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1大气湍流相位屏模型
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%% example_ft_sh_phase_screen.m 利用谐波方法产生随机相位屏的例子clc;Dx = 2; % length of one side of square phase screen [m]，相位屏边长，单位是mDy = 2;Nx = 256; % number of grid points per side，取样点数为256Ny = Nx;N=Nx;L0 = 10; % outer scale [m]，湍流外径l0 = 0.001;% inner scale [m]，湍流内径Cn2 = 1e-12; % coherence diameter [m^(-2/3)].当Cn设为1e-14时，1550nm时，r0=0.010255m；3800nm时，r0=0.03008m。r0的计算见公式9.42Lambda=1550*1e-9; %波长，单位mK_k = 2*pi / Lambda; % optical wavenumber [rad/m]，光波数Delta_z=5e2; %分段距离，单位msubh=3;%%谐波次数 % SW and PW coherence diameters [m]，球面波和平面波的干涉半径 r0sw = (0.423 * K_k^2 * Cn2 * 3/8 * Delta_z)^(-3/5); %%球面波 r0pw = (0.423 * K_k^2 * Cn2 * Delta_z)^(-3/5); %%平面波 delta_x=Dx/Nx; %% grid step along x axis; x方向网格间隔delta_y=Dy/Ny; %%采样间隔 x = (-Nx/2 : Nx/2-1) * delta_x; %spatial grid，离散后在不同采样点处对应的x坐标值y = (-Ny/2:Ny/2-1)*delta_y; %采样点对应的y坐标值r_val=sqrt(x((Nx/2+1):Nx).^2+y((Ny/2+1):Ny).^2); %%原点-边缘的r值[x y]=meshgrid(x, y); %%变成nx*ny的矩阵 Structure_ther=6.88*(r_val/r0pw).^(5/3); %%理论结构方程值 mask = circ(x, y, 1);% D_val_hill = structure_function_hill(Cn2, Nx, Ny, Dx, Dy, Lambda, L0, l0, Delta_z); %%hill谱的fft结构方程% %figure,pcolor(x,y,D_val);% figure,plot(1:(Ny/2),D_val_hill(Nx/2+1,(Ny/2+1):Ny))% % D_val_hill_sub = structure_function_hill_sub(Cn2, Nx, Ny, Dx, Dy, Lambda, L0, l0, Delta_z, subh) %%hill谱的subharmonic结构方程% subh1=10;% D_val_hill_sub1 = structure_function_hill_sub(Cn2, Nx, Ny, Dx, Dy, Lambda, L0, l0, Delta_z, subh1)% figure,plot(1:(Ny/2),D_val_hill_sub(Nx/2+1,(Ny/2+1):Ny),1:(Ny/2),D_val_hill_sub1(Nx/2+1,(Ny/2+1):Ny)) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%网上下载的一个程序里面的结果% wvl=Lambda;% D=Dx;% dz=Delta_z;% N=Nx;% CN=Cn2;% % delta=D/N;% x=(-N/2:N/2-1)*delta;% y=x;% [X Y]=meshgrid(x,y);% del_f=1/(N*delta);% fx=(-N/2:N/2-1)*del_f;% [kx ky]=meshgrid(2*pi*fx);% k=2*pi/wvl;% [th ka]=cart2pol(kx,ky);% km=5.92/l0;% k0=2*pi/L0;% % r0=0.185*(wvl^2/(dz*CN))^(3/5);% PSD_phi=0.033*CN*exp(-(ka/km).^2)./(ka.^2+k0^2).^(11/6);% PSD_phi(N/2+1,N/2+1)=0;% cn=2*pi*k.^2*dz.*PSD_phi*(2*pi*del_f).^2;% phz_hi=ifft2((randn(N)+1i*randn(N)).*sqrt(cn));%????matlab±??í??FFT???¨??????????cn????????±??????????????????±del_f=1;% phz_hi=real(phz_hi);% % figure;imagesc(phz_hi);colorbar;% %% ????????% phz_lo=zeros(size(phz_hi));% for p=1:3% del_fp=1/(3^p*D); % fx1=(-1:1)*del_fp;% [kx1 ky1]=meshgrid(2*pi*fx1);% [th1 k1]=cart2pol(kx1,ky1);% km=5.92/l0;% k0=2*pi/L0;%outscale frequency% PSD_phi1=0.033*CN*exp(-(k1/km).^2)./(k1.^2+k0^2).^(11/6);% PSD_phi1(2,2)=0;% %random draws of Fourier coefficient% cn1=2*pi*k.^2*dz.*PSD_phi1*(2*pi*del_fp).^2;% cn1=(randn(3)+1i*randn(3)).*sqrt(cn1);% SH=zeros(N);% for ii=1:9% SH=SH+cn1(ii)*exp(1i*(kx1(ii)*X+ky1(ii)*Y));% end% phz_lo=phz_lo+SH;% end% phz_lo=real(phz_lo)-mean(real(phz_lo(:)));% phz=phz_hi+phz_lo;% figure;imagesc(phz_hi);colorbar;% figure;imagesc(phz);colorbar;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % generate a random draw of an atmospheric phase screen生成相位屏 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%检测将相位屏零频分量是否设为0时，产生的相位屏的区别%%%%%%%%%%%%%%%%%%%%%%%%%%%从产生的相位屏上来看，不设置为0的图形颜色更鲜明，黑的地方更黑，但图形都是一样的%%%%%%%%%%%%%%%%%%%%%%%%%%%不过设为0之后的值特别小，是不是不太对？所以我没有将其设为0%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [phz_central_zero phz_central_notzero] = ft_phase_screen_zero_or_notzero(r0, N, delta, L0, l0); %%检测将零频分量是否设置成为0时的结果是否一样% %[phz_lo phz_hi] = ft_sh_phase_screen(r0, N, delta, L0, l0,subh);% %phz=phz_hi;% %phz=phz_lo;% %phz = phz_lo + phz_hi;%%最终的随机相位屏是低频部分和高频部分的加和% figure % 新建画图窗口，即保存以前图形，重新画一个新的% subplot(2,1,1),pcolor(x,y,phz_central_zero);% colormap gray% colormap gray% shading interp% colorbar% subplot(2,1,2),pcolor(x,y,phz_central_notzero);% colormap gray% shading interp% colorbar%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%检测是否使用fftshift时，产生的相位屏的区别%%%%%%%%%%%%%%%%%%%%%%%%%%%从产生的相位屏上来看，先用fftshift，就产生不出想要的图样，不明白为什么%%%%%%%%%%%%%%%%%%%%%%%%%%%最后是否再使用ifftshift，只是对最后产生的图样进行了对角线的挪移%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [phz_1 phz_2] = ft_phase_screen_use_cn2(Cn2, Nx, Ny, Dx, Dy, Lambda, L0, l0, Delta_z); % %[phz_lo phz_hi] = ft_sh_phase_screen(r0, N, delta, L0, l0,subh);% %phz=phz_hi;% %phz=phz_lo;% %phz = phz_lo + phz_hi;%%最终的随机相位屏是低频部分和高频部分的加和% figure % 新建画图窗口，即保存以前图形，重新画一个新的% subplot(2,1,1),pcolor(x,y,phz_1);% colormap gray% shading interp% colorbar% subplot(2,1,2),pcolor(x,y,phz_2);% colormap gray% shading interp% colorbar%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%我觉得，如果直接用fft变换产生相位屏的话，不应该将频谱中的原点位置（应该是矩阵中的(N/2+1,N/2+1)位置）的值设为零%%%而要使用subharmonic方法时，需要将中心位置设为零，因为进一步对原点位置进行了更细的划分了 [phz_lo phz_hi]= ft_sh_phase_screen_use_cn2(Cn2, Nx, Ny, Dx, Dy, Lambda, L0, l0, Delta_z, subh);%%phz_lo只是谐波产生的低频部分，phz_hi是中心分量为0时的FFT[phz_z phz_nz] = ft_phase_screen_use_cn2(Cn2, Nx, Ny, Dx, Dy, Lambda, L0, l0, Delta_z); phz_1=phz_hi+phz_lo; %%总的谐波产生的相位屏 phz_2=phz_hi; %%FFT方法 [phz_lo_1 phz_hi_2] = ft_sh_phase_screen(r0pw, Nx, delta_x, L0, l0,subh);figurepcolor(x,y,phz_lo_1+phz_hi_2);%imagesc(phz_2); colormap gray shading interpcolorbar figure % 新建画图窗口，即保存以前图形，重新画一个新的subplot(2,1,1),pcolor(x,y,phz_1);%imagesc(phz_1); colormap gray shading interpcolorbarsubplot(2,1,2),pcolor(x,y,phz_2);%imagesc(phz_2); colormap gray shading interpcolorbar [cs1 cs2]= ft_sh_phase_screen(r0pw, Nx, delta_x, L0, l0,subh);mask = ones(Nx);CCC1=str_fcn2_ft(phz_hi_2, mask, delta_x);CCC2=str_fcn2_ft(phz_lo_1+phz_hi_2, mask, delta_x);CCC3=str_fcn2_ft(cs1+cs2, mask, delta_x);CCC4=Structure_ther;figureplot(1:(Ny/2),CCC2(Nx/2+1,(Ny/2+1):Ny),'b',1:(Ny/2),CCC3(Nx/2+1,(Ny/2+1):Ny),'r',1:(Ny/2),CCC1(Nx/2+1,(Ny/2+1):Ny),'g')%pcolor(x,y,CCC);%imagesc(phz_2); phz = phz_lo + phz_hi;%%最终的随机相位屏是低频部分和高频部分的加和figure % 新建画图窗口，即保存以前图形，重新画一个新的pcolor(x,y,phz);% min(phz(:))% max(phz(:))% imagesc(phz)colormap gray(255) %图形是灰色的shading interp %对图形网格线着色.faceted:网格线为黑色；flat:网格线分块着色；interp：着色的光顺性最好colorbar mesh(x,y,phz);view(0,90); %%画三维图，%三维曲面图，view是改变视角contourf(x,y,phz) %等高线图pcolor(x,y,phz);shading interp%伪彩色图surf(x,y,phz);plot3(x,y,phz);%画三维曲线图stem3(x,y,phz);contour3(x,y,phz);imagesc(phz);1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.51.52.53.54.55.56.57.58.59.60.61.62.63.64.65.66.67.68.69.70.71.72.73.74.75.76.77.78.79.80.81.82.83.84.85.86.87.88.89.90.91.92.93.94.95.96.97.98.99.100.101.102.103.104.105.106.107.108.109.110.111.112.113.114.115.116.117.118.119.120.121.122.123.124.125.126.127.128.129.130.131.132.133.134.135.136.137.138.139.140.141.142.143.144.145.146.147.148.149.150.151.152.153.154.155.156.157.158.159.160.161.162.163.164.165.166.167.168.169.170.171.172.173.174.175.176.177.178.179.180.181.182.183.184.185.186.187.188.189.190.191.192.193.194.195.196.197.198.199.200.
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