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Notebook[{

Cell[CellGroupData[{
Cell["Fitting Diffraction Grating Data", "Title"],

Cell["Introduction", "Subtitle"],

Cell[TextData[{
  "Here's an example program on how to use ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " to fit your diffraction grating data.  A few things you need to do first. \
 1) using logger pro export your data to a text file 2) the data file has \
some header lines at the top, erase those and save the file.\n\nFinally, \
don't be afraid to use the help browser.  It's very HELPFUL.  Just search \
anything you don't understand and it'll tell you what it is, how to use it, \
and give some examples."
}], "Text"],

Cell[CellGroupData[{

Cell["Opening and Reading a file", "Subtitle"],

Cell[TextData[{
  "First you need to open the text file, so use the OpenRead command and it \
takes as input the file name surrounded by quatation marks.  Set this equal \
to dataFile.  ",
  StyleBox["Change the location to match that of your data file",
    FontWeight->"Bold",
    FontColor->RGBColor[1, 0, 0]],
  "."
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(dataFile = 
      OpenRead["\<C:\Documents and \
Settings\powl3-3109b\Desktop\Jordan\sampleData.txt\>"]\)], "Input"],

Cell[BoxData[
    \(InputStream[
      "C:\\Documents and \
Settings\\powl3-3109b\\Desktop\\Jordan\\sampleData.txt", 5]\)], "Output"]
}, Open  ]],

Cell["\<\
Then read the list of data from the text file and save it as a list called \
dataList.  To do this use the ReadList command as follows.  The {Number, \
Number} part reads things in as pairs so, for each time you have an \
associated voltage.\
\>", "Text"],

Cell[BoxData[
    \(\(dataList = ReadList[dataFile, {Number, Number}];\)\)], "Input"],

Cell["Here's an exmple of a plot.", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(lp = 
        ListPlot[dataList, PlotRange \[Rule] {{5, 17}, {0, 7}}];\)\)], "Input"],

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Cell[CellGroupData[{

Cell["Massaging the Data", "Subtitle"],

Cell["\<\
First I'm gonna cut down the data and focus on the region in the middle that \
looks the most like an airy disk.  To do this I run a For loop and only take \
the data that fits between time 8.7 and 13.6.  And I'm gonna save it in a \
list called cutDataList.\
\>", "Text"],

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        start = i]; \[IndentingNewLine]If[\(dataList[\([i]\)]\)[\([1]\)] \
\[Equal] 13.6, \ finish = i];\[IndentingNewLine]]\), "\[IndentingNewLine]", 
    \(\(cutDataList = Take[dataList, {start, finish}];\)\)}], "Input"],

Cell["Here's a Picture of the new data", "Text"],

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}, Open  ]],

Cell[CellGroupData[{

Cell["Fitting", "Subtitle"],

Cell["\<\
Next I load the statistics software needed to do the fit program.\
\>", "Text"],

Cell[BoxData[
    \(<< Statistics`NonlinearFit`\)], "Input"],

Cell["\<\
Finall I run the command fit command that is called Nonlinear Regress.  It is \
executed as follows:

NonlinearRegress[data,model,variables,{parameter,start value}]

Now this takes some time to get correct.  It helps not to let all your \
parameters vary at first.  Fix a few you know from looking at the data like \
the amplitude or the off set.\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(\(Clear[a, b, c, d];\)\), "\[IndentingNewLine]", 
    \(fp = 
      NonlinearRegress[cutDataList, \ 
        a*\((Sin[b*x - c]/\((b*x - c)\))\)^2 + d\ , 
        x, {{a, 6}, {c, 15}, {b, 1.39}, {d,  .3}}, 
        RegressionReport \[Rule] {BestFit, ParameterTable}]\)}], "Input"],

Cell[BoxData[
    RowBox[{"{", 
      RowBox[{\(BestFit \[Rule] \(\(0.30619370225230047`\)\(\[InvisibleSpace]\
\)\) + \(5.791853778294638`\ Sin[\(\(29.617577616200993`\)\(\[InvisibleSpace]\
\)\) - 2.660111157746425`\ x]\^2\)\/\((\(-29.617577616200993`\) + \
2.660111157746425`\ x)\)\^2\), ",", 
        RowBox[{"ParameterTable", "\[Rule]", 
          TagBox[GridBox[{
                {"\<\"\"\>", "\<\"Estimate\"\>", "\<\"Asymp. SE\"\>", \
"\<\"TStat\"\>", "\<\"PValue\"\>"},
                {"a", "5.791853778294638`", "0.0031619242011055922`", 
                  "1831.7497226117787`", 
                  "1.225913935851471481876002416516389`15.954589770191005*^-\
1729"},
                {"c", "29.617577616200993`", "0.017096329482532105`", 
                  "1732.3939414283204`", 
                  "5.54129041589032885790996981`15.954589770191005*^-1706"},
                {"b", "2.660111157746425`", "0.0015342782177379774`", 
                  "1733.7866933080036`", 
                  "2.527782333812309854382503377`15.954589770191005*^-1706"},
                {"d", "0.30619370225230047`", "0.0013401368622144416`", 
                  "228.47942690446268`", 
                  "2.79858056990923410408257528`15.954589770191005*^-850"}
                },
              RowSpacings->1,
              ColumnSpacings->3,
              RowAlignments->Baseline,
              ColumnAlignments->{Left}],
            Function[ BoxForm`e$, 
              TableForm[ 
              BoxForm`e$, TableHeadings -> {{a, c, b, d}, {"Estimate", 
                "Asymp. SE", "TStat", "PValue"}}]]]}]}], "}"}]], "Output"]
}, Open  ]],

Cell["Here's a Plot of the fit against the data:", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
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        0.30619370225230047`\[InvisibleSpace] + \((5.791853778294638`\ Sin[\(\
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x]\^2)\)/\((\(-29.617577616200993`\) + 2.660111157746425`\ x)\)\^2, {x, 8.7, 
          13.6}, PlotRange \[Rule] {0, 7}, 
        Epilog \[Rule] Point /@ cutDataList];\)\)], "Input"],

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