zernikect.m

zernike多项式的前36项的表达方式

function ss=zernikeCT( x, y,zerN)
if zerN>=5 
	d10=x;
    d11=x*y;
    d01=y;
    d20=x*x;
    d02=y*y;
    ss(1)=d01;
    ss(2)=d10;
    ss(3)=2*d11;
    ss(4)=2*(d20+d02)-1;
    ss(5)=d20-d02;
end
if zerN>=9
    d21=d20*y;
    d12=d11*y;
    d30=d20*x;
    d03=y*d02;
    ss(6)=3*d21-d03;
    ss(7)=3*(d21+d03)-2*d01;
    ss(8)=3*(d30+d12)-2*d10;
    ss(9)=d30-3*d12;
end
if zerN>=14
    d22=d21*y;
    d31=d30*y;
    d13=d11*d02;
    d40=x*d30;
    d04=y*d03;
    ss(10)=4*(d31-d13);
    ss(11)=8*(d31+d13)-6*d11;
    ss(12)=1-6*(d20+d02-d40-2*d22-d04);
    ss(13)=3*(d02-d20)+4*(d40-d04);
    ss(14)=d40-6*d22+d04; 
end
if zerN>=20 
    d23=x*d13;
    d14=x*d04;
    d41=d40*y;
    d32=d31*y;
    d50=x*d40;
    d05=d04*y;
    ss(15)=5*d41+d05-10*d23;
    ss(16)=10*d23+15*d41+4*d03-12*d21-5*d05;
    ss(17)=10*d05+20*d23+10*d41-12*d03-12*d21+3*d01;
    ss(18)=10*d14+20*d32+10*d50-12*d12-12*d30+3*d10;
    ss(19)=-10*d32+5*d50-15*d14-4*d30+12*d12;
    ss(20)=d50-10*d32+5*d14;  
end
if zerN>=27 
    d33=d32*y;
    d24=x*d14;
    d42=d41*y;
    d15=x*d05;
    d51=d50*y;
    d60=x*d50;
    d06=y*d05;
    ss(21)=6*d51-20*d33+6*d15;
    ss(22)=24*d51-24*d15-20*d31+20*d13;
    ss(23)=30*d15+60*d33+30*d51-40*d13-40*d31+12*d11;
    sss=20*d60+60*d42+60*d24+20*d06-30*d04-60*d22;
    ss(24)=sss-30*d40+12*d02+12*d20-1;
    sss=-(15*d24)+15*d42+15*d60-20*d40+6*d20-15*d06;
    ss(25)=sss+20*d04-6*d02;
    sss=6*d60+6*d06-5*d40+30*d22;
    ss(26)=sss-5*d04-30*d42-30*d24;
    ss(27)=d60-15*d42+15*d24-d06;    
end
if zerN>=35
    d34=x*d24;
    d43=d42*y;
    d25=x*d15;
    d52=d51*y;
    d61=d60*y;
    d16=x*d06;
    d70=x*d60;
    d07=y*d06;
    ss(28)=7*d61-35*d43+21*d25-d07;
    sss=-35*d43+35*d61-63*d25+7*d07;
    ss(29)=sss-30*d41+60*d23-6*d05;
    sss=-21*d07+21*d25+105*d43+30*d05;
    ss(30)=sss-60*d23-10*d03+63*d61-90*d41+30*d21;
    sss=35*d61+105*d43+105*d25+35*d07-60*d05;
    ss(31)=sss-120*d23-60*d41+30*d03+30*d21-4*d01;
    sss=35*d70+105*d52+105*d34+35*d16-60*d14;
    ss(32)=sss-120*d32-60*d50+30*d12+30*d30-4*d10;
    sss=-105*d34-21*d52+21*d70+60*d32-30*d50;
    ss(33)=sss+10*d30-63*d16+90*d14-30*d12;
    sss=-63*d52+7*d70-35*d34+35*d16-6*d50;
    ss(34)=sss+60*d32-30*d14;
    ss(35)=d70-21*d52+35*d34-7*d16; 
end