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C5-test-bench-id31/test_id31_1_metrology.m
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210
C5-test-bench-id31/test_id31_1_metrology.m
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%% test_id31_1_metrology.m
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%% Clear Workspace and Close figures
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clear; close all; clc;
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%% Intialize Laplace variable
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s = zpk('s');
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%% Path for functions, data and scripts
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addpath('./mat/'); % Path for Data
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addpath('./src/'); % Path for functions
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addpath('./STEPS/'); % Path for STEPS
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addpath('./subsystems/'); % Path for Subsystems Simulink files
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%% Data directory
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data_dir = './mat/';
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%% Colors for the figures
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colors = colororder;
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%% Frequency Vector
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freqs = logspace(log10(1), log10(2e3), 1000);
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%% Sampling Time
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Ts = 1e-4;
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%% Specifications for Experiments
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specs_dz_peak = 50; % [nm]
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specs_dy_peak = 100; % [nm]
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specs_ry_peak = 0.85; % [urad]
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specs_dz_rms = 15; % [nm RMS]
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specs_dy_rms = 30; % [nm RMS]
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specs_ry_rms = 0.25; % [urad RMS]
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%% Geometrical parameters of the metrology system
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H = 150e-3;
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l1 = (150-48-42)*1e-3;
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l2 = (76.2+48+42-150)*1e-3;
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% Computation of the Transformation matrix
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Hm = [ 0 1 0 -l2 0;
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0 1 0 l1 0;
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-1 0 0 0 -l2;
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-1 0 0 0 l1;
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0 0 -1 0 0];
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%% Angular alignment
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% Load Data
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data_it0 = h5scan(data_dir, 'alignment', 'h1rx_h1ry', 1);
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data_it1 = h5scan(data_dir, 'alignment', 'h1rx_h1ry_0002', 3);
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data_it2 = h5scan(data_dir, 'alignment', 'h1rx_h1ry_0002', 5);
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% Offset wrong points
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i_it0 = find(abs(data_it0.Rx_int_filtered(2:end)-data_it0.Rx_int_filtered(1:end-1))>1e-5);
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data_it0.Rx_int_filtered(i_it0+1:end) = data_it0.Rx_int_filtered(i_it0+1:end) + data_it0.Rx_int_filtered(i_it0) - data_it0.Rx_int_filtered(i_it0+1);
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i_it1 = find(abs(data_it1.Rx_int_filtered(2:end)-data_it1.Rx_int_filtered(1:end-1))>1e-5);
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data_it1.Rx_int_filtered(i_it1+1:end) = data_it1.Rx_int_filtered(i_it1+1:end) + data_it1.Rx_int_filtered(i_it1) - data_it1.Rx_int_filtered(i_it1+1);
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i_it2 = find(abs(data_it2.Rx_int_filtered(2:end)-data_it2.Rx_int_filtered(1:end-1))>1e-5);
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data_it2.Rx_int_filtered(i_it2+1:end) = data_it2.Rx_int_filtered(i_it2+1:end) + data_it2.Rx_int_filtered(i_it2) - data_it2.Rx_int_filtered(i_it2+1);
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% Compute circle fit and get radius
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[~, ~, R_it0, ~] = circlefit(1e6*data_it0.Rx_int_filtered, 1e6*data_it0.Ry_int_filtered);
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[~, ~, R_it1, ~] = circlefit(1e6*data_it1.Rx_int_filtered, 1e6*data_it1.Ry_int_filtered);
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[~, ~, R_it2, ~] = circlefit(1e6*data_it2.Rx_int_filtered, 1e6*data_it2.Ry_int_filtered);
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%% Rx/Ry alignment of the spheres using the micro-station
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figure;
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hold on;
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plot(1e6*data_it0.Rx_int_filtered, 1e6*data_it0.Ry_int_filtered, '-', ...
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'DisplayName', sprintf('$R_0 = %.0f \\mu$rad', R_it0))
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plot(1e6*data_it1.Rx_int_filtered, 1e6*data_it1.Ry_int_filtered, '-', ...
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'DisplayName', sprintf('$R_1 = %.0f \\mu$rad', R_it1))
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plot(1e6*data_it2.Rx_int_filtered, 1e6*data_it2.Ry_int_filtered, '-', 'color', colors(5,:), ...
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'DisplayName', sprintf('$R_2 = %.0f \\mu$rad', R_it2))
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hold off;
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xlabel('$R_x$ [$\mu$rad]'); ylabel('$R_y$ [$\mu$rad]');
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axis equal
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
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xlim([-600, 300]);
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ylim([-100, 800]);
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%% Eccentricity alignment
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% Load Data
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data_it0 = h5scan(data_dir, 'alignment', 'h1rx_h1ry_0002', 5);
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data_it1 = h5scan(data_dir, 'alignment', 'h1dx_h1dy', 1);
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% Offset wrong points
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i_it0 = find(abs(data_it0.Dy_int_filtered(2:end)-data_it0.Dy_int_filtered(1:end-1))>1e-5);
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data_it0.Dy_int_filtered(i_it0+1:end) = data_it0.Dy_int_filtered(i_it0+1:end) + data_it0.Dy_int_filtered(i_it0) - data_it0.Dy_int_filtered(i_it0+1);
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% Compute circle fit and get radius
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[~, ~, R_it0, ~] = circlefit(1e6*data_it0.Dx_int_filtered, 1e6*data_it0.Dy_int_filtered);
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[~, ~, R_it1, ~] = circlefit(1e6*data_it1.Dx_int_filtered, 1e6*data_it1.Dy_int_filtered);
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%% Dx/Dy alignment of the spheres using the micro-station
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figure;
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hold on;
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plot(1e6*data_it0.Dx_int_filtered, 1e6*data_it0.Dy_int_filtered, '-', ...
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'DisplayName', sprintf('$R_0 = %.0f \\mu$m', R_it0))
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plot(1e6*data_it1.Dx_int_filtered, 1e6*data_it1.Dy_int_filtered, '-', ...
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'DisplayName', sprintf('$R_1 = %.0f \\mu$m', R_it1))
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hold off;
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xlabel('$D_x$ [$\mu$m]'); ylabel('$D_y$ [$\mu$m]');
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axis equal
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legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
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xlim([-1, 21]);
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ylim([-8, 14]);
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%% Estimated acceptance of the metrology
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% This is estimated by moving the spheres using the micro-hexapod
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% Dx
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data_dx = h5scan(data_dir, 'metrology_acceptance_new_align', 'dx', 1);
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dx_acceptance = zeros(5,1);
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for i = [1:size(dx_acceptance, 1)]
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% Find range in which the interferometers are measuring displacement
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dx_di = diff(data_dx.(sprintf('d%i', i))) == 0;
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if sum(dx_di) > 0
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dx_acceptance(i) = data_dx.h1tx(find(dx_di(501:end), 1) + 500) - ...
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data_dx.h1tx(find(flip(dx_di(1:500)), 1));
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else
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dx_acceptance(i) = data_dx.h1tx(end) - data_dx.h1tx(1);
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end
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end
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% Dy
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data_dy = h5scan(data_dir, 'metrology_acceptance_new_align', 'dy', 1);
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dy_acceptance = zeros(5,1);
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for i = [1:size(dy_acceptance, 1)]
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% Find range in which the interferometers are measuring displacement
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dy_di = diff(data_dy.(sprintf('d%i', i))) == 0;
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if sum(dy_di) > 0
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dy_acceptance(i) = data_dy.h1ty(find(dy_di(501:end), 1) + 500) - ...
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data_dy.h1ty(find(flip(dy_di(1:500)), 1));
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else
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dy_acceptance(i) = data_dy.h1ty(end) - data_dy.h1ty(1);
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end
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end
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% Dz
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data_dz = h5scan(data_dir, 'metrology_acceptance_new_align', 'dz', 1);
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dz_acceptance = zeros(5,1);
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for i = [1:size(dz_acceptance, 1)]
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% Find range in which the interferometers are measuring displacement
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dz_di = diff(data_dz.(sprintf('d%i', i))) == 0;
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if sum(dz_di) > 0
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dz_acceptance(i) = data_dz.h1tz(find(dz_di(501:end), 1) + 500) - ...
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data_dz.h1tz(find(flip(dz_di(1:500)), 1));
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else
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dz_acceptance(i) = data_dz.h1tz(end) - data_dz.h1tz(1);
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end
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end
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%% Interferometer noise estimation
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data = load("test_id31_interf_noise.mat");
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Ts = 1e-4;
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Nfft = floor(5/Ts);
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win = hanning(Nfft);
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Noverlap = floor(Nfft/2);
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[pxx_int, f] = pwelch(detrend(data.d, 0), win, Noverlap, Nfft, 1/Ts);
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% Uncorrelated noise: square root of the sum of the squares
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pxx_cart = pxx_int*sum(inv(Hm).^2, 2)';
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rms_dxy = sqrt(trapz(f(f>1), pxx_cart((f>1),1))); % < 0.3 nm RMS
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rms_dz = sqrt(trapz(f(f>1), pxx_cart((f>1),3))); % < 0.3 nm RMS
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rms_rxy = sqrt(trapz(f(f>1), pxx_cart((f>1),4))); % 5 nrad RMS
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figure;
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hold on;
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plot(f, sqrt(pxx_cart(:,1)), 'DisplayName', sprintf('$D_{x,y}$, %.1f nmRMS', rms_dxy));
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plot(f, sqrt(pxx_cart(:,3)), 'DisplayName', sprintf('$D_{z}$, %.1f nmRMS', rms_dz));
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plot(f, sqrt(pxx_cart(:,4)), 'DisplayName', sprintf('$R_{x,y}$, %.1f nradRMS', rms_rxy));
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set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
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xlabel('Frequency [Hz]'); ylabel('ASD $\left[\frac{nm,\ nrad}{\sqrt{Hz}}\right]$')
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xlim([1, 1e3]); ylim([1e-3, 1]);
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leg = legend('location', 'northeast', 'FontSize', 8, 'NumColumns', 1);
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leg.ItemTokenSize(1) = 15;
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%% X-Y scan with the micro-hexapod, and record of the vertical interferometer
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data = h5scan(data_dir, 'metrology_acceptance', 'after_int_align_meshXY', 1);
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x = 1e3*detrend(data.h1tx, 0); % [um]
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y = 1e3*detrend(data.h1ty, 0); % [um]
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z = 1e6*data.Dz_int_filtered - max(data.Dz_int_filtered); % [um]
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mdl = scatteredInterpolant(x, y, z);
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[xg, yg] = meshgrid(unique(x), unique(y));
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zg = mdl(xg, yg);
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% Fit a sphere to the data
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[sphere_center,sphere_radius] = sphereFit(1e-3*[x, y, z]);
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%% XY mapping of the Z measurement by the interferometer
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figure;
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[~,c] = contour3(xg,yg,zg,30);
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c.LineWidth = 3;
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xlabel('$D_x$ [$\mu$m]');
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ylabel('$D_y$ [$\mu$m]');
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zlabel('$D_z$ [$\mu$m]');
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zlim([-1, 0]);
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xticks(-100:50:100); yticks(-100:50:100); zticks(-1:0.2:0);
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