June 2014 

NASA/CR–2014-218276 

Simulating Wake Vortex Detection with the 

Sensivu Doppler Wind Lidar Simulator 

Dan Ramsey and Chi Nguyen 

Aerospace Innovations, LLC, Yorktown, Virginia 
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June 2014 

NASA/CR–2014-218276 

Simulating Wake Vortex Detection with the 

Sensivu Doppler Wind Lidar Simulator 

Dan Ramsey and Chi Nguyen 

Aerospace Innovations, LLC, Yorktown, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

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and Space Administration
NASA ATMOSPHERIC ENVIRONMENT SAFETY TECHNOLOGIES NRA 

WAKE VORTEX HAZARD INVESTIGATION

Simulating Wake Vortex 

Detection with the Sensivu 

Doppler Wind Lidar Simulator 

Dan Ramsey and Chi Nguyen 

Aerospace Innovations LLC 

Yorktown, VA 

April 21, 2014 

In support of NASA’s Atmospheric Environment Safety Technologies NRA 

research topic on Wake Vortex Hazard Investigation, Aerospace Innovations 

(AI) investigated a set of techniques for detecting wake vortex hazards from 

arbitrary viewing angles, including axial perspectives. This technical report 

describes an approach to this problem and presents results from its 

implementation in a virtual lidar simulator developed at AI. Threedimensional data volumes from NASA’s Terminal Area Simulation System 

(TASS) containing strong turbulent vortices were used as the atmospheric 

domain for these studies, in addition to an analytical vortex model in 3-D 

space. By incorporating a third-party radiative transfer code (BACKSCAT 

4), user-defined aerosol layers can be incorporated into atmospheric models, 

simulating attenuation and backscatter in different environmental conditions 

and altitudes. A hazard detection algorithm is described that uses a twocomponent spectral model to identify vortex signatures observable from 

arbitrary angles. 

1
1 Introduction 

Over the past few decades, researchers have successfully measured and characterized aircraft 

wake vortices with several types of sensors, perhaps most effectively with the pulsed coherent 

Doppler wind lidar. A typical measurement strategy involves scanning transverse cross-sections 

of the aircraft flight path to detect the relatively large tangential velocities present in the vortex 

pair (Figure 1). 

Figure 1.Visualization of vortex tangential velocities viewable from a transverse scan. From 

this perspective, line-of-sight Doppler instruments can observe the easily detectable tangential 

velocities. The axial perspective, however, is what poses a unique risk to aircraft during 

encounter, and it poses a particularly difficult detection challenge. 

The axial perspective of the vortex hazard, however, has the potential to induce a severe 

rolling moment during an aircraft encounter, and this unique risk has motivated a renewed 

interest in axial detection of wake vortices. 

Using novel approaches developed recently in this field [2,3], this simulation study aims to 

demonstrate the feasibility of identifying vortex signatures observable from arbitrary viewing 

angles, particularly those substantially parallel to the flight path. 

2 Simulation of Heterodyne Detection Lidar 

Sensivu is the name of AI’s virtual wind lidar instrument. In the present application, it 

models the heterodyne detection method, whereby the received laser pulse is optically mixed with 

a local oscillator beam to produce a modulated signal with known frequency. The detector 

measures the energy reflected by aerosols suspended in the atmosphere, and the Doppler 

2
frequency shift of this return signal can be used to infer line-of-sight characteristics of the 

atmosphere (Figure 2). 

Figure 2.Lidar frequency spectrum schematic. Bulk characteristics of the sampling volume can 

be inferred from the lidar spectrum, and line-of-sight velocities will appear as shifts in the peak 

of the spectral curve. Vortex velocities, however, comprise a relatively small fraction of the 

sampling volume, and measuring them requires a different approach. 

2.1 Signal Simulation 

Preconfigured lidar system parameters are used to simulate a Gaussian laser pulse, which 

propagates through a medium of uniformly distributed random scatterers. Each excited scatterer 

emits a Huygens wavelet with random amplitude and phase. The combined backscattered signal 

from all scatterers in the field results in an alternating photocurrent from the detector plane, 

which is digitized in discrete samples and recorded as individual raw signals for each transmitted 

pulse.[1] 

To simulate the raw signal, Sensivu uses one of three user-selected lidar models: Constant 

CNR, Lisim6, and Radiometric. 

Constant CNR. This model uses a signal with constant carrier-to-noise ratio (CNR) specified 

by the user. Individual signals will vary from the specified value, but the simulation is designed 

such that bulk statistics will exhibit the user-specified CNR. We expect that this model may be 

useful to tailor the simulation to field lidar data. 

Here, we define wideband CNR in as the average ratio of signal power to noise power: 

 = 	

〈




〉

〈


〉

Where 
 is the heterodyne signal current and 
 is the receiver noise current. In the

estimated power spectrum, we measure wideband CNR using an estimate of the signal and noise 

3
power. We first establish a mean and standard deviation of the noise level by measuring the

magnitude of the power spectrum spectrum well outside of the signal bandwidth (
.

1

We establish a noise threshold four standard deviations above the mean noise level, and we 

consider any adjacent spectral lines within the signal bandwidth that rise above this

threshold to comprise our signal spectrum. Summing these lines yields an estimate for signal 

power: 

 = 	  

	∊	

The wideband CNR is then estimated as 

 =

 − 

 

where  is the number of bins in the signal bandwidth, and  is the total number of

bins in the spectrum.[6] 

Lisim-6. Lisim-6 is a model with a fixed transmission and backscatter characteristics based on 

previous work in this field. This model incorporates an atmosphere with constant transmission 

coefficients and specified profiles for backscatter coefficient and refractive turbulence that vary 

with altitude. 

Radiometric. Similar to Lisim-6, this model incorporates a user-specified model atmosphere to 

simulate transmission and backscatter based on the lidar wavelength. 

The transmission and backscatter data used in this model are products of the radiative 

transfer code BACKSCAT 4.02. From user-configured atmospheric layers and setup parameters, 

the code uses the LOWTRAN7/FASCODE aerosol models and atmospheric model to produce a 

table of table of aerosol and Rayleigh backscatter and attenuation coefficients as a function of 

altitude.[7,8] 

The radiometric model interpolates coefficients from this table based on the arbitrary beam 

path and incorporates them into the signal simulation algorithm. 

1Alternatively, we could use the mean level of the power spectrum from a range gate beyond the 

effective range of the lidar. 

2BACKSCAT 4.0 (circa 1994) was developed by Sparta, Inc. [8], and is currently distributed by 

Ontar Corporation (ontar.com), packaged with a lidar simulation program called Betaspec 2.0, a lidar 

simulator developed by the University of South Florida [7]. BACKSCAT 4.0 is included with the 

Sensivu 2.0 installation as an executable file. Because it is a 16-bit application, it cannot be run 

directly from 64-bit windows systems. To accommodate this program, we have included the opensource DOS emulator, DosBOX (dosbox.com), which is called from within Sensivu whenever 

atmospheric parameters must be generated from BACKSCAT 4.0. 

4
2.2 Scatterer Velocity Simulation 

The signal contribution from each scatterer exhibits a Doppler shift from the particle’s 

velocity relative to the sensor line-of-sight (LOS) axis. Hence, each scatterer must be assigned a 

LOS velocity representative of the atmospheric volume that is reflecting the lidar pulse. 

Sensivu gets velocity information from one of two sources: an analytical vortex model or a 

TASS dataset. 

2.2.1 Analytical Vortex Model 

The Burnham-Hallock vortex model [9] specifies tangential velocities !" for a single vortex

as a function of distance from the vortex core ", fixed core radius "#, and total circulation $.

!" = 	

$

2&

"

"#

 + "

In Sensivu, the user specifies parameters for a pair of Burnham-Hallock vortices with 

independent circulation values and core radii, plus separation distance and tilt angle to 

determine their relative position. The velocities of the pair are superimposed, and the resulting 

velocity cross-section is treated as constant along the vortex axis (x), with zero vortex velocity in 

the x-direction. 

Figure 3.Vector plot of a sample Burnham-Hallock vortex pair used in Sensivu. (Separation = 

40m, tilt angle=10 ̊, ()=565m2/s, (*=500m2/s, +,)=2m, +,*=3m.) This cross section is

constant along the x-axis, with zero vortex velocity in the x-direction. 

During simulation, a 2-D velocity is calculated for each scatterer along the beam axis 

depending on its position. Each of these values is then projected on the lidar LOS vector to 

obtain the lidar-viewable Doppler velocities for each scatterer. 

5
2.2.2 TASS Data Sets 

The other source used to simulate vortex velocities is a static 3-D data set generated by 

NASA’s Terminal Area Simulation System (TASS). Figure 4 shows a sample dataset generated 

by TASS. The data set shown here models a Boeing 747 wake after 97.5 seconds, part of a 

simulation effort intended to simulate a wake encounter environment suspected in the American 

Airlines Flight 587 accident in 2001. [4] 

The data set for this time slice consists of three *.faa files, containing orthogonal u, v, and w 

velocity components in a regular grid. The domain size is 960m by 648m by 360m in the alongtrack (x), cross-track (y), and vertical directions (z), respectively. Spatial resolution is 1.5m in y 

and z, and 2m in the x-direction. [4] 

Sensivu can also process single *.faa files, which contain all three velocity components in a 

single file. 

Figure 4.Visualization of the 3-D TASS volume used in the development of Sensivu. The 

velocity magnitude isosurface (7 m/s) is plotted to visualize the vortex pair. Velocities of the 

simulation “scatterers” are interpolated from regularly spaced velocity data in this domain. 

For each pulse propagating through the simulation domain, Sensivu generates uniformly 

distributed scatterer positions along the beam axis. It then treats these locations as interpolation 

points within the regular grid. An interpolated u, v, and w value is assigned for each scatterer, 

and each of these vectors is then projected onto the beam axis to obtain a line-of-sight velocity 

for each particle. 

2.3 Frequency Spectrum Estimation 

To resolve the lidar signal along the beam axis, the return signal is sampled in overlapping 

range gates. Each range gate is then weighted with a window function, and a zero-padded Fast 

6
Fourier Transform is performed to estimate a power spectrum in the frequency domain. Each 

spectrum therefore corresponds to a range window whose resolution in space varies depending on 

the number of samples in each range gate and the length of the laser pulse. 

The spectra exhibit significant variation from pulse to pulse, owing to a number of random 

factors. For this reason, spectra from several pulses are usually averaged to obtain a 

representative spectrum for each measurement point. 

2.4 Scan Pattern 

To detect spectral signatures from axial perspectives, we followed the sinusoidal scanning 

strategy employed in Ref. 3, where a single mirror scans horizontally while a pair of rotating 

prisms creates a controlled, rapid vertical oscillation (Figure 5). 

Figure 5. The scan pattern employed in this study. Rapid vertical oscillation combined with 

slower horizontal sweeps yields a dense sinusoidal scan pattern. One scan frame is shown here, 

and each dot in the figure above represents an individual pulse. 

With this method, we obtain a series of pulses distributed across a horizontal and vertical 

angular window. The sensing volume therefore takes the shape of an ever widening rectangular 

wedge (Figure 6). 

7
Figure 6.Illustration of scan volume intersecting a Burnham-Hallock vortex pair. For a static 

sensor, the sampling volume will grow wider up to the range limit. Sampling the signal in 

overlapping range gates allows us to resolve the spectral data into “planes” or “frames” that 

exhibit the characteristics of the atmosphere at a given range. 

2.5 Moving Sensor Simulation 

To explore the special requirements of airborne forward-looking sensors, Sensivu incorporates 

an option for forward airspeed. This affects the minimum required digital sampling rate, requires 

modification of the return signal, and can require expanding the data set if the scanning volume 

exceeds the TASS data limits. 

Figure 7.To accommodate the additional distance traveled during the scan, the scanning 

volume must be extended beyond the region shown in Figure 6. 

2.5.1 Increased Sampling Rate 

The detectable frequency range estimated by discrete sampling is limited by the sampling 

rate. Beyond the Nyquist rate (1/2 the sampling rate), it is not possible to discern the frequency 

components of the signal. 

If the sensor is moving forward, this creates a Doppler shift in the return signal. At a forward 

airspeed of 150m/s, a 2-μm signal transmitting at 25MHz will be shifted to 173MHz. A system 

sampling at 256MHz (with a Nyquist limit of 128MHz) will not measure this signal adequately. 

A higher frequency rate, say 500MHz, is required to capture the spectrum at this speed (Figure 

8). 

8
Figure 8.Illustration of Doppler shift at 150m/s airspeed. Here, forward motion of the sensor 

causes the transmitted pulse at 25MHz (heterodyne frequency) to be shifted to 173MHz when 

the aerosol return is detected at the receiver. 

2.5.2 Sampling Volume Geometry with a Moving Signal 

Because the sensor is moving, each pulse is transmitted from a different location. In earlier 

versions of Sensivu, each individual pulse/signal was trimmed to fit within a coherent volume in 

space. To encourage compatibility with existing sensor systems, however, this system was 

modified. Spectral data is collected using fixed range gating parameters: number of samples in 

each range gate, overlap between gates, number of gates, and so on. 

If the aircraft speed is known, each range gate spectrum can be assigned a position in space, 

and the spectra themselves can be further binned into a predefined number of longitudinallydistributed volumes. During spectral averaging, spectra from each of these volumes are added 

together to obtain a spectral estimate for that space. 

2.5.3 Misalignment Error due to Sensor Motion 

Because the sensor head is both rotating and translating in space, pulses are transmitted in a 

different orientation and position than when they are received. As a result, the receiver is 

misaligned by some angle when the signal is received at time 2R/c. 

To account for this misalignment during simulation, the effective angular misalignment is 

calculated for each signal sample (Figure 9). 

9
Figure 9.Illustration of effective angular misalignment. Because the sensor has rotated and 

translated since transmitting the pulse, there is an angular offset to the target in question. 

With an angular offset, we are able to use an expression for CNR loss in heterodyne systems 

related to this offset angle and the diffraction angle at the lidar wavelength[1]. 

-	 = 	./0 1

−	23

34



5

Here, 34 is the diffraction angle,

34 = 	

6

&7

7 is the Gaussian beam waist, and 6 is the lidar wavelength. To illustrate the order of 

magnitude of this error: a 2-μm lidar with 5-cm beam waist, scanning at 20 deg/s, might exhibit 

a 3.5 dB loss due to this alignment error. 

2.5.4 Data Set Expansion 

The TASS data sets are fixed size (Figure 4). If using the TASS dataset for a simulation 

where the scatterers are sampled outside of this volume, the TASS dataset must be expanded to 

fit the simulation envelope. 

At runtime, Sensivu determines the limits of the simulation envelope and mirrors the TASS 

data along the boundaries in three dimensions until the simulation space can be accommodated. 

Although it is resource intensive, this method ensures that the dataset is adequately sized for the 

simulation. Figure 10 demonstrates the expanded dataset. 

10
Figure 10. When using the TASS dataset to simulate vortex velocities, the dataset is mirrored 

along its boundaries until expanded to the required size. 

3 Axial Detection Algorithm 

The Doppler spectrum contains an estimate of the signal power for each frequency bin 

measurable at a given sampling rate. The median peak of the distribution can be interpreted as 

dominant frequency of the return signal. Therefore, the shift of this peak from the heterodyne 

frequency of the transmitted pulse can be used to estimate the expected line-of-sight velocity for 

the bulk of the sampled volume (Figure 2). 

In classic transverse scanning, vortex tangential velocities typically appear as a minor 

perturbation at the base of the spectral curve rather than a shift in the bulk peak. As the lidar 

look angle shifts toward the vortex axis, these perturbations become even more indistinct, and 

we look to other methods to discern vortex signatures in the lidar signal. 

3.1 Zone-Based Spectrum Averaging 

In planar scanning patterns, the simplest way to reduce random effects in the spectrum is to 

average the spectra from a fixed number of sequential pulses. Because of the different scanning 

pattern described here, however, we employ a zone-based resampling and averaging scheme. 

First, the peak values of all spectra are centered in the frequency band to reduce variation 

when averaging, and each spectrum is assigned a weight based on signal quality in CNR terms. 

Next, the angular scan window is divided into a uniform grid, with the center of each cell 

represented by an azimuth and elevation angle from the sensor reference frame. For each cell, the 

averaged spectrum includes the accumulation of all pulses within a solid-angle “radius” of the cell 

center. 

11
Figure 11.Illustration of zone-b

of each cell is accumulated to 

method is repeated at each res

spectra. 

The result is a series of range g

grid that becomes larger with incre

3.2 Bi-Gaussian Model Para

We then fit the averaged spect

reducing the spectral data to a lim

The model consists of the supe

(fn), amplitude (sn), and standard

value at each frequency(f) multipli

to reduce the degrees of freedom, t

For each spectrum, the six mo

the data in a least-squares sense us

based averaging. Any pulse within a solid angle from the

to generate the average spectrum for that cell. This 2-D ave

h resampled range gate to generate a 3-D spatial matrix of av

nge gate “planes” with averaged spectral data spaced o

increasing range (Figures 7, 8). 

Parameter Estimation

spectrum for each measurement cell(i,j)to a spectral m

limited set of model parameters for each point. 

superposition of two Gaussian curves, each with a p

dard deviation (σn). The noise floor N(f) is modeled 

ltiplied by a gain value(n). After normalizing the expr

, the model takes the following form: [3] 

odel parameters are varied within specified limits

se using an iterative optimization routine (Figure 12).

the center 

averaging 

of averaged 

ced on a Cartesian 

al model, thereby 

a peak frequency 

eled as a constant 

expression further

imits and fitted to 

.

12
Figure 12.Illustration of bi-Gaussian spectral model. The model curve (M2

) is the sum of the 

first and second Gaussian curves. The six model parameters are varied within predefined limits 

until a least squares convergence is reached. The detection field D(i,j) for each range gate is 

based on the relative magnitude of the 2nd Gaussian curve. 

4 Vortex Signatures in the Model Parameters 

4.1 S2 Model Parameter 

Since the secondary Gaussian curve is intended to model the vortex-induced spectral 

broadening, the model parameters that describe it are good candidates for identifying vortex 

signatures. Indeed, the clearest vortex signatures are visible in the s2

 parameter, which is the 

amplitude of the secondary curve relative to the amplitude of the primary curve. Figure 13 is an 

example of a vortex pair signature visible in the s2

 data. 

13
Figure 13. Example of the vortex signatures present in the s2

 model parameter. Five selected 

range gates are shown on the left. On the right, a schematic shows the overall scanning 

orientation. An azimuth offset of 25 ̊ from the vortex axis makes the signature appear to drift 

from right to left across the field of view with increasing range. 

Other parameters, such as the width of the secondary Gaussian or the area captured under 

the secondary curve, seem to be more prone to spurious results that do not correlate with vortex 

signatures. Hence, we use the s2 parameter as the clearest indicator of the vortex hazard. 

5 Hazard Magnitude and Position Estimates 

To estimate the vortex hazard, peaks in the s2 parameter are measured in relation to the 

background statistics. First, speckle noise is filtered in each range plane using a 3x3 median 

filter. Next, the characteristics of the background data are estimated (mean and standard 

deviation), and the peaks in s2 attributable to vortices are expressed in terms of multiples of 

standard deviations above the background mean. 

5.1 Position Accuracy 

In the simulation space, the vortex pair is a linear feature along the X-direction. Any given 

“hit” in a scan plane has an x coordinate that corresponds to a nearest “slice” in the TASS data. 

Using this slice, the y and z coordinates corresponding to the vortex positions were read from 

truth data supplied by NASA with the simulation cases. 

Because the algorithm only identifies a single peak in a given frame, we use the average of 

the two vortex positions as a reference from which to estimate the positional accuracy of the 

Sensivu hazard algorithm.3

3

 In the absence of a hard threshold for false alarm filtering, the track hits were manually filtered. 

Therefore, any algorithm track hits that identified a spurious peak not associated with the vortex 

14
Y Z

Mean Error -5.8m -10.4m 

Standard Deviation 9.5m 8.4m

(N=87)

The results show a nominal bias, however it is well within the separation distance between 

the vortices (approximately 50m). 

Figure 14 shows how, for small angles offset from the vortex axis, the algorithm often picks 

the larger of the two vortex signatures as the single peak. For larger angles, the peak is typically 

more centrally located in the vortex pair. 

Figure 14. Simulation truth positions (+) compared with algorithm peak detection position 

results (O). The left image is a 5 ̊ observation angle, and the right image is the same TASS 

data viewed from a 10 ̊angle. The Sensivu algorithm picks up the largest peak in the scan 

frame and treats it as the vortex hazard. For small viewing angles such as this, two peaks are 

usually visible, but only one is chosen as the primary hazard. For larger viewing angles, the 

signature was discarded. As a result, the accuracy of the position estimates reflects a human-in-theloop outlier screening. 

15
peak is typically more centrally located. On average, the error places the position within the 

vortex pair ellipse, however these results incorporate human-in-the-loop screening of spurious 

hits for marginal data. 

5.2 Dependence of Apparent Hazard Magnitude on Viewing Angle 

Since the tangential components of the vortex flow become more dominant as the line-ofsight approaches a perpendicular viewing angle, we expected the apparent strength of the vortex 

to follow a similar pattern. Indeed, with all other variables held approximately equal, there 

appears to be a linear relationship between viewing angle and apparent strength. 

Figure 15. Measured s2

 parameter peak value at various viewing angles to a simulated vortex 

pair. Azimuth was varied from 5 degrees to 45 degrees relative to the vortex axis. All strength 

measurements are from a single range gate centered at a distance of 1493m from the lidar. 

Wind field was NASA’s TASS Case 18 (Ref. 10), which simulates a B747 “out of ground 

effect” wake vortex embedded within a low turbulence atmosphere (eddy dissipation rate = 

4x10-5 m2s

-3). N = 52, circulation truth values: μ = 550m2

s

-1

, σ = 7.6m2s

-1 (15-20m average); μ 

= 499m2s

-1

, σ = 20.4m2s

-1 (10-15m average). 

Qualitatively, a few things change as the viewing angle changes from an axial perspective to 

a more oblique perspective. First, as we observed quantitatively, the vortex signature is more 

prominent relative to the background. Second, the footprint of the vortex pair signature becomes 

“smeared” along the direction of the angular offset. Each range gate samples a 3-D volume, and 

the depth of this volume is responsible for this measurement artifact. Third, the characteristic 

shape of the vortex signature changes. From an axial perspective, individual vortices can often be 

discerned, but as the viewing angle becomes wider, the signature takes on the shape of the vortex 

pair ellipse, with the central “downwash” zone exhibiting the peak signature. Figure 16 illustrates 

some examples of these qualitative differences. 

16
Figure 16. Qualitative comparison of vortex signatures at different viewing angles. Azimuth 

angle was varied from 5 ̊ to 40 ̊, but each image above is taken from the range gate centered 

at 1493m, which in turn is centered on the same location in the 3-D TASS volume (Case 18, 

0s). Note that the pseudocolor scaling changes dynamically between simulation runs, so no 

absolute comparisons of magnitude can be made between images. One can, however, observe 

that the background topography appears to diminish relative to the vortex signature as the 

viewing angle becomes greater. 

5.3 CNR and Range Considerations 

The lidar equation for coherent detection lidar reveals the R-2 relationship between CNR and 

target range. Put in a different way, a more distant target will result in a weaker spectral peak 

relative to the noise floor. As the noise floor rises in relation to the signal portion of the 

spectrum, it will occlude more of the secondary Gaussian curve, which signals the vortex 

presence. Therefore, it is reasonable to expect a weaker vortex signature at longer range. 

Figure 17. Track hits for three individual simulation runs at 5, 20, and 40 degrees offset from 

the vortex pair axis. All else equal, apparent strength is correlated positively with CNR. 

Indeed, if all other parameters are held constant, a track hit in higher CNR conditions will 

appear stronger than one in lower CNR conditions. 

17
5.4 Performance Envelope 

Because this detection algorithm relies heavily on the aerosol return, this simulation can be 

expected to apply to coherent lidar systems operating in wavelengths from 1μm to approximately 

10μm. At these wavelengths, the atmospheric conditions of the sensing volume must also support 

a minimum aerosol density in order to detect vortex signatures in the spectra. Although the 

aerosol density is dependent upon local conditions, our trade studies indicate that this algorithm 

is generally successful in the atmospheric boundary layer, typically below a ceiling of 

approximately 2km to 3km AGL. 

6 Opportunities for Future Work 

6.1 Sensor Application 

A natural extension of this work would be applying this algorithm to offline post-processing 

of data from real-world sensors. Most existing data would likely not suffice, as ground-based 

measurement campaigns have typically involved two-dimensional planar scanning of transverse 

wake cross-sections. Implementing this algorithm would require hardware capable of rapidly 

scanning in a 3-D pattern. 

While some integration and modification would certainly be required, the general architecture 

implemented in Sensivu would make the transition to real-world systems a matter of data 

conversion and processing. 

The nonlinear model fitting approach is computationally intensive, and this system is not 

currently a candidate for real-time processing. On a PC workstation, processing one simulation 

run (one scan) takes up to 30 minutes. Although Moore’s Law and parallel processing hardware 

may lead to a scenario where a real-time application is feasible, this algorithm is perhaps best 

classified as a candidate technology for future sensors rather than an immediately applicable 

solution. 

6.2 Direct Detection Application 

The core assumption underlying the development of the processing algorithms described here 

is that the tell-tale vortex signatures are manifested in the lidar returns as distortions or 

excursions from the typical signals returned by the bulk atmosphere volumes. 

During this study, an investigation into visible and UV wavelengths revealed that this 

principle might be applied to direct detection lidar as well, albeit in a radically different way. 

Although a detailed investigation quickly outgrew the scope of this work, there may be an 

opportunity to investigate model fitting approaches to direct detection Doppler lidars that 

incorporate fringe imaging. By investigating distortions in the characteristic Airy shape function, 

a similar approach would fit an analogous model to the data, expecting a set of parameters to 

reveal vortex signatures. 

18
7 Conclusions 

This work was undertaken to “support and facilitate NASA’s efforts to link wake vortex 

behavior and hazard indicators to factors that are detectable by sensors from arbitrary viewing 

angles and at sufficient range to allow for hazard mitigation or avoidance by an aircraft.” [12] To 

accomplish this objective, a simulation tool was developed that can use NASA’s TASS data sets 

with embedded vortices as sensing volumes. Leveraging existing atmospheric transmission codes, 

a multispectral simulation tool was developed that simulates coherent detection lidar systems 

with wavelengths ranging from 1μm to approximately 10μm. To test concepts related to airborne 

platforms, the simulation also provides for forward motion with optional settings. 

Encouraged by a method described in references 2 and 3, an algorithm was developed that 

can identify vortex signatures from arbitrary viewing angles by fitting a two-component spectral 

model to the simulated data. The feasibility of this method was demonstrated for a range of 

acceptable local sampling conditions in the atmospheric boundary layer. 

While positional accuracy appears sufficient for avoidance purposes, the current 

implementation of the hazard identification algorithm falls short of an ability to discern wake 

characteristics that would drive hazard mitigation technologies. Circulation, a basic measure of 

the vortex hazard, cannot be estimated with sufficient precision, as the observable variables do 

not sufficiently explain the variability in the estimated hazard strength observed in the TASS 

volumes, at least for a single hazard “hit”. By identifying the vortex pair as a linear feature, 

however, the observation angle can be inferred, which is a primary driver of the apparent 

strength. 

In this work, characteristics of 3-D wake vortices were linked to sensor measurables for a 

wide class of sensors likely to be employed in future systems. While the method seems promising, 

it should be noted with the caveat that the approach is limited to a narrow section of the 

atmosphere, and the computational intensity of the approach precludes it from a simple real-time 

implementation. 

The authors’ aim is that the results will generate knowledge used by decision makers to steer 

the development of either airborne or ground-based sensors for vortices, which would provide the 

information necessary for optimum safe and efficient operations in the NextGen environment as 

well as supporting evaluation of formation flight concepts. 

19
8 References 

1] T. Fujii and T. Fukuchi, ed., Laser Remote Sensing, Ch.7. Taylor and Francis, 2005.

2] S. Lugan, L. Bricteux, B. Macq, P. Sobieski, G. Winckelmans and D. Douxchamps, 

“Simulation of LIDAR-Based Aircraft Wake Vortex Detection Using a Bi-Gaussian 

Spectral Model,”IEEE International Geoscience and Remote Sensing Symposium 

(IGARSS 2007), Barcelona, Spain, Jul. 23-27, 2007.

3] D. Douxchamps, Y. Verschueren, S. Lugan, S. Mutuel, B. Macq, and K. Chihara, “OnBoard Axial Detection of Wake Vortices using a 2-μm LiDAR,”IEEE Transactions on 

Aerospace and Electronic Systems, Vol. 44, No. 4, October 2008, p. 1276-1290.

4] G. Switzer, “Documentation for Three Wake Vortex Model Data Sets from Simulation 

of Flight 587 Wake Vortex Encounter Accident Case,” Final Report, RTI/8438/006-

02F, January 2003.

5] C. Nguyen, D. Ramsey, “Sensivu 3.0 User Guide,”unpublished (included with Sensivu 

3.0 documentation), April 2014.

6] S. Tucker, M. Hardesty, A. Brewer, “Optical Remote Sensing with Coherent Doppler 

Lidar,” University of Colorado Lecture, April 4, 2011.

7] “Betaspec 2.0 User Manual,” September 2009, University of South Florida.

8] D. Longtin, M. Cheifetz, J. Jones, J. Hummel, “Backscat Lidar Simulation Version 4.0:

Technical Documentation and Users Guide,” Sparta, Inc., June 1994. (DTIC Report 

AD-A285 851)

9] D. Burnham, and J. Hallock, “Chicago Monostatic Acoustic Vortex Sensing System,”

Report No. DOT-TSC-FAA-79-103. IV, July 1982.

10] G. Switzer, and F. Duparcmeur, “Wake Vortex Data Set #18 for Sensor Development,” 

unpublished, December 2010.

11] J. Vaughan, “The Fabry-Perot Interferometer—History, Theory, Practice, and 

Applications,” Adam Hilger/IOP Publishing, 1989.

12] Amendment No. 8 to the NASA Research Announcement (NRA), “Research

Opportunities in Aeronautics – 2010 (ROA-2010),” NNH10ZEA001N, Released June 2, 

2010.

20
9 Appendix: Sample Data Set 

Included here are data from a trade study which varied the azimuth angle from 5 degrees to 

45 degrees (relative to the vortex axis) in 5-degree increments. This parametric study was 

performed on the Case 18 data set at six time slices (0s, 12s, 24s, 36s, 48s, 60s). 

Each of the simulations consisted of one scan frame, and the results shown here are a series 

of 2-D maps of the s2 parameter fitted to the spectral data. 

The physical location of the lidar and data set were oriented such that the range gate at 

1493m was centered on the same TASS data region for each simulation run. For wider viewing 

angles, the vortex pair may appear multiple times due to the reflection of the original data set in 

order to accommodate the entire sensing volume. 

Other than the lidar position and orientation, all other simulation and processing parameters 

were held constant for this study. The following parameters are a selection of those used as 

initial conditions for the simulation: 

Simulation or Processing Parameter Value

Altitude 1000 m 

Azimuth angle scan range 12 degrees 

Azimuth center [From 5 degrees to 45 degrees] 

Elevation angle scan range 3 degrees 

Elevation angle center 0 degrees (horizontal) 

Period for one scan sweep .55 s 

Wind data source TASS Case 18 (B747; EDR=4e-5) 

[0, 12, 24, 36, 48, and 60 sec] 

First signal sample range 1000 m 

Last signal sample range 2500 m 

Lidar wavelength 2.02 μm 

Pulse repetition rate 5k pulses/s 

Pulse energy 5 mJ 

Pulse width 400 ns 

Pulse to pulse frequency fluctuation 

(standard deviation) 1 MHz 

Nominal heterodyne frequency 25 MHz 

Sampling rate 128 MHz 

Pulse width fluctuation (std. dev.) 20 ns 

Pulse timing jitter (std. dev.) 50 ns 

Transmitter optical efficiency) .99 

Antenna efficiency (truncation * heterodyne 

efficiency) .41 

Receiver optical efficiency .99 

Beam splitter optical efficiency .80 

Quantum efficiency .1 

Heterodyne receiver excess noise ratio 1.1 

Receiver bandwidth 8e7 

Receiver aperture diameter 10 cm 

Beam quality (M2) 1 

Season Spring/Summer 

Atmosphere model US Standard (1976) 

Boundary layer height 2 km 

Aerosol type Maritime 

Relative humidity 70% 

Surface visibility 23 km 

Wind speed at 10m 10 m/s 

FFT size 512 

Samples per range gate 192 

Overlap between gates 2/3 

Resampling ‘radius’ solid angle .5 degrees 

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REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Simulating Wake Vortex Detection With the Sensivu Doppler Wind Lidar 

Simulator

5a. CONTRACT NUMBER

NNL12AA24C 

 6. AUTHOR(S)

Ramsey, Dan; Nguyen, Chi

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center 

Hampton, Virginia 23681 

 

 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

 8. PERFORMING ORGANIZATION

 REPORT NUMBER

10. SPONSOR/MONITOR'S ACRONYM(S)

NASA

13. SUPPLEMENTARY NOTES

Langley Technical Monitor: Larry Goins

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Unclassified - Unlimited

Subject Category 06

Availability: NASA CASI (443) 757-5802

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email: help@sti.nasa.gov)

14. ABSTRACT

In support of NASA’s Atmospheric Environment Safety Technologies NRA research topic on Wake Vortex Hazard 

Investigation, Aerospace Innovations(AI) investigated a set of techniques for detecting wake vortex hazards from arbitrary 

viewing angles, including axial perspectives. This technical report describes an approach to this problem and presents results 

from its implementation in a virtual lidar simulator developed at AI. Threedimensional data volumes from NASA’s Terminal 

Area Simulation System (TASS) containing strong turbulent vortices were used as the atmospheric domain for these studies, in 

addition to an analytical vortex model in 3-D space. By incorporating a third-party radiative transfer code (BACKSCAT 4), 

user-defined aerosol layers can be incorporated into atmospheric models, simulating attenuation and backscatter in different 

environmental conditions and altitudes. A hazard detection algorithm is described that uses a twocomponent spectral model to 

identify vortex signatures observable from arbitrary angles. 

15. SUBJECT TERMS

Atmospheric hazards; Atmospheric simulation; Avionics; Lidar; Remote sensing; Wake vortex

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