%% Beynon zone plate
% OPTICS LETTERS / Vol. 17, No. 7 / April 1, 1992
%
% This file generates the Beynon zone plate, which behaves exactly like
% Gabor zone plate with a single focus. In contrast to Gabor plate,
% the Beynon plate has binary transmittance function,
% this makes it attractive for practical applications where continuous
% analog functions are difficult to use.
%
close all;
% clear all;
clc;
N = 40; % number of angular Sectors (technically you can input small numbers, but for your own responsibility)
lambda = .6328; % light wavelength [um]
f = 5000; % focal length [um]
D = 500; % zone plate diameter [um] (aperture)
%% Some precalculations
R = D/2; % zone plate outer radius [um]
r = sqrt(lambda*f); % fist zone radius
rhores = R*10; % radial resolution
phires = 3600; % angular resolution
halfalpha = pi/N; % half-angle of sector
rho = linspace(0,R,rhores); % polar coordinates (radial)
phi = linspace(0,2*pi,phires); % polar coordinates (angular)
theta = halfalpha * sin(pi*(rho/r).^2/2).^2; % transmittance function in polar coordinates
theta(rhores) = 0; % by this string last value forced to zero, that required for polymesh generation (small negligible error occur)
X=rho.*cos(theta); % return to Cartesian coordinates
Y=rho.*sin(theta); % return to Cartesian coordinates
%% Drawing of the Beynon zone plate with aperture 2*R, N-number of angular sectors and with f-foci distance
figure('name','Beynon','color','white');clf;
pgon1 = polyshape(X,Y); % upper halfsector
pgon2 = polyshape(X,-Y); % lower halfsector
sector = union(pgon1,pgon2); % one complite sector
alpha =360/N; % angle in degrees between conjugated sectors
for n1=1:(N+1)*2
sector = rotate(sector,alpha);
plot(sector,'FaceColor','k','FaceAlpha',1,'LineStyle','none');
axis equal;
hold on
end
grid('off');
axis('off');
title('Beynon zone plate');
% exportgraphics(gcf,'Beynon.tiff','Resolution',600);
% saveas(gcf,'Beynon.png')
