Документ взят из кэша поисковой машины. Адрес оригинального документа : http://lizard.phys.msu.su/home/science/Dmitriev-Ivanov-Xoxlov-09-FPM-Diffuser.pdf
Дата изменения: Wed Feb 9 10:20:11 2011
Дата индексирования: Mon Oct 1 20:07:18 2012
Кодировка:

. . , . . , . .
. . . e-mail: dmitriev@lt.phys.msu.su 538.935+517.958+537.84 : , , , , , . : , . . , , . --, . . . . , - . , . Abstract A. V. Dmitriev, A. V. Ivanov, A. R. Khokhlov, Numerical simulation of light propagation through a diffuser, Fundamentalnaya i prikladnaya matematika, vol. 15 (2009), no. 6, pp. 33--41. Diffusers are important elements of many illumination systems, for example, in computer and mobile phone displays or advertising panels, etc. In this article, the light propagation in a diffuser with optically soft inclusions is described with the help of the Fokker--Planck equation, i.e., a transfer equation with a diffusion term in the space of radiation propagation directions. The coefficient of angle diffusion is calculated using the Mie theory. The equation is solved numerically using the stochastic analog method, and the space and angle distribution of the radiation that passed through the diffuser is calculated. The results can be useful for diffuser parameters optimization, and the method can be applied to many problems of turbid media with optically soft particles.

, , . , , ,
, 2009, 15, 6, . 33--41. c 2009 , « »


34

. . , . . , . .

. -, - . , , , . : , , . . , . (), . , . , , , , , . , - , . , , . : . -, , . : . . [1, 9, 11, 13], ; . , [9] 1 1 I (t, n, r) + nI (t, n, r) = cm t lsc 1 d x( )I (t, n , r) - I (t, n, r). 4 lex (1)

I -- , t --, r -- , cm -- -, n n -- , n , x( ) -- ( ),




35

-- n n . l l
sc

sc

l

ex

-- : 1 , Nex

=

1 , Nsc

lex =

N -- ( ), sc ex -- . , , . , , n r, , . . - ( ), , , . . [8, 9] . . . , , , . «» , ґ , - . , ` , . [3], -- [3, 7] . -- [8, 9]. , n n , , I (n) I (n ), - - n, --, n, -- n . -- [3, 7], , .


36

. . , . . , . .

: 1 2I , sin2 2 1 d I x( )I (t, n , r) = I (t, n, r)+ D sin 4 sin + d x = 1, 4 , I . D -- : 1 D= 8


d x( )sin3 .
0

, D . . . [8, 9] , x1 , : 1 D = (3 - x1 ), 6 3 x1 = 2


d x( )cos sin .
0

(2)

D. [6] 1 I sin sin + 1 2I = - div([n в [n в grad]]I ) = -([n в [n в]]I ), sin2 2

-- : 1 I (t, n, r) + nr I (t, n, r)+ cm t 1 l
ex

-

1 lsc

I (t, n, r) =

D n {[n в [n вn ]]I (t, n, r)}. lsc , , -. =-




37

, rz = 0 rz = Lz . , , . . - [9, 12]. , (2), [2, 10, 14]. . [4, 5]. , , . , , . . . , , , . . : rk nk
+1 +1

= rk + hcnk , = R R(nk , 23 k ) ik в nk ,2 |ik в nk | -2hD ln 3
k+1

cos 23

k+2

nk ,

k -- , h -- , ik -- , nk , {j } -- , (0, 1), R(o, ) -- o :
R(o, ) = 2 (ox - o2 - o2 )sin2 2 +cos2 2 2sin 2 ox oy sin 2 - oz cos 2 2sin y z 2 2 2 2 2 =2sin 2 ox oy sin 2 + oz cos 2 (oy - ox - oz )sin 2 +cos 2 2sin 2sin
2 ox oz sin 2 - oy cos 2 2 2 2 oy oz sin 2 - ox cos 2 o2 - o2 )sin2 2 +cos2 2 x y ox oz sin 2 + oy cos

.

2sin

2

oy oz sin 2 + ox cos

2

(o2 - z

[-Lx /2,Lx /2] в [-Ly /2,Ly /2] Nx в Ny . , ,


38

. . , . . , . .

. , . , ( 60 ). . 60 · 4r , r -- . , : 2 (1 - y 2 ), y =1- , x= 1- , -- , x, y -- . , , , 2 x2 + y 2 < r [0, ] N . , Ieff , , . , . N , , , : N Nx Ny · 60 · 4r . , , , ; l
max

(20 В 100)Lz .

, C++, Python Fortran Linux , , , eps gif. . 1--4 , . , , , .




39

. 1. , , , ( )

. 2. , , , ( )


40

. . , . . , . .

. 3. , . -- , ,

. 4. , . () ()

« - 2009--2013 » ( -2312).


[1] . ., . . . . -- .: , 1983. [2] ., . . -- ., 1986. [3] . . . -- .: - . -; , 2004. [4] . . // . . -- 1996. -- . 8, 11. -- . 3--40. [5] . . // . . -- 2007. -- . 19, 10. -- . 89--104. [6] . ., . . . -- ., 1981. [7] . ., . . . -- .: , 2001.




41

[8] [9] [10] [11] [12]

. . . -- 1967. -- . 177, 4. -- . 812--815. . . . -- .: , 1972. . . -- .: . . ., 1961. . . -- ., 1953. Babenko V. A., Astafyeva L. G., Kuzmin V. N. Electromagnetic Scattering in Disperse Media. -- Berlin: Springer, 2003. [13] Mishchenko M. M., Davis L. D., Lacis A. A. Scattering, Absorption, and Emission of Light by Small Particles. -- Cambridge University Press, 2002. [14] Wiscombe W. J. Improved Mie scattering algorithms // Appl. Optim. -- 1980. -- Vol. 19. -- P. 1505--1509.