7dB. Good agreement can be found between practice and theory at distances greater than 2 m. Figure 7共c兲shows the measurements of tolerance in distance. Most of the measurements are better than theory, probably because of the pessimistic criterion used, and a general tendency of an initial growing, followed by a quick fall, predicted by the theory 共continuous curves兲, can be observed for the three series of measurements ( ␸ ⫽30, 45 and 60 deg兲. Some points, however, especially at the incidence angle of 30 deg, depart from the general trend likely due to problems in the target positioning. According to a criterion of nonzero tolerance in distance, the maximum working distance can be considered as ⬃16m for ␸ ⫽30 and 45 deg and 14 m for ␸ ⫽60deg. Figures 8共a兲and 8共b兲show, respectively, the Doppler signal power and spectral width for the target rotating at an angular speed of approximately 1300 rpm. The corresponding Doppler shifts measured are 54 MHz for ␸ ⫽30deg, 76 MHz for ␸ ⫽45deg and 93 MHz for ␸ ⫽60deg, corresponding with the theoretical values. Note that the signal power peak 关see Fig. 8共a兲兴 observed in the spectrum analyzer experiments experienced a slight fall due to the extra spectral widening, predicted by Eq. 共12兲. Due to this visibility reduction, the maximum working range falls to approximately 12 m. Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 403Optical Engineering, Vol. 40 No. 3, March 2001 The measured spectral widths 关see Fig. 8共b兲兴 correlate acceptably to the calculated values. 6 Conclusions A very simple system that enables us to perform Doppler measurements of the velocity of hard targets was presented. Few optical elements, common nonexpensive electro-optic components and auto aligning are its main advantages. An optical analysis that includes computations regarding the characteristics of the different beams and the coherence between the different signals was performed. Also a power budget was calculated. A criterion for calculating the tolerance in the distance adjustment of the system was proFig. 7 (a) Calculated (continuous lines) and measured (symbols) (a) Doppler signal power, (b) Doppler signal bandwidth, and (c) tolerance in the distance adjustment of the lidar as a function of distance and for three different incidence angles ␸ for the target rotating at 400 rpm. Fig. 8 Calculated (continuous lines) and measured (symbols) (a) Doppler signal power and (b) Doppler signal bandwidth as a function of distance and for three different incidence angles ␸ for the target rotating at 1300 rpm. Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 404 Optical Engineering, Vol. 40 No. 3, March 2001 posed. Finally, experimental results obtained with a laboratory rotating target were presented. The experimental results show the capability of the system to perform Dopplershift measurements at distances up to 16 m. Acknowledgments This work was supported by the Spanish Government through grants CICYT TIC 431-93 and AMB96-1144-C0202. References 1. L. E. Drain, The Laser Doppler Technique, Wiley, Norwich, Great Britain 共1980兲. 2. M. J. Rudd, ‘‘A laser Doppler velocimeter employing the laser as a mixer-oscillator,’’ J. Sci. Instrum. 1共Ser. 2兲, 723–726 共1968兲. 3. I. C. Potter, ‘‘Frequency response of the 6328-Å helium-neon laser interferometer,’’ J. Appl. Phys. 40共12兲, 4770–4776 共1969兲. 4. J. H. Churnside, ‘‘Laser Doppler velocimetry by modulating a CO2 laser with backscattered light,’’ Appl. Opt. 23共1兲, 61–66 共1984兲. 5. J. H. Churnside, ‘‘Signal-to-noise in a backscattered-modulated Doppler velocimeter,’’ Appl. Opt. 23共13兲, 2097–2106 共1984兲. 6. S. Shinohara et al., ‘‘Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,’’ Appl. Opt. 25共9兲, 1417–1419 共1986兲. 7. M. H. Koelnik et al., ‘‘Laser Doppler velocimeter based on the selfmixing effect in a fiber-coupled semiconductor laser: theory,’’ Appl. Opt. 31共18兲, 3401–3408 共1992兲. 8. A. Rodrı ´guez, A. Comeron et al., ‘‘Sistema lidar coherente monoesta ´tico de baja potencia para medida de velocidad lineal y de rotacio ´n de blancos so ´lidos,’’ Patent No. 9702070, Oficina Espan ˜ oladePatentes y Marcas 共1997兲. 9. A. Rodrı ´guez, ‘‘Sistemas lidar coherentes e incoherentes de baja potencia para la deteccio ´n de velocidad de blancos so ´lidos,’’ PhD Thesis disertation, Universitat Polite ´cnica de Catalunya 共Dec. 1998兲. 10. B. J. Rye, ‘‘Antenna parameters for incoherent backscatter heterodyne lidar,’’ Appl. Opt. 18共9兲, 1390–1398 共1979兲. 11. B. J. Rye and R. G. Frehlich, ‘‘Optimal truncation and optical efficiency of an apertured coherent lidar focused on an incoherent backscatter target,’’ Appl. Opt. 31共15兲, 2891–2899 共1992兲. 12. A. E. Siegman, ‘‘The antenna properties of optical heterodyne receivers,’’ Proc. IEEE 54共10兲, 1350–1356 共1966兲. 13. A. Yariv, Quantum Electronics, 3rd ed., Wiley, New York 共1989兲. 14. H. Kogelnik and T. Li, ‘‘Laser beams and resonators,’’ Appl. Opt. 5共10兲, 1550–1567 共1966兲. 15. N. Abramson, The Making and Evaluation of Holograms, Academic Press 共1981兲. 16. M. C. Teich, ‘‘Infrared heterodyne detection,’’ Proc. IEEE 56共1兲, 37–46 共1968兲. 17. J. W. Goodman, Statistical Optics, Wiley, New York 共1985兲. 18. R. E. Hufnagel, ‘‘Propagation through atmospheric turbulence,’’ Chap. 6 in The Infrared Handbook, William L. Wolfe and George J. Zissis, Eds., Office of Naval Research, Dept. of the Navy, Washington, DC 共1978兲. 19. J. M. Senior, Optical Fiber Communications: Principles and Practice, Prentice-Hall, Englewood Cliffs, NJ 共1985兲. Alejandro Rodriguez received his telecommunication engineer degree from the Technical University of Madrid (UPM) in 1993 and his PhD in telecommunication engineering from the Technical University of Catalonia (UPC) in 1998. Since 1995 he has been an associate professor with the Department of Signal Theory and Communications, UPC. His research interests include low power coherent and incoherent laser radar systems and atmospheric lidar systems. Dr. Rodriguez is a member of SPIE. Adolfo Comeron received his telecommunication engineer degree from the Telecommunication Engineer School of Barcelona in 1976 and his DEA and DrIng degrees from the Paris-XI University, Orsay, in 1977 and 1980, respectively. He is currently professor with the Technical University of Catalonia, Barcelona, Spain. His research activities have included the study of nonlinear devices at IR wavelengths and the development of microwave and millimeter-wave receivers for satellite communication systems, and he is currently focused on free-space optical communications and remote detection and sensing at optical wavelengths. Dr. Comeron is a member of SPIE. David Garcia received a degree in telecommunications in 1993 and the telecommunication engineering degree in 1998, both from the Technical University of Catalonia (UPC). Since 1996 he has been an associate professor with the Department of Signal Theory and Communications (UPC). His research interests include low power coherent laser radar and laser Doppler anemometry systems. Rodriguez, Comeron, and Garcia: Homodyne laser radar system... 405Optical Engineering, Vol. 40 No. 3, March 2001