6.7 KiB
Attocube - Test Bench
Estimation of the Spectral Density of the Attocube Noise
Long and Slow measurement
The first measurement was made during ~17 hours with a sampling time of $T_s = 0.1\,s$.
load('./mat/long_test2.mat', 'x', 't')
Ts = 0.1; % [s]
Let's fit the data with a step response to a first order low pass filter (Figure fig:long_meas_time_domain_fit).
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
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
.
The obtained displacement is shown in Figure fig:long_meas_time_domain_zoom.
t1 = 11; t2 = 17; % [h]
x = x(t > t1*60*60 & t < t2*60*60);
x = x - mean(x);
t = t(t > t1*60*60 & t < t2*60*60);
t = t - t(1);
The Power Spectral Density of the measured displacement is computed
win = hann(ceil(length(x)/20));
[p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
Short and Fast measurement
An second measurement is done in order to estimate the high frequency noise of the interferometer. The measurement is done with a sampling time of $T_s = 0.1\,ms$ and a duration of ~100s.
load('./mat/test.mat', 'x', 't')
Ts = 1e-4; % [s]
The time domain measurement is shown in Figure fig:short_meas_time_domain.
The Power Spectral Density of the measured displacement is computed
win = hann(ceil(length(x)/20));
[p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
Obtained Amplitude Spectral Density of the measured displacement
The computed ASD of the two measurements are combined in Figure fig:psd_combined.