Introduction
Light detection and ranging (lidar) for remote sensing of wind has become a
well-established and widely used instrument in atmospheric science and wind
energy . Among
different variants of lidars, coherent Doppler lidars (CDLs) are of primary
interest for remote measurement of wind as well as characterization of
turbulence structures for the lower atmosphere
. Due to their nature of
operation, CDLs measure the radial velocity of the wind which does not
necessarily coincide with the true velocity vector. Thus, one ideally needs
to employ three lidars, with a sufficient angular separation, for probing the
measurement volumes of interest to be able to derive the full wind velocity
vector. One of the challenges in existing CDLs is the detection of the radial
velocity direction. Among the few commercially available continuous wave (CW)
systems none is capable of determining the radial velocity direction.
A few research CW CDLs, capable of determining the sign of the radial
velocity, have been developed over the years. For instance,
used two CO2 lasers with
frequency-offset locking to discriminate the radial velocity direction. The
system benefits from a down-conversion principle known as heterodyne receiver
with intermediate-frequency (IF) sampling . However,
the reported signal-to-noise ratio around zero velocity in this system
was poor. More recently, a CW CDL capable of determining the radial velocity
sign/direction is the first-generation “Windscanner” also
benefiting from a heterodyne receiver with IF sampling. In this system an
acousto-optic modulator (AOM) is used to provide a frequency shift (offset)
between the local oscillator (LO) signal and the transmit signal. As an
all-fiber directional CW CDL, the first-generation Windscanner has been a
valuable research instrument for directional remote sensing of wind. A
detailed analysis of systems benefiting from the heterodyne front-ends with
IF sampling is beyond the scope of this paper. It suffices to mention that they
may suffer from a number of drawbacks in terms of (more) extraneous noise,
(lower) detection bandwidth (BW), as well as (more) intensive data
acquisition and processing. Some of these issues are briefly discussed in the
remainder of this paper.
Recently, an all-fiber directional CW CDL employing an image-reject homodyne
optical front-end was successfully demonstrated by . This
reported system utilizes an all-fiber 90∘ hybrid ,
conventionally employed in high-speed optical communications, to optically
down-convert the desired signals to baseband. As opposed to the heterodyne
receivers with IF sampling, the optical down conversion is carried out with
passive components only. As a result, the noise behavior of the system,
especially around the zero Doppler shift, is improved. Besides, the system
reduces the BW of the photo-detectors as well as the analog-to-digital converter by a factor of 2.
have shown that, due to the presence of two signal components
with independent noise sources, a cross-spectral analysis technique can be
utilized to remove the unnecessary noise sources in the system, eliminating
the additional intensive signal processing for the removal of the background
noise.
To evaluate the performance of the all-fiber image-reject system
see, its performance was compared against a sonic anemometer
in a field campaign. The measurements were specifically carried out to
measure the vertical component of the wind vector: the vertical component is
usually very small and appears in the frequency region where CW CDLs
generally suffer from a multitude of noise sources, such as offset noise,
interferometric noise, 1/f noise, etc. For comparison purposes, the results
of this campaign are compared with the results of a different campaign
carried out in 2013 where three first-generation Windscanners (benefiting from
an AOM-based heterodyne receiver with IF sampling) were utilized to measure
the 3-D wind vector. For the latter, only the results associated with measured
radial velocities close to zero are discussed in this paper so that a fair
comparison between the above-mentioned systems can be made.
This paper starts with a brief and simple introduction, in terms of baseband
signal models, to the image-reject architecture and how it compares to the
heterodyne architecture with IF sampling. We also discuss the advantages and
disadvantages of a signal processing approach, introduced in and
further analyzed in , to remove the dominant
noise sources and eliminate spectral whitening. Then, we will present some of
the measurement results relevant to this paper for two separate measurement
campaigns where the first-generation Windscanners and a prototype CW CDL,
benefiting from image-reject homodyne receiver , were deployed
for remote sensing of wind.
Finally, the paper is wrapped up with a few concluding remarks. Throughout
this paper, we will use ICDL and HCDL to refer to the CW CDL benefiting from
image-reject front-end and first-generation Windscanner CW CDLs (an AOM-based
heterodyne receiver with IF sampling), respectively.
Image-reject optical receiver in CW CDLs and spectral processing
One of the most well-known and widely used optical front-end architectures in
CW CDLs is the homodyne receiver with real mixing . A
detailed analysis of this system, as well as other architectures, is not the
purpose of this paper. The interested reader can refer to and
for more information. In such a system, a simplified transmit
signal can be expressed as
s(t)∝cos2πfct,
where fc is the optical carrier frequency. As a result, the
baseband signal associated with backscatter from a single moving particle can
be written as
i(t)=αcos2πΔft,
where α, among other things, represents the net effect of transmit
optical power, atmospheric transmission, scattering, telescope area, and the
receiver efficiency. In Eq. () we have ignored any parameters (such
as phase shift) secondary to the concepts discussed in this paper. Please
note that Eq. () represents both negative and positive Doppler
shifts. As a result, due to its symmetric spectrum with respect to the zero
frequency it is impossible to infer the direction of the radial velocity.
Figure illustrates an example of a HCDL where the role of the
acousto-optic modulator (AOM) is to shift the LO frequency
to an IF offset to enable the discrimination of negative and positive radial
velocities. Assuming similar operating conditions, the detected
signal, in the baseband form, for the transmit signal in Eq. () is
i(t)=αcos2πfIFt±2πΔft.
As we can see from Eq. (), it is relatively simple to extract the
sign of the radial velocity as well as its magnitude; the sign can be
inferred by comparing the Doppler shift with respect to the IF. However, we
know from experience that a few imperfections contribute to the corruption of
the desired Doppler signal components close to IF. We believe the main
sources of spurious signals are leakage from the optical circulator, back
reflections from the telescope, and a
challenging offset noise removal at the IF. Besides, possible AOM
imperfections, such as a dirty AOM radio frequency drive and the
zeroth-order component leakage, may contribute to additional noise in the
system. As a result, an accurate measurement of small Doppler shifts
(associated with wind speeds close to zero) becomes more cumbersome and
sometimes even impossible.
Heterodyne receiver with IF sampling (HCDL). To be able to capture the
full return signal power a balanced mixer/detector needs to be employed; for details
please see . MO and EDFA represent the master oscillator and erbium-doped
fiber amplifier, respectively. Optical circulator isolates the transmit, s(t), and
the receive signal, r(t). Lo(t) represents the local oscillator signal, A/D
is the analog-to-digital converter, and DSP is the digital signal processor unit.
A thorough analysis of an all-fiber image-reject homodyne receiver has been provided
in . This system utilized a receiver employing two signal detection
arms: in-phase (I) and quadrature-phase (Q) components. The combination of the I and
Q signal components results in a complex-valued signal
i(t)=iI(t)+jiQ(t)=α22cos2πΔft±jα22sin2πΔft,
where j=-1. Furthermore, iI(t) and iQ(t) are the baseband I
and Q components, respectively. It can readily be seen that by comparing the
I and Q components in Eq. (), the radial velocity sign can be
inferred. Furthermore, we have shown in that there are two
approaches to retrieve the velocity component from the spectral analysis of
Eq. (), i.e., auto-spectral analysis of the complex signal or the
cross-spectral analysis of the in-phase and quadrature components. For the
remainder of this paper, we use the term cross-spectral approach when
referring to the cross-spectrum between the in-phase and quadrature
components of the baseband signal in Eq. (). The cross-spectral
approach seems to be the obvious option in the majority of measurements due
to its ability to remove, at least on average, the uncorrelated noise sources
such as the dominant detector's shot noise. The main advantage of this
approach, for the majority of scenarios, is the elimination of additional
signal processing algorithms, such as spectral whitening, that may introduce
additional estimation noise. However, as will be shown shortly, the
cross-spectral approach cannot be reliably employed for a small number of
measurement cases using the ICDL where the Doppler spectra leak across the
zero frequency.
Following Eqs. (25) and (26) in it is evident that the
cross-spectral approach works best when the spectral components are to the
one side of the zero frequency. In other words, the Doppler shifts associated
with the backscatter are either all positive or negative: they do not
leak across the zero frequency. This is, of course, the case for the majority
of scenarios. However, as we will show in this paper, the estimation of
Doppler shifts distributed around zero frequency for cross-spectral approach
becomes skewed and biased. For instance, if the vertical velocity component
measurement associated with a large sampling volume is carried out, it is
highly probable to observe a wide distribution of velocities which cross the
zero frequency. This is indirectly due to the incapability of lidars to
provide point measurements; CDLs always provide a volume measurement. In the
event of CW CDLs, the sampling volume is primarily a function of the output
lens diameter and measurement range.
Optical signal intensity as a function of distance from the output lens
of a telescope. For an effective aperture diameter of 2 cm, the FWHM at a focus distance
of 2.7 m is about 72 mm. Due to beam truncation at the output lens in our system, the measured FWHM is 140 mm.
For an untruncated Gaussian beam, the transmit laser beam's optical intensity (OI) has a Lorentzian distribution defined by
OI=Γπ(F-d)2+Γ2,
where λ is the wavelength; d and F are the distance and focus
distance of the light with respect to the output lens of the telescope,
respectively. Furthermore,
Γ=4λF2πDeff2,
where Deff is the output lens effective diameter, i.e., where the
transmit beam radial intensity drops to 1/e2
see. For an effective antenna diameter of 2 cm
and a focus distance of 2.7 m the full width at half maximum (FWHM) of the beam
(as shown in Fig. ) is 72 mm
see. In our experiment the lens
diameter (not the effective diameter) was a mere D=2.2 cm. Due to beam
truncation see at the output lens of the telescope in our
system the FWHM at the focus distance deviated from the untruncated beam in
Eq. (). Our measurements indicated a FWHM of 140 mm at a focus
distance of 2.7 m at the time of measurement. This width corresponds
approximately to the 115 mm gap of the sonic anemometer
used for the verification of the measurement results, elaborated in Sect. . Following Eq. () it can be inferred that the FWHM
varies quadratically as a function of the focus distance.
To demonstrate the performance of the cross-spectral approach, in the event
of Doppler spectral power at both sides of zero frequency, let us assume a
simple case of optical backscatter from two individual aerosol particles. The
two particles have Doppler shifts equal in magnitude but opposite in sign,
with baseband coefficients α and β associated with positive and
negative Doppler shifts, respectively. Thus, assuming the transmit signal in
Eq. () and following the image-reject architecture elaborated in
, the following baseband complex signal can be formulated
i(t)=iI(t)+jiQ(t)=2α+β2cos2πΔft+j2α-β2sin2πΔft.
Moreover, assuming the desired Doppler signal information is contained in the imaginary part of the cross-spectrum between I and Q
,
ℑPiIiQ=(α+β)(α-β)8δf+Δf-δf-Δf,
where ℑPiIiQ represents the imaginary component of the cross-spectrum between I and Q.
To assess the performance of the cross-spectral approach, let us consider three different scenarios:
If β→ 0, thenℑPiIiQ=α28δf+Δf-δf-Δf,which is a better spectral estimator, compared to the auto-spectral method,
as elaborated in and . This is a
very common measurement scenario since simultaneous occurrence of Doppler
spectral components with opposite sign is rare and is expected in specific
conditions, e.g., vertical wind component measurement in turbulent flow or
large sampling volume.
If β=α, thenℑPiIiQ=0.In this case, contrary to the auto-spectral procedure, the estimator fails to detect
the presence of a Doppler signal. However, the center of gravity and median estimators,
explained in what follows, are able to produce the correct average Doppler shift
associated with the sampling volume.
If β≠α and β≠0, then Eq. () detects a single signal
component which might be negative or positive depending whether β>α
or β<α. This may result in an inaccurate detection/estimation of the
Doppler shift and introduce a bias in the measured volume-averaged velocity estimate away from zero.
As a result, although cross-spectral approach provides a reliable and convenient
way for Doppler shift estimation in the majority of cases, it fails to provide
unbiased velocity estimates when Doppler components spread across the zero frequency.
Cross-spectral approach in the event of spectral components appearing
on both sides of zero frequency. Examples of auto-spectra are shown in the
left column while the corresponding cross-spectra are shown in the right.
On the other hand, more often than not, we are interested in the mean value
of the Doppler shift as it represents the dominant wind velocity in the
sampling volume. Thus, is it possible to utilize the cross-spectral approach
when one is interested in the average value of the wind velocity in the
sampling volume? To answer this question, let us take the two practical
estimators conventionally used for the sampling-volume average wind velocity
estimation, i.e., the center of gravity and median estimators.
The mean (center of gravity) Doppler shift estimator, operating on a power spectral density (treated as a probability distribution
function (PDF) of Doppler shifts), is
μf=∫fPr(f)df/∫Pr(f)df,
where μf is the mean Doppler shift.
It can be easily shown that
∫fPr(f)df=2∫fℑPiIiQ(f)-df,
where ℑPiIiQ(f)- is the one-sided spectrum
see. At first glance the center of gravity estimator should
be able to operate on the cross-spectral approach. However, to estimate the
center of gravity, the spectrum needs to be
normalized, hence the normalization factor in the denominator of
Eq. (). Replacing Pr(f) in Eq. () with
ℑPiIiQ(f)- associated with the spectrum in
Fig. d results in Δf which deviates from the true center
of gravity estimate, i.e., (α2-β2)Δf/(α2+β2).
The median estimator of the Doppler shifts is defined by
∫-∞f̃P(f)df=12∫-∞+∞P(f)df,
where f̃ is the median frequency. It is easy to show that the
median estimator for the average velocity retrieval fails to provide an
accurate estimate when operating on ℑPiIiQ(f)-. As
a result, the auto-spectrum of the signal, Pr(f), needs to be utilized.
The median estimator turns out to exhibit a lower variance
, when compared to the center of gravity estimator. Once
the median (or mean) value of Doppler shifts is estimated, it is easy to
find the corresponding median wind speed by
ṽ=12λf̃.
Using the auto-spectrum in Eqs. () and () requires the
dominant background noise to be removed (a rather signal-processing-intensive
procedure that can introduce an additional estimation error).
Following the above discussion, the cross-spectral approach cannot be
reliably used when estimating either the mean or median value of the vertical
wind component since there is a possibility for spectral cancellation across
the zero frequency. The chances for spectral cancellation are even higher
when measurements are carried out in turbulent flows and large sampling volumes. As
shown in Eq. (), the sampling volume increases quadratically as a
function of distance from the transceiver antenna. Thus, more precautions
should be taken when measurements are carried out for long ranges.
Field campaign at Risø campus of the Technical University of Denmark.
(a) shows the position of the ICDL's output antenna with respect to the sonic anemometer. (b) is an expanded view of the mounting plate for the antenna, viewed from the backside of the plate seen in (a).
On the other hand, the cross-spectral approach is a very effective way for
mean/median Doppler shift estimation in the event of Doppler spectra being
confined to either side of the zero frequency. Hence, a combination of
cross-spectral and auto-spectral approach can be employed for an efficient
estimation of mean wind velocity in ICDLs. For instance, a real-time
automated algorithm can primarily benefit from a cross-spectral approach to
estimate the Doppler shifts. If the estimated shift is inside a predefined
confidence interval (e.g., ±1 m s-1), the auto-spectral approach can be
revoked to estimate the mean value of the Doppler shift.
In this paper, we have simply relied on the auto-spectral approach for the
median Doppler shift estimation. This is justified by the fact that in this
particular campaign we have purposefully performed the measurements for the
vertical wind velocity component only. As we will see in Sect. ,
the results illustrate a significant improvement over the measurements
performed by a HCDL.
Measurement results
The PDF of estimated median velocities; in both figures, blue and
red represent the measurements performed by the sonic anemometer and heterodyne CW CDL
(HCDL), respectively. Please observe the gap in the PDF of velocities
associated with the HCDL in (a). The overshoots (when compared to the blue
PDF) correspond to the accumulation of the estimated velocities associated
with the frequencies away from zero as well as the inaccurately estimated
velocities associated with the frequencies inside the gap.
Two separate and independent measurement campaigns were carried out to verify
the results from the deployed CW CDLs against a sonic anemometer. In the
first measurement campaign, carried out at the Risø campus of the
Technical University of Denmark (October–November 2013), three HCDLs and one
3-D CSAT sonic anemometer (Cambell scientific) were utilized. The HCDLs were
carefully positioned around the mast shown in Fig. 4a and focused on the
measurement center of the sonic anemometer, which for this experiment was
located around 6 m from the ground. The three wind lidars were tilted and
measured at an angle of approximately 35∘. The FWHM of the
measurement volume was 90 mm, which is comparable to the path length of the
sonic anemometer (115 mm). The main purpose of this experiment at the time
was to investigate the possibility of calibrating the sonic anemometer using
the wind lidar. As mentioned before, only a subset of data representing wind
measurements close to zero velocity, taken from only one HCDL, are used for
comparison purposes in this paper.
The PDF of the estimated median velocities close to zero, measured
by the sonic anemometer and ICDL. Blue and red represent the sonic anemometer and lidar
measurements, respectively. As we can infer from the gap in this figure, the
ICDL also suffers from an estimation inaccuracy around zero. This can be
attributed to spurious effects (such as DC offset, 1/f noise, filtering,
etc.) around the zero frequency. The noise behavior, however, is
significantly improved when compared to the HCDL results presented in Fig. ().
In a later measurement campaign, carried out in January 2014, we made use of
a prototype ICDL elaborated in . The parameters for the system
are listed in Table . To measure the vertical component of the
wind, where observations of near-zero velocities are maximized, the beam at
the output of the telescope was aligned vertically and the beam was focused
at the measurement center of the sonic anemometer. Figure shows the
field deployment of the instrument for this specific campaign. Due to the
direction of wind during both measurement campaigns, the effect of mast
shadowing was minimal.
Measurement campaign system parameters. pt, BW,
and fs represent the optical output power, detection bandwidth, and
sampling frequency, respectively. Furthermore, N and M represent the
number of discrete Fourier transform (DFT) points and spectral averaging, respectively. Periodograms
were used for the estimation of spectra as elaborated in
.
F [m]
D [cm]
FWHM [mm]
λ [nm]
pt [W]
BW [MHz]
fs [MHz]
N
M
2.7
2.2
140
1565
0.95
50
120
512
3900
Figure a and b illustrate the PDF of the measured velocities for the measurement
campaign carried out by the HCDL. Figure b is an example associated with PDF of velocities away from the IF
(zero Doppler shift) while Fig. a illustrates the PDF of velocities around the IF offset, i.e., zero radial velocity.
As it can be seen from Fig. a and b the performance of the lidar, compared against the sonic anemometer,
is consistent across the displayed velocity range. However, the measured close-to-zero velocities are either
impossible to estimate or significantly biased, when compared to the sonic anemometer.
This is mainly due to the presence of spurious effects around the IF offset.
Figure illustrates the PDF of the velocities measured by the ICDL,
acquired during the latest field campaign. It is obvious that, when compared
to the HCDL, the estimated mean velocities around zero are more consistent
with the measurements performed by the sonic anemometer. This is mainly the direct
consequence of using passive components for radial sign detection, elaborated
in , as opposed to the AOM (an active component), introducing
additional spurious effects. Moreover, the need for notch filters, band-pass
filters with a very narrow frequency band, for attenuating the strong IF
offset is eliminated. From experience, the analog notch filters are costly,
difficult to design, and often suffer from non-symmetric response. They also
suffer from environmental effects such as temperature dependency. The
image-reject receiver, though, benefits from a high-pass filter for removing
the DC offset, which is more robust and has better frequency response
characteristics.
Figure a and b show the estimated median
velocities sorted in ascending order. The velocity range has been selected to
be in the vicinity of the zero frequency shift. The estimated mean wind
velocities, associated with the measurement volume, show a one-to-one
correspondence between the sonic anemometer and lidar. Wind speed values in
Fig. a and b
are associated with data in Figs. a and , respectively.
In these figures, the red
curve is a linear fit to the measured data. An ideal one-to-one
correspondence between the lidar and sonic anemometer should result in a straight line
with a slope of one, passing through the center. For the campaign associated
with the HCDL, Fig. a, a significant deviation from the
reference instrument is observed (as expected). The deviations for the ICDL,
Fig. b, are far less pronounced and consistently follow the
sonic anemometer, except in a very narrow range around zero velocity.
The estimated median velocities sorted in ascending order and
stacked against the sonic anemometer (blue). The red line is a linear fit to the blue
curve which extends to several m s-1 in both directions. For an ideal lidar
(and sonic anemometer) the blue curve would be a one-to-one line.