jssylttc |
2012-04-23 19:23 |
如何从zernike矩中提取出zernike系数啊
下面这个函数大家都不会陌生,计算zernike函数值的,并根据此可以还原出图像来, <<d # 我输入10阶的n、m,r,theta为38025*1向量,最后得到的z是29525*10阶的矩阵, ZXQ5fBx 这个,跟我们用zygo干涉仪直接拟合出的36项zernike系数,有何关系呢? _oc6=Z 那些系数是通过对29525*10阶的矩阵每列的值算出来的嘛? bDWLHdu
a &{8:XJe*,% Fc`IRPW< y p{Dl }cMkh function z = zernfun(n,m,r,theta,nflag) :} =lE"2 %ZERNFUN Zernike functions of order N and frequency M on the unit circle. )Q`Ycz- % Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N ASy?^Jrs5 % and angular frequency M, evaluated at positions (R,THETA) on the Gf.ywqE$Y$ % unit circle. N is a vector of positive integers (including 0), and )KFxtM- % M is a vector with the same number of elements as N. Each element e:
Sd#H! % k of M must be a positive integer, with possible values M(k) = -N(k) ~2rQ80_ % to +N(k) in steps of 2. R is a vector of numbers between 0 and 1, l3b=8yn. % and THETA is a vector of angles. R and THETA must have the same [6l0|Y % length. The output Z is a matrix with one column for every (N,M) > .NLmzUX % pair, and one row for every (R,THETA) pair. [G8EX3 % $Be hU % Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike H3$py|}lL % functions. The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), #w|v.35%? % with delta(m,0) the Kronecker delta, is chosen so that the integral )=GPhC/sw % of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, b(N\R_IQ~ % and theta=0 to theta=2*pi) is unity. For the non-normalized 7 w,D2T % polynomials, max(Znm(r=1,theta))=1 for all [n,m]. i=<;$+tW % V $I8iVGL % The Zernike functions are an orthogonal basis on the unit circle. e]1'D % They are used in disciplines such as astronomy, optics, and 1]''@oh{6U % optometry to describe functions on a circular domain. L3\#ufytb % \12G,tBH % The following table lists the first 15 Zernike functions. u4FD}nV % ')q4d0B`" % n m Zernike function Normalization \ejHM}w3, % -------------------------------------------------- 3\}u#/Vb % 0 0 1 1 $`GlXiV % 1 1 r * cos(theta) 2 H'#06zP>5 % 1 -1 r * sin(theta) 2 =M-=94 % 2 -2 r^2 * cos(2*theta) sqrt(6) & | |