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PROCEEDINGS OF SPIE
SPIEDigitalLibrary.org/conference-proceedings-of-spie
Near ground surface turbulence
measurements and validation: a
comparison between different
systems
Chensheng Wu, Daniel A. Paulson, Miranda Van Lersel,
Joseph Coffaro, Melissa Beason, et al.
Chensheng Wu, Daniel A. Paulson, Miranda Van Lersel, Joseph Coffaro,
Melissa Beason, Christopher Smith, Robert F. Crabbs, Ronald Phillips, Larry
Andrews, Christopher C. Davis, "Near ground surface turbulence
measurements and validation: a comparison between different systems,"
Proc. SPIE 10770, Laser Communication and Propagation through the
Atmosphere and Oceans VII, 107700K (18 September 2018); doi:
10.1117/12.2322723
Event: SPIE Optical Engineering + Applications, 2018, San Diego, California,
United States
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Near ground surface turbulence measurements and validation: A
comparison between different systems
Chensheng Wua*, Daniel A. Paulsona, Miranda Van Lersela, Joseph Coffarob, Melissa Beasonb, Christopher
Smithb, Robert F. Crabbsb, Ronald Phillipsb, Larry Andrewsb, Christopher C. Davisa
aDepartment of Electrical and Computer Engineering, University of Maryland College Park, College
Park, Maryland 20742, USA;
bCollege of Optics, University of Central Florida, Orlando, Florida 32816, USA.
ABSTRACT
Recently, the number of optical systems that operate along near horizontal paths within a few meters of the ground has
increased rapidly. Examples are LIDAR or optical sensors imbedded in a vehicle, long range surveillance or optical
communication systems, a LIFI network, new weather monitoring stations, as well as directed energy systems for
defense purposes. Near ground turbulence distortion for optical waves used in those systems cannot be well described by
conventional turbulence and beam propagation theory. Phenomena such as anisotropy, micro mirage effects, a temporal
negative relation between diurnal dips and altitude, and condensation induced measurement errors are frequently
involved. As a result, there is a high risk of defective designs or even failures in those optical systems if the near ground
turbulence effects are not well considered. To illustrate such risk, we make Cn2 measurements by different approaches
and cross compare them with associated working principles. By demonstrating the reasons for mismatched Cn2 results,
we point out a few guidelines regarding how to use the general anisotropy theorem and the risk of ignoring it. Our
conclusions can be further supported by an advanced plenoptic sensor that provides continuous wavefront data.
Keywords: Turbulence measurements, turbulence distortion, plenoptic sensor, LIDAR, LIFI, optical communication,
general anisotropy theorem, RTD
1. INTRODUCTION
We have found that conventional isotropic turbulence theory doesn’t fit the real atmospheric turbulence situations within
the first few meters near the ground. This is where the many advanced optical systems are deployed, such as the
imbedded sensors in an automatic driving vehicle, LIDARs for remote sensing and imaging, surveillance systems, free
space optical communication systems, as well as directed energy laser systems. Mistreating real anisotropic turbulence
as isotropic turbulence could lead to great deficiencies and errors in data processing and rendering in those optical
systems. For example, image restoration algorithms [1, 2] for a surveillance system may take much more unnecessary
processing time by using ground truth aligned with the vertical axis than using ground truth aligned with the horizontal
axis. The difference is caused by the fact that anisotropic turbulence will typically have more turbid power concentrated
in the vertical direction. Similarly, conventional large aperture scintillometers may underestimate turbulence levels near
the ground [3, 4], providing data that doesn’t agree with visual observations (including turbulence estimation through
our own eyes). Therefore, understanding how anisotropic turbulence would affect devices and systems built upon
isotropic turbulence principles has paramount significance for safe operation and precise measurements [5]. The work
described in this paper serves to provide an important comparison between different platforms in measuring near ground
turbulence levels.
2. THEORY AND COMPARISON APPROACHES
2.1 Basics in general turbulence anisotropy modeling
It is common for optical turbulence studies to use very compact power spectrum models to describe the turbulence status
without involving complicated theoretical models from fluid dynamic viewpoints [6]. The compact turbulence power
spectrum models are typically realized through phase screen simulations and verified through experiments [7, 8]. In
Laser Communication and Propagation through the Atmosphere and Oceans VII, edited by Jeremy P. Bos,
Alexander M. J. van Eijk, Stephen Hammel, Proc. of SPIE Vol. 10770, 107700K
© 2018 SPIE · CCC code: 0277-786X/18/$18 · doi: 10.1117/12.2322723
Proc. of SPIE Vol. 10770 107700K-1
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order to conveniently characterize the power spectrum of anisotropic turbulence and reuse most of the phase screen
methods, Andrews and Phillips have proposed an extremely compact modeling based on Dr. Kon’s initial modeling of
non-Kolmogorov turbulence [9]. It is commonly referred as a “general anisotropy theorem”, which handles the mutual
transformation between isotropic and anisotropic turbulence power spectra with anisotropic ratios µx, and µy to scale the
horizontal and vertical axes, respectively. In anisotropic turbulence, it does not degrade with a conventional (-11/3)
power law with increased spatial frequency |κ|, and the actual degradation slope of the power spectrum is indicated by
index -(3+α) in the “general anisotropy theorem”. The parameter α represents a general power law of the media’s
structure function. In conventional isotropic turbulence, µx and µy are simply unity and α=2/3. Therefore, a conventional
turbulence situation is included in the “general anisotropy theorem” as a singular case. And the overall anisotropic
turbulence spectrum, as has been widely accepted in the turbulence field by many researchers such as Xiao [10], Toselli
[11], Baykal [12], Beason [13] and Bos [14] with various mutations of the form, can be written as:
( )
()
( )
2
( 3)/2
22 22 2
,,, n xy
xyz
xx yy z
AC
α
α µµ
κκκα µκ µκ κ
+
Φ=
++
. (1)
( ) ()
2
2 cos 2.
4
A
απ
α
α
π
Γ+
= (2)
In Eq. (1),
2
n
C
represents the generalized structure constant which replaces
2
n
Cin a conventional turbulence theorem.
The generalized structure constant parameter has the unit of m-α, which is a representation of the turbulence strength. We
don’t include inner scale and outer scale factors for simplicity of discussion. A more comprehensive work on an
anisotropic power spectrum with these two factors can be found in Beason et. al [15]. Needless to say, the overall use of
the new model causes significant conflict with a conventional turbulence measurement that estimates the
2
n
C
with unit
m-2/3. In other words, although researchers are still using levels such as 10-15 m-α, 10-14 m-α, and 10-13 m-α to indicate the
turbulence strength, such modeling values don’t provide an intuitive understanding of turbulence strength.
To fix this problem, it is more reasonable to convert back to a “loose” measurement using the Rytov variance [16] to
understand the strength of turbulence at various situations. Empirically, when the Rytov variance gets larger than unity,
the channel is regarded as having strong turbulence. A unified equation to express the Rytov variance has been
developed by Andrews et. al. [17], as:
( )
( ) ( )
( )
( )
1
22
2
322
22
222
0
1
1 sin
1 ( 1) cos sin
2
,, 4 (3 ) 2
sin 1
4
R xy n
xy
L
C kL d
α
α
π
α
α πα
α λ θθ
σ µµα θ
π
α π µµ
πα
+
+
Γ + Γ−
+
=− ⋅+
+
+
∫
(3)
In Eq. (3), the unified Rytov variance is enveloped by sin(πα), where α is the distance power law of the refractive index
structure function [18]. In order to get meaningful results from the general anisotropy theory, the power law index α is
typically evaluated between 0 and 1 (most researchers regulate the boundaries as 0.1 and 0.9). The term sin(πα) also
serves as a major envelope for the unified Rytov variance that results in a general concave shape over α.
2.2 Implementing cross comparisons between different devices
Commercial scintillometers:
Commercial scintillometers such as the BLS900 are typically used to measure
2
n
C
based on the large aperture
scintillometer theorem [19] and conventional Kolmogorov turbulence modeling. Normally, the legitimate use of
scintillometers should give them sufficient elevation from the ground to work in a suitable isotropic turbulence regime.
In our cross comparison experiments, we deliberately put the BLS900 scintillometers close to the ground to produce
2
n
C
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values in non-Kolmogorov turbulence and use them to compute the Rytov variance based on the conventional theorem.
Such Rytov variance values, when compared with actual Rytov variance derived through the formalized “general
anisotropy theorem”, can reveal how “far off” data obtained by mistreating anisotropic turbulence as isotropic turbulence
will be.
A multi-aperture transmissometer:
To get the actual Rytov variance from the formalized “general anisotropy theorem”, we have used a newly described
multi-aperture transmissometer (MAT) system [20]. The MAT system contains 13 distributed small photodetectors that
are synchronized in data collection to reflect instantaneous beam irradiance distribution over a receiver plane. The MAT
system is capable of extracting the long term beam profile to estimate the location of the beam center, beam shape and
beam transmission through an atmospheric channel.
Because it is much easier to use the on-axis scintillation equation from the general anisotropy theorem, the long term
beam profile reconstructed by the MAT system will be used to select the closest detector to the “dynamic” beam center.
The beam center is “dynamically” changing [21] due to beam wander and temporal built up of temperature, which
causes a slow drift on the propagation axis of the beam. Therefore, the Rytov variance calculation defined in Eq. (3) can
be estimated through the closest detector.
According to the “general anisotropy theorem”, the on-axis scintillation index is very useful in interpreting the Rytov
variance under a fixed state of turbulence (stationary anisotropy ratios and power law index). Especially for weak
turbulence regimes, which is generally assumed true when the Rytov variance is less than unity, the on-axis scintillation
index is proportional to the Rytov variance. In deep turbulence cases where the Rytov variance is significantly larger
than unity, the two terms are positively correlated through a non-linear equation [17].
Two resistance thermometer device systems:
To determine the states of turbulence, we have used a high precision multi-probe RTD (resistance thermometer device)
system to extract the temperature structure function over time. The RTD system has multiple probes mounted in a row to
show how temperature fluctuations gets de-correlated with increased spacing, which is theoretically described as a
structure function of the media. The power law of the structure function gives the value of α. Anisotropy can be easily
revealed by the reconstructed structure functions from vertically and horizontally deployed RTD systems. Intuitively, the
RTD system provides distance-value pairs of the media’s structure function, which is generally characterized by the
2
T
C
value and power index α. The output difference between the two RTD systems reveals important information about the
anisotropy state of the channel.
It is also interesting to point out that in processing the RTD system data, one can also fix the power law of the media’s
structure function as 2/3 in conventional Kolmogorov turbulence. This will generate a result of
2
T
C
that can be used to
indicate the conventional
2
n
C
.
2.3 Experimental setup
We first compare the RTD systems by producing the conventional
2
n
C
and anisotropic
2
n
C
through disabling or enabling
the power index fittings in the algorithm, respectively. The two RTD systems are experimentally deployed as supporting
devices for the ONR (Office of Naval Research) Project APSHEL (Atmospheric Propagation Sciences for High Energy
Lasers) on May Test 2018. The test took place in the Shuttle Landing Facility (SLF) in Space Florida. An overall picture
of the system deployment can be shown as:
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(a) (b)
p
+!
a.,
-
Figure 1. (a) Overall view of the test channel with main test range between 1km ~ 2km; (b) Experimental setup of the RTD
probe systems (one vertical and the other horizontal); (c) Picture of the 8-probe RTD system.
The purpose of the RTD system comparison is to provide evidence of anisotropy in turbulence experiments near the
ground, as well as determining the error of measuring turbulence level by assuming isotropic turbulence.
We next compare the RTD system data with the MAT system data to examine the unitless comparison based on the
unified Rytov variance. The MAT system was deployed during the same APSHEL May Test 2018. The experimental
setup is shown as:
Figure 2. (a) Deployment of the MAT system; (b) Side by side deployment of the BLS900 and the MAT system
Proc. of SPIE Vol. 10770 107700K-4
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4MI .01114.1110.
Laser TransmisSometer
Receiver
Laser Transaissometer
Transmitter
To provide additional turbulence data, we also used a commercial scintillometer BLS900 at approximately 4 meters
elevation above the ground to ensure its operation in an isotropic turbulence regime. The supportive data from the
BLS900 helps to reveal the actual variation trend of the turbulence levels, while the near ground measurements may be
influenced by many other factors in the experiment, such as build-up of inferior mirage effects. In other words, the
comparison between the RTD systems and the MAT system will only be made if and only if they agree with the general
trend of
2
n
C
provided by the BLS900 that is 4 meters high above the ground.
We last make a cross comparison between the MAT system and the BLS900 system when both of them are deployed
near the ground with elevation around 1.5 meters. The test was conducted at the Townes Institute Science and
Technology Experimentation Facility (TISTEF) at the Kennedy Space Center (Florida) from 18 October 2017 to 19
October 2017. The experimental setup can be shown as:
Figure 3. (a) Receiver site setup in TISTEF test; (b) Overall setup in TISTEF test
Because the grass-top channel in TISTEF is more resilient to temperature gradient build-up, the BLS900 can be
deployed near the ground with steady alignment. The purpose of the test is to detect weak degrees of anisotropy and
study whether the BLS900 can still be used in this environment with an acceptable error range.
3. EXPERIMENTAL RESULTS
3.1 RTD systems
The RTD systems’ comparison results can be shown as:
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10 -12
10-14
10 -15
04/30 @12AM 05/01 @12AM 05/02 @12AM 05/03 @12AM 05/04 @12AM
Time
(a)RTD retrieved Cn2 data
Horizontal 4 -probe RTD and
Treat Turbulence as Isotropic
Horizontal 4 -probe RTD and
Treat Turbulence as Anisotropic
Vertical 8 -probe RTD and
Treat Turbulence as Anisotropic
;'"+
.
P.
. ; : r `,
`%;, '.;:,.
::_' ;..
i:`t. ':.
ti
T
. .
,.
s' p y1 i, 's 4 ,..:*
;«iti : :sar %`-(! ;.
,^~¡" : ;,:.
:ÿ'.vy.I,/
2(b)RTD retrieved power law
Horizontal 4 -probe RTD and
Treat Turbulence as Anisotropic
Vertical 8 -probe RTD and
Treat Turbulence as Anisotropic
ti *. ' ., .
:..;;..
,: .: ; ,;" .:g :.
-%..
',h ~ ''t.' PN;M. S'ws ,.
+t va.s :% .J'. -;' .
;'' ~¡:r; wá,
. ti
0
04/30 @12AM 05/01 @12AM 05/02 @12AM 05/03 @12AM 05/04 @12AM
Time
Figure 4. (a) Retrieved
2
n
C
or
2
n
C
levels; (b) Retrieved power law indices over horizontal and vertical deployments of the
RTD probe systems with a duration of 10 minutes per sample.
In figure 4(a), the conventional
2
n
C
is evaluated through the 4 probe RTD system by fitting the structure function:
( )
22 2/3
12 T
T T CR−= . (4)
The
2
n
C
is evaluated through the 4 probe RTD and the 8 probe RTD by fitting the structure function:
( )
22
12 T
T T CR
α
−=
. (5)
In Eqs. (4-5), T1 and T2 represent the temperature values at two space points separated by distance R. The right angle
bracket represents the ensemble average over a certain period of time. In our experiment, we empirically average over 10
minutes. Each probe pair will provide one sample point for the fitting, where the 4 probe RTD system has 6 samples and
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the 8 probe RTD system has 28 samples. We didn’t measure the conventional
2
n
C
value from the 8 probe RTD system
because its geometric extent may exceed the outer scale of turbulence, while the 4 prove RTD system has a much shorter
distance range that allows for such operation.
It is evident that in a near ground turbulence environment, turbulence doesn’t necessarily satisfy the 2/3 power structure
function. In specific, the fitting result in plot 4(b) show that the horizontal direction seems to have a power index less
than 2/3, while the vertical direction seems to have a power index higher than 2/3. On the other hand, the result in plot
4(a) suggests that the measured scintillation levels (which are translated through the temperature fluctuation level in the
RTD systems) are almost the same along different measurement directions. Plot 4(a) also suggests that the use of
2
n
C
in
the general anisotropy models doesn’t deviate much from the conventional structure coefficient
2
n
C
in quantifying the
strength of turbulence. Therefore, the classification of weak, medium, and strong turbulence based on 10-15, 10-14 as well
as 10-13 is approximately correct in anisotropic turbulence. One additional observation is that the retrieved power indices
from the vertical and horizontal directions have the same trend.
These observations can be well explained through the “general anisotropy theorem” by introducing the anisotropy ratios
µx and µy. In fact, the same trend of power indices in plot 4(b) suggests that these two curves can be unified into one α*
curve by scaling the x and y geometry differently. Consequently, we can revise the structure function as:
( )
( )
( )
*
2*
22
12 Tx Ty
T T C X or C Y
α
α
µµ
−=
. (6)
For simplicity and symmetry reasons, we analyze the fitting process along the x axis before and after adding the µx
scaling as:
( ) ( )
( )
2
2 2* *
12
log log log log log X :
T Tx
C X TT C X
α αµ
+ = −= + =
. (7)
In “pseudo” equation (7), X is the real world scale and X* is the adjusted scaling geometry in the “general anisotropy
theorem”. We use the prefix word “pseudo” to refer to the fact that equation (7) deals with a fitting algorithm based on
real data instead of a genuine theoretical equation. Both fittings are anchored with the same
2
T
C
value in correspond to
the real turbulence level. In other words, when the unified power law index α* is translated into real world scales, it
renders the actual power index α without affecting other coefficients in the modeling. In an extreme case with a pair of
ideal RTD probes that have infinite accuracy, an analytical solution for the new fitting is possible and can be written as:
( )
( )
*
log
log
x
X
X
αα µ
=
. (8)
In order to get a unified power index α* for the measurement data shown in figure 4(b), µx needs to be evaluated larger
than unity an µy needs to be less than unity. For example, we can arbitrarily assign X = 0.1 (as X is typically evaluated
within 1 meter range) and µx =2, so that we have α*=1.43α. By restricting that the average value of the unified power
index α* should be 2/3, we can extract the long term µx and µy based on the measurement data shown in figure 4. As a
result, µx =2.24 and µy =0.93 for our experiment. The result agrees very well with many theoretical studies on
anisotropic turbulence modeling [10-14] where the major turbulence axis is evaluated has µ~1 and the minor turbulence
axis has µ~2, 5, or 10 in their simulations. Beason’s work [13, 15] also point out with experiment that the major axis is
more oriented along the vertical axis with an aspect ratio of µy/ µx~0.33. This agrees with our experimental result
reasonably well where our µy/ µx~0.41.
We should also point out that the 8-probe RTD system sometimes suggests a power index between 1~2 (where the
normal range should be 0~1) in plot 4(b), this seem to agree with Toselli’s theory [11], which suggest the spectrum
power law index (3+α) to be ranged with 3~5. This wider range doesn’t violate fundamental fluid dynamics. However, it
requires further experiments to determine whether α should be evaluated between 0~1 (as suggested by most
researchers) or 0~2 (as suggested by Toselli and others). The major reason is that sharp temperature gradient can be
occasionally witnessed within the short range of the probes (as the measurement is close to the ground). Therefore, for
the data fitting conducted in this work, the data with α>1 has been removed as “outliers”.
Proc. of SPIE Vol. 10770 107700K-7
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102
10 -2
04/30 @12AM
.. `-v.,
r: l ``Mt.=.,`.
7f .; t. ,.!,i; '7
..,.`i : r,.' :} v:f,,.
.1t ;: ?k v 1 r Ì
,, ,.y, t,
'? '.t t!.i< ^.tiy, .: .i.
'1 `
.If'
4 -probe, horizontal, original Rytov
4- probe, horizontal, unified Rytov
8- probe, vertical, unified Rytov
MAT, tracked center, SI
BLS900, SI (4m elevation)
05/01 @- 12AM 05/02 @12AM 05/03 @12AM 05/04 @12AM
Time
3.2 RTD and MAT comparison
Because the unified Rytov variance in equation 3 requires parameters µx, µy, and α for evaluation. We can use the
retrieved results in section 3.1 for calculation. In specific, we give µx =2.24 and µy =0.93 and α= α* as the unified power
index result with mean value of 2/3 for the RTD systems’ data. In calculating the “assembled” Rytov variances from the
RTD systems, we also assume the wavelength is 633 nm to match with the He-Ne laser used for the MAT system. We
use the pre-fix word “assembled” because we have used the local RTD data to estimate
2
n
C
, µx, µy, α and combined them
with the channel information to get the unified Rytov variance by equation 3. Such calculation is true if and only if the
ground condition is uniform, such as the flat concrete path in SLF.
For the MAT system, we simply use the tracked center detector to get the on-axis scintillation index and compare it with
the RTD results and BLS900 result as:
Figure 5. Cross comparison of Rytov variance values
The scintillation index from the BLS900 is derived by using its
2
n
C
output and the channel information for the large
aperture scintillometer equation:
2 2 7/3 3
4
In
C DL
C
σ
−
=
. (9)
In equation (9), C=4.48, L=2km, and the aperture diameter D is evaluated as 2.54 cm to match with the detector size on
the MAT system. Note that we don’t use the actual aperture size of the BLS900 for equation (9) as the purpose of such
calculation is to estimate the scintillation index of a MAT detector in a Kolmogorov turbulence regime that is 4 meters
above the ground (rather than the scintillation index data on the BLS900). It is evident that turbulence induced
scintillation will be greatly reduced with higher elevation from the ground, as is plotted in figure 5 by the scattered
magenta dots. It is also clear that the systems operating near the ground (1.5 meter elevation) also provide reliable results
as they agree with the SI curve’s trend measured higher above (4 meter elevation).
The MAT system doesn’t produce long duration data (such as 24 hours of continuous data) due to the significant
magnitude of horizontal beam wander. Although the MAT system is designed with a redundant number of distributed
detectors to take care of moderate beam wandering, the beam drift caused by temperature gradients near the ground can
push the beam outside the MAT receiver aperture. Other factors such as power loss, prohibited laser operation at the SLF
during night time, and accidental mirror rotation on the transmitter site also add to the data discontinuity on the MAT
system data. Future improvement will be made by adding a beam tracking and pointing system on the transmitter site to
maintain a reliable alignment.
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101
G) o
CQco
lu
co
°
-a
EDio2
BLS900, conventional Rytov
MAT, unified Rytov
1Q-3
10/18/2017@l2AM
A 'le
17ri .. I.
f. . '- lAix'14 ..
1: .. 1-... ),..; .! . 4 r.
Z.ii.;''.;..% r..
liri?.::,..:!...4'.: ''f! ;
.:S:d
';,L '..z.
.-;.1... 1I.: ,:. N
..., j.:.. :!: '...,:-.A., -,': :.: ''. ':iiPI
:. )?¡ 2
:J.; t- .:*.- .. , :, ,*
'A:. ss,.. : I i:...g;
iii ...: :1
' .: ... ..
%,
10/19/2017@12AM
Time
10/20/2017@12AM
For near ground turbulence measurement, the scattered red dots represent the estimation of the conventional Rytov
variance to mimic the case of mistreating the near ground channel as having Kolmogorov turbulence. The conventional
Rytov variance equation is expressed as:
2 2 7/6 11/6
1.23
In
Ck L
σ
=
. (10)
Compared with the unified Rytov variance along the vertical and horizontal axis, as well as the actual on-axis
scintillation index, our experiment suggests that:
22 2 2
(isotropic) (anisotropic, major axis) (anisotropic, minor axis) ~ ( , )
II I I
MAT on axis
σσ σ σ
>= >= −
. (11)
Unlike the mixed results with
2
n
C
and
2
n
C
co-plotted in figure 4(a), the use of the Rytov variance concept has clearly
separated turbulence strength measurements to address the potential problem of ignoring anisotropic turbulence. In
general, anisotropic turbulence will reduce optical scintillation under the same level of
2
n
C
. In retro-respect, this means
that conventional turbulence measurement approaches will give an underestimated value of
2
n
C
. In fact, theoretical work
[10-14] has already provided similar conclusions that lower scintillation levels will be seen in an anisotropic turbulence
regime. The factor of scintillation reduction in our experiment is approximately 4. In other words, ignoring the
anisotropic turbulence state near the ground would underestimate the channel turbulence level by a factor of 4 in the SLF
test!
3.3 MAT and BLS900 comparison
When the MAT system and the BLS900 system were co-deployed at the same height (~1.5 meter) during the TISTEF
test over a grass top channel, both systems were well aligned and left unattended for long duration (>24 hours). We
compared the derived Rytov variance from the BLS900 (as the outcome of ignoring anisotropy) with the MAT system
suggested scintillation index near the long-term beam center (reconstructed beam center over 2 minutes). The latter one
is affected by anisotropic turbulence, as it is essentially a point measurement that reveals the on-axis unified Rytov
variance in equation (3). The comparison result can be shown as:
Figure 6. Cross comparison of Rytov variance by BLS900 and unified on-axis Rytov variance by the MAT system over a
grass-top channel in TISTEF (10/18/2017~10/19/2017)
It is clear from figure 6 that the BLS900 suggested scintillation index (SI) is approximately correct when operating under
moderate turbulence condition near the ground. The maximum reported
2
n
C
on the BLS900 is 2e-13 m-2/3 during the
TISTEF test. The overall underestimating effect for SI ranges from 1 to 1.93 on an hour-to-hour based comparison. And
the mean ratio between MAT suggested Rytov variance and the BLS900 suggested Rytov variance is 1.12 over the 24
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hour period. In other words, arbitrarily ignoring the anisotropic states of near ground turbulence will not cause severe
problems under medium to low levels of turbulence.
4. CONCLUSION
The introduction of the “general anisotropy theorem” may have caused certain confusions in the turbulence field, such as
the changing unit for turbulence structure constant in deriving the turbulence power spectrum and the geometric scaling
of space. However, the essence of the “general anisotropy theorem” is to maintain conventional understanding of
turbulence models to the largest extend, not to replace any established concept. Our detailed cross comparison
experiments between multiple systems demonstrate that:
1. The numerical scales of
2
n
C
in measuring isotropic turbulence strength are not significantly altered by the
numerical scales of
2
n
C
in anisotropic turbulence regimes. The values of the two terms convey very similar
measure of turbulence and can be mutually used between isotropic and anisotropic models.
2. Because anisotropic turbulence will reduce the observed optical scintillation, the unified Rytov variance should
be used to give the right measure of
2
n
C
under anisotropic turbulence regime. Otherwise, the result will
underestimate the turbulence strength.
3. The state of anisotropy can be determined by using the media’s structure functions to determine μx, μy and α.
The RTD systems used in our experiments can be used to determine anisotropy state. Alternatively, optical
methods such as imagers [15], plenoptic sensors [22], or light field cameras [23, 24] can also be applied to
analyze the incident optical waves and extract correlation information for structure functions.
In summary, the “general anisotropic theorem” integrates with conventional turbulence models reasonably well and is
more reliable to use in a near ground channel [25]. Ignoring anisotropic turbulence may cause large errors in a strong
turbulence regime, and minor errors in moderate or lower levels of turbulence regimes.
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