Adding a script that plots images OD images from the raw hdf5 files and a script to carry out some calculations for the Accordion Lattice.
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114
EstimatesForAccordionLattice.m
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114
EstimatesForAccordionLattice.m
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%% Physical constants
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PlanckConstant = 6.62607015E-34;
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PlanckConstantReduced = 6.62607015E-34/(2*pi);
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FineStructureConstant = 7.2973525698E-3;
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ElectronMass = 9.10938291E-31;
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GravitationalConstant = 6.67384E-11;
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ProtonMass = 1.672621777E-27;
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AtomicMassUnit = 1.660539066E-27;
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BohrRadius = 5.2917721067E-11;
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BohrMagneton = 9.274009994E-24;
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BoltzmannConstant = 1.38064852E-23;
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StandardGravityAcceleration = 9.80665;
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SpeedOfLight = 299792458;
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StefanBoltzmannConstant = 5.670373E-8;
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ElectronCharge = 1.602176634E-19;
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VacuumPermeability = 1.25663706212E-6;
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DielectricConstant = 8.8541878128E-12;
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ElectronGyromagneticFactor = -2.00231930436153;
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AvogadroConstant = 6.02214076E23;
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ZeroKelvin = 273.15;
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GravitationalAcceleration = 9.80553;
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VacuumPermittivity = 1 / (SpeedOfLight^2 * VacuumPermeability);
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HartreeEnergy = ElectronCharge^2 / (4 * pi * VacuumPermittivity * BohrRadius);
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AtomicUnitOfPolarizability = (ElectronCharge^2 * BohrRadius^2) / HartreeEnergy; % Or simply 4*pi*VacuumPermittivity*BohrRadius^3
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% Dy specific constants
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Dy164Mass = 163.929174751*1.660539066E-27;
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Dy164IsotopicAbundance = 0.2826;
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DyMagneticMoment = 9.93*9.274009994E-24;
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%% Lattice spacing
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Wavelength = 532e-9;
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theta = linspace(1.5, 18.0, 100);
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LatticeSpacing = Wavelength ./ (2.*sin((theta*pi/180)/2));
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figure(1);
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set(gcf,'Position',[100 100 950 750])
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plot(theta, LatticeSpacing * 1E6, LineWidth=2.0)
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xlim([0 19]);
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ylim([0.5 21]);
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xlabel('Angle (deg)', FontSize=16)
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ylabel('Lattice spacing (µm)', FontSize=16)
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title(['\bf Upper bound = ' num2str(round(max(LatticeSpacing * 1E6),1)) ' µm ; \bf Lower bound = ' num2str(round(min(LatticeSpacing * 1E6),1)) ' µm'], FontSize=16)
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grid on
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%% Scaling of vertical trap frequency with lattice spacing
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Wavelength = 532e-9;
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a = 180 * (AtomicUnitOfPolarizability / (2 * SpeedOfLight * VacuumPermittivity));
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Power = 5;
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waist_y = 250E-6;
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waist_z = 50E-6;
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TrapDepth = ((8 * a * Power) / (pi * waist_y * waist_z)) / (BoltzmannConstant * 1E-6); % in µK
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thetas = linspace(1.5, 18.0, 100);
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LatticeSpacings = zeros(1, length(thetas));
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Omega_z = zeros(1, length(thetas));
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for idx = 1:length(thetas)
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theta = 0.5 * thetas(idx) .* pi/180;
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LatticeSpacings(idx) = Wavelength ./ (2.*sin(theta));
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Omega_z(idx) = sqrt(((16 * a * Power) / (pi * Dy164Mass * waist_y * waist_z)) * ...
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((2 * (cos(theta)/waist_z)^2) + ((Wavelength * sin(theta)/pi)^2 * ...
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((1/waist_y^4) + (1/waist_z^4))) + (pi / LatticeSpacings(idx))^2));
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end
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nu_z = Omega_z ./ (2*pi);
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figure(2);
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set(gcf,'Position',[100 100 950 750])
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plot(LatticeSpacings * 1E6, nu_z * 1E-3, LineWidth=2.0)
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xlim([0.5 21]);
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xlabel('Lattice spacing (µm)', FontSize=16)
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ylabel('Trap frequency (kHz)', FontSize=16)
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title(['\bf Upper bound = ' num2str(round(max(nu_z * 1E-3),2)) ' kHz ; \bf Lower bound = ' num2str(round(min(nu_z * 1E-3),2)) ' kHz'], FontSize=16)
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grid on
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%% Scaling of Recoil Energy - All energy scales in an optical lattice are naturally parametrized by the lattice recoil energy
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LatticeSpacing = linspace(2E-6, 20E-6, 100);
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RecoilEnergy = PlanckConstant^2 ./ (8 .* Dy164Mass .* LatticeSpacing.^2);
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figure(3);
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set(gcf,'Position',[100 100 950 750])
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semilogy(LatticeSpacing * 1E6, RecoilEnergy/PlanckConstant, LineWidth=2.0, DisplayName=['\bf Max = ' num2str(round(max(RecoilEnergy / PlanckConstant),1)) ' Hz; Min = ' num2str(round(min(RecoilEnergy / PlanckConstant),1)) ' Hz'])
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xlim([0.5 21]);
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xlabel('Lattice spacing (µm)', FontSize=16)
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ylabel('Recoil Energy (Hz)', FontSize=16)
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title('\bf Scaling of Recoil Energy - All energy scales in an optical lattice are naturally parametrized by the lattice recoil energy', FontSize=12)
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grid on
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legend(FontSize=12)
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%% Interference pattern spacing in ToF - de Broglie wavelength associated with the relative motion of atoms
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ExpansionTime = linspace(1E-3, 20.0E-3, 100);
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figure(4);
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set(gcf,'Position',[100 100 950 750])
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labels = [];
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for ls = [2E-6:2E-6:5E-6 6E-6:6E-6:20E-6]
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InteferencePatternSpacing = (PlanckConstant .* ExpansionTime) ./ (Dy164Mass * ls);
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plot(ExpansionTime*1E3, InteferencePatternSpacing* 1E6, LineWidth=2.0, DisplayName=['\bf Lattice spacing = ' num2str(round(max(ls * 1E6),1)) ' µm'])
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hold on
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end
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xlim([0 22]);
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xlabel('Free expansion time (milliseconds)', FontSize=16)
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ylabel('Interference pattern period (µm)', FontSize=16)
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title('\bf Interference of condensates - Fringe period is the de Broglie wavelength associated with the relative motion of atoms', FontSize=12)
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legend(labels, 'Location','NorthWest', FontSize=12);
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grid on
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legend show
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223
plotImages.m
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plotImages.m
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%% Parameters
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groupList = ["/images/MOT_3D_Camera/in_situ_absorption", "/images/ODT_1_Axis_Camera/in_situ_absorption", "/images/ODT_2_Axis_Camera/in_situ_absorption", "/images/Horizontal_Axis_Camera/in_situ_absorption", "/images/Vertical_Axis_Camera/in_situ_absorption"];
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folderPath = "C:/Users/Karthik/Documents/GitRepositories/Calculations/24/";
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run = '0086';
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folderPath = strcat(folderPath, run);
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cam = 5;
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angle = 90;
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center = [2100, 1150];
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span = [500, 500];
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fraction = [0.1, 0.1];
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pixel_size = 4.6e-6;
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%% Compute OD image, rotate and extract ROI for analysis
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% Get a list of all files in the folder with the desired file name pattern.
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filePattern = fullfile(folderPath, '*.h5');
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files = dir(filePattern);
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refimages = zeros(span(1) + 1, span(2) + 1, length(files));
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absimages = zeros(span(1) + 1, span(2) + 1, length(files));
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for k = 1 : length(files)
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baseFileName = files(k).name;
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fullFileName = fullfile(files(k).folder, baseFileName);
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fprintf(1, 'Now reading %s\n', fullFileName);
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atm_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/atoms")), angle));
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bkg_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/background")), angle));
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dark_img = im2double(imrotate(h5read(fullFileName, append(groupList(cam), "/dark")), angle));
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refimages(:,:,k) = subtract_offset(crop_image(bkg_img, center, span), fraction);
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absimages(:,:,k) = subtract_offset(crop_image(calculate_OD(atm_img, bkg_img, dark_img), center, span), fraction);
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end
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%% Fringe removal
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optrefimages = removefringesInImage(absimages, refimages);
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absimages_fringe_removed = absimages(:, :, :) - optrefimages(:, :, :);
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nimgs = size(absimages_fringe_removed,3);
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od_imgs = cell(1, nimgs);
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for i = 1:nimgs
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od_imgs{i} = absimages_fringe_removed(:, :, i);
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end
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%%
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figure(1)
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clf
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r = 120;
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x = 250;
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y = 250;
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for k = 1 : length(od_imgs)
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imagesc(xvals, yvals, od_imgs{k})
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hold on
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th = 0:pi/50:2*pi;
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xunit = r * cos(th) + x;
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yunit = r * sin(th) + y;
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h = plot(xunit, yunit, Color='yellow');
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xlabel('µm', 'FontSize', 16)
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ylabel('µm', 'FontSize', 16)
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axis equal tight;
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hcb = colorbar;
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hL = ylabel(hcb, 'Optical Density', 'FontSize', 16);
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set(hL,'Rotation',-90);
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colormap jet;
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set(gca,'CLim',[0 1.0]);
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set(gca,'YDir','normal')
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title('DMD projection: Circle of radius 200 pixels', 'FontSize', 16);
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drawnow;
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end
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%% Helper Functions
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function ret = get_offset_from_corner(img, x_fraction, y_fraction)
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% image must be a 2D numerical array
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[dim1, dim2] = size(img);
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s1 = img(1:round(dim1 * y_fraction), 1:round(dim2 * x_fraction));
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s2 = img(1:round(dim1 * y_fraction), round(dim2 - dim2 * x_fraction):dim2);
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s3 = img(round(dim1 - dim1 * y_fraction):dim1, 1:round(dim2 * x_fraction));
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s4 = img(round(dim1 - dim1 * y_fraction):dim1, round(dim2 - dim2 * x_fraction):dim2);
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ret = mean([mean(s1(:)), mean(s2(:)), mean(s3(:)), mean(s4(:))]);
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end
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function ret = subtract_offset(img, fraction)
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% Remove the background from the image.
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% :param dataArray: The image
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% :type dataArray: xarray DataArray
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% :param x_fraction: The fraction of the pixels used in x axis
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% :type x_fraction: float
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% :param y_fraction: The fraction of the pixels used in y axis
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% :type y_fraction: float
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% :return: The image after removing background
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% :rtype: xarray DataArray
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x_fraction = fraction(1);
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y_fraction = fraction(2);
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offset = get_offset_from_corner(img, x_fraction, y_fraction);
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ret = img - offset;
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end
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function ret = crop_image(img, center, span)
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% Crop the image according to the region of interest (ROI).
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% :param dataSet: The images
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% :type dataSet: xarray DataArray or DataSet
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% :param center: The center of region of interest (ROI)
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% :type center: tuple
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% :param span: The span of region of interest (ROI)
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% :type span: tuple
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% :return: The cropped images
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% :rtype: xarray DataArray or DataSet
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x_start = floor(center(1) - span(1) / 2);
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x_end = floor(center(1) + span(1) / 2);
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y_start = floor(center(2) - span(2) / 2);
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y_end = floor(center(2) + span(2) / 2);
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ret = img(y_start:y_end, x_start:x_end);
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end
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function ret = calculate_OD(imageAtom, imageBackground, imageDark)
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% Calculate the OD image for absorption imaging.
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% :param imageAtom: The image with atoms
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% :type imageAtom: numpy array
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% :param imageBackground: The image without atoms
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% :type imageBackground: numpy array
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% :param imageDark: The image without light
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% :type imageDark: numpy array
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% :return: The OD images
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% :rtype: numpy array
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numerator = imageBackground - imageDark;
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denominator = imageAtom - imageDark;
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numerator(numerator == 0) = 1;
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denominator(denominator == 0) = 1;
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ret = -log(double(abs(denominator ./ numerator)));
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if numel(ret) == 1
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ret = ret(1);
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end
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end
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function [optrefimages] = removefringesInImage(absimages, refimages, bgmask)
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% removefringesInImage - Fringe removal and noise reduction from absorption images.
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% Creates an optimal reference image for each absorption image in a set as
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% a linear combination of reference images, with coefficients chosen to
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% minimize the least-squares residuals between each absorption image and
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% the optimal reference image. The coefficients are obtained by solving a
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% linear set of equations using matrix inverse by LU decomposition.
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%
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% Application of the algorithm is described in C. F. Ockeloen et al, Improved
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% detection of small atom numbers through image processing, arXiv:1007.2136 (2010).
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%
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% Syntax:
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% [optrefimages] = removefringesInImage(absimages,refimages,bgmask);
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%
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% Required inputs:
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% absimages - Absorption image data,
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% typically 16 bit grayscale images
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% refimages - Raw reference image data
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% absimages and refimages are both cell arrays containing
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% 2D array data. The number of refimages can differ from the
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% number of absimages.
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%
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% Optional inputs:
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% bgmask - Array specifying background region used,
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% 1=background, 0=data. Defaults to all ones.
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% Outputs:
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% optrefimages - Cell array of optimal reference images,
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% equal in size to absimages.
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%
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% Dependencies: none
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%
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% Authors: Shannon Whitlock, Caspar Ockeloen
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% Reference: C. F. Ockeloen, A. F. Tauschinsky, R. J. C. Spreeuw, and
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% S. Whitlock, Improved detection of small atom numbers through
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% image processing, arXiv:1007.2136
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% Email:
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% May 2009; Last revision: 11 August 2010
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% Process inputs
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% Set variables, and flatten absorption and reference images
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nimgs = size(absimages,3);
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nimgsR = size(refimages,3);
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xdim = size(absimages(:,:,1),2);
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ydim = size(absimages(:,:,1),1);
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R = single(reshape(refimages,xdim*ydim,nimgsR));
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A = single(reshape(absimages,xdim*ydim,nimgs));
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optrefimages=zeros(size(absimages)); % preallocate
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if not(exist('bgmask','var')); bgmask=ones(ydim,xdim); end
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k = find(bgmask(:)==1); % Index k specifying background region
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% Ensure there are no duplicate reference images
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% R=unique(R','rows')'; % comment this line if you run out of memory
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% Decompose B = R*R' using singular value or LU decomposition
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[L,U,p] = lu(R(k,:)'*R(k,:),'vector'); % LU decomposition
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for j=1:nimgs
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b=R(k,:)'*A(k,j);
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% Obtain coefficients c which minimise least-square residuals
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lower.LT = true; upper.UT = true;
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c = linsolve(U,linsolve(L,b(p,:),lower),upper);
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% Compute optimised reference image
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optrefimages(:,:,j)=reshape(R*c,[ydim xdim]);
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end
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end
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