diff --git a/index.html b/index.html index c42282b..f4e49e6 100644 --- a/index.html +++ b/index.html @@ -3,7 +3,7 @@ "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> - + Attocube - Test Bench @@ -35,23 +35,23 @@

Table of Contents

-
-

1 Estimation of the Spectral Density of the Attocube Noise

+
+

1 Estimation of the Spectral Density of the Attocube Noise

-
-

1.1 Long and Slow measurement

+
+

1.1 Long and Slow measurement

The first measurement was made during ~17 hours with a sampling time of \(T_s = 0.1\,s\). @@ -64,17 +64,45 @@ Ts = 0.1; % [s]

-
+

long_meas_time_domain_full.png

Figure 1: Long measurement time domain data

-We can see in Figure 1 that there is a transient period where the measured displacement experiences some drifts. +Let’s fit the data with a step response to a first order low pass filter (Figure 2). +

+ +
+
f = @(b,x) b(1)*(1 - exp(-x/b(2)));
+
+y_cur = x(t < 17*60*60);
+t_cur = t(t < 17*60*60);
+
+nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function
+B0 = [400e-9, 2*60*60];                        % Choose Appropriate Initial Estimates
+[B,rnrm] = fminsearch(nrmrsd, B0);     % Estimate Parameters ‘B’
+
+
+ +

+The corresponding time constant is (in [h]): +

+
+2.0576
+
+ + +

+figs/long_meas_time_domain_fit.pdf +

+ +

+We can see in Figure 1 that there is a transient period where the measured displacement experiences some drifts. This is probably due to thermal effects. We only select the data between t1 and t2. -The obtained displacement is shown in Figure 2. +The obtained displacement is shown in Figure 2.

@@ -88,7 +116,7 @@ t = t - t(1);
-
+

long_meas_time_domain_zoom.png

Figure 2: Kept data (removed slow drifts during the first hours)

@@ -105,8 +133,8 @@ The Power Spectral Density of the measured displacement is computed
-
-

1.2 Short and Fast measurement

+
+

1.2 Short and Fast measurement

An second measurement is done in order to estimate the high frequency noise of the interferometer. @@ -120,11 +148,11 @@ Ts = 1e-4; % [s]

-The time domain measurement is shown in Figure 3. +The time domain measurement is shown in Figure 3.

-
+

short_meas_time_domain.png

Figure 3: Time domain measurement with the high sampling rate

@@ -141,15 +169,15 @@ The Power Spectral Density of the measured displacement is computed
-
-

1.3 Obtained Amplitude Spectral Density of the measured displacement

+
+

1.3 Obtained Amplitude Spectral Density of the measured displacement

-The computed ASD of the two measurements are combined in Figure 4. +The computed ASD of the two measurements are combined in Figure 4.

-
+

psd_combined.png

Figure 4: Obtained Amplitude Spectral Density of the measured displacement

@@ -160,7 +188,7 @@ The computed ASD of the two measurements are combined in Figure

Author: Dehaeze Thomas

-

Created: 2020-10-29 jeu. 10:41

+

Created: 2020-10-29 jeu. 11:05

diff --git a/index.org b/index.org index 93a3434..b13dde6 100644 --- a/index.org +++ b/index.org @@ -70,6 +70,40 @@ The first measurement was made during ~17 hours with a sampling time of $T_s = 0 #+RESULTS: [[file:figs/long_meas_time_domain_full.png]] +Let's fit the data with a step response to a first order low pass filter (Figure [[fig:long_meas_time_domain_fit]]). + +#+begin_src matlab + f = @(b,x) b(1)*(1 - exp(-x/b(2))); + + y_cur = x(t < 17*60*60); + t_cur = t(t < 17*60*60); + + nrmrsd = @(b) norm(y_cur - f(b,t_cur)); % Residual Norm Cost Function + B0 = [400e-9, 2*60*60]; % Choose Appropriate Initial Estimates + [B,rnrm] = fminsearch(nrmrsd, B0); % Estimate Parameters ‘B’ +#+end_src + +The corresponding time constant is (in [h]): +#+begin_src matlab :results value replace :exports results + B(2)/60/60 +#+end_src + +#+RESULTS: +: 2.0576 + +#+begin_src matlab :exports none + figure; + hold on; + plot(t_cur/60/60, 1e9*y_cur); + plot(t_cur/60/60, 1e9*f(B, t_cur)); + hold off; + xlabel('Time [h]'); ylabel('Displacement [nm]'); +#+end_src + +#+name: fig:long_meas_time_domain_fit +#+caption: Fit of the measurement data with a step response of a first order low pass filter +[[file:figs/long_meas_time_domain_fit.pdf]] + We can see in Figure [[fig:long_meas_time_domain_full]] that there is a transient period where the measured displacement experiences some drifts. This is probably due to thermal effects. We only select the data between =t1= and =t2=.