| Date 06/09/2010 |
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| Script S2_2_18.m | |||
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%Longitudinal and transverse spherical aberrations %see CORRIGENDA in Contents section of the web site %================================================= % %the radius R of the first surface of the in mm %thickness t of the lens in mm %the refractive index of the lens R=20; t=3; n=1.67; % %below alfag=20° we are in condition of paraxial %approximation and can write alfa = sin(alfa) %with an error less than 2% alfa_g=eps:1:20; %the length of the array alfa_g N=length(alfa_g); %angle in radians alfa=alfa_g*pi/180; %y are heights less than or equal to r1 y=R*sin(alfa); r1=y(end) %the corresponding d values with the maximun value dmax d=R*(1-cos(alfa)); %============================================================= %for the following angles alfap, beta and alfas see Fig.2.57 % %the angles alfap of refraction on the %first spherical surface of the lens alfap=asin(sin(alfa)/n); %the angles beta of incidence on the %second plane surface of the lens beta=alfa-alfap; %the angles alfas of refraction on the %second plane surface of the lens alfas=asin(n*sin(beta)) %============================================================= % %the values yp (see Fig. 2.58) AD=(t-d).*tan(beta); yp=y-AD %values zp distances of point images from the %plane surface of the lens (longitudinal aberrations) zp=yp./tan(alfas) %the longitudinal extension of the point image delta_zp=zp(1)-zp(end) %power and focal length of the lens P=(n-1)/R; f=1/P %distance of the principal point from the %plane surface of the lens h=-(f-zp(1)) % %d is the distance, in mm, from position zp(N) to the place %of a scren where the point image is observed d=10; ys=(yp(N)/zp(N))*d r2=ys; %the value of transverse aberration disk=pi*r2^2 %================================================= % |
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