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recip_2Dlattice.m
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recip_2Dlattice.m
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classdef recip_2Dlattice < handle
%reciprocal 2D lattice object
%Dependencies eDiff_Wavenumber
% eDiff_ScatteringFactor
% phase2color
properties (SetAccess = public, GetAccess = public)
spotcut = 2; % radial cut off
kzval = 0; % default kz value
keV = 80; % incident electron beam energy (keV)
rnd = 8; % position tolerance (# decimal points)
kzMode = 'ewald'; %
intcut = 0; % Intensity cutoff (Normalized)
killZero = 1; % 0-> show 0, 1-> hide 0, 2-> gray 0
includeScat= true;
% Lattice Parameters
bs
b1
b2
as
a1
a2
area % Unit Cell Area
lambda % Inter-vdw spacing
stacking
title_str =''; % Title for figures
intensityFactor = 1; % Scaling factor for ploting bragg peaks
% For Tilt Series
tilt_start
tilt_end
tilt_n = 2.^8;
tilt_angle
tilt_axis = 0;
% 3D kz extent
kzExtent;
end
methods
function setTitle(self,val)
self.title_str=val;
end
function setSpotcut(self,val)
self.spotcut=val;
end
function setKzVal(self,val)
self.kzval=val;
end
function setkeV(self,val)
self.keV=val;
end
function setrnd(self,val)
self.rnd=val;
end
function setKzMode(self,val)
self.kzMode=val;
end
function setIntcut(self,val)
self.intcut=val;
end
function setKillZero(self,val)
self.killZero=val;
end
function setIncludeScat(self,val)
self.includeScat=val;
end
function setArea(self,val)
self.area = val;
end
function setKzExtent(self,val)
self.kzExtent = val;
end
function setLambda(self,val)
self.lambda=val;
end
function setIntensityFactor(self,val)
self.intensityFactor = val;
end
function setTiltStart(self,val)
self.tilt_start = val;
end
function setTiltEnd(self,val)
self.tilt_end = val;
end
function setTiltAxis(self,val)
self.tilt_axis = val;
end
function setTiltAngle(self,val)
self.tilt_angle = val;
end
function setTiltN(self,val)
self.tilt_n = val;
end
function [pos,h,k] = recip2DMeshGrid(self)
[pos,h,k] = indexedMeshGrid(self.spotcut,self.b1,self.b2);
% Get rid of overlapping peaks
pos = round(pos,self.rnd);
[~,ia,~] = unique(pos,'rows');
pos = pos(ia,:);
h = h(ia);
k = k(ia);
end
function [ kz ] = kzProvider(self,kx,ky)
switch self.kzMode
case 'constant'
kz = self.kzval*ones(length(kx),1);
case 'ewald'
K = eDiff_Wavenumber(self.keV);
k_rho_sq = (kx.^2+ky.^2);
kz = K-sqrt(K^2 -k_rho_sq);
case 'tilted_ewald'
k = eDiff_Wavenumber(self.keV);
phi = self.tilt_angle;
theta = self.tilt_axis;
qzo = k*cos(phi);
qxo = k*sin(phi)*cos(theta);
qyo = k*sin(phi)*sin(theta);
kz = qzo - sqrt(k^2 - (kx-qxo).^2 - (ky-qyo).^2);
otherwise
error('invalid mode')
end
end
function [pos] = rotPos(self,pos,theta)
% rotate positioin matrix in xy plane
% pos: n x 3 position matrix [x0,y0,z0;x1,y1,z1;..]
% Written by Suk Hyun Sung, sukhsung@umich.edu
% Jan. 05 2018
% construct tilt_axis matrix
rotmatrix = [cos(theta),-sin(theta);sin(theta),cos(theta)];
% extract xy coordinates only
xy = pos(:,1:2);
% rotate xy coordinates
xy_rot = xy*rotmatrix;
% assign output
pos(:,1:2) = xy_rot;
end
% Generic function for drawing scatter plot with color
% corresponding to phase and size corresponding to magnitude
function posmagDrawPhase(self,pos,mag,fig)
figure(fig);
% load global variables
% handle empty variables
% suppress zero beam
if self.killZero ==1
mag(round(pos(:,1),2) == 0 & round(pos(:,2),2) ==0) = 0;
end
% calculate intensity and normalize
int = mag.*conj(mag);
int = int/max(int);
% remove intensities below cutoff
pos(int<=self.intcut,:) =[];
mag(int<=self.intcut,:) =[];
int(int<=self.intcut) = [];
phase = angle(mag);
rgb = phase2color(phase);
if self.killZero == 2
rgb(round(pos(:,1),2) == 0 & round(pos(:,2),2) ==0,:) = .8275; %setting center beam to gray
end
% scatter point area is proportional to int
int = self.intensityFactor .* sqrt(int);
scatter3(pos(:,1),pos(:,2),pos(:,3),700*int,rgb,'.')
end
% Draw 2D recip structure according to current kzmode and kzval
function [pos, mag] = draw2D(self,fig)
figure(fig);
[pos,mag] = self.calculate();
self.posmagDrawPhase(pos,mag,fig);
title(self.title_str)
end
% Draw full 3D recip structure
function [pos, mag] = draw3D(self,drawUnitCell,fig)
figure(fig);
self.setKzMode('constant');
kzs = linspace(-self.kzExtent,self.kzExtent,2^8);
intensityScal = 5;
self.intensityFactor = intensityScal * self.intensityFactor;
pos =[]; mag = [];
for kz = kzs
self.setKzVal(kz);
[pos_cur,mag_cur] = self.calculate;
pos = [pos;pos_cur];
mag = [mag;mag_cur];
end
self.posmagDrawPhase(pos,mag,fig);
if drawUnitCell
% Draw a hexagon around first order Bragg peak
hold on
[x, y] = self.unitCellOutline();
plot(x,y,'k')
end
title(self.title_str)
axis equal off
view([17,36])
self.intensityFactor = self.intensityFactor/intensityScal;
end
% Draw full 3D recip structure
function [pos, mag] = draw3DHK(self,hs,ks,drawUnitCell,fig)
figure(fig);
self.setKzMode('constant');
kzs = linspace(-self.kzExtent,self.kzExtent,2^8);
intensityScal = 5;
self.intensityFactor = intensityScal * self.intensityFactor;
pos =[]; mag = [];
for kz = kzs
self.setKzVal(kz);
[pos_cur,mag_cur] = self.calculateHK(hs,ks);
pos = [pos;pos_cur];
mag = [mag;mag_cur];
end
self.posmagDrawPhase(pos,mag,fig);
if drawUnitCell
% Draw a hexagon around first order Bragg peak
hold on
[x, y] = self.unitCellOutline();
plot(x,y,'k')
end
title(self.title_str)
axis equal off
view([17,36])
self.intensityFactor = self.intensityFactor/intensityScal;
end
% Draw side view of structure given hk indices
function [pos, mag] = drawSideView(self,hs,ks,xpos,fig)
self.setKzMode('constant')
self.setIntcut(0)
intensityScal = 1;
self.intensityFactor = intensityScal * self.intensityFactor;
kzs = linspace(-self.kzExtent,self.kzExtent,2^8);
pos = []; mag = [];
for kz = kzs
self.setKzVal(kz);
[pos_cur,mag_cur] = self.calculateHK(hs,ks);
pos_cur(:,1) = xpos;
pos_cur(:,2) = zeros(size(xpos));
pos = [pos;pos_cur];
mag = [mag;mag_cur];
end
self.posmagDrawPhase(pos,mag,fig);
title(self.title_str)
view([0 0])
self.intensityFactor = self.intensityFactor/intensityScal;
end
% Used by getTiltSeries to draw tilt axis on a 2D diffraction
% pattern with colors corresponding to position NOT PHASE
function drawTiltAxis(self,pos,mag,fig)
% load global variables
% handle empty variables
% suppress zero beam
if self.killZero == 1
mag(round(pos(:,1),2) == 0 & round(pos(:,2),2) ==0) = 0;
end
% calculate intensity and normalize
int = mag.*conj(mag);
int = int/max(int);
% remove intensities below cutoff
pos(int<=self.intcut,:) =[];
int(int<=self.intcut,:) =[];
rgb = pos2color(pos);
% Draw
ax = axes('Parent',fig);
hold(ax,'on')
axis(ax,'equal')
scatter(pos(:,1),pos(:,2),1000*int,rgb,'.')
phi = self.tilt_axis+pi/2;
plot( self.bs(1)*linspace(-cos(phi),cos(phi)),self.bs(1)*linspace(-sin(phi),sin(phi)));
if isempty(self.title_str)
self.setTitle('')
end
title(self.title_str)
end
function [tiltrange, I] = getTiltSeries(self, kzmode, displaymode, displaypattern, fig)
figure(fig);
hold on;
curkeV = self.keV;
self.setKzMode('tilted_ewald');
if strcmp(kzmode, 'constant')
% Set arbitrary high beam energy to simulate flat ewald
self.setkeV(10^8);
end
tiltrange = linspace(self.tilt_start,self.tilt_end,self.tilt_n);
I = [];
kz_holder = [];
for tilt = tiltrange
self.tilt_angle = tilt;
[pos, mag] = self.calculate;
if self.killZero ==1
mag(round(pos(:,1),2) == 0 & round(pos(:,2),2) ==0) = 0;
end
int = mag.*conj(mag);
int = int./max(int);
pos(int<=self.intcut,:) =[];
mag(int<=self.intcut,:) = [];
%%%%%%% applying cosine correction baked in
mag = mag./(cos(tilt)); %before multiplying by conjugate -> cos^2
kz_holder = [kz_holder, pos(:,3)];
I = [I, mag.*conj(mag)];
end
I = I./max(I(:));
pos0 = pos;
mag0 = ones(size(pos0));
rgb = pos2color(pos0);
if(strcmp('angle',displaymode))
for i = length(rgb):-1:1
plot(tiltrange(:).*180/pi, I(i,:),'LineWidth',2,'Color',rgb(i,:));
end
elseif(strcmp('kz',displaymode))
for i = 1:length(rgb)
plot(kz_holder(i,:), I(i,:),'LineWidth',2,'Color',rgb(i,:));
end
else
error('Incorrect Display Mode');
end
if isempty(self.title_str)
self.setTitle('')
end
title(self.title_str)
if displaypattern
self.drawTiltAxis(pos0,mag0,figure);
end
self.setkeV(curkeV);
end
function [tiltrange, I] = getTiltSeriesHK(self, hs,ks,kzmode, displaymode, displaypattern, fig)
figure(fig);
hold on;
curkeV = self.keV;
self.setKzMode('tilted_ewald');
if strcmp(kzmode, 'constant')
% Set arbitrary high beam energy to simulate flat ewald
self.setkeV(10^8);
end
tiltrange = linspace(self.tilt_start,self.tilt_end,self.tilt_n);
I = [];
kz_holder = [];
for tilt = tiltrange
self.tilt_angle = tilt;
[pos, mag] = self.calculateHK(hs,ks);
if self.killZero ==1
mag(round(pos(:,1),2) == 0 & round(pos(:,2),2) ==0) = 0;
end
int = mag.*conj(mag);
int = int./max(int);
pos(int<=self.intcut,:) =[];
mag(int<=self.intcut,:) = [];
%%%%%%% applying cosine correction baked in
mag = mag./(cos(tilt)); %before multiplying by conjugate -> cos^2
kz_holder = [kz_holder, pos(:,3)];
I = [I, mag.*conj(mag)];
end
I = I./max(I(:));
pos0 = pos;
mag0 = ones(size(pos0));
rgb = pos2color(pos0);
if(strcmp('angle',displaymode))
for i = length(rgb):-1:1
plot(tiltrange(:).*180/pi, I(i,:),'LineWidth',2,'Color',rgb(i,:));
end
elseif(strcmp('kz',displaymode))
for i = 1:length(rgb)
plot(kz_holder(i,:), I(i,:),'LineWidth',2,'Color',rgb(i,:));
end
else
error('Incorrect Display Mode');
end
if isempty(self.title_str)
self.setTitle('')
end
title(self.title_str)
if displaypattern
self.drawTiltAxis(pos0,mag0,figure);
end
self.setkeV(curkeV);
end
function mag = applyScat(self,pos,mag,element)
% Calculate scattering factor and apply to recip-space magnitude vector
% Utilizes eDiff_ScatteringFactor by R Hovden.
% Written by Suk Hyun Sung, sukhsung@umich.edu
% Jan. 05 2018
r = sqrt(pos(:,1).^2+pos(:,2).^2 +pos(:,3).^2);
fe = eDiff_ScatteringFactor(element,r/(2*pi));
mag = mag.*fe;
end
end
methods (Abstract)
[pos,mag] = calculate(self);
mag = calculateHK(self,h,k);
[x, y] = unitCellOutline(self);
end
end