Zernike_36_泽尼克_直角坐标系zernike多项式程序_zernike多项式_zernike_zernikematla

function J =Zernike_36(W,dim) x=linspace(-1,1,dim); y=linspace(-1,1,dim); [x,y] = meshgrid(x,y); % Z3=-1+2*(x.^2+y.^2);%离焦 % Z4=x.^2-y.^2;%像散，轴线0，90 % Z5=2*x.*y;%像散，轴线+-45 % Z6=-2*x+3*x.*(x.^2+y.^2);%沿X轴的三级慧差r % Z7=-2*y+3*y.*(x.^2+y.^2);%沿Y轴的三级慧差 % Z8=1-6*(x.^2+y.^2)+6*(x.^2+y.^2).^2;%三级球差 % % sq = (x.^2+y.^2); % s2 = sqrt(2); % s3 = sqrt(3); % s5 = sqrt(5); % s7 = sqrt(7); % % Z9 = 2*s2*y.*(3*x.^2-y.^2); % Z10 = 2*s2*x.*(x.^2-3*y.^2); % Z11 = s5*(6*sq.^2-6*sq+1); % Z12 = s2*s5*(x.^2-y.^2).*(4*sq-3); % Z13 = 2*s2*s5*x.*y.*(4*sq.^2-3); % Z14 = s2*s5*(sq.^2-8*x.^2*y.^2); % Z15 = 4*s2*s5*(x.^2-y.^2); % Z16 = 2*s3*x.*(10*sq.^2-12*sq+3); % % Z17 = 2*s3*y.*(10*sq.^2-12*sq+3); % Z18 = 2*s3*x.*(x.^2-3*y.^2).*(5*sq-4); % Z19 = 2*s3*y.*(3*x.^2-y.^2).*(5*sq-4); % Z20 = 2*s3*x.*(16*x.^4-20*x.^2.*sq+5*sq.^2); % Z21 = 2*s3*y.*(16*y.^4-20*y.^2.*sq+5*sq.^2); % Z22 = s7*(20*sq.^3-30*sq.^2+12*sq-1); % Z23 = 2*s2*s7*x.*y.*(15*sq.^2-20*sq+6); % Z24 = s2*s7*(x.^2-y.^2).*(15*sq.^2-20*sq+6); % Z25 = 4*s2*s7*x.*y.*(x.^2-y.^2).*(6*sq-5); % Z26 = s2*s7*(8*x.^4-8*x.^2.*sq+sq.^2).*(6*sq-5); % Z27 = s2*s7*(32*x.^4-32*x.^2.*sq+6*sq.^2); % Z28 = s2*s7*(32*x.^6-48*x.^4.*sq+18*x.^2.*sq.^2-sq.^3); Z4=-1+2*(x.^2+y.^2); Z5=x.^2-y.^2; Z6=2*x.*y; Z7=-2*x+3*x.*(x.^2+y.^2); Z8=-2*y+3*y.*(x.^2+y.^2); Z9=1-6*(x.^2+y.^2)+6*(x.^2+y.^2).^2; Z10=x.^3-3*x.*y.^2; Z11=3*x.^2.*y-y.^3; Z12=-3*x.^2+3*y.^2+4*x.^2.*(x.^2+y.^2)-4*y.^2.*(x.^2+y.^2); Z13=-6*x.*y+8*x.*y.*(x.^2+y.^2); Z14=3*x-12*x.*(x.^2+y.^2)+10*x.*(x.^2+y.^2).^2; Z15=3*y-12*y.*(x.^2+y.^2)+10*y.*(x.^2+y.^2).^2; Z16=-1+12*(x.^2+y.^2)-30*(x.^2+y.^2).^2+20*(x.^2+y.^2).^3; Z17=x.^4-6*x.^2.*y.^2+y.^4; Z18=4*x.^3.*y-4*x.*y.^3; Z19=-4*x.^3+12*x.*y.^2+5*x.^3.*(x.^2+y.^2)-15*x.*y.^2.*(x.^2+y.^2); Z20=-12*x.^2.*y+4*y.^3+15*x.^2.*y.*(x.^2+y.^2)-5*y.^3.*(x.^2+y.^2); Z21=6*x.^2-6*y.^2-20*x.^2.*(x.^2+y.^2)+20*y.^2.*(x.^2+y.^2)+15*x.^2.*(x.^2+y.^2).^2-15*y.^2.*(x.^2+y.^2).^2; Z22=12*x.*y-40*x.*y.*(x.^2+y.^2)+30*x.*y.*(x.^2+y.^2).^2; Z23=-4*x+30*x.*(x.^2+y.^2)-60*x.*(x.^2+y.^2).^2+35*x.*(x.^2+y.^2).^3; Z24=-4*y+30*y.*(x.^2+y.^2)-60*y.*(x.^2+y.^2).^2+35*y.*(x.^2+y.^2).^3; Z25=1-20*(x.^2+y.^2)+90*(x.^2+y.^2).^2-140*(x.^2+y.^2).^3+70*(x.^2+y.^2).^4; Z26=x.^5-10*x.^3.*y.^2+5*x.*y.^4; Z27=5*x.^4.*y-10*x.^2.*y.^3+y.^5; Z28=-5*x.^4+30*x.^2.*y.^2-5*y.^4+6*x.^4.*(x.^2+y.^2)-36*x.^2.*y.^2.*(x.^2+y.^2)+6*y.^4.*(x.^2+y.^2); Z29=-20*x.^3.*y+20*x.*y.^3+24*x.^3.*y.*(x.^2+y.^2)-24*x.*y.^3.*(x.^2+y.^2); Z30=10*x.^3-30*x.*y.^2-30*x.^3.*(x.^2+y.^2)+90*x.*y.^2.*(x.^2+y.^2)+21*x.^3.*(x.^2+y.^2).^2-63*x.*y.^2.*(x.^2+y.^2).^2; Z31=30*x.^2.*y-10*y.^3-90*x.^2.*y.*(x.^2+y.^2)+30*y.^3.*(x.^2+y.^2)+63*x.^2.*y.*(x.^2+y.^2).^2-21*y.^3.*(x.^2+y.^2).^2; Z32=-10*x.^2+10*y.^2+60*x.^2.*(x.^2+y.^2)-60*y.^2.*(x.^2+y.^2)-105*x.^2.*(x.^2+y.^2).^2+105*y.^2.*(x.^2+y.^2).^2+56*x.^2.*(x.^2+y.^2).^3-56*y.^2.*(x.^2+y.^2).^3; Z33=-20*x.*y+120*x.*y.*(x.^2+y.^2)-210*x.*y.*(x.^2+y.^2).^2+112*x.*y.*(x.^2+y.^2).^3; Z34=5*x-60*x.*(x.^2+y.^2)+210*x.*(x.^2+y.^2).^2-280*x.*(x.^2+y.^2).^3+126*x.*(x.^2+y.^2).^4; Z35=5*y-60*y.*(x.^2+y.^2)+210*y.*(x.^2+y.^2).^2-280*y.*(x.^2+y.^2).^3+126*y.*(x.^2+y.^2).^4; Z36=-1+30*(x.^2+y.^2)-210*(x.^2+y.^2).^2+560.*(x.^2+y.^2).^3-630*(x.^2+y.^2).^4+252*(x.^2+y.^2).^5; % Z(:,:,37)=1-42*(x.^2+y.^2)+420*(x.^2+y.^2).^2-1680.*(x.^2+y.^2).^3+3150*(x.^2+y.^2).^4-2772*(x.^2+y.^2).^5+924*(x.^2+y.^2).^6; % fid3=fopen('Z3.txt','wt'); fid4=fopen('Z4.txt','wt'); fid5=fopen('Z5.txt','wt'); fid6=fopen('Z6.txt','wt'); fid7=fopen('Z7.txt','wt'); fid8=fopen('Z8.txt','wt'); fid9=fopen('Z9.txt','wt'); fid10=fopen('Z10.txt','wt'); fid11=fopen('Z11.txt','wt'); fid12=fopen('Z12.txt','wt'); fid13=fopen('Z13.txt','wt'); fid14=fopen('Z14.txt','wt'); fid15=fopen('Z15.txt','wt'); fid16=fopen('Z16.txt','wt'); fid17=fopen('Z17.txt','wt'); fid18=fopen('Z18.txt','wt'); fid19=fopen('Z19.txt','wt'); fid20=fopen('Z20.txt','wt'); fid21=fopen('Z21.txt','wt'); fid22=fopen('Z22.txt','wt'); fid23=fopen('Z23.txt','wt'); fid24=fopen('Z24.txt','wt'); fid25=fopen('Z25.txt','wt'); fid26=fopen('Z26.txt','wt'); fid27=fopen('Z27.txt','wt'); fid28=fopen('Z28.txt','wt'); fid29=fopen('Z29.txt','wt'); fid30=fopen('Z30.txt','wt'); fid31=fopen('Z31.txt','wt'); fid32=fopen('Z32.txt','wt'); fid33=fopen('Z33.txt','wt'); fid34=fopen('Z34.txt','wt'); fid35=fopen('Z35.txt','wt'); fid36=fopen('Z36.txt','wt'); fid38=fopen('ZW.txt','wt'); for i=1:1:dim for j=1:1:dim if(W(i,j)~=0) % fprintf(fid3,'%f ',Z3(i,j)); fprintf(fid4,'%f ',Z4(i,j)); fprintf(fid5,'%f ',Z5(i,j)); fprintf(fid6,'%f ',Z6(i,j)); fprintf(fid7,'%f ',Z7(i,j)); fprintf(fid8,'%f ',Z8(i,j)); fprintf(fid9,'%f ',Z9(i,j)); fprintf(fid10,'%f ',Z10(i,j)); fprintf(fid11,'%f ',Z11(i,j)); fprintf(fid12,'%f ',Z12(i,j)); fprintf(fid13,'%f ',Z13(i,j)); fprintf(fid14,'%f ',Z14(i,j)); fprintf(fid15,'%f ',Z15(i,j)); fprintf(fid16,'%f ',Z16(i,j)); fprintf(fid17,'%f ',Z17(i,j)); fprintf(fid18,'%f ',Z18(i,j)); fprintf(fid19,'%f ',Z19(i,j)); fprintf(fid20,'%f ',Z20(i,j)); fprintf(fid21,'%f ',Z21(i,j)); fprintf(fid22,'%f ',Z22(i,j)); fprintf(fid23,'%f ',Z23(i,j)); fprintf(fid24,'%f ',Z24(i,j)); fprintf(fid25,'%f ',Z25(i,j)); fprintf(fid26,'%f ',Z26(i,j)); fprintf(fid27,'%f ',Z27(i,j)); fprintf(fid28,'%f ',Z28(i,j)); fprintf(fid29,'%f ',Z29(i,j)); fprintf(fid30,'%f ',Z30(i,j)); fprintf(fid31,'%f ',Z31(i,j)); fprintf(fid32,'%f ',Z32(i,j)); fprintf(fid33,'%f ',Z33(i,j)); fprintf(fid34,'%f ',Z34(i,j)); fprintf(fid35,'%f ',Z35(i,j)); fprintf(fid36,'%f ',Z36(i,j)); fprintf(fid38,'%f ',W(i,j)); end end end % fid=fopen('Z3.txt','rt'); % H1=fscanf(fid,'%f'); fid=fopen('Z4.txt','rt'); H2=fscanf(fid,'%f'); fid=fopen('Z5.txt','rt'); H3=fscanf(fid,'%f'); fid=fopen('Z6.txt','rt'); H4=fscanf(fid,'%f'); fid=fopen('Z7.txt','rt'); H5=fscanf(fid,'%f'); fid=fopen('Z8.txt','rt'); H6=fscanf(fid,'%f'); fid=fopen('Z9.txt','rt'); H7=fscanf(fid,'%f'); fid=fopen('Z10.txt','rt'); H8=fscanf(fid,'%f'); fid=fopen('Z11.txt','rt'); H9=fscanf(fid,'%f'); fid=fopen('Z12.txt','rt'); H10=fscanf(fid,'%f'); fid=fopen('Z13.txt','rt'); H11=fscanf(fid,'%f'); fid=fopen('Z14.txt','rt'); H12=fscanf(fid,'%f'); fid=fopen('Z15.txt','rt'); H13=fscanf(fid,'%f'); fid=fopen('Z16.txt','rt'); H14=fscanf(fid,'%f'); fid=fopen('Z17.txt','rt'); H15=fscanf(fid,'%f'); fid=fopen('Z18.txt','rt'); H16=fscanf(fid,'%f'); fid=fopen('Z19.txt','rt'); H17=fscanf(fid,'%f'); fid=fopen('Z20.txt','rt'); H18=fscanf(fid,'%f'); fid=fopen('Z21.txt','rt'); H19=fscanf(fid,'%f'); fid=fopen('Z22.txt','rt'); H20=fscanf(fid,'%f'); fid=fopen('Z23.txt','rt'); H21=fscanf(fid,'%f'); fid=fopen('Z24.txt','rt'); H22=fscanf(fid,'%f'); fid=fopen('Z25.txt','rt'); H23=fscanf(fid,'%f'); fid=fopen('Z26.txt','rt'); H24=fscanf(fid,'%f'); fid=fopen('Z27.txt','rt'); H25=fscanf(fid,'%f'); fid=fopen('Z28.txt','rt'); H26=fscanf(fid,'%f'); fid=fopen('Z29.txt','rt'); H27=fscanf(fid,'%f'); fid=fopen('Z30.txt','rt'); H28=fscanf(fid,'%f'); fid=fopen('Z31.txt','rt'); H29=fscanf(fid,'%f'); fid=fopen('Z32.txt','rt'); H30=fscanf(fid,'%f'); fid=fopen('Z33.txt','rt'); H31=fscanf(fid,'%f'); fid=fopen('Z34.txt','rt'); H32=fscanf(fid,'%f'); fid=fopen('Z35.txt','rt'); H33=fscanf(fid,'%f'); fid=fopen('Z36.txt','rt'); H34=fscanf(fid,'%f'); fid=fopen('ZW.txt','rt'); L=fscanf(fid,'%f'); % fclose(fid3); fclose(fid4); fclose(fid5); fclose(fid6); fclose(fid7); fclose(fid8); fclose(fid9);