Static Measurements

• 5530: Straightness Plot: Yz
• Filename: r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt
• Acquisition date: 09/01/2019 13:49:42
• Current date: 08/03/2019 08:46:35
• Measurement Type: STRAIGHTNESS vertical
• Travel Mode: Bidirectional
• Number of Target Positions: 401
• Number of total data pairs: 2406
• Number of total data runs:6
• Position Value Units: millimeters
• Error Value Units: micrometers

In a very schematic way, the measurement is explained on figure 1. The positioning error $d$ is measure as a function of $x$. Because the measurement is done in a static way, the dynamics of the station (represented by the mass-spring-damper system on the schematic) does not play a role in the measure.

The obtained data corresponds to the guiding errors.

First, we plot the straightness error as a function of the position (figure 2).

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figure;
hold on;
for i=1:data(end, 1)
  plot(data(data(:, 1) == i, 3), data(data(:, 1) == i, 4), '-k');
end
hold off;
xlabel('Target Value [mm]'); ylabel('Error Value [$\mu m$]');

Then, we compute mean value of each position, and we remove this mean value from the data. The results are shown on figure 3.

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mean_pos = zeros(sum(data(:, 1)==1), 1);
for i=1:sum(data(:, 1)==1)
  mean_pos(i) = mean(data(data(:, 2)==i, 4));
end

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figure;
hold on;
for i=1:data(end, 1)
  filt = data(:, 1) == i;
  plot(data(filt, 3), data(filt, 4) - mean_pos, '-k');
end
hold off;
xlabel('Target Value [mm]'); ylabel('Error Value [$\mu m$]');

We here make the assumptions that, during a scan with the translation stage, the Z motion of the translation stage will follow the guiding error measured.

We then create a time vector $t$ from 0 to 1 second that corresponds to a typical scan, and we plot the guiding error as a function of the time on figure 4.

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t = linspace(0, 1, length(data(data(:, 1)==1, 4)));

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figure;
hold on;
plot(t, data(data(:, 1) == 1, 4) - mean_pos, '-k');
hold off;
xlabel('Time [s]'); ylabel('Error Value [um]');

We first compute some parameters that will be used for the PSD computation.

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dt = t(2)-t(1);

Fs = 1/dt; % [Hz]

win = hanning(ceil(1*Fs));

We remove the mean position from the data.

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x = data(data(:, 1) == 1, 4) - mean_pos;

And finally, we compute the power spectral density of the displacement obtained in the time domain.

The result is shown on figure 5.

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[pxx, f] = pwelch(x, win, [], [], Fs);

pxx_t = zeros(length(pxx), data(end, 1));

for i=1:data(end, 1)
  x = data(data(:, 1) == i, 4) - mean_pos;
  [pxx, f] = pwelch(x, win, [], [], Fs);
  pxx_t(:, i) = pxx;
end

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figure;
hold on;
plot(f, sqrt(mean(pxx_t, 2)), 'k-');
hold off;
xlabel('Frequency (Hz)');
ylabel('Amplitude Spectral Density $\left[\frac{m}{\sqrt{Hz}}\right]$');
set(gca, 'XScale', 'log'); set(gca, 'YScale', 'log');