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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 2 — Jan. 28, 2013
  • pp: 1872–1897
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Continuous wave synthetic low-coherence wind sensing Lidar: motionless measurement system with subsequent numerical range scanning

Ernst Brinkmeyer and Thomas Waterholter  »View Author Affiliations


Optics Express, Vol. 21, Issue 2, pp. 1872-1897 (2013)
http://dx.doi.org/10.1364/OE.21.001872


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Abstract

A continuous wave (CW) Lidar system for detection of scattering from atmospheric aerosol particles is presented which is useful in particular for remote sensing of wind velocities. It is based on a low-coherence interferometric setup powered by a synthetic broadband laser source with Gaussian power density spectrum. The laser bandwidth is electronically adjustable and determines the spatial resolution which is independent of range. The Lidar system has no moving parts. The location to be resolved can be shifted numerically after the measurement meaning that a single measurement already contains the full range information. The features of constant resolution and numerical range scanning are in sharp contrast to ordinary CW Lidar systems.

© 2013 OSA

1. Introduction

Optical low-coherence reflectometry (OLCR), also called OCDR (Optical Coherence Domain Reflectometry), is a powerful continuous-wave (CW) white-light interferometric technique used primarily for testing fiber optical components and integrated optical waveguides [1

1. R. C. Youngquist, S. Carr, and D.E.N. Davies, “Optical coherence domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987). [CrossRef] [PubMed]

6

6. P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathé, C. Zimmer, and H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5(5), 565–567 (1993). [CrossRef]

]. An OLCR setup consists of a broadband source, e.g. a superluminescent diode (SLD), and a Mach-Zehnder-type interferometer. When unbalanced, the optical powers of signal and reference arm add up at the receiver and no coherent interference signal is detected. On the contrary, an interferometric signal is obtained if the optical path difference is smaller than the coherence length (which is inversely proportional to the optical bandwidth). During the measurement the optical length in the reference arm usually is changed so that different parts of the device under test enter - one after the other - the coherence range causing an interference signal. Therefore, the range of path change determines the measurement range (commonly of the order of centimeters and limited by a mechanically moved reference mirror) while the optical bandwidth and the coherence length of the source, respectively, determine the spatial resolution (which can be as low as a few micrometers). Within the coherence length the detection can possibly be quantum limited (down to about one signal photon per temporal resolution element).

An alternative CW reflectometric measurement technique, called optical frequency-domain reflectometry (OFDR), is based on a narrowband source which is swept in its optical frequency during the measurement (see e.g. [7

7. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. 11(8), 1377–1384 (1993). [CrossRef]

]). It is the optical counterpart of frequency-modulated continuous-wave (FMCW) radar. Since the swept frequency range can be as large as 10 THz very high spatial resolutions can be obtained. Basically, however, FMCW-Lidar is not suited for velocity measurements because different locations lead to different detector frequencies as different target velocities do likewise via the Doppler effect. That problem can be solved by sequential up- and downshifts of the optical frequency for moving hard targets. That is not an option, however, for distributed moving targets such as aerosols in the atmosphere [8

8. C. J. Karlsson, F. A. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 1.55 m for range, speed, vibration and wind measurements,” Appl. Opt. 39, 3716–3726 (2000). [CrossRef]

]. Very recently attempts have been made in that direction with a particular combination of CW and pulsed Lidar using frequency-stepped lasers realized by amplified and frequency shifting fiber optical recirculating delay lines [9

9. P. Lindelöw and J. J. Mohr, “Coherent lidar modulated with frequency stepped pulse trains for unambiguous high duty cycle range and velocity sensing in the atmosphere,” International Geoscience and Remote Sensing Symposium (IGARSS), pages 2787–2790 (2008).

, 10

10. A. T. Pedersen, “Frequency swept fibre laser for wind speed measurements,” PhD thesis at the Technical University of Denmark, December 2011.

].

Furthermore, there are continuous wave (CW) Lidar systems systems – widely used for wind sensing – the spatial resolution of which is based on focusing the emitted light to a particular location [11

11. M. Harris, “Introduction to continuous-wave Doppler lidar,” in Remote Sensing for Wind Energy, A. Peña and C. B. Hasager, eds. (RisøDTU, 2011), pp. 41–64.

13

13. E. Simley, L. Y. Pao, R. Frehlich, B. Jonkman, and N. Kelley, “Analysis of wind speed measurements using continuous wave Lidar for wind turbine control,” 49th AIAA Aerospace Sciences Meeting, Orlando, Florida (2011).

]. They rely on the fact that the close-to-focus range primarily contributes to the received backscattered signal. A typical spatial resolution obtained in that way is Δz = 10 m at a measurement distance z = 100 m and it scales about quadratically with z.

On the other hand many reflectometric optical measurement methods in fiber optics and Lidar use pulsed sources. In such a case the pulse width determines the spatial resolution and it usually is of the order of meters.

2. Proposed OLCR Lidar system

A schematic view of the proposed setup is shown in Fig. 1. It consists of an interferometer with a single-mode fiber delay line in the reference path which serves as a local oscillator (LO). The signal path is partly fiber-optical comprising an acousto-optical frequency shifter (acousto-optic modulator, AOM; frequency shift fAOM) and an optical circulator, both preferably in fiber pigtailed versions. The other part of the signal path is in free space with the incident laser light propagating into the atmosphere and the backscattered light from aerosols returning to the circulator. Signal and reference light are subsequently combined by means of a 3dB directional coupler with photodetectors at either output. The two electrical signals are subtracted from each other in order to get so-called balanced detection with the DC-signal nulled and the interference signal doubled in order to cancel the relative intensity noise (RIN) of the source. Therefore, RIN is not further considered in this paper. For the time being the center of the coherence zone in the atmosphere is determined by the choice of the delay in the reference path. The states of polarization of signal and reference light are supposed to be matched by proper – preferably fiber optical – polarization adjustment. The local oscillator power is assumed to be large enough so that the thermal detector noise is negligible as compared to the LO shot noise.

Fig. 1 Low coherence CW-Lidar setup

A vital part of the measurement setup is a CW broadband source with Gaussian optical power density spectrum SL and adjustable spectral width ΔνL of the order of 10 to 100 MHz:
SL(ν)=S^Lexp[(νν0ΔνL/2)2]
(1)
Its finite bandwidth is caused by a fluctuating optical phase Θ(t) of the electric field E while the amplitude is constant:
E(t)=E^exp(jω0t)exp[jΘ(t)]
(2)
The corresponding temporal degree of coherence γ11(τ) is - according to the Wiener-Khintchine theorem - equal to the Fourier transform of SL(ν), the absolute value of which also is a Gaussian function
|γ11(τ)|=exp[(πΔνL2τ)2]=exp[(ττc)2]
(3)
where τc = 2/(πΔνL) denotes the coherence time. The coherence time and the coherence length Δzc = c ·τc, respectively, where c is the speed of light, are the origin of spatial resolution. Details of this source are presented in Sec.3.

To begin with let us assume that backscattered light solely comes from a small length element δz in the atmosphere located at a distance z with an optical power δP being returned into the transmitting fiber. Moreover, let us assume - for the time being - that the scattering particles are fixed. The corresponding delay time with respect to the reference arm is td = 2z/cnreflref/c, where lref and nref denote the length and effective refractive index of the delay fiber, respectively. In that case the currents of the photodetectors (a) and (b) are
δia,b(t)={δP2+PLO2±2δP2PLO2cos[ωAOMt+Θ(t+td)Θ(t)+Ψ(z)]}
(4)
where PLO is the local oscillator power delivered through the reference fiber, ωAOM the frequency shift caused by the AOM, Ψ(z) an unknown phase, and ℛ = ηDe / () the responsivity of the detectors. After subtraction we obtain
δi(t)=δia(t)δib(t)=δi^2exp{j[ωAOMt+ϕ(t;td)+ψ(z)]}+c.c.
(5)
where ϕ(t; td) = Θ(t + td) − Θ(t) and δi^=2PLOδP. For a given δP the effective value of δi(t) is independent of td. Its expected power spectral density - the expectation of the absolute value squared of its Fourier transform - δS(f;td) = |ℱ {δi(t)}|2, however, strongly depends on td being narrowband for tdτc and broadband for tdτc. In the latter case the expected power density spectrum is proportional to the convolution product of SL(f + ν0) * SL(ffAOM + ν0) which yields a frequency dependence according to exp[(ffAOM)2/(2(ΔνL/2)2)]. That means that the electrical spectrum S(f;tdτc) is 2 times broader than the optical power spectrum of the source: Δf=2ΔνL (remark: for standard laser diodes with Lorentzian power spectrum the electrical spectrum is known to be twice as broad [15

15. A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).

,16

16. T. Okoshi, K. Kikucho, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 12, 630–631 (1980). [CrossRef]

]). The broad spectrum for tdτc is sometimes called ”incoherent interference” [17

17. W. V. Sorin, “Noise sources in optical measurements,” in Fiber Optic Test and Measurement, D. Derrickson, ed. (Prentice-Hall, 1998).

]. For tdτc the electrical spectrum would be a δ-function for an infinite measurement time T. With a finite measurement time T the spectrum will have a non-zero width Δfrec of about 1/T. Actually we define the respective spectral width by Δfrec=2/(πT) so that in the two limiting cases the electrical power density spectrum is given by
δS(f)=(δi^)2T2π{1Δfrec{sin[π(ffAOM)T]π(ffAOM)T}2fortdτc1Δfexp[(ffAOMΔf/2)2]fortdτc.
(6)
Two scattering elements with equal δP, one in either range, will thus yield a narrow peak on top of a broad spectrum with a peak ratio of Δf / Δfrec. When regarding a scattering element at a general delay time td the narrowband spectral part decays as |γ11(td)|2 and the broadband part increases accordingly so that the integral - given by Parseval’s theorem - remains constant:
δS(f;td)=(δi^)2T2π(1Δfrecexp[2(tdτc)2]{sin[π(ffAOM)T]π(ffAOM)T}2+1Δf{1exp(2(tdτc)2)}exp[(ffAOMΔf/2)2]).
(7)
It is convenient to subdivide the measurement range into coherence zones of length Δzc = c ·τc and numbering these zones according to Fig. 2. The center of the central coherence zone mc = 0 is defined as the location where the optical paths of signal and reference are the same (i.e. it is primarily determined by the fiber delay line). We will call that zone the matched zone in the following. In terms of delay time td the matched zone is given by −τc < td < τc. Each zone consists of a great number of length elements δz and the expected total electrical power density spectrum of each zone 〈ΔS(mc)〉 results from the sum of all contributions δS contained in it because of the random phase delays of different length elements. Moreover, this statement holds separately for the narrowband and the broadband part of the spectrum with widths Δfrec and Δf, respectively. The relative contribution of a zone #mc to the narrowband spectrum therefore is given by
qnarrow(mc)=12τc(2mc1)τc(2mc+1)τcexp[2(tdτc)2]dtd=π32{erf[2(2mc+1)]erf[2(2mc1)]}={0.6formc=00.014formc=±1<61010for|mc|2
(8)
Obviously, only the central zone mc = 0 (matched zone) substantially contributes to the narrow part of the spectrum. In an analogous manner the relative contribution of zone #mc to the broadband part of the electrical power spectrum is given by
qbroad(mc)=1qnarrow(mc)={0.4formc=00.986formc=±11for|mc|2
(9)

Fig. 2 Division of measurement range into zones of length Δzc

In an actual measurement, the narrowband part of the electrical power density spectrum has to be identified. According to Eq. (8) it is governed by the scattered power from the matched zone so that its width Δzc can be considered as the spatial resolution of our ”coherence gated” CW Lidar system. Hence, the spatial resolution is constant in a given measurement. Moreover, with our synthetic laser source presented in section 3 the coherence length Δzc can be electronically varied at will in a wide range. In an ordinary CW Lidar, on the contrary, spatial discrimination relies on focusing the transmitted laser beam to a particular location (see e.g. [18

18. C. M. Sonnenschein and F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10(7), 1600–1604 (1971) [CrossRef] [PubMed]

20

20. J. Y. Wang, “Optimum truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474 (1988). [CrossRef] [PubMed]

] and the appendix of this paper). As a result high spatial resolution can hardly be achieved with ordinary CW Lidar, the resolution obtained decreases with distance and the resolution is only moderately well determined since the spatial sensitivity variation is approximately given by a Lorentzian (rather than a Gaussian) function.

If 〈ΔP(mc)〉 denotes the expected scattered optical power in the transmitting fiber from zone #mc the expected peak values of the narrowband and broadband spectral parts are
ΔSnarrow(p)(mc)=ALO1ΔfrecΔP(mc)qnarrow(mc)
(10)
ΔSbroad(p)(mc)=ALO1ΔfΔP(mc)qbroad(mc)
(11)
where ALO=22PLOT/π. Due to Eq. (8) and Eq. (9) the peak values of the narrowband and broadband spectral parts can be well approximated by
Snarrow(p)ALO1Δfrec0.6Pcoh
(12)
Sbroad(p)ALO1ΔfPcoh(μ0.6)
(13)
where Pcoh = ΔP(mc = 0) is the received scattered power originating from the central zone (matched zone), Ptot the total received backscattered power, and μ = 〈Ptot〉 / 〈Pcoh〉. The total expected spectrum therefore consists of a narrow spectral peak with a peak value of Snarrow(p)+Sbroad(p) residing on a broad socket of height Sbroad(p).

The powers Pcoh and Ptot are random variables because they consist of contributions of many scatterers the electric fields of which are superimposed with random phases. Therefore they behave like the intensity I in a speckle pattern [21

21. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckles and Related Phenomena, J.C. Dainty, ed. (Springer, 1984).

]. For a coherent superposition the standard deviation σI of the intensity is known to be equal to the mean intensity 〈I〉 (unity contrast). Since the electric power spectral density Snarrow(p) of the narrow spectral part is proportional to the optical power Pcoh = ΔP(mc = 0) it follows the same statistics:
σnarrow=Snarrow
(14)
The same applies to the broad spectral part
σbroad=Sbroad
(15)
although one might suppose that the superposition of light from different zones #mc would yield an averaging effect, i.e. a reduction of the contrast. That is not the case because the addition takes place on an amplitude rather than an intensity basis (see Eq. (4) and Eq. (5)). Therefore, the negative exponential statistics of coherent speckle patterns is preserved [21

21. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckles and Related Phenomena, J.C. Dainty, ed. (Springer, 1984).

] and the contrast is unity as stated in Eq. (15).

Thus, different - but fixed - spatial arrangements of the scattering particles cause different optical powers, different detector currents and different electric power spectral densities as quantified in Eq. (12)Eq. (15). Actually, when the particles move, they will get in and out of the illuminated volume, in particular by transverse wind components, and their relative positions will change with time. That phenomenon yields a temporal fluctuation of the detector current amplitude. As a consequence the narrowband part of the spectrum will be broadened from Δfrec to some value Δfsp (speckle induced spectral broadening) which is of the order or below 1 MHz in most cases being of interest here. We approximate the resulting spectral shape by a Gaussian function and replace Δfrec by Δfsp in Eq. (12). In the applications outlined below we will always choose Δf ≫ Δfsp so that the speckle broadening is irrelevant for the broad spectral part Sbroad(f). Hence, the expectation of the electric power density spectrum is
S(f)=Snarrow(p)exp[(ffAOMΔfsp/2)2]+Sbroad(p)exp[(ffAOMΔf/2)2]
(16)
The situation is highlighted in Fig. 3 for three values of the ratio 〈Ptot〉 / 〈Pcoh〉 (1, 10, and 100, respectively), and spectral widths Δf=238.2MHz=54MHz (corresponding to a spatial resolution Δzc = 5 m) and Δfsp = 1 MHz. The main task - addressed in the following - is to identify the spectral location of the narrow peak in the presence of stochastic fluctuations (note that the spectra shown in Fig. 3 are expected values only).

Fig. 3 Simulated normalized electrical power density spectrum for power ratios 〈Ptot〉 / 〈Pcoh〉 = [1, 10, 100]

Let us call the vicinity of the spectral peak the ”upper level” and the adjacent spectral range the ”lower level” and let us define the signal-to-noise ratio SNR according to
SNR=(SupSlow)2σup2+σlow2
(17)
with Sup being the electrical power spectral density of the upper level, Slow the respective value of the lower level and σup2 and σlow2 the noise induced variances. For the time being we will assume that the shot noise is negligible so that only speckle noise is relevant. With the relations Sup=Snarrow(p)+Sbroad(p), Slow=Sbroad(p), σuplow=Suplow and the ad hoc abbreviation ξ=Sbroad(p)/Snarrow(p)
SNR=Snarrow(p)2Sup2+Slow2=11+2ξ+2ξ2
(18)
According to Eq. (12) and Eq. (13) the quantity ξ can be expressed by μ = 〈Ptot〉 / 〈Pcoh
ξ=Δfsp(μ0.6)Δf0.6
(19)
As an example the above values Δf = 54 MHz (corresponding to Δzc = 5 m) and Δfsp = 1 MHz shall be used: in the pleasant case of μ = 1 we have ξ = 1.2 · 10−2 and SNR ≈ 1 while in the extreme case of μ = 100 we get ξ = 3.07 and SNR ≈ 0.04. In any case the SNR must be improved by averaging. Taking the average of Mav independent electrical power density spectra yields (with our definition of Eq. (17)) an SNR improvement by a factor of Mav and hence
SNRsp=Mav1+2ξ+2ξ2
(20)
where the index sp denotes the fact that the case of speckle noise dominance is considered so far. This relation reveals that usually about 100 averages will be sufficient in this regime.

In the case where the speckle noise is negligible and the shot noise (SN) due to the local oscillator power PLO prevails the SNR is given by
SNRSN=MavSnarrow(p)22σSN2=MavSnarrow(p)22(2ePLOT)2=MavSnarrow22(ALOπe/)2
(21)
The SNR in general and in particular in the transition range between speckle and shot noise dominance can be well approximated by
SNR1=SNRsp1+SNRSN1
(22)
The shot noise term is dominant for 〈Pcoh〉 < Pcrit. Due to Eq. (20) and Eq. (21) Pcrit ≈ 3Δfsp in the majority of cases which is about 1 pW for Δfsp = 1 MHz.

3. Synthetic broadband laser source with adjustable power density spectrum

The optical power density spectrum is an important attribute of continuous wave (CW) lasers in general and laser diodes in particular. In single longitudinal mode operation the finite spectral linewidth is caused by the presence of incoherent spontaneous emission inside the active medium. Depending on the laser under considerations and the operation conditions the linewidth may vary from the sub-kHz to the multi-MHz range. The shape of the spectrum is known to be Lorentzian. The electric field E(t) of the emitted light has an almost constant amplitude. Its phase Θ(t), however, fluctuates randomly due to the spontaneous transitions which continually add power to the oscillation field thereby causing the spectral broadening observed. The phase noise can be modeled by using the Fokker-Planck equation.

Some applications such as ordinary interferometry, conventional Doppler Lidar or coherent optical communications require narrowband sources, e.g. with linewidths below 10 kHz. As already summed up in the introductory remark of Sec. 1 broadband sources on the other hand with bandwidths in the THz range are used in white-light interferometry, optical low-coherence reflectometry (OLCR) and low-coherence tomography.

In Sec. 2 it has been shown that optical low-coherence reflectometry can also be the basis of CW Lidar systems with resolution in the range of meters. Such Lidar systems are particularly beneficial for remote wind velocity measurement (see Sec. 5). One of their key elements is a source with adjustable spectral width in the range of tens of MHz and a Gaussian rather than a Lorentzian spectrum since the respective temporal coherence function γ11 falls off much more rapidly.

The optical source we propose and use afterwards consists of a laser diode and an electro-optical phase modulator as schematically shown in Fig. 4. The laser diode employed is supposed to oscillate in a single transverse and single longitudinal mode and it is considered to be sufficiently monochromatic for our purposes, say having a linewidth of 100 kHz or below. Such laser diodes are readily available, in particular in the 1500 nm range of optical communication. The output light is transmitted through an optical phase modulator which also is an off-the-shelf telecom component, using e.g. LiNbO3 as electro-optic material. The modulator is assumed to be driven by a noise-like electrical signal. It is evident, hence, that the electric field of the optical output is given by
E(t)=E^exp(jω0t)exp[jΘ(t)]
(23)
Its power density spectrum is given by taking the squared absolute value of its Fourier transform
SL(fopt)=|E^exp(j2πfoptt)exp[jΘ(t)]dt|2
(24)
where fopt = νν0 denotes the baseband frequency variable. The key question is which Θ(t) (and which associated drive voltage U(t)) is required to obtain a spectrum as specified by Eq. (2) with Gaussian shape and predefined optical bandwidth ΔνL. That question is equivalent to the problem of finding a function Θ(t) with the property
{exp[jΘ(t)]}=exp[12(foptΔνL/2)2]exp[jψ(fopt)]
(25)
where ψ(fopt) is an arbitrary real function. The authors are unaware of a mathematical proof of existence of a suitable function Θ(t). If a solution exists it is for sure not unique. Furthermore, the question has to be raised how to find a concrete and tangible solution which can be used in experiments.

Fig. 4 Setup for source with adjustable spectral width

Due to lack of respective answers we applied the following heuristic and iterative approach: We start with a random phase function ψ(fopt) and calculate a first approximation to Θ(t) by applying Eq. (25)
Θ(t)=arg{1{exp[12(foptΔνL/2)2]exp[jψ(fopt)]}}
(26)
With the result of Eq. (26) we subsequently calculate a new function ψ(fopt) according to
ψ(fopt)=arg{{exp[jΘ(t)]}exp[+12(foptΔνL/2)2]}=arg{{exp[jΘ(t)]}}
(27)
The procedure of Eq. (26) and Eq. (27) is repeated until an acceptable approximation to the goal, Eq. (25), is reached. We do not have a proof of convergence for this iteration procedure. It turned out to work, however, in any case we tried so far and yields useful results for practical applications. Examples will be shown in the following.

The procedure outlined above has been carried out by a simple MATLAB code. Usually, we used a time discretization of δt = 1 ns and N = 214 = 16384 data points. The optical bandwidths used were in the range of 10 MHz < ΔνL < 100 MHz corresponding to coherence lengths Δzc = c · 2/(πΔνL) between 2 m and 20 m. Examples of the power density spectra obtained with ΔνL = 10 MHz and 100 MHz are shown in Fig. 5(a) and 5(b) along with the target Gaussian spectra which - apart from weak spectral fluctuations - are very closely reached. Cutouts of the phase Θ(t) in a time interval of 1μs (i.e. 1000 data points) are shown at the bottom. In an actual application the complete set of discrete data Θn, n = 1 ... N, has to be stored one single time in a digital memory and used to drive the phase modulator. For repeated measurements it can be used again or other predetermined representations may be used. The mean number of phase jumps per time interval increases with increasing spectral bandwidth ΔνL. In the example of Fig. 5(b) there are about 400 phase jumps out of 16000 phase values, i.e. the jump rate is around 2.5 percent. If the phase modulator has a maximum frequency above 1 GHz (actually 40 GHz versions are readily available) the rate of phase jumps is not significant. Otherwise, the actual phase function will be slightly corrupted when compared to the numerical one.

Fig. 5 Normalized optical power density spectrum for ΔνL = 10 MHz (a) and ΔνL = 100 MHz (b), green curve: Gaussian target spectrum, blue curve: iteration result; bottom: cutout of phase Θ(t)

As mentioned above the temporal degree of coherence γ11(τ) of the output radiation field is determined by the inverse Fourier transform of the power density spectrum SL(ν). A Gaussian spectrum according to Eq. (1) yields an absolute value of γ11(τ) as given above in Eq. (3). In the remainder of this paper we will use a single numerical data set as an example – both for simulations (section 6) and for experimentally driving the phase modulator (section 7) - with ΔνL = 38.2 MHz and Δzc = 5 m, respectively. The corresponding optical power density spectrum and the associated temporal degree of coherence are shown in Fig. 6(a) and 6(b). The latter is presented in a logarithmic scale 20 log10 |γ11| because the actual numerical curve (shown in blue) and the ideal gaussian one (shown in green) are indistinguishable on a linear scale. According to Fig. 6(b) the deviation of |γ11(τ)| from the target function Eq. (3) is of the order of 10−3 outside the coherence peak.

Fig. 6 Result from iteration and Gaussian target function for ΔνL = 38.2 MHz: a) Normalized optical power density spectrum; b) temporal degree of coherence |γ11|

In a low-coherence reflectometer as well as in a low coherence Lidar the absolute value |γ11| is of utmost importance because the measured signal should be a measure of the power originating from the coherence zone |τ| < τc, only. Actually, contributions in the measured electrical power density spectrum originating from reflections outside the coherence range are suppressed by |γ11|2. From Fig. 6(b) it is obvious that an excellent suppression is obtained when using the synthetic phase noise source presented above - much better than the Lorentzian-type spatial sensitivity obtained by beam focusing in ordinary CW-Lidars.

4. Post-measurement numerical range scanning

The signal to be detected stems from length elements close to the point where signal and reference path are of equal optical length (which we called above the matched zone). That location therefore is given by the length of the reference fiber and can be changed by changing the length of the reference fiber lref. In this section we will show that the matched zone can also be shifted afterwards by a suitable numerical evaluation of the measured data.

According to Sec. 2, Eq. (4) and Eq. (5) the detector signal and its spectrum caused by scattered light from a length element δz strongly depends on the phase difference ϕ(t;td) = Θ(t + td) − Θ(t). The matched zone is the vicinity of the location z = nref ·lref/2 where the delay time td = 0. In order to shift the matched zone to another location the analytical signal corresponding to the real detector signal - which is readily available by suppressing the spectral part at negative frequencies and consists of terms exp {j[ωAOMt + Θ(t + td) − Θ(t)]}, cp. Eq. (4) - can be multiplied by a function
hshift(t;Δtshift)=exp{j[Θ(t+Δtshift)Θ(t)]}
(28)
resulting in terms
hshift(t;Δtshift)exp{j[ωAOMt+Θ(t+td)Θ(t)]}=exp{j[ωAOMt+Θ(t+td)Θ(t+Δtshift)]}
(29)
where the matched zone is shifted to td = Δtshift and z = (nreflref + c · Δtshift)/2, respectively.

That procedure is made possible because the phase data Θ(t) are known (see Sec. 3) in sharp contrast to the situation in optical low-coherence reflectometry with natural laser sources. Thus, a single measurement can be repeatedly evaluated in order to get the response of different locations. That is by far more convenient and less time consuming than physically changing the setup and repeating the measurement and also means a tremendous advantage of our measurement scheme compared to ordinary CW-Lidars. Furthermore the numerical range-scanning feature of our system implies that the delay fiber in the reference arm can even be omitted.

5. Low-coherence Doppler wind Lidar system

Lidar systems are known to be useful for a large variety of applications [22

22. C. Weitkamp, Lidar Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005)

]. One of them is the remote measurement of wind velocities which is based on the Doppler frequency shift caused by moving scattering particles. The Doppler effect directly translates the line-of-sight velocity vLOS (to be determined) to the optical frequency shift
fD=2vLOSλ
(30)
Using pulsed sources and measuring the time of flight is one way to obtain spatial resolution: Δzpulse = c ·τpulse/2 where τpulse denotes the pulse duration. The shorter the pulse duration the better is the spatial resolution, the poorer is, however, the frequency and velocity resolution, respectively. An alternative is to use an ordinary CW Lidar which is much less complicated and gets its spatial resolution by focusing the transmitted beam, with the limitations, however, mentioned above.

In this paper we propose a CW Doppler wind Lidar system where the spatial resolution primarily originates from the coherence properties of the source. The scheme has been presented already in Fig. 1 and discussed in Sec. 2. The only change to be made is to replace the fixed frequency shift fAOM caused by the AOM by fAOM + fD. The detector signal is digitized and the electrical power spectral density is calculated by FFT. As shown in Sec. 2 this spectrum has a narrow peak which nearly exclusively stems from the matched zone (mc = 0) of width Δzc. Contributions of other locations (with other velocities, in general) are strongly suppressed according to a Gaussian function exp[−2(td/τc)2].

6. Simulation results

In Sec. 2 an OLCR Lidar method has been proposed and analyzed. Regardless and independent of the formulae derived there we present results of numerical simulations in this section which mimic the actual scattering and detection process. The simulation starts with an optical field with constant amplitude and synthetic noisy phase (cp. Sec. 3) so that the optical power density spectrum is a Gaussian with a predetermined spectral width. The time domain data are sampled with a time increment of 1 ns and 214 = 16384 data points corresponding to 16μs are taken for a single measurement. The responses of individual length elements - many of them in each coherence zone #mc with random optical phases which, moreover, change randomly from measurement to measurement - are superimposed yielding a speckle-like total signal. In each coherence zone #mc the line-of-sight velocity and, hence, the Doppler frequency shift is assumed to be constant. The power weighting of different coherence zones is actually given by the transmitted beam (see appendix) and the scattering properties of the atmosphere. For demonstration reasons we choose truncated weighting profiles of the form
w_=[w(Mc2)w(Mc2+1)w(1)w(0)=1w(1)w(Mc21)w(Mc2)]
(31)
In all simulation to follow we chose a laser wavelength λ = 1500 nm and a 1/e width of the optical power density spectrum to be ΔνL = 38.2 MHz (corresponding to Δf = 54 MHz and a resolution length Δzc = 5 m; cp. Sec. 2). The narrow spectral peak is simulated by random amplitude fluctuations of the detector signal (bursts with Gaussian temporal shape) and is chosen to exhibit a width Δfsp = 0.9 MHz (cp. Sec. 2). The AOM frequency shift is set to fAOM = 80 MHz and the Doppler frequency shifts in the coherence zone #mc is chosen to be mc · 2.5 MHz, with the exception of the central coherence zone mc = 0 where - in order to make a discernible distinction - the Doppler frequency shift is chosen to be fD = 1.27 MHz. Thus the spectral peak in the electrical power density spectrum is expected to be at 81.27 MHz. The number of averages is fixed to Mav = 100 so that the total simulated measurement time is 1.6 ms.

In the Fig. 710 the received power level is assumed to be large enough so that the speckle noise is dominant rather than the LO shot noise. In Fig. 7 the scattered light is assumed to originate from Mc = 11 coherence zones with uniform power weighting w̱ = [1 1 1 1 1  1  1 1 1 1 1] so that μ = 11. It shows the narrow spectral peak from the central zone residing on the broad socket originating from the remaining zones. The central part is magnified in the inset of Fig. 7. The peak to socket ratio is about 0.9/0.2 and hence close to the expected value of 4.46 calculated from Eq. (12) and Eq. (13). The SNR as defined by Eq. (17) is about 57, close to the expected value. The center of gravity of the narrow peak was determined to be 81.24 MHz which is very close to the true position of 81.27 MHz. The simulation results shown in Fig. 8 hold for the same conditions, except for the fact that the power weighting w(mc = −1) of the coherence zone directly adjacent to the central zone is increased to 10. In accordance with Eq. (13) and Eq. (20) that results in an increased socket (and a slightly decreased SNR). There is a weak indication of a second peak at 77.5 MHz which corresponds to the adopted Doppler shift of −2.5 MHz of the zone mc = −1. In Fig. 9 the weighting of the three zones mc = −4 through mc = −2 is increased to 10 so that μ = 38. No indication is noticeable of additional Doppler peaks. Thus, Fig. 8 and 9 prove the excellent OLCR suppression of Doppler peaks away from the central coherence zone so that strong scatterers like clouds are not particularly detrimental. In Fig. 10 the SNR for uniform weighting is given as a function of the number Mav of averages. It is found by repeating the averaging process several times and yields a result which slightly outnumbers the values of Sec. 2, Eq. (20) which predicts SNR = 57 after 100 averages. It has to be taken into account, however, that the SNR after averaging is a random variable, too, so that after a single averaging process - of e.g. 100 averages - the SNR can be smaller or larger than the expected value.

Fig. 7 Normalized power spectral density for uniformly weighted zones w(mc) ≡ 1; inset: central peak
Fig. 8 Normalized power spectral density for increased scattered power from outside the matched zone: w̱ = [1 1 1 1 10  1 1 1 1 1 1]
Fig. 9 Normalized power spectral density for increased scattered power from outside the matched zone: w̱ = [1 1 10 10 10  1  1 1 1 1 1]
Fig. 10 SNR for uniform weighting w(mc) ≡ 1 as function of averages Mav

In Fig. 11 the power weighting in the eleven zones is assumed to be uniform again. However, the expected received scattered power from the matched zone is assumed to be 〈Pcoh〉 = 250 fW only (i.e. 〈p(z)〉 = 50 fW/m) so that the shot noise of the local oscillator is dominant. Nevertheless, the narrow peak is clearly visible. The expected SNR after 100 averages (found by repeating the averaging process 100 times) was determined to be 16. That is in splendid accordance with Eq. (21) which yields SNRSN = 17 in this case (assuming a responsivity of ℛ = 1A/W in Eq. (21) as well as in the simulation). Moreover, the mean value of the center frequency is found to be 81.30 MHz with a standard deviation of 0.15 MHz which is very close to the frequency of 81.27 MHz assigned to the matched zone even in this noisy case. In Fig. 12 the expected received power 〈Pcoh〉 is increased to 1 pW which is about the value of the critical power between shot noise and speckle noise dominance.

Fig. 11 Normalized power spectral density for uniformly weighted zones w(mc) ≡ 1 with 〈Pcoh〉 = 250 fW
Fig. 12 Normalized power spectral density for uniformly weighted zones w(mc) ≡ 1 with 〈Pcoh〉 = 1 pW

In Fig. 13(a) and 13(b) the signal data of Fig. 7 are re-evaluated by applying the procedure presented in Sec. 4 in order reveal the scattering from other locations. In Fig. 13(a) the matched zone is shifted by +4Δzc = +20 m, in Fig. 13(b) by −3Δzc = −15 m, i.e. to the coherence zones mc = 4 and mc = −3, respectively. The narrow Doppler peaks at 90 MHz and 72.5 MHz are clearly visible.

Fig. 13 Simulation of post-hoc shifting the matched zone; a) shift by +4Δzc = +20 m; b) shift by −3Δzc = −15 m

7. Experimental results

Experimental work with the low-coherence Lidar system presented above has been done in the laboratory so far. The actual setup closely follows the schematic view of Fig. 1 with the source being a combination of a laser diode and a phase modulator according to Fig. 4. For the time being some of the components used are laboratory instruments. For future field measurements they can easily be replaced by OEM modules so that our approach will share the properties of small footprint, light weight, low cost and simple data processing with other CW Lidars. The results shown below focus on the crucial specific features of our approach rather than on those - such as heterodyne and quantum limited detection - which it has in common with established Lidar systems:
  • operation and characterization of our synthetic broadband source with Gaussian power density spectrum of adjustable width
  • demonstration of the low coherence Lidar principle: spectral discrimination between scattered power from the matched zone and from other locations
  • numerical range scanning: post measurement shift of the matched zone

7.1. Synthetic broadband laser source

The synthetic laser source is realized as described in Sec. 3. It consists of a narrowband laser diode with a wavelength λ = 1550 nm and a phase modulator. The latter is driven by data as obtained from the iterative procedure also described in Sec. 3. In all the measurements discussed below a single data set with 214 values is used which generates a Gaussian optical power density spectrum with a width of ΔνL = 38.2 MHz corresponding to a coherence length of ΔνL = 5 m. The same data set has also been used in the simulations of Sec. 6.

To experimentally determine the bandwidth of our artificially broadened source we make use of the delayed-self-heterodyne-method [15

15. A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).

, 16

16. T. Okoshi, K. Kikucho, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 12, 630–631 (1980). [CrossRef]

], which is widely used for the measurement of narrow optical bandwidths. Its setup consists of a strongly imbalanced fiber optical Mach-Zehnder-interferometer, where the length difference of the arms of the interferometer has to exceed the coherence length of the optical source under test, in other words the delay time td has to exceed the coherence time τc. The expected coherence length in our case is 5 m. To meet the above requirement we use a length difference of 500 m of optical fiber, resembling 725 m of air or a time delay of td = 2.4μs. At the interferometer output two incoherent signals interfere and lead to the so called ”incoherent interference” with an electrical power spectral density (PSD) the width of which is expected to be 2 times broader than the optical power spectrum of the source (for Gaussian PSD); see Sec. 2.

The experimental result, normalized by the total electrical power Pel, is shown in Fig. 14. As expected it has a rugged appearance. However, a Gaussian fit which is also shown in Fig. 14 yields a 1/e-width of Δfel = 55.4 MHz, corresponding to an optical bandwidth of ΔνL=55.4MHz/2=39.2MHz which is very close to the expected value of ΔνL = 38.2 MHz. The smooth expected Gaussian spectrum would be obtained by averaging many spectra either with different delays td or by using different numerical data sets Θn for the phase modulation which are readily available.

Fig. 14 Normalized measured electrical power spectral density of the synthetic broad-band source with delayed-self-heterodyne-method, Δfel = 55.4 MHz, ΔνL=Δfel/2=39.2MHz, N = 16384 data points, δf = 1/(N * δt), Mav = 1, 16384 data points

7.2. Experimental demonstration of low coherence Lidar principle

To test the low coherence Lidar in the lab, the setup is set to a measurement distance of z = 10 m, i.e. the laser beam is focused to that distance and the matched zone is positioned there by choosing an appropriate length of the fiber optical reference arm. The measurement resolution is set to Δz = 5 m through the choice of the laser bandwidth of ΔνL = 38.2 MHz. These test conditions remain the same for all measurements.

Four measurements using a retroreflecting film as at target were carried out and the respective results are shown in Fig. 15 and Fig. 16. The target is placed once in the center of zone mc = 0 at z = 10 m and once in the center of zone mc = −1 at z = 5 m. At each position we are taking measurements once on a static target and once on a moving target. The moving target is simulated by fixing the retroreflecting film to a rotating cylinder, the static target is the same, but with the rotation stopped. From the narrow peaks in Fig. 15(a) and 16(a) we can determine the speed of movement from the Doppler shift Eq. (30). From Fig. 15(a) we find for the static target in zone mc = 0 a narrow peak at f = fAOM = 80 MHz corresponding to a Doppler shift of fD = 0 MHz as expected with no movement. In Fig. 16(a) the PSD of the moving target is shown and clearly a shift of the narrow peak is visible, which can be determined to be fD = −2.54 MHz, denoting a movement speed of vLOS = −2.0 m/s with λ = 1550 nm, i.e. away from the observer.

Fig. 15 Lidar Measuremtent with static target; (a) Normalized power density spectrum with target at z = 10 m, inside matched zone mc = 0, inset: closeup of central peak of; (b) Normalized power density spectrum with target at z = 5 m inside zone mc = −1
Fig. 16 Lidar Measuremtent with moving target; (a) Normalized power density spectrum with target at z = 10 m, inside matched zone mc = 0, inset: closeup of central peak of; (b) Normalized power density spectrum with target at z = 5 m inside zone mc = −1

Placing the target at a distance z = 5 m, inside zone mc = −1 leads to the spectra shown in Fig. 15(b) and Fig. 16(b) for the static target case and the moving target case, respectively. Here we can see the broad and low amplitude spectra with a bandwidth of about 39 MHz, identifying these measurements clearly as signals from outside the matched zone. Thus, these examples demonstrate the range resolving and speed measurement abilities of our low coherence Lidar.

7.3. Post measurement shift of matched zone

As already detailed in Sec. 4 the exact knowledge of the phase Θ(t) provides the possibility of moving the matched zone numerically after the measurement to any desired location. To demonstrate this feature we set up an experiment with two targets in the beam path, one moving target at a distance of z = 10 m centered at zone #mc = 0 and one static target at a distance of z = 5 m centered at zone #mc = −1. The static target is formed by laterally moving a reflecting film inside the beam, thus reflecting a fraction of about 25% of the light. The rest is passed on to the moving target. Fig. 17(a) shows the originally measured PSD with a peak at 77 MHz, revealing a target at a speed of vLOS = −2.3 m/s inside the resolution range. A reevaluation after multiplication of the measurement data with
hshift(t;Δtshift)=exp[j(Θ(t+Δtshift)Θ(t))]
(32)
with Δtshift = 34 ns (cp. Sec. 4) results in the PSD shown in Fig. 17(b) where the matched zone is shifted to z = 5 m. In this figure a peak at 80 MHz is visible, denoting a static target in the resolution range, with a broadband underground, denoting some signal from outside the resolution range, which is our moving target. This indicates that we have successfully shifted the matched zone from z = 10 m to z = 5 m.

Fig. 17 (a) Evaluation of data for moving target at z = 10 m ; (b) Reevaluation of data: numerical shift of matched zone to location of static target at z = 5 m

8. Summary and conclusions

A continuous-wave Lidar system has been presented, primarily meant for remote sensing of wind velocities. It is based on principles of optical low-coherence reflectometry (OLCR), using, however, a laser source with artificially broadened optical power density spectrum, e.g. with Gaussian shape. On that basis it is featuring a number of specific characteristics, in particular:
  • constant and electronically adjustable spatial resolution in the order of meters
  • strong discrimination between scattering contributions of different locations
  • numerical range scanning after the measurement

All of these three characteristics are in sharp contrast to ordinary CW wind sensing systems. When compared to pulsed Lidar systems it stands out by its simple setup and the absence of the problem of velocity versus spatial resolution.

Our Lidar concept may also be useful for other applications such as range-resolved depolarization diagnosis and range-resolved determination of gas concentrations by means of differential absorption Lidar (DIAL), provided scattering particles are available.

Appendix: Transmitted laser beam and received backscattered power

The problem of transmitting light into the atmosphere and receiving backscattered light in a monostatic Lidar system has been addressed previously (see e.g. [18

18. C. M. Sonnenschein and F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10(7), 1600–1604 (1971) [CrossRef] [PubMed]

20

20. J. Y. Wang, “Optimum truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474 (1988). [CrossRef] [PubMed]

]). It is crucial in the case of an ordinary CW-Lidar because the spatial resolution in that case is based on focusing the laser beam. It also plays an important role in a low-coherence Lidar as proposed in Sec. 2 because it determines - together with the scattering properties of the atmosphere - the signal level and the level of the broadband background of the measured electrical power density spectrum. In this appendix we revisit the problem in more detail in fiber optical terms and we derive formulae for the launching efficiency and the received power per length element, respectively, in closed form.

Fig. 18 Gaussian beam of the Lidar setup

Fig. 19 Factors considered for calculation of η(x,y,z)

All this will reduce the launching efficiency η calculated from Eq. (38). With some minor approximations the final result is
η(x,y,z)=ηlong(z)exp[(δxf)2+(δyf)2wη2]
(41)
where
ηlong(z)=4/{[w˜0(z)w0+w0w˜0(z)]2+[kw0w˜0(z)2Rcurv]2}w˜02(z)=w02[1+(δzfδz0zR0)2]Rcurv=(δzfδz0)[1+zR02(δzfδz0)2]1wη2=2w˜02+Re{[k22(1f1Rcurv+j2kw˜02)2]/(1w02+1w˜02+jk2Rcurv)}k=2π/λ;δxfxfz;δyfxfz
It is interesting to note that η(x = 0, y = 0, z′ = 0) = ηlong(z′ = 0) ≈ 1.

Fig. 20 Received power per length element p(z) and launching efficiency η̄(z)

On the contrary, a CW-Lidar with coherence resolution as presented in Sec. 2 can offer a better and constant spatial resolution (e.g. Δzc = 5 m; cp. Sec. 2). Moreover, it is only marginally affected by out-of-focus scatterers.

References and links

1.

R. C. Youngquist, S. Carr, and D.E.N. Davies, “Optical coherence domain reflectometry: a new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987). [CrossRef] [PubMed]

2.

K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fiber source and erbium doped power amplifier,” Electron. Lett. 29, 365–367 (1993). [CrossRef]

3.

A. Kohlhaas, C. Frömchen, and E. Brinkmeyer, “High-resolution OCDR for testing integrated optical waveguide: dispersion-corrupted experimental data corrected by a numerical algorithm,” J. Lightwave Technol. 9, 1493–1502 (1991). [CrossRef]

4.

D. M. Baney and W. V. Sorin, “Extended-range optical low coherence reflectometry using a recirculation delay technique,” IEEE Photon. Technol. Lett. 5, 1109–1102 (1993). [CrossRef]

5.

W. V. Sorin, “Optical reflectometry for component characterization,” in Fiber Optic Test and Measurement, D. Derrickson, ed. (Prentice-Hall, 1998).

6.

P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathé, C. Zimmer, and H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett. 5(5), 565–567 (1993). [CrossRef]

7.

U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol. 11(8), 1377–1384 (1993). [CrossRef]

8.

C. J. Karlsson, F. A. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 1.55 m for range, speed, vibration and wind measurements,” Appl. Opt. 39, 3716–3726 (2000). [CrossRef]

9.

P. Lindelöw and J. J. Mohr, “Coherent lidar modulated with frequency stepped pulse trains for unambiguous high duty cycle range and velocity sensing in the atmosphere,” International Geoscience and Remote Sensing Symposium (IGARSS), pages 2787–2790 (2008).

10.

A. T. Pedersen, “Frequency swept fibre laser for wind speed measurements,” PhD thesis at the Technical University of Denmark, December 2011.

11.

M. Harris, “Introduction to continuous-wave Doppler lidar,” in Remote Sensing for Wind Energy, A. Peña and C. B. Hasager, eds. (RisøDTU, 2011), pp. 41–64.

12.

I. Antoniou, “Remote sensing the wind using Lidars and Sodars,” Proceedings of the 2007 European Union Wind Energy Conference, Milan, Italy (2007).

13.

E. Simley, L. Y. Pao, R. Frehlich, B. Jonkman, and N. Kelley, “Analysis of wind speed measurements using continuous wave Lidar for wind turbine control,” 49th AIAA Aerospace Sciences Meeting, Orlando, Florida (2011).

14.

E. Brinkmeyer and T. Waterholter, “Lidar-Messsystem,” pending European patent application P89429, November12, 2012.

15.

A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).

16.

T. Okoshi, K. Kikucho, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett. 12, 630–631 (1980). [CrossRef]

17.

W. V. Sorin, “Noise sources in optical measurements,” in Fiber Optic Test and Measurement, D. Derrickson, ed. (Prentice-Hall, 1998).

18.

C. M. Sonnenschein and F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt. 10(7), 1600–1604 (1971) [CrossRef] [PubMed]

19.

M. Harris, G. Constant, and C. Ward, “Continuous-wave bistatic laser doppler wind sensor,” Appl. Opt. 40(9), 1501–1506 (2001). [CrossRef]

20.

J. Y. Wang, “Optimum truncation of a lidar transmitted beam,” Appl. Opt. 27, 4470–4474 (1988). [CrossRef] [PubMed]

21.

J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckles and Related Phenomena, J.C. Dainty, ed. (Springer, 1984).

22.

C. Weitkamp, Lidar Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005)

23.

D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J. 56, 703–718 (1977).

24.

F. L. Pedrotti, Introduction to Optics (Prentice-Hall, 1993).

OCIS Codes
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(010.3640) Atmospheric and oceanic optics : Lidar
(030.1640) Coherence and statistical optics : Coherence
(060.2310) Fiber optics and optical communications : Fiber optics
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(280.1100) Remote sensing and sensors : Aerosol detection
(280.1310) Remote sensing and sensors : Atmospheric scattering
(280.1350) Remote sensing and sensors : Backscattering

ToC Category:
Remote Sensing

History
Original Manuscript: November 12, 2012
Revised Manuscript: December 19, 2012
Manuscript Accepted: January 4, 2013
Published: January 17, 2013

Virtual Issues
January 24, 2013 Spotlight on Optics

Citation
Ernst Brinkmeyer and Thomas Waterholter, "Continuous wave synthetic low-coherence wind sensing Lidar: motionless measurement system with subsequent numerical range scanning," Opt. Express 21, 1872-1897 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1872


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References

  1. R. C. Youngquist, S. Carr, and D.E.N. Davies, “Optical coherence domain reflectometry: a new optical evaluation technique,” Opt. Lett.12, 158–160 (1987). [CrossRef] [PubMed]
  2. K. Takada, T. Kitagawa, M. Shimizu, and M. Horiguchi, “High-sensitivity low coherence reflectometer using erbium-doped superfluorescent fiber source and erbium doped power amplifier,” Electron. Lett.29, 365–367 (1993). [CrossRef]
  3. A. Kohlhaas, C. Frömchen, and E. Brinkmeyer, “High-resolution OCDR for testing integrated optical waveguide: dispersion-corrupted experimental data corrected by a numerical algorithm,” J. Lightwave Technol.9, 1493–1502 (1991). [CrossRef]
  4. D. M. Baney and W. V. Sorin, “Extended-range optical low coherence reflectometry using a recirculation delay technique,” IEEE Photon. Technol. Lett.5, 1109–1102 (1993). [CrossRef]
  5. W. V. Sorin, “Optical reflectometry for component characterization,” in Fiber Optic Test and Measurement, D. Derrickson, ed. (Prentice-Hall, 1998).
  6. P. Lambelet, P. Y. Fonjallaz, H. G. Limberger, R. P. Salathé, C. Zimmer, and H. H. Gilgen, “Bragg grating characterization by optical low-coherence reflectometry,” IEEE Photon. Technol. Lett.5(5), 565–567 (1993). [CrossRef]
  7. U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” J. Lightwave Technol.11(8), 1377–1384 (1993). [CrossRef]
  8. C. J. Karlsson, F. A. Olsson, D. Letalick, and M. Harris, “All-fiber multifunction continuous-wave coherent laser radar at 1.55 m for range, speed, vibration and wind measurements,” Appl. Opt.39, 3716–3726 (2000). [CrossRef]
  9. P. Lindelöw and J. J. Mohr, “Coherent lidar modulated with frequency stepped pulse trains for unambiguous high duty cycle range and velocity sensing in the atmosphere,” International Geoscience and Remote Sensing Symposium (IGARSS), pages 2787–2790 (2008).
  10. A. T. Pedersen, “Frequency swept fibre laser for wind speed measurements,” PhD thesis at the Technical University of Denmark, December 2011.
  11. M. Harris, “Introduction to continuous-wave Doppler lidar,” in Remote Sensing for Wind Energy, A. Peña and C. B. Hasager, eds. (RisøDTU, 2011), pp. 41–64.
  12. I. Antoniou and , “Remote sensing the wind using Lidars and Sodars,” Proceedings of the 2007 European Union Wind Energy Conference, Milan, Italy (2007).
  13. E. Simley, L. Y. Pao, R. Frehlich, B. Jonkman, and N. Kelley, “Analysis of wind speed measurements using continuous wave Lidar for wind turbine control,” 49th AIAA Aerospace Sciences Meeting, Orlando, Florida (2011).
  14. E. Brinkmeyer and T. Waterholter, “Lidar-Messsystem,” pending European patent application P89429, November12, 2012.
  15. A. Yariv, Optical Electronics in Modern Communications (Oxford Univ. Press, 1997).
  16. T. Okoshi, K. Kikucho, and A. Nakayama, “Novel method for high resolution measurement of laser output spectrum,” Electron. Lett.12, 630–631 (1980). [CrossRef]
  17. W. V. Sorin, “Noise sources in optical measurements,” in Fiber Optic Test and Measurement, D. Derrickson, ed. (Prentice-Hall, 1998).
  18. C. M. Sonnenschein and F. A. Horrigan, “Signal-to-noise relationships for coaxial systems that heterodyne backscatter from the atmosphere,” Appl. Opt.10(7), 1600–1604 (1971) [CrossRef] [PubMed]
  19. M. Harris, G. Constant, and C. Ward, “Continuous-wave bistatic laser doppler wind sensor,” Appl. Opt.40(9), 1501–1506 (2001). [CrossRef]
  20. J. Y. Wang, “Optimum truncation of a lidar transmitted beam,” Appl. Opt.27, 4470–4474 (1988). [CrossRef] [PubMed]
  21. J. W. Goodman, “Statistical Properties of Laser Speckle Patterns,” in Laser Speckles and Related Phenomena, J.C. Dainty, ed. (Springer, 1984).
  22. C. Weitkamp, Lidar Range-Resolved Optical Remote Sensing of the Atmosphere (Springer, 2005)
  23. D. Marcuse, “Loss analysis of single-mode fiber splices,” Bell Syst. Tech. J.56, 703–718 (1977).
  24. F. L. Pedrotti, Introduction to Optics (Prentice-Hall, 1993).

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