Attocube - Test Bench
Table of Contents
1 Estimation of the Spectral Density of the Attocube Noise
Figure 1: Test Bench Schematic
Figure 2: Picture of the test bench. The Attocube and mirror are covered by a “bubble sheet”
1.1 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]
Figure 3: Long measurement time domain data
Let’s fit the data with a step response to a first order low pass filter (Figure 4).
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
Figure 4: Fit of the measurement data with a step response of a first order low pass filter
We can see in Figure 3 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 5.
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);
Figure 5: Kept data (removed slow drifts during the first hours)
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);
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.
G_lpf = 1/(1 + s/2/pi); p_1 = p_1./abs(squeeze(freqresp(G_lpf, f_1, 'Hz'))).^2;
Only frequencies below 2Hz are taken into account (high frequency noise will be measured afterwards).
p_1 = p_1(f_1 < 2); f_1 = f_1(f_1 < 2);
1.2 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/short_test_plastic.mat') Ts = 1e-4; % [s]
x = detrend(x, 0);
The time domain measurement is shown in Figure 6.
Figure 6: Time domain measurement with the high sampling rate
The Power Spectral Density of the measured displacement is computed
win = hann(ceil(length(x)/10)); [p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
1.3 Obtained Amplitude Spectral Density of the measured displacement
The computed ASD of the two measurements are combined in Figure 7.
Figure 7: Obtained Amplitude Spectral Density of the measured displacement
2 Effect of the “bubble sheet” and Aluminium tube
Figure 8: Aluminium tube used to protect the beam path from disturbances
2.1 Aluminium Tube and Bubble Sheet
load('./mat/long_test_plastic.mat'); Ts = 1e-4; % [s]
x = detrend(x, 0);
win = hann(ceil(length(x)/10)); [p_1, f_1] = pwelch(x, win, [], [], 1/Ts);
2.2 Only Aluminium Tube
load('./mat/long_test_alu_tube.mat'); Ts = 1e-4; % [s]
x = detrend(x, 0);
The time domain measurement is shown in Figure 6.
win = hann(ceil(length(x)/10)); [p_2, f_2] = pwelch(x, win, [], [], 1/Ts);
2.3 Nothing
2.4 Comparison
Figure 9: Comparison of the noise ASD with and without bubble sheet