153 lines
3.7 KiB
Matlab
153 lines
3.7 KiB
Matlab
%% 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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addpath('./mat/');
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% Long and Slow measurement
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% The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$.
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load('long_test_plastic.mat', 'x', 't')
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Ts = 0.1; % [s]
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figure;
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plot(t/60/60, 1e9*x)
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xlim([0, 17.5]);
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xlabel('Time [h]'); ylabel('Displacement [nm]');
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% #+name: fig:long_meas_time_domain_full
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% #+caption: Long measurement time domain data
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% #+RESULTS:
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% [[file:figs/long_meas_time_domain_full.png]]
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% Let's fit the data with a step response to a first order low pass filter (Figure [[fig:long_meas_time_domain_fit]]).
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f = @(b,x) b(1)*(1 - exp(-x/b(2)));
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y_cur = x(t < 17.5*60*60);
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t_cur = t(t < 17.5*60*60);
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nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
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B0 = [400e-9, 2*60*60]; % Choose Appropriate Initial Estimates
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[B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’
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% The corresponding time constant is (in [h]):
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B(2)/60/60
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% #+RESULTS:
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% : 2.0658
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figure;
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hold on;
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plot(t_cur/60/60, 1e9*y_cur);
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plot(t_cur/60/60, 1e9*f(B, t_cur));
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hold off;
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xlim([0, 17.5])
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xlabel('Time [h]'); ylabel('Displacement [nm]');
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% #+name: fig:long_meas_time_domain_fit
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% #+caption: Fit of the measurement data with a step response of a first order low pass filter
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% #+RESULTS:
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% [[file:figs/long_meas_time_domain_fit.png]]
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% We can see in Figure [[fig:long_meas_time_domain_full]] that there is a transient period where the measured displacement experiences some drifts.
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% This is probably due to thermal effects.
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% We only select the data between =t1= and =t2=.
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% The obtained displacement is shown in Figure [[fig:long_meas_time_domain_zoom]].
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t1 = 10.5; t2 = 17.5; % [h]
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x = x(t > t1*60*60 & t < t2*60*60);
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x = x - mean(x);
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t = t(t > t1*60*60 & t < t2*60*60);
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t = t - t(1);
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figure;
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plot(t/60/60, 1e9*x);
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xlabel('Time [h]'); ylabel('Measured Displacement [nm]')
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% #+name: fig:long_meas_time_domain_zoom
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% #+caption: Kept data (removed slow drifts during the first hours)
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% #+RESULTS:
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% [[file:figs/long_meas_time_domain_zoom.png]]
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% The Power Spectral Density of the measured displacement is computed
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win = hann(ceil(length(x)/20));
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[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
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% As a low pass filter was used in the measurement process, we multiply the PSD by the square of the inverse of the filter's norm.
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G_lpf = 1/(1 + s/2/pi);
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p_1 = p_1./abs(squeeze(freqresp(G_lpf, f_1, 'Hz'))).^2;
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% Only frequencies below 2Hz are taken into account (high frequency noise will be measured afterwards).
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p_1 = p_1(f_1 < 2);
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f_1 = f_1(f_1 < 2);
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% Short and Fast measurement
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% An second measurement is done in order to estimate the high frequency noise of the interferometer.
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% The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s.
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load('short_test_plastic.mat')
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Ts = 1e-4; % [s]
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x = detrend(x, 0);
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% The time domain measurement is shown in Figure [[fig:short_meas_time_domain]].
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figure;
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plot(t, 1e9*x)
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xlabel('Time [s]'); ylabel('Displacement [nm]');
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% #+name: fig:short_meas_time_domain
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% #+caption: Time domain measurement with the high sampling rate
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% #+RESULTS:
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% [[file:figs/short_meas_time_domain.png]]
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% The Power Spectral Density of the measured displacement is computed
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win = hann(ceil(length(x)/20));
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[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
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% Obtained Amplitude Spectral Density of the measured displacement
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% The computed ASD of the two measurements are combined in Figure [[fig:psd_combined]].
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figure;
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hold on;
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plot(f_1(8:end), sqrt(p_1(8:end)), 'k-');
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plot(f_2(8:end), sqrt(p_2(8:end)), 'k-');
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hold off;
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set(gca, 'Xscale', 'log'); set(gca, 'Yscale', 'log');
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ylabel('ASD [$m/\sqrt{Hz}$]'); xlabel('Frequency [Hz]');
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