Svetlana Avramov-Zamurovic, Professor
Weapons and Systems Department
United States Naval Academy
Olga Korotkova, Physics Department, University of Miami, FL
Charles Nelson Electrical and Computer Engineering Department, USNA
Reza Malek-Madani, Director of Research, Mathematics Department, USNA

Research Accomplishments

Instrumentation and Equipment to support
Field Experiments

Student involvement: Field Experiments as
Laboratory Exercises in Courses
May-16
United States Naval Academy
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Field experiments:True
environmental changes
along the entire path are
occurring
simultaneously,
influencing laser light
propagation
Modeling
(Mathematics)
Field
Experiments
(Engineering)
Physical
Phenomenon:
Laser
Propagation
(Physics)
May-16
United States Naval Academy
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


Seven field experiments successfully executed at USNA
Laser beam characterized via PDF
Four PDF models investigated
 Gamma-Gamma and Log-Normal by Andrews and Philips, Gamma-
Laguerre by Barakat and Rice–Nakagami modification by Beckman


PDF of beam allowed us to clearly establish the difference between
laser beam propagation above water and over land
Data processing programs developed in MATLAB
Major project achievements published

Laser light modulated using SLM

Students engaged in experimental aspect of the project

 MIDN Iiams independent research student and MIDN Withsett honors
student
 Field experiments are used as a laboratory exercise in courses
▪ Control systems and their application to weapons (week per semester, 2 semesters, 3
sections, 50 students)
▪ Directed Energy (week per semester, 2 semesters, 30 students)
▪ Introduction to laser research (6 weeks per semester, 9 students)
May-16
United States Naval Academy
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May-16
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
PDF of fluctuating intensity W(h) shows with which chance the beam’s
intensity attains a certain level.
b
Probability(a  h  b)   W (h)dh
W(h)
a

0
h
a b
h(l )   W (h)hl dh
0
Determination of the PDF from moments is an academically noble problem:
(famous Hausdorff moment problem)
 Knowledge of the PDF of the intensity is crucial for solving inverse
problems of finding the statistics of a medium

May-16
United States Naval Academy
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
The goal:


Deliver laser light energy onto a target by maintaining the highest level
of light intensity for as long as necessary to interfere with the target.
Probability Density Function provides information on how often
particular light intensity occurs at the beam center, making PDF a model
of choice to measure the beam quality on the target.
PDF contains the information about the properties of the
environment the laser light passed through.
 The method:

 PDF models are based on light scattering physics employing various
mathematical functions and on statistical moments calculated from
data.

Data histogram is used to evaluate the fidelity of a PDF model.
May-16
United States Naval Academy
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

Gamma distribution modulated by series of generalized
Laguerre polynomials proposed by Barakat
 Medium and source independent
 Uses first n moments of detected intensity
 Valid in the presence of scatterers
Gamma- Gamma distribution based on the work of
Nakagami et. al. and presented by Andrews and Philips
 Medium and source dependent
 Uses 2 first moments
 Valid only in clear air atmosphere
May-16
United States Naval Academy
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 
2( ) 2  2  1
P( I ) 
I
K   (2  I )
( )(  )
( x)
- Gamma-function
K m ( x)
- Modified Bessel function of the second kind.

 ln2 x
and
1
exp(
2
ln x
) 1

1
exp( ln2 y )  1
 ln2 yare normalized variances of the fluctuating intensity due to
large and small turbulent inhomogeneities, respectively.
For the Gaussian beam model and the Kolmogorov power spectrum model:
 ln2 x 
0.49
7/6
[1  0.56(1   ) 12/5
]
B
2
B
where  2 is the normalized variance of
B
fluctuating intensity in the center of the beam:

1
 2L 
1 
2 
 kW0 
2
 ln2 y
0.51 B2

5/6
[1  0.69 12/5
B ]
 I 2    I 2
 
 I 2
2
B
for collimated beams, with L being propagation distance
from the source to the receiver, k is wave number and W0
is the initial beam radius (after the expander).
1. Calculation of statistical moments of fluctuating intensity from data
k max
hk ( x, y) l
k 1
k max
h ( x, y )  
(l )
Fluctuating intensity
h
k
Index of realization
k max Total number of realizations
( x, y ) Coordinates of the pixel
2. Fitting the moments into the Probability Density Function
Note:
h (l )   W (h)h l dh

Source:





Medium:


Low power laser (4mW), Midshipmen and faculty safety
High quality beam shape (He-Ne red laser, Gaussian beam)
Beam diameter suitable for medium range propagation (d=1 cm)
Light intensity sensor (camera) used to observe beam statistics before propagation
Maritime environment at US Naval Academy grounds (propagation across body of water and
above field, 500m source-target distance)
Target:

May-16
Light intensity fluctuations recorded at the beam center (observed directly using light intensity
sensor)
United States Naval Academy
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
All of the realizations were
added to create cumulative
intensity plot, Pmax.

From Pmax location with
maximum intensity was
determined, (xm, ym).

Intensity vector , I, used for
calculating PDF was formed
by selecting intensity at the
location (xm, ym) for each
realization.
Cumulative light intensity
plot
Maximum intensity
used for determination of
(xm, ym).
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May-16
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
We measure Gaussian laser beam propagation over the land in the proximity of
the water and above the water.

Based on two different methods, Gamma-Laguerre, and Gamma-Gamma we
reconstruct from collected data the single-point Probability Density Function
(PDF) of the fluctuating intensity of a laser beam propagating through the
marine type atmospheric turbulence.

We measure light intensity at the target directly using light camera sensor.

We present comparison of models with data histogram and find good
agreement. In particular, Gamma-Laguerre model emphasizes the tails agreeing
better with data histogram. This can be due to prevailed water particle scattering
and absorption above the water column which suppress optical intensity
fluctuations.

Our results will find uses for any applications involving radiation transfer through
marine-type atmospheric turbulence.
May-16
United States Naval Academy
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





C. Nelson,
S. AvramovZamurovic,
O. Korotkova,
R. Malek-Madani,
R. Sova,
F. Davidson







The United States
Naval Academy

The University of
Miami

The Johns Hopkins
University

Applied Physics
Laboratory,

The Johns Hopkins
University
May-16




Mid-Atlantic coast near Wallops Island, VA. September of 2009
Bi-directional shore-to-ship data link
Commercially available adaptive optics terminals
Range 5.1 – 17.8 km, to include near optical horizon,
Tower on Cedar Island, VA and a Johns Hopkins University Applied
Physics Laboratory research vessel Chelsea
Statistical analysis of the power-in-fiber adaptive optics detector and
two power-in-bucket detectors that have different receiver
diameters
The detectors are placed alongside the adaptive optics terminal.
Data histogram reconstruction and comparison with the data from
the 0.64 and 2.54 cm power-in-bucket detectors, and 2.54 cm powerin-fiber detector detectors is given
Analytical probability density function models based on the
Lognormal, Gamma-Laguerre, and Gamma-Gamma with Aperture
Averaging distributions are developed for data sets for each detector
Dependence of the results on propagation distance, detector
aperture size, and varying levels of optical turbulence are
investigated
United States Naval Academy
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Chessie, “Speck”

Field Test off of Atlantic Coast

2 – 22 km optical horizon

Bi-directional shore-to-ship data
link between old 56’ Coast Guard
lookout tower and John Hopkinhs
University and Applied Physics
Laboratory research vessel,
“Chessie”.

1.0” Adaptive Optics Power-inFiber as well as 0.25” and 1.0”
Power-in-Bucket
1.0” PIB
0.25” PIB

1.0” PIF AO
May-16
United States Naval Academy
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LSE LN – 0.975
LSE GG – 0.805
LSE GL – 0.775
**Tail – 1st 30 bins**
LSE LN – 0.0343
LSE GG – 0.0225
LSE GL – 0.0149

Low Turbulence –
(Cn2~1.5*10-14 m-2/3)




1.0” PIF AO
5.1 km to 17.8 km
Good data fits in low
turbulence across all
of the distributions
Note – this is aperture
averaged data
LSE LN – 1.606
LSE GG – 0.595
LSE GL – 0.324
**Tail – 1st 30
bins**
LSE LN – 0.552
LSE GG – 0.269
LSE GL – 0.0574
GL had best LSE fit
May-16
United States Naval Academy
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
O. Korotkova , C. Nelson and R. Malek-Madani, “Probability density function of partially coherent
beams propagating in the atmospheric turbulence”, SPIE Photonics West Sensing Conference,
January 2012.

R. Malek-Madani, S. Avramov-Zamurovic, O. Korotkova and J. Watkins, “An experimental study of
the probability density function of a turbulence induced fluctuating laser beam”, Directed Energy
Beam Control Conference, May 2011.

C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, F. Davidson, “PDF
computations for power-in-the-bucket measurements of an IR laser beam propagating in the
maritime environment”, SPIE Defense, Security, and Sensing Conference, April 2011.

S. Avramov-Zamurovic ,O. Korotkova and R. Malek-Madani, “Probability Density Function Of
Fluctuating Intensity of Laser Beam Propagating in Marine Atmospheric Turbulence”, SPIE
Photonics West Sensing Conference, January 2011.

S. Avramov-Zamurovic, O. Korotkova and R. Malek-Madani,” Laser Beam Characterization of
Propagation through a Marine Atmospheric Channel”, Thirteenth Annual Directed Energy
Symposium, November 2010.
May-16
United States Naval Academy
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
Journal



O. Korotkova, S. Avramov-Zamurovic, R. Malek-Madani, and C. Nelson, "Probability density
function of the intensity of a laser beam propagating in the maritime environment," Opt.
Express 19, 20322-20331 (2011)
C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, F. Davidson,
“PDF computations for power-in-the-bucket measurements of an IR laser beam propagating
in the maritime environment”, submission planned for Optical Engineering Journal
Conference Proceedings



May-16
O. Korotkova , C. Nelson and R. Malek-Madani, “Probability density function of partially
coherent beams propagating in the atmospheric turbulence”, SPIE Photonics West Sensing
Conference proceedings, Atmospheric and Oceanic Propagation of Electromagnetic Waves,
(2012).
S. Avramov-Zamurovic ,O. Korotkova and R. Malek-Madani, “Probability Density Function Of
Fluctuating Intensity of Laser Beam Propagating in Marine Atmospheric Turbulence”, SPIE
Photonics West Sensing Conference proceedings, Atmospheric and Oceanic Propagation of
Electromagnetic Waves, Volume 7924, (2011).
C. Nelson, S. Avramov-Zamurovic, R. Malek-Madani, O. Korotkova, R. Sova, F. Davidson,
“PDF computations for power-in-the-bucket measurements of an IR laser beam propagating
in the maritime environment”, SPIE Defense, Security, and Sensing Conference proceedings,
2011.
United States Naval Academy
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May-16
United States Naval Academy
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
The effort to observe the laser beam propagation in maritime environment
started on the Academy grounds in the spring of 2010 with a laser on a homemade mount, a white poster board and a rented camera from the media center.
Qualitative observations from these tests were reported in number of
publications.

Since then equipment and instrumentation was systematically acquired to
achieve capability to methodically study laser propagation and provide high
quality field measurements that can be used in modeling.





May-16
Laser beam of choice is He-Ne red, with beam size at the order 1 cm for medium range
propagation and safety
Laser light is modulated at the transmission using spatial light modulator
Fast high resolution cameras simultaneously observe the beam at transmission and
reception with rates up to 1200 frames per second to account for fast changing
atmospheric parameters
All of the cameras are equipped with specialized filters for optimum recording and all of
the optical component are optimized for 1 cm beam diameter
Cameras are producing up to 200 000 frames over the course of 3 min observation and
the laptop computers successfully receive this information and process it so that the
PDF calculations are obtained in the field for immediate evaluation
United States Naval Academy
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
High level of system integration and journal
publication level of measurement results is
achieved:
 Selecting single component at the time and including
it in the system only after extensive field testing
 Hiring technician dedicated to the project
▪ Interfacing the instrumentation
▪ Maintaining safety, security and organization of equipment
and instrumentation
▪ Organizing the experimental data to be accessible to the
interested parties
▪ Setting up the system demos for students
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United States Naval Academy
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The laser beam is
reflected from the
SLM to create
partially coherent
beam and sent to
beam splitter.
Beam splitter
distributes part of
the beam to be sent
through the
atmospheric channel
across the water.
May-16
Beam expander x20
used to reach 1 cm beam
diameter adequate for
long distance
propagation.
United States Naval Academy
Red He-Ne 2
mW laser with
0.8 mm beam
diameter.
The rest of the beam
(50%) is sent to the
light sensor. This
camera records the
statistics of the beam
at the source.
25
The laser beam
recorded using
camera
capable to
document 4096
different levels of
light intensities at
the rate of 1200
frames per second
May-16
Weather station
records the
atmospheric
conditions.
.
United States Naval Academy
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May-16
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
Introduction to Laser Light


Propagation of periodic signals
Gaussian beam
Refraction and reflection
MATLAB



Project (4 weeks, individually or in small teams )

Measure beam size to determine beam waist and
evaluate second derivative values for the paraxial
equation approximation (range 1 cm to 1m)

Measure beam power and diameter as a function
of distance and compare with theoretical
predictions (range 1 m to 100m)

Evaluate beam propagation over water at
HydroLab in weak turbulence using mirror to
reflect beam back to starting destination (range 50
to 200 m)

Teams 1 and 2 compare beam performance over
the range of 500 m. Record weather data.
Basics:




Reading assignment A. Schawlow, 1968, Scientific
American Journal
Calculating functions
Processing images of laser light recoded in
experiments using marices
Experiments

Basic operation of
▪
▪
▪



May-16
Laser source s
Light intensity sensors (digital cameras)
Beam splitters and beam expanders
Laser beam propagation recorded in weak turbulence
using beam analyzer. Observe beam shape and
spreading due to propagation distance
Thermal disturbance introduced and beam response
observed and recorded
Laser light modulation using liquid crystal variable
retarder and recording using a camera. Binary signal
transmission.
United States Naval Academy

Team 1
Record beam propagation over the
land (Sherman Field)

Team 2
Record beam propagation over
water (College creek)
28

Introduction to Laser Research
 6 weeks per semester
 Individual project
 Offered one semester, 9 students

Control Systems and
their Applications to
Weapons
 A week per semester
 Offered for 2 semesters,
3 sections, 50 students
May-16
United States Naval Academy
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
Weapons and Systems Engineering Honors Program
 Students are invited to participate in the program based on their
performance in major classes during the sophomore year
 Honors students are committed to research for three semesters
▪ Honors research and design introduction to research methods outcome
research project proposal (juniors, 3 credit)
▪ Independent research class one-on-one mentored research based on the
proposal (seniors, 3 credits)
▪ Capstone project research project practical implementation (seniors, 4
credits)

MIDN Whitsett, junior
 Started experimenting with laser beam propagation in laboratory
setting this semester.
 Formulating a proposal on laser beam modulation for effective
intensity distribution on target
May-16
United States Naval Academy
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May-16
United States Naval Academy
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
Phase and Amplitude spatial modulation to
create laser beams with defined
characteristics

Spatial modulation for learning the current
state of the atmosphere and adapting beam
characteristics (phase and amplitude) to
minimize the distortion of the beam due to
the atmospheric turbulence
May-16
United States Naval Academy
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May-16
United States Naval Academy
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May-16
United States Naval Academy
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Experimental Data, 09-14-2009
(evening run, tight beam, ideal conditions 4km  21.3 km)
/5
2
2
WLT  W 1  1.63 12
R  , WST  W LT  rc
L.C. Andrews and R.L. Phillips, Laser Beam Propagation through
Random Media (SPIE Press, Bellingham, WA, 2005).
May-16
United States Naval Academy
1503-7.5nmi.avi
35

Computers



1 Lucy Lenovo ThinkPad, 2.2 GHz, 4 GB RAM
2 Bob and Erin Dell Mobile Precision M6400, quad core 2.53 GHz , 4 GB RAM with 1066 MHz memory
2 Tom and John Dell Mobile Precision M6600, 2.4 GHz six core , 16 GB RAM with 1600 MHz extreme performance memory

Interface from cameras to computers :
▪
▪

USB for B&W Thor cameras and Beam Analyzer
Laptop docking station with enclosure since Hamamatsu camera has motherboard type of interface
Light Intensity Sensors
Camera Type
Spatial Resolution
Light Intensity
Resolution
Time Resolution
Beam Analyzer
1024 x 1280
sensor 6.8 x 8.5 mm
diagonal 10.8 mm
pixel 6.7 µm
1024
(65 536)
10 fps
Total 128 frames
B&W camera
for students
Thor
2
1280 x 1024
sensor 5.95 x 4.76 mm
diagonal 7.6 mm
pixel 4.65 µm
256
15 fps
B&W camera
for research
Hamamatsu
Sally Mary April
1920 x 1440
sensor 6.97 x 5.23 mm
diagonal 8.7 mm
Pixel 3.63 µm
4096
45 to 1200 fps
(spatial resolution)
1
May-16
United States Naval Academy
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

Liquid Crystal Variable Retarder
provides any phase shift of polarized
light from zero to several times the light
wavelength by applying the right
voltage controller, (Thor)
diameter
10.0 mm
Spatial light modulator (SLM)
modulates light according to a fixed
spatial (pixel) pattern provided from
MATLAB matrices via controller
(Boulder Nonlinear Systems)




May-16
High Speed and High Efficiency
Format 512 x 512 matrix, Pixel size15 x 15 μm
Switching frequency 60 Hz
100 linear levels for 2π phase stroke
United States Naval Academy
Reflective window
7.68 x 7.68 mm
37

Polarimeter analyzes the state of
polarization and the degree of
polarization of optical signals (Thor)
 Measurement rate 333 Samples/s
 Azimuth Angle Accuracy ±0.25°
 Ellipticity Angle Accuracy ±0.25°
 Degree of Polarization
Accuracy:±0.5% Full Scale
May-16
United States Naval Academy

Scintillometer detects variations
in the refractive index due to heat
fluxes in the atmosphere. From
scintillation measurements the
sensible heat flux and evapotranspiration are derived

100m to 1km (10 cm aperture) 250m
to 4.5 (aperture 15 cm) km
 Cn2 Scintillation bandwidth 10-17 to
10-12
38

Laser Beam Source



Low power <2 mW ( class 2A safety)
He-Ne based for high quality Gaussian
beam suitable for mathematical analysis
polarized (2) non-polarized (2)
Laser Beam Expanding, Filtering and
Splitting





May-16
Beam Expanded 1 cm (appropriate for
long distance link) Beam expanders (2)
Only red lasers used => red notch filters
on cameras Red filters (2)
Very sensitive light intensity sensors
used => cameras protected with neutral
filters Sets of 10 neutral filters (2)
Simultaneous record of transmitted and
received laser light => beam splitting at
the source Beam splitters (2)
Mirrors (2+1)
United States Naval Academy

Supporting equipment










Kinematic heads for alignment (10)
Laser power meter (1)
Binoculars (1)
Mobile optics breadboard (2)
Portable power generators (2)
Tripods (5)
Tent (1)
Cart for transportation (1)
Home-made field table
Home-made laser and expander mount
39