THE REFRACTIVE EFFECTS OF LASER PROPAGATION THROUGH THE OCEAN AND WITHIN THE OCEAN

The Refractive Effects of Laser Propagation through the Ocean Surface and within the

Ocean.

LTJG Pavlos Xiradakis HNDonald Walters

Bred Borden

footprint

θ

I(θ)

THESIS OUTLINE

•Scenario•Optical Oceanography Background•Modeling the Ocean Surface•Simulation of the wind generated ocean surface•Snell’s Law•Attenuation inside the ocean•Refraction at sea surface•Results•Computational Difficulties•Conclusions•Questions

scenario

a(λ) β(λ)

AbsorptionAnd

Scattering

AbsorptionAnd

Scattering

Sea surface

Laser footprint???

Refraction with the waves slope

Firing a laser beam

Optical Oceanography background1. Inherent Optical Properties

– absorption coefficient α(λ)– scattering coefficient b(λ)– volume scattering function β(θ)

2. Apparent optical properties– Vertical Attenuation coefficient for the

downward Irradiance– Irradiance Reflectance

3. Cox and Munk Results:

Slope variance increases linearly with wind speed

4. Wave spectrum

dx

z(x) FFT

df

Modeling the ocean surface I

Pierson Moskowitz Spectrum

Mean squared slope diverges logarithmically

2

3 2 4( ) exp[ ( )]

2

gS k

k k U

3

1( ) [ ]l hS B B

Elfouhaily spectrum

Spectrum includes a gaussian cut offMean squared slope does not diverge

Modeling the ocean surface IIAgreement with Cox Munk Results

Changing parameters in our Matlab code until there is a satisfactory approximation of the Cox Munk Observations

Initialresult

Increasing the data points

ChangingKm

Making KmVariable

Simulation of the wind generated ocean surfaceUsing our wave spectrum we create an 1D model

• a. Start with an 1-D array of random Gaussian numbers

• b. Fourier transform this array in frequency coordinates

• c. Filter this spectrum with the Elfouhaily spectrum

• d. Inverse Fourier transform back to x coordinates

• e. Scale the results to correct for 1/N factors

SNELL’S LAW

Geometrical optics approach:• Snell’s law applied to our ocean model

neglecting attenuation effects• Variance of the angles of the emerging

photons was estimated• A magnification effect takes place

θ θ

φ

φ

Sea surface

footprint

Attenuation Inside the Ocean ITheoretical approach

• There are no analytical means to predict the photon movement in a random, scattering and absorbing medium

• Absorption and scattering coefficients provide information about all the possible ways a photon moves and interacts in a scattering medium,

• Following many photons provides a probability distribution • A Monte Carlo, computer simulation was used

• Kirk Code in FORTRAN 77 was translated into FORTRAN 95– Eliminate backward referenced go to statements and resultant spaghetti code– Water depth is divided into 21 layers– Depth interval at each layer is 10 m– Solar elevation angle 90 degrees in each case – Three different cases examined– Follow 106 photons, x,y,z and and

• A separate MATLAB code reads the output and plots the results

Attenuation inside the ocean IISimulation results

1st Layer

Case I small extinctionCase III higher extinction

Case II moderate extinction


2nd Layer

Case I small extinction


Case III higher extinction


21st Layer





21st Layer 2D

Case III high extinction



Refraction at the Sea Surface Simulation Results




COMPUTATIONAL DIFFICULTIES

• Differences between FORTRAN 77 - 95• Little enden vs big enden for binary data

– Byte order difference between MAC and a PC• Byte is 8 bits of a 32 bit, binary number• High byte first (big enden) ABCD• High byte last (little enden) DCBA

• Matlab program must parse the 4 dimensional, binary, data array from the Fortran program

Conclusions

• Absorption is the dominant effect compared to scattering inside the ocean

• Extinction within the ocean is more important than refraction at the sea surface

• Scattering will mainly determine the spreading of the laser beam footprint at the ocean surface

Before asking questions,remember…

Εν οίδα, ότι ουδέν οίδα Σωκράτης

I know just one, that I know nothing Socrates

THE REFRACTIVE EFFECTS OF LASER PROPAGATION THROUGH THE OCEAN AND WITHIN THE OCEAN

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