球面柱面螺旋面等各种形式的干涉图

1、设参考光为平面波，则干涉图的强度变化为：其中，为物波面的位相函数。我们希望形成的干涉条纹有径向形状，以反映这种径向位相变化。在回转对称波面的清况下，很自然的就希望有极坐标形式来表示波面的位相变化。两种干涉图：（1）条纹是径向分布的，称为径向条纹干涉图；（2）条纹为圆形分布的，称为圆条纹干涉图。这些干涉图是在极坐标中描述的。上式中，当时出现相消干涉。当我们需要画出干涉图时，如需要画出二元干涉图，那么需要有亮条纹的上下限，即进行二元的硬性限幅。p为一定值时，则r, q的取值满足时，为暗条纹下限；r, q的取值满足时，为暗条纹上限；径向条纹干涉图选择参考光波的位相只沿方位方向变化，则得到的干涉条纹就

2、是径向分布的。(8. 2. 10)其中m为条纹数。干涉条纹的方程式为：下限： 上限其中m为干涉图上的径向条纹总数。画干涉图时，(1) 根据(r, q)的范围，确定p的取值范围；(2) 根据干涉条纹的方程式，(fsolve?)求解出下限的(r, q)坐标值与上限的(r, q)坐标值；(3) 分别拟合同一p值对应的上限值与下限值；(4) 极坐标与直角坐标的转换：cart2pol用contourf函数画出，colormap(gray)contourf(X,Y,Z,100,linestyle,none)colormap(gray)axis equalcontourf(X,Y,Z,100,'li

3、nestyle','none')colormap(gray)axis equalaxis off圆条纹干涉图圆条纹干涉图的参考光波位相为其中C为条纹数。那么干涉条纹方程为物光为单位球面波，C = 10时得到螺旋波面的计算全息图螺旋波面的波面方程为取m = 6, M = 30，得到的再现波面的干涉图为由再现波面的干涉图可见螺旋波面的位相变化在方位维是线性的，但外层波面的位相梯度比较小，而向着波面中心移动时，波面的位相梯度就变得很陡。锥形波面的再现波面干涉图取c = 30， C = 10得到的锥形波面的再现波面干涉图如图所示，因为波面在径向的梯度是常数，所以频域中每一衍射级

4、是一个圆，再现波面的干涉图是一系列同心圆。柱状位相物体干涉图柱状物体定义：%r = 0:0.01:5;th = 0:0.01:2*pi; th, r = meshgrid(th, r);m1,n1 = size(th);% Ìõ×´ÎïÌåµÄ¶¨Òå% ¾ù²¼µÄÁùÌõ£¬Ã¿Ìõ¿

5、í1/6*pi ph0 = zeros(m1,n1); % ƽ¶¥¿í¶Èw = pi/10; % ×óбÆ¿í¶Èal = pi/30; % ÓÒбÆ¿í¶Èar = pi/30; %ƽÒÆÁ¿tt = pi/12; for i=1:m

6、1 for j=1:n1 for k=1:6 if th(i,j) <= k*(1/3)*pi - tt && th(i,j) > k*(1/3)*pi-w - tt ph0(i,j) = 1; elseif th(i,j)< k*(1/3)*pi-w -tt && th(i,j)>= k*(1/3)*pi-w-al - tt ph0(i,j) = 1/al.* (th(i,j) - (k*pi/3 - w - al- tt); elseif th(i,j) > k*(1/3)*pi- tt && th(i,j) &

7、lt;= k*(1/3)*pi + ar- tt ph0(i,j) = -1/ar.* (th(i,j) - (k*pi/3 + ar- tt); end end endend % ²Î¿¼¹âΪÎÞÇãбµÄƽÃ沨phr1 = 1; % ¸ÉÉæͼ±í´ïÊ

8、;½I1 = 4.* (cos(0.5 .* (ph0 - phr1).2; % »æͼ X,Y,Z = pol2cart(th,r,I1);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)axis equalaxis off% ²Î¿¼¹âΪÓÐÇãбµÄƽ

9、Ã沨 /10*pix,y = pol2cart(th,r);phr2 = 5*pi.*y;x,y,ph01 = pol2cart(th,r,ph0); % ¸ÉÉæͼ±í´ïʽI2 = 4.* (cos(0.5 .* (ph01 - phr2).2; %r2,th2,I2 = cart2pol(x,y,I2); % »æͼ %X,Y,Z = pol2cart(th,r,I2);figur

10、e,contourf(x,y,I2,100,'linestyle','none')colormap(gray)axis equalaxis off% ²Î¿¼¹âΪÇòÃ沨phr3 = 10*r;% ¸ÉÉæͼ±í´ïʽI3 = 4.* (cos(0.5 .* (ph0 - phr3).2; %

11、»æͼ X,Y,Z = pol2cart(th,r,I3);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)axis equalaxis off条状物体% Ìõ×´ÎïÌåµÄ¶¨Òå% ¾ù²¼µÄÁùÌõ

12、3;¬Ã¿Ìõ¿í1/6*pi ph0 = zeros(m1,n1); % ƽ¶¥¿í¶Èw = 0; % ×óбÆ¿í¶Èal = pi/30; % ÓÒбÆ¿í¶Èar = pi/30; %ƽÒÆ

13、;Á¿tt = pi/12; for i=1:m1 for j=1:n1 for k=1:6 if th(i,j) <= k*(1/3)*pi - tt && th(i,j) > k*(1/3)*pi-w - tt ph0(i,j) = 1; elseif th(i,j)< k*(1/3)*pi-w -tt && th(i,j)>= k*(1/3)*pi-w-al - tt ph0(i,j) = 1/al.* (th(i,j) - (k*pi/3 - w - al- tt); elseif th(i,j) > k

14、*(1/3)*pi- tt && th(i,j) <= k*(1/3)*pi + ar- tt ph0(i,j) = -1/ar.* (th(i,j) - (k*pi/3 + ar- tt); end end endend % ²Î¿¼¹âΪÎÞÇãбµÄƽÃ沨phr1 = 1; % ¸ÉÉæÍ&

15、#188;±í´ïʽI1 = 4.* (cos(0.5 .* (ph0 - phr1).2; % »æͼ X,Y,Z = pol2cart(th,r,I1);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)axis equalaxis off% ²Î¿¼¹âΪÓÐÇã&#

16、208;±µÄƽÃ沨 /10*pix,y = pol2cart(th,r);phr2 = 5*pi.*y;x,y,ph01 = pol2cart(th,r,ph0); % ¸ÉÉæͼ±í´ïʽI2 = 4.* (cos(0.5 .* (ph01 - phr2).2; %r2,th2,I2 = cart2pol(x,y,I2); % »æͼ

17、; %X,Y,Z = pol2cart(th,r,I2);figure,contourf(x,y,I2,100,'linestyle','none')colormap(gray)axis equalaxis off% ²Î¿¼¹âΪÇòÃ沨phr3 = 10*r;% ¸ÉÉæͼ±í´ïʽI3 =

18、4.* (cos(0.5 .* (ph0 - phr3).2; % »æͼ X,Y,Z = pol2cart(th,r,I3);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)axis equalaxis off位相盘装物体% Íâ0ÄÚ1£¬·Ö½çÏßΪr=0.5 r = 0:0.01:5;th = 0:0.

19、01:2*pi; th, r = meshgrid(th, r);m1,n1 = size(th); ph0 = zeros(m1,n1); for i=1:m1 for j=1:n1 if r(i,j)>=3 && r(i,j) < 4 ph0(i,j)=0.5*sin(pi*(r(i,j)-3.5)+0.5; elseif r(i,j) >=4 ph0(i,j)=1; end endend% ²Î¿¼¹âΪÎÞÇãб

20、;µÄƽÃ沨phr1 = 1; % ¸ÉÉæͼ±í´ïʽI1 = 4.* (cos(0.5 .* (ph0 - phr1).2; % »æͼ X,Y,Z = pol2cart(th,r,I1);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)ax

21、is equalaxis offfigure,>> plot(r(:,1),ph0(:,1)% ²Î¿¼¹âΪÓÐÇãбµÄƽÃ沨 /10*pix,y = pol2cart(th,r);phr2 = 2*pi.*x;x,y,ph01 = pol2cart(th,r,ph0); % ¸ÉÉæͼ&#

22、177;í´ïʽI2 = 4.* (cos(0.5 .* (ph01 - phr2).2; %r2,th2,I2 = cart2pol(x,y,I2); % »æͼ %X,Y,Z = pol2cart(th,r,I2);figure,contourf(x,y,I2,100,'linestyle','none')colormap(gray)axis equalaxis off% ¾¶ÏòÌõÎÆ

23、;¸ÉÉæͼphr4 = 20*th; % ¸ÉÉæͼ±í´ïʽI4 = 4.* (cos(0.5 .* (ph0 - phr4).2; % »æͼ X,Y,Z = pol2cart(th,r,I4);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)axis equal

24、axis off位相环状物体% λÏàÅÌ×´ÎïÌå% ¶¨Òå % Íâ0ÄÚ1£¬·Ö½çÏßΪr=0.5 r = 0:0.01:5;th = 0:0.01:2*pi; th, r = meshgrid(th, r);m1,n1 = size(th); ph0 = zeros(m1,n1)

25、; for i=1:m1 for j=1:n1 if r(i,j)>=3 && r(i,j) < 4 ph0(i,j)=0.5*sin(2*pi*(r(i,j)-3.25)+0.5; end endend% ²Î¿¼¹âΪÎÞÇãбµÄƽÃ沨phr1 = 1; % ¸ÉÉæͼ±í´ïʽI1 = 4.* (cos(0.5 .* (ph0 - phr1).2; % »æͼ X,Y,Z = pol2cart(th,r,I1);figure,contourf(X,Y,Z,100,'linestyle','none')colormap(gray)axis equalaxis of