(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 150654, 2875] NotebookOptionsPosition[ 149626, 2837] NotebookOutlinePosition[ 149998, 2853] CellTagsIndexPosition[ 149955, 2850] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Calculation of linear prolate spheroidal functions \ and eigen values", FontFamily->"New Century Schlbk", FontSize->14, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]]], "Title", CellChangeTimes->{{3.4170002883745575`*^9, 3.4170003017115574`*^9}, { 3.417000344870558*^9, 3.4170003502825575`*^9}}], Cell["\<\ From Optical Imaging and Spectroscopy (Wiley - OSA 2009) By David J. Brady www.opticalimaging.org Figure 10.15\ \>", "Subsubtitle", CellChangeTimes->{{3.448224217106*^9, 3.4482242191879997`*^9}}], Cell[TextData[{ "\n\tAs discussed in \n\n\tW. P. Latham and M. L. Tilton, \"Calculation of \ prolate functions for optical analysis,\" Appl. Opt. 26, 2653- (1987)\n\nthe \ linear prolate spheroidal functions satisfy \n\n", Cell[BoxData[ FormBox[ SubscriptBox["\[Lambda]", "n"], TraditionalForm]]], Cell[BoxData[ FormBox[ SubscriptBox["\[Psi]", "n"], TraditionalForm]]], "(x)=", Cell[BoxData[ FormBox[ RowBox[{ SubsuperscriptBox["\[Integral]", RowBox[{"-", "1"}], "1"], RowBox[{ SuperscriptBox["e", "icxy"], RowBox[{ SubscriptBox["\[Psi]", "n"], "(", "x", ")"}], RowBox[{"\[DifferentialD]", "x"}]}]}], TraditionalForm]]], "\n\nThis notebook finds the eigenvalues and wavefunctions for these \ functions using Gauss-Legendre integration" }], "Text", CellChangeTimes->{{3.4170003559715576`*^9, 3.4170004103595576`*^9}, { 3.4170004677935576`*^9, 3.4170006666965575`*^9}}], Cell[BoxData[ RowBox[{"<<", "NumericalDifferentialEquationAnalysis`"}]], "Input"], Cell[BoxData[{ RowBox[{ RowBox[{"orderN", "=", "100"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"glw", "=", RowBox[{"GaussianQuadratureWeights", "[", RowBox[{"orderN", ",", 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