小弟不是學(xué)光學(xué)的，所以想請各位大俠指點啊！謝謝啦 J-Wphc!m  
就是我用ansys計算出了鏡面的面型的數(shù)據(jù)，怎樣可以得到zernike多項式的系數(shù)，然后用zemax各階得到像差！謝謝啦！ +\~Mx>Cn  

可以用matlab編程，用zernike多項式進行波面擬合，求出zernike多項式的系數(shù)，擬合的算法有很多種，最簡單的是最小二乘法，你可以查下相關(guān)資料，挺簡單的

澤尼克多項式的前9項對應(yīng)象差的

非常感謝啊，我手上也有zernike多項式的擬合的源程序，也不知道對不對，不怎么會有 \hFIg3  
function z = zernfun(n,m,r,theta,nflag) Jp]eFaqp  
%ZERNFUN Zernike functions of order N and frequency M on the unit circle. :s`\j
J  
%   Z = ZERNFUN(N,M,R,THETA) returns the Zernike functions of order N x1{gw 5:  
%   and angular frequency M, evaluated at positions (R,THETA) on the -A17tC20J1  
%   unit circle.  N is a vector of positive integers (including 0), and 63n<4VSH  
%   M is a vector with the same number of elements as N.  Each element s6J`i&uu  
%   k of M must be a positive integer, with possible values M(k) = -N(k) B&RgUIrFoY  
%   to +N(k) in steps of 2.  R is a vector of numbers between 0 and 1, #OVf2
"  
%   and THETA is a vector of angles.  R and THETA must have the same #iAEcC0k5  
%   length.  The output Z is a matrix with one column for every (N,M) V+2C!)f(  
%   pair, and one row for every (R,THETA) pair. 5rx;?yvn  
% B M$+r(#t  
%   Z = ZERNFUN(N,M,R,THETA,'norm') returns the normalized Zernike ]:vo"{*C  
%   functions.  The normalization factor sqrt((2-delta(m,0))*(n+1)/pi), 01" b9`jU  
%   with delta(m,0) the Kronecker delta, is chosen so that the integral &?gvW//L2  
%   of (r * [Znm(r,theta)]^2) over the unit circle (from r=0 to r=1, QSq0{  
%   and theta=0 to theta=2*pi) is unity.  For the non-normalized .#ASo!O5q  
%   polynomials, max(Znm(r=1,theta))=1 for all [n,m]. 27-GfC=7*  
% aZ{]t:]  
%   The Zernike functions are an orthogonal basis on the unit circle. CDTM<0`%  
%   They are used in disciplines such as astronomy, optics, and 9akIu.H  
%   optometry to describe functions on a circular domain. /vLdm-4  
% q:/<^|  
%   The following table lists the first 15 Zernike functions. D<d4"*qo  
% *eonXJYD  
%       n    m    Zernike function           Normalization .#[==  
%       -------------------------------------------------- &KS*rHgt?  
%       0    0    1                                 1 u+Q<>>lU  
%       1    1    r * cos(theta)                    2 ).b,KSi  
%       1   -1    r * sin(theta)                    2 -%eBip,'yl  
%       2   -2    r^2 * cos(2*theta)             sqrt(6) j6_
tFJT  
%       2    0    (2*r^2 - 1)                    sqrt(3) cq,0?2R`t  
%       2    2    r^2 * sin(2*theta)             sqrt(6) $'obj  
%       3   -3    r^3 * cos(3*theta)             sqrt(8) }hy, }2(8  
%       3   -1    (3*r^3 - 2*r) * cos(theta)     sqrt(8) t/TWLhx/  
%       3    1    (3*r^3 - 2*r) * sin(theta)     sqrt(8) z nxAP|  
%       3    3    r^3 * sin(3*theta)             sqrt(8) mWPA]g(  
%       4   -4    r^4 * cos(4*theta)             sqrt(10) OEFALt  
%       4   -2    (4*r^4 - 3*r^2) * cos(2*theta) sqrt(10) p\ }Ep  
%       4    0    6*r^4 - 6*r^2 + 1              sqrt(5) ?]]d 
s]  
%       4    2    (4*r^4 - 3*r^2) * cos(2*theta) sqrt(10) <//#0r*  
%       4    4    r^4 * sin(4*theta)             sqrt(10) O.% $oV  
%       -------------------------------------------------- 3</gK$f2  
% ?'$Y
j>R6  
%   Example 1: m=hUHA,p4  
% O<o>/HH$  
%       % Display the Zernike function Z(n=5,m=1) Q'B2!9=LB  
%       x = -1:0.01:1; fT.GYvt`  
%       [X,Y] = meshgrid(x,x); :|tWKA  
%       [theta,r] = cart2pol(X,Y); ~DYv6-p%  
%       idx = r<=1; dRD t.U!T  
%       z = nan(size(X)); WQ1~9# 长兴县| 丰顺县| 廊坊市| 绍兴县| 定远县| 西充县| 琼中| 安龙县| 昂仁县| 建德市| 嘉荫县| 甘孜县| 谷城县| 遂川县| 井冈山市| 望江县| 安阳县| 义马市| 都匀市| 红河县| 雅江县| 定安县| 长宁县| 德州市| 岚皋县| 嘉祥县| 高安市| 栾川县| 通道| 盐山县| 奉新县| 遂川县| 龙州县| 华坪县| 银川市| 和平区| 新巴尔虎右旗| 穆棱市| 沧源| 巴中市| 上栗县|