The main purpose of this study is to evaluate the near-zero wind velocity
measurement performance of two separate 1.5

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

A few research CW CDLs, capable of determining the sign of the radial
velocity, have been developed over the years. For instance,

Recently, an all-fiber directional CW CDL employing an image-reject homodyne
optical front-end was successfully demonstrated by

To evaluate the performance of the all-fiber image-reject system

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

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.

One of the most well-known and widely used optical front-end architectures in
CW CDLs is the homodyne receiver with real mixing

Figure

Alternatively, the transmit (or receive) signal can be frequency shifted. In first-generation Windscanners, the transmit signal is frequency shifted.

Assuming similar operating conditions, the detected signal, in the baseband form, for the transmit signal in Eq. (In CW CDLs, the presence of
non-ideal characteristics of the optical circulator and anti-reflection
coating may give rise to an unwanted signal in the vicinity of the
zero-velocity Doppler component. The unwanted signal is known as the
interferometric noise.

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

A thorough analysis of an all-fiber image-reject homodyne receiver has been provided
in

Following Eqs. (25) and (26) in

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

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

To assess the performance of the cross-spectral approach, let us consider three different scenarios:

If

If

If

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

It can be easily shown that

The median estimator of the Doppler shifts is defined by

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. (

Field campaign at Risø campus of the Technical University of Denmark.

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.,

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 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

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 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,

In a later measurement campaign, carried out in January 2014, we made use of
a prototype ICDL elaborated in

Measurement campaign system parameters.

Figure

In Fig.

Figure

Figure

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

The presented results in this paper verify the relevant performance
improvement claims in

The authors would like to thank Xinzhao Chu from University of Colorado in Boulder and Mikael Sjöholm, Nikolas Angelou, and Karen Enevoldsen from the Technical University of Denmark for their invaluable help. This project is mainly funded by the WindScanner project from the Danish Strategic Research Council (DSF), Danish Agency for Science, Technology and Innovation; Research Infrastructure 2009; Grant No. 2136-08-0022. Additional funds from DSF grant no. 09-067216 (the DTU “Flow Center”) are also appreciated. Ingeborg and Leo Dannin Grant for Scientific Research funded the NI computer used in this work. Edited by: G. Ehret