LASER BEAM PROPAGATION THROUGH FOG

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LASER BEAM PROPAGATION THROUGH FOG

M. Duchet, B. Flocon, J. Sap

To cite this version:

LASER BEAM PROPAGATION THROUGH FOG

M. Duchet, B. Flocon and J. Sap .

Abstract.- The atmosphere is characterized by its molecular absorption coefficient and the fog by the initial radius of droplets which can be drifted by the wind. Absorption and scattering coeffi-cients of droplets are calculated by the MIE's theory from their radius and complex index. In the laser beam, droplets are partially vaporized (we neglect thermal conductivity).

Propagation equations are solved by numerical means giving steady state in a first slice of atmos-phere and by incremental process in the following slices - until the focal plane is reached. Two examples are given here :

- A = 10.6 um : without fog, we found the well known laser spot showing thermal blooming and = with fog we can see a strong hole boring phenomenon ;

- X = 4 um : the hole boring is very weak.

1) STATEMENT OF THE PROBLEM (figure 1)

Let us call E (x, y, z) the normalized laser

emitted field on each of the points of (x, y)

cross-section plane to the 0z propagation

direction, that is :

{J 1 E (x, y, z) |

2

dx dy = 1

The P power beam intensity is then :

I (x, y, z) = P E E * (x, y, z) e"

A [z)

A (z) is the extinction factor such as :

A (z) = «m z + |o (aa f ) S + od f f f) dz1

f'oreover, according to the MIE's theory : aabs = V Nl a l2 <x' y* z> Mabs ( al ) « d i f f = v h a l2 <*' y* z> Md i f f ( al >

N^ being the concentration of the a1 radius water droplets, M . and Md i f f being the absorption and scattering HIE's coefficients.

The equation to solve is :

i

2 j k i £ + - ^ + •££ + k2 (n2 - 1) E = 0

3z 3x2 3yz

k = — A = wavelength X

n = medium optical index

n

2

- 1 = * [ I (x

1

, y, z) dx'

v t a z J-oo

o

JOURNAL DE PHYSIQUE Colloque C9, supplément au n°ll, Tome 41, novembre 1980, page C9-U5

Laser Division, Laboratoire de Marooussis, Centre de Reeherohe de la C.G.E., Route de Nozay, JI1460 Marooussis, France.

Electronic and Opti-c Division.

Résumé.- L'atmosphère est définie par son coefficient d'absorption moléculaire et le brouillard par le rayon initial des gouttelettes transportées par un vent transversal. Les coefficients d'absorp-tion et de diffusion des gouttelettes sont calculés d'après la théorie de MIE à partir de la connais-sance de leur indice complexe et de leur rayon. Dans le faisceau, les gouttelettes sont partielle-ment vaporisées (on néglige l'effet de conductibilité thermique).

Les équations de propagation sont résolues par voie numérique donnant l'état d'équilibre d'une pre-mière tranche d'atmosphère et ainsi de suite pour les tranches suivantes jusqu'au plan focal. On donne deux exemples :

- A = 10,6 um : sans brouillard, on trouve la tache bien connue montrant l'effet de défocalisa-tion thermique et avec brouillard on voit nettement le percement de celui-ci causé par le faisceau ;

- X = 4 um : le percement causé par le faisceau est très faible.

C9-116 JOURNAL DE PHYSIQUE

Vo

= transverse wind speed This equation i s solved i n t h r e e phases :

= beam slewing r a t e 1) a p p l i c a t i o n o f t h e p o p e r a t o r between

-

2

A = _{310' N ( y}

-

_{1) a, P}

_k2

_{Cs Z and Z}

₊

_-

_6Z

1

.. 2

[

CGS, a p a r t from P ( w a t t s ) 2) a p p l i c a t i o n o f the

aT

operator between N = molecular r e f r a c t i v i t y (cm3 g - l ) Z and Z

+

6Z

y = Cp/CV s p e c i f i c heat r a t i o 3) a p p l i c a t i o n o f t h e

u

operator between am = molecular. a b s o r p t i o n c o e f f i c i e n t Z

+

and Z

+

6Z

2

Cs = sound speed through t h e medium

\?re have :

2)

FOG

EODELING

The f o g i s modeled b y water d r o p l e t s o f @ d e n t i - c a l i n i t i a l values. The energy absorbed by a : d r o p l e t induces i t s p a r t i a l evaporation. We

A _{solve t h e steady s t a t e , where t h e d r o p l e t}

U 0 + Q Z

p r o f i l e i s s t a b l e . We suppose t h a t t h e wind

+ " d i f f

moves l a t e r a l l y t h e d r o p l e t s w i t h t h e same velo- c i t y

.

I f we i n t r o d u c e t h e new v a r i a b l e s X, Y, Z such as :

az

1

a = I e - I r a d i u s

- = -

_{f = f o c a l l e n g t h} az D ( z )

_F?

_{= s c a l e f a c t o r} i t comes, E3 bein@ t h e f i e l d i n t h e X, Y, Z c o o r d i nates :

a2

a2 AT =

-

+

-

( t r a n s v e r s e b u c k l i n g o p e r a t o r ) ax2 aY2 3) L e t us c a l l al ( x a y, z, t ) t h e d r o p l e t r a d i u s a t t time and a t (x, y, z ) p o i n t . \?e want t o know i t s r a d i u s a t a t

+

T time. D u r i n g T t h e d r o p l e t has moved a

Vo

T length, t h e r e f o r e :

x ( t

+

T) = x ( t )

+

V,T

The dW1 absorbed energy i s given by

I

(x, Y, z, t ) !Tabs (al) IT a12 (x, Ya z, t ) d t

1

This energy leads t o vapor p r o d u c t i o n w i t h t h e r e l a t i o n :

I

h being t h e l a t e n t h e a t o f v a p o r i z a t i o n I E 3 I 2 d X 1

We have :

d a l =

-

I

(x,

y,

2 7 t ) dx

example. He see t h a t f o r 50 droplets/cm3 t h e maximal i n t e n s i t y i s about 0.3 % o f t h a t o b t a i n - ed w i t h o u t fog, compared t o 42 % a t 10.6 pa. The

4 pm l a s e r does n o t show a good e f f i c i e n c y t o f o g h o l e boring, as can be seen on f i g u r e 7

which represents the d r o p l e t s r a d i u s p r o f i l e . Figures 8 and 9 g i v e t h e f o c a l i n t e n s i t y p r o f i l e .

T h i s equation i s solved by numerical means. The i t e r a t i o n goes on i n each s e c t i o n u n t i l . t h e steady s t a t e .

We have considered a 300 kld gaussian beam w i t h a

1

m e-2 diameter, f o c a l i s e d a t 1000 m, t w i c e d i f f r a c t i o n - 1 i m i ted, subjected t o a 10 m/s t r a n s v e r s e wind, f o r d i f f e r e n t f o g concentra- t i o n s . On f i g u r e 2 we have an approximated i d e a o f t h e corresponding v i s i b i l i t i e s . I n t h i s t a b l e we observe t h e maximum i n t e n s i t i e s i n presence o f f o g compared w i t h those obtained i n non-saturable aerosols o f t h e same i n i t i a l c h a r a c t e r i s t i c s . tc!e n o t i c e a g a i n i n i n t e n s i t y , t h e 10.6 prr: l a s e r beam having d i s s i p a t e d a f r a c t i o n o f f o g ( f o g h o l e b o r i n g phenomenon). Figure3shows the d r o p l e t r a d i u s p r o f i l e . Figures

4

and 5 g i v e t h e i n t e n s i t y n r o f i l e s . b) A = 4 ,pm

.The t a b l e on f i g u r e 6 presents a

4

pm example w i t h a 6 . 1 0 - ~ c m - ~ molecular absorption, the o t h e r parameters being i d e n t i c a l t o t h e f o r m r

CONCLUSION

A h i g h l e v e l propagation code through f o g has been elaborated. T t takes e f f e c t o f the d i f f r a c t i o n and t h e thermal blooming phenomena i n a s a t u r a b l e medium. The 10.6 vn! l a s e r shows a good f o g h o l e b o r i n g p o s s i b i l i t y y c o n t r a r i l y t o t h e 4 pm l a s e r . Laser power : 300 k W

.

Wavelength : 10.6 ) ~ m Quality factor : 2 Molecular absorption : 2 c m - I Wind speed : 10 mls Target distance : I 0 0 0 m Focal length : 1 000 m Slewing rate : 0

Troncature radius : 5 0 cm at e - * intensity level . - . - . - . . - - --

Concentration of dropfetal

ViaibUny (m)

Equlvalmt water denany Equlvald 'd (m-')

d Cotecular abiorptbn)

JOURNAL DE PHYSIQUE Droplets radius A OJm

1

4 ' 100 3

-

Droplets I

cm3

50 2

-

10 A distance ( cm ) Laser beam axis

F i g m e

3 -

DtopLeLh h a d i w p06.iee .in

p h n e (10

urn)

No fog

.

Fog : 30 droplets I cm

8 vls!bd~ty

t !

Maximum intensity : \.. I ,' Maxtmum intenslty :

17 466 wlcm2 tor x

-

-

2.4 cm 16 357 wlcm2 tor x

-

- 2.1 cm

F 4 . 4 -

IvLteuuLtg

pad.iee

-iM

.the

a%tg&

pLane(70pm)

4

Wind

4

Fog

:

50 droplets/cm

3

Visibility

: 5 0 0

m

~ a x i m u m

intensity

: 7 3 6 7 W/cm

2

Laser power : Wavelength : Quality factor : Molecular absorption : Wind speed : Target distance : Focal length : Slewing rate : Troncature radius : 300 k W 4

Pm

2

.6

10 -7 cm-I 10 m/s 1 000 m I 000 m 0

50 cm at e-2 intensity level

Droplets radius

Wind

Droplets/cm

3

Q

dktance (cm)

Lasw

beam

a x k

- Concentration of droplets1 cm3

'

fW

for x

-.

-

0.84 cm

10 - 1 600 0.288 lo-' 6 1c7 66 224 -0.477 -- vlsibliny (m)

Equivalent water density (glcm3)

4, (molecular absorption) (cilil)

-

-Maximum intensity on target (LV/cm2)

-- -.-

Abscissa of maximum intensity (cm)

NO fog _{Fog : 10 droplets I cm}

_{ACKNObfLEDGEE?ENTS}

This work was sponsored

by

the French Direction des

Recherches e t Etudes Techniques

( D R E T ) .

Y

I cm

-

A - 4 p m

Maximum intensity : Maximum intensity :