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< h1 class = "title" > Static Measurements< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
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< li > < a href = "#org9dbeefe" > 1. Ty Stage< / a >
< ul >
< li > < a href = "#org98becb2" > 1.1. Notes< / a > < / li >
< li > < a href = "#orgbab4f4e" > 1.2. Data Pre-processing< / a > < / li >
< li > < a href = "#orgbb084a6" > 1.3. Matlab - Data Import< / a > < / li >
< li > < a href = "#orgb7b2129" > 1.4. Data - Plot< / a > < / li >
< li > < a href = "#org01e23ef" > 1.5. Translate to time domain< / a > < / li >
< li > < a href = "#org13bc3d4" > 1.6. Compute the PSD< / a > < / li >
< / ul >
< / li >
< li > < a href = "#orgc7af6bd" > 2. < span class = "todo TODO" > TODO< / span > Spindle< / a > < / li >
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< / ul >
< / div >
< / div >
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< div id = "outline-container-org9dbeefe" class = "outline-2" >
< h2 id = "org9dbeefe" > < span class = "section-number-2" > 1< / span > Ty Stage< / h2 >
< div class = "outline-text-2" id = "text-1" >
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< p >
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< a id = "org0ab6482" > < / a >
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< / p >
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< div class = "note" >
< p >
All the files (data and Matlab scripts) are accessible < a href = "data/static_ty.zip" > here< / a > .
< / p >
< / div >
< / div >
< div id = "outline-container-org98becb2" class = "outline-3" >
< h3 id = "org98becb2" > < span class = "section-number-3" > 1.1< / span > Notes< / h3 >
< div class = "outline-text-3" id = "text-1-1" >
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< ul class = "org-ul" >
< li > < b > 5530< / b > : Straightness Plot: Yz< / li >
< li > < b > Filename< / b > : < code > r:\home\PDMU\PEL\Measurement_library\ID31\ID31_u_station\TY\12_12_2018\linear deviation _tyz_401_points.txt< / code > < / li >
< li > < b > Acquisition date< / b > : 09/01/2019 13:49:42< / li >
< li > < b > Current date< / b > : 08/03/2019 08:46:35< / li >
< li > < b > Measurement Type< / b > : STRAIGHTNESS vertical< / li >
< li > < b > Travel Mode< / b > : Bidirectional< / li >
< li > < b > Number of Target Positions< / b > : 401< / li >
< li > < b > Number of total data pairs< / b > : 2406< / li >
< li > < b > Number of total data runs< / b > :6< / li >
< li > < b > Position Value Units< / b > : millimeters< / li >
< li > < b > Error Value Units< / b > : micrometers< / li >
< / ul >
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< col class = "org-left" / >
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< thead >
< tr >
< th scope = "col" class = "org-left" > Environmental Data< / th >
< th scope = "col" class = "org-left" > Min< / th >
< th scope = "col" class = "org-left" > Max< / th >
< th scope = "col" class = "org-left" > Avg< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > Air Temp (C)< / td >
< td class = "org-left" > 024,57< / td >
< td class = "org-left" > 024,61< / td >
< td class = "org-left" > 024,59< / td >
< / tr >
< tr >
< td class = "org-left" > Air Prs (mm)< / td >
< td class = "org-left" > 742,56< / td >
< td class = "org-left" > 743,29< / td >
< td class = "org-left" > 742,83< / td >
< / tr >
< tr >
< td class = "org-left" > Air Hmd (%)< / td >
< td class = "org-left" > 024,00< / td >
< td class = "org-left" > 024,00< / td >
< td class = "org-left" > 024,00< / td >
< / tr >
< tr >
< td class = "org-left" > MT1 Temp (C)< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > 020,00< / td >
< / tr >
< tr >
< td class = "org-left" > MT2 Temp (C)< / td >
< td class = "org-left" > 024,40< / td >
< td class = "org-left" > 024,44< / td >
< td class = "org-left" > 024,42< / td >
< / tr >
< tr >
< td class = "org-left" > MT3 Temp (C)< / td >
< td class = "org-left" > 024,32< / td >
< td class = "org-left" > 024,36< / td >
< td class = "org-left" > 024,34< / td >
< / tr >
< / tbody >
< / table >
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< p >
In a very schematic way, the measurement is explained on figure < a href = "#orgb91392e" > 1< / a > .
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.
< / p >
< p >
The obtained data corresponds to the guiding errors.
< / p >
< div id = "orgb91392e" class = "figure" >
< p > < img src = "./figs/guiding_errors.png" alt = "guiding_errors.png" / >
< / p >
< p > < span class = "figure-number" > Figure 1: < / span > Schematic of the measurement< / p >
< / div >
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< / div >
< / div >
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< div id = "outline-container-orgbab4f4e" class = "outline-3" >
< h3 id = "orgbab4f4e" > < span class = "section-number-3" > 1.2< / span > Data Pre-processing< / h3 >
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< div class = "org-src-container" >
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< pre class = "src src-shell" > sed < span class = "org-string" > 's/\t/ /g;s/\,/./g'< / span > < span class = "org-string" > "mat/linear_deviation_tyz_401_points.txt"< / span > > data/data_tyz.txt
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< / pre >
< / div >
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< pre class = "src src-shell" > head < span class = "org-string" > "mat/data_tyz.txt"< / span >
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< th scope = "col" class = "org-right" > Pos< / th >
< th scope = "col" class = "org-right" > TargetValue< / th >
< th scope = "col" class = "org-right" > ErrorValue< / th >
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< h3 id = "orgbb084a6" > < span class = "section-number-3" > 1.3< / span > Matlab - Data Import< / h3 >
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< h3 id = "orgb7b2129" > < span class = "section-number-3" > 1.4< / span > Data - Plot< / h3 >
< div class = "outline-text-3" id = "text-1-4" >
< p >
First, we plot the straightness error as a function of the position (figure < a href = "#orge60d823" > 2< / a > ).
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
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hold on;
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< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i< / span > =< span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > :data< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-constant" > end, < / span > < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span >
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > data< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-constant" > i< / span > , < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , data< span class = "org-rainbow-delimiters-depth-2" > (< / span > data< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-constant" > i< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > '-k'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
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hold off;
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xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Target Value < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > mm< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > Error Value < span class = "org-rainbow-delimiters-depth-2" > [< / span > $< span class = "org-type" > \< / span > mu m$< span class = "org-rainbow-delimiters-depth-2" > ]< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "orge60d823" class = "figure" >
< p > < img src = "figs/raw_data_tyz.png" alt = "raw_data_tyz.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 2: < / span > Time domain Data< / p >
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< / div >
< p >
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Then, we compute mean value of each position, and we remove this mean value from the data.
The results are shown on figure < a href = "#org6b6ea44" > 3< / a > .
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< / p >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > mean_pos = zeros< span class = "org-rainbow-delimiters-depth-1" > (< / span > sum< span class = "org-rainbow-delimiters-depth-2" > (< / span > data< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i< / span > =< span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > :sum< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-constant" > data< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-2" > (< / span > < / span > < span class = "org-constant" > :, < / span > < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < / span > < span class = "org-constant" > ==< / span > < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span >
mean_pos< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-constant" > i< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = mean< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > data< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-constant" > i< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
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hold on;
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< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i< / span > =< span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > :data< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-constant" > end, < / span > < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span >
filt = data< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-constant" > i< / span > ;
plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > filt, < span class = "org-highlight-numbers-number" > 3< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , data< span class = "org-rainbow-delimiters-depth-2" > (< / span > filt, < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > mean_pos, < span class = "org-string" > '-k'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > end< / span >
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hold off;
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xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Target Value < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > mm< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > '< / span > Error Value < span class = "org-rainbow-delimiters-depth-2" > [< / span > $< span class = "org-type" > \< / span > mu m$< span class = "org-rainbow-delimiters-depth-2" > ]< / span > '< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "org6b6ea44" class = "figure" >
< p > < img src = "figs/processed_data_tyz.png" alt = "processed_data_tyz.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 3: < / span > caption< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org01e23ef" class = "outline-3" >
< h3 id = "org01e23ef" > < span class = "section-number-3" > 1.5< / span > Translate to time domain< / h3 >
< div class = "outline-text-3" id = "text-1-5" >
< p >
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.
< / p >
< p >
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 < a href = "#orgb3c2727" > 4< / a > .
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > t = linspace< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 0< / span > , < span class = "org-highlight-numbers-number" > 1< / span > , length< span class = "org-rainbow-delimiters-depth-2" > (< / span > data< span class = "org-rainbow-delimiters-depth-3" > (< / span > data< span class = "org-rainbow-delimiters-depth-4" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-4" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
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hold on;
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plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > t, data< span class = "org-rainbow-delimiters-depth-2" > (< / span > data< span class = "org-rainbow-delimiters-depth-3" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > -< / span > mean_pos, < span class = "org-string" > '-k'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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hold off;
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xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Time < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > s< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; ylabel< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > 'Error Value < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > [< / span > < / span > < span class = "org-string" > um< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > ]< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
< / div >
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< div id = "orgb3c2727" class = "figure" >
< p > < img src = "figs/time_domain_tyz.png" alt = "time_domain_tyz.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 4: < / span > caption< / p >
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< / div >
< / div >
< / div >
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< div id = "outline-container-org13bc3d4" class = "outline-3" >
< h3 id = "org13bc3d4" > < span class = "section-number-3" > 1.6< / span > Compute the PSD< / h3 >
< div class = "outline-text-3" id = "text-1-6" >
< p >
We first compute some parameters that will be used for the PSD computation.
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > dt = t< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > t< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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Fs = < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > /< / span > dt; < span class = "org-comment" > % [Hz]< / span >
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win = hanning< span class = "org-rainbow-delimiters-depth-1" > (< / span > ceil< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-type" > *< / span > Fs< span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< / pre >
< / div >
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< p >
We remove the mean position from the data.
< / p >
< div class = "org-src-container" >
< pre class = "src src-matlab" > x = data< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-highlight-numbers-number" > 1< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > mean_pos;
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< / pre >
< / div >
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< p >
And finally, we compute the power spectral density of the displacement obtained in the time domain.
< / p >
< p >
The result is shown on figure < a href = "#org7446cbb" > 5< / a > .
< / p >
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< div class = "org-src-container" >
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< pre class = "src src-matlab" > < span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > x, win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
pxx_t = zeros< span class = "org-rainbow-delimiters-depth-1" > (< / span > length< span class = "org-rainbow-delimiters-depth-2" > (< / span > pxx< span class = "org-rainbow-delimiters-depth-2" > )< / span > , data< span class = "org-rainbow-delimiters-depth-2" > (< / span > end, < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-keyword" > for< / span > < span class = "org-variable-name" > i< / span > =< span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > :data< / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-constant" > end, < / span > < span class = "org-constant" > < span class = "org-highlight-numbers-number" > 1< / span > < / span > < span class = "org-constant" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span >
x = data< span class = "org-rainbow-delimiters-depth-1" > (< / span > data< span class = "org-rainbow-delimiters-depth-2" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-highlight-numbers-number" > 1< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < span class = "org-type" > ==< / span > < span class = "org-constant" > i< / span > , < span class = "org-highlight-numbers-number" > 4< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < span class = "org-type" > -< / span > mean_pos;
< span class = "org-rainbow-delimiters-depth-1" > [< / span > pxx, f< span class = "org-rainbow-delimiters-depth-1" > ]< / span > = pwelch< span class = "org-rainbow-delimiters-depth-1" > (< / span > x, win, < span class = "org-rainbow-delimiters-depth-2" > []< / span > , < span class = "org-rainbow-delimiters-depth-2" > []< / span > , Fs< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
pxx_t< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-type" > :< / span > , < span class = "org-constant" > i< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > = pxx;
< span class = "org-keyword" > end< / span >
< / pre >
< / div >
< div class = "org-src-container" >
< pre class = "src src-matlab" > < span class = "org-type" > figure< / span > ;
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hold on;
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plot< span class = "org-rainbow-delimiters-depth-1" > (< / span > f, sqrt< span class = "org-rainbow-delimiters-depth-2" > (< / span > mean< span class = "org-rainbow-delimiters-depth-3" > (< / span > pxx_t, < span class = "org-highlight-numbers-number" > 2< / span > < span class = "org-rainbow-delimiters-depth-3" > )< / span > < span class = "org-rainbow-delimiters-depth-2" > )< / span > , < span class = "org-string" > 'k-'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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hold off;
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xlabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-string" > 'Frequency < / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > (< / span > < / span > < span class = "org-string" > Hz< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-2" > )< / span > < / span > < span class = "org-string" > '< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
ylabel< span class = "org-rainbow-delimiters-depth-1" > (< / span > 'Amplitude Spectral Density $< span class = "org-type" > \< / span > left< span class = "org-rainbow-delimiters-depth-2" > [< / span > < span class = "org-type" > \< / span > frac< span class = "org-rainbow-delimiters-depth-3" > {< / span > m< span class = "org-rainbow-delimiters-depth-3" > }{< / span > < span class = "org-type" > \< / span > sqrt< span class = "org-rainbow-delimiters-depth-4" > {< / span > Hz< span class = "org-rainbow-delimiters-depth-4" > }< / span > < span class = "org-rainbow-delimiters-depth-3" > }< / span > < span class = "org-type" > \< / span > right< span class = "org-rainbow-delimiters-depth-2" > ]< / span > $'< span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
< span class = "org-type" > set< / span > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < span class = "org-variable-name" > gca< / span > , < span class = "org-string" > 'XScale', 'log'< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > )< / span > < / span > < span class = "org-string" > ; set< / span > < span class = "org-string" > < span class = "org-rainbow-delimiters-depth-1" > (< / span > < / span > < span class = "org-string" > gca, 'YScale', 'log'< / span > < span class = "org-rainbow-delimiters-depth-1" > )< / span > ;
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< / pre >
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< div id = "org7446cbb" class = "figure" >
< p > < img src = "figs/psd_tyz.png" alt = "psd_tyz.png" / >
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< / p >
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< p > < span class = "figure-number" > Figure 5: < / span > PSD of the Z motion when scanning with Ty at 1Hz< / p >
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< div id = "outline-container-orgc7af6bd" class = "outline-2" >
< h2 id = "orgc7af6bd" > < span class = "section-number-2" > 2< / span > < span class = "todo TODO" > TODO< / span > Spindle< / h2 >
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< div id = "postamble" class = "status" >
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< p class = "author" > Author: Dehaeze Thomas< / p >
< p class = "date" > Created: 2019-05-14 mar. 09:52< / p >
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< p class = "validation" > < a href = "http://validator.w3.org/check?uri=referer" > Validate< / a > < / p >
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