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ptycho/utils_electron/make_tem_probe.m

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+function [probe, mask] = make_tem_probe(dx, N, param)
+%MAKE_TEM_PROBE Generate probe functions produced by object lens in 
+% transmission electron microscope.
+% Written by Yi Jiang based on Eq.(2.10) in Advanced Computing in Electron 
+% Microscopy (2nd edition) by Dr.Kirkland
+% 
+% Outputs:
+%   probe: complex probe functions
+%   mask: 2D Fourier mask function determined by alpha_max
+%
+% Inputs: 
+%   dx: pixel size in angstrom
+%   N: number of pixels in each side of the 2D probe
+%   param: probe parameters and other settings
+
+% parse inputs
+parse_param = inputParser;
+parse_param.KeepUnmatched = true;
+parse_param.addParameter('df', 0, @isnumeric) %first-order aberration (defocus) in angstrom
+parse_param.addParameter('C3', 0, @isnumeric) %third-order spherical aberration in angstrom
+parse_param.addParameter('C5', 0, @isnumeric) %fifth-order spherical aberration in angstrom
+parse_param.addParameter('C7', 0, @isnumeric) %seventh-order spherical aberration in angstrom
+parse_param.addParameter('f_a2', 0, @isnumeric) %twofold astigmatism in angstrom
+parse_param.addParameter('theta_a2', 0, @isnumeric) %azimuthal orientation in radian
+parse_param.addParameter('f_a3', 0, @isnumeric) %threefold astigmatism in angstrom
+parse_param.addParameter('theta_a3', 0, @isnumeric) %azimuthal orientation in radian
+parse_param.addParameter('f_c3', 0, @isnumeric) %coma in angstrom
+parse_param.addParameter('theta_c3', 0, @isnumeric) %azimuthal orientation in radian
+
+parse_param.addParameter('shifts', [0,0], @isnumeric) %shift probe center in angstrom
+parse_param.addParameter('N_z', 1, @isnumeric) %number of focal planes
+parse_param.addParameter('voltage', 300, @isnumeric) %beam voltage
+parse_param.addParameter('alpha_max', 30, @isnumeric) %semi-convergence angle
+parse_param.addParameter('plotting', 0, @islogical) %plot probes
+
+parse_param.parse(param)
+p = parse_param.Results;
+
+lambda = 12.398/sqrt((2*511.0+p.voltage).*p.voltage); %angstrom
+
+amax = p.alpha_max*1e-3; %in rad
+amin = 0;
+
+klimitmax = amax/lambda;
+klimitmin = amin/lambda;
+dk = 1/(dx*N);
+
+if p.N_z==1
+    dff = p.df;
+else
+    dff = linspace(-floor(p.N_z/2),ceil(p.N_z/2)-1,p.N_z)*p.df; %angstrom
+end
+
+kx = linspace(-floor(N/2),ceil(N/2)-1,N);
+[kX,kY] = meshgrid(kx,kx);
+
+kX = kX.*dk;
+kY = kY.*dk;
+kR = sqrt(kX.^2+kY.^2);
+theta = atan2(kY,kX);
+chi = zeros(N,N,p.N_z);
+probe = zeros(N,N,p.N_z);
+
+mask = single(kR<=klimitmax).*single(kR>=klimitmin);
+for i= 1:p.N_z
+    chi(:,:,i) = -pi*lambda*kR.^2*dff(i);
+    if p.C3~=0; chi(:,:,i) = chi(:,:,i) + pi/2*p.C3*lambda^3*kR.^4; end
+    if p.C5~=0; chi(:,:,i) = chi(:,:,i) + pi/3*p.C5*lambda^5*kR.^6; end
+    if p.C7~=0; chi(:,:,i) = chi(:,:,i) + pi/4*p.C7*lambda^7*kR.^8; end
+    if p.f_a2~=0; chi(:,:,i) = chi(:,:,i) + pi*p.f_a2*lambda*kR.^2*sin(2*(theta-p.theta_a2)); end
+    if p.f_a3~=0; chi(:,:,i) = chi(:,:,i) + 2*pi/3*p.f_a3*lambda^2*kR.^3*sin(3*(theta-p.theta_a3)); end
+    if p.f_c3~=0; chi(:,:,i) = chi(:,:,i) + 2*pi/3*p.f_c3*lambda^2*kR.^3*sin(theta-p.theta_c3); end
+
+    phase = exp(-1i.*chi(:,:,i)).*exp(-2*pi*1i*p.shifts(1).*kX).*exp(-2*pi*1i*p.shifts(2).*kY);
+    probe(:,:,i) = mask.*phase;
+    probe(:,:,i) = fftshift(ifft2(ifftshift(probe(:,:,i))));
+    probe(:,:,i) = probe(:,:,i)/sum(sum(abs(probe(:,:,i))));
+end
+
+if p.plotting
+    figure
+    subplot(1,2,1)
+    imagesc(abs(mask))
+    axis image
+    title('Fourier mask magnitude')
+
+    subplot(1,2,2)
+    colormap parula
+    iaxis{1} = ([1 N]-floor(N/2)+1)*dx/10;
+    iaxis{2} = ([1 N]-floor(N/2)+1)*dx/10;
+    imagesc3D(iaxis{1},iaxis{2},abs(probe)) 
+    xlabel('nm')
+    ylabel('nm')
+    axis image
+      
+    title('Probe magnitude')
+end
+
+%probe = probe/(L/N)^2; %normalize the probe. Because in reciprocal space
+%the zero frequency amplitute is 1, so, the summation is also one.
+end
+