(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 37358, 790] NotebookOptionsPosition[ 19749, 468] NotebookOutlinePosition[ 36995, 778] CellTagsIndexPosition[ 36952, 775] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Megapixel Equivalence of Film", "Subsubtitle", CellChangeTimes->{{3.4420740803866353`*^9, 3.442074089599883*^9}}], Cell["\<\ Resolution of digital cameras is often given in megapixels (MP). In order to \ compare film resolution with digital capture resolution we use the \ diffraction limited resolution of the lens at a particular f-stop as well as \ the resolution of the film given by the film's MTF and derive a comparative \ estimate. The Rayleigh limit determines the maximum aerial resolution of a lens having \ f-number f and light wavelength of \[Lambda], with units of line pairs per mm \ when \[Lambda] is in mm:\ \>", "Text", CellChangeTimes->{{3.442053816198163*^9, 3.442053849155554*^9}, { 3.4420541863804593`*^9, 3.4420542268386354`*^9}, {3.442066317424043*^9, 3.442066341568762*^9}, 3.4420732345303535`*^9, {3.442073321325158*^9, 3.4420736198043504`*^9}, {3.4420743647054653`*^9, 3.4420743670989075`*^9}, {3.4420744019289904`*^9, 3.442074447484496*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"rayleigh", "[", RowBox[{"f_", ",", "\[Lambda]_"}], "]"}], " ", ":=", " ", FractionBox["1", RowBox[{"1.22", " ", "f", " ", "\[Lambda]"}]]}]], "Input", CellChangeTimes->{{3.4420527256900897`*^9, 3.4420527516273856`*^9}, { 3.4420528069269023`*^9, 3.4420528126250963`*^9}, {3.442052844420816*^9, 3.442052889635832*^9}}], Cell["\<\ For recording media with MTF of r2 in line pairs per mm, recording image \ having rayleigh limit r1 in line pairs per mm, R is defined as:\ \>", "Text", CellChangeTimes->{{3.4420539745258274`*^9, 3.442054098614258*^9}, { 3.4420542759893103`*^9, 3.442054299092531*^9}, {3.442066385461877*^9, 3.442066389357478*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"R", "[", RowBox[{"r1_", ",", "r2_"}], "]"}], " ", ":=", " ", RowBox[{ FractionBox["1", "r1"], "+", FractionBox["1", "r2"]}]}]], "Input", CellChangeTimes->{{3.4420529210209618`*^9, 3.4420529372643185`*^9}, { 3.4420529926639795`*^9, 3.442053036647224*^9}, {3.4420531032329693`*^9, 3.442053118965592*^9}}], Cell["\<\ Where the recording media has dimensions x and y (mm), and equating a line \ pair as 2 pixels, we can estimate the equivalent resolution of film in \ megapixels as:\ \>", "Text", CellChangeTimes->{{3.4420541563372593`*^9, 3.4420541703373904`*^9}, { 3.4420542483796096`*^9, 3.442054248770171*^9}, {3.4420543157965508`*^9, 3.442054384184888*^9}, {3.4420664125207853`*^9, 3.442066422034466*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{ RowBox[{"mp", "[", RowBox[{"f_", ",", "\[Lambda]_", ",", "mtf_", ",", "x_", ",", "y_"}], "]"}], " ", ":=", " ", FractionBox[ RowBox[{"4", " ", "x", " ", "y"}], RowBox[{ SuperscriptBox["10", "6"], SuperscriptBox[ RowBox[{"(", RowBox[{"R", "[", RowBox[{ RowBox[{"rayleigh", "[", RowBox[{"f", ",", "\[Lambda]"}], "]"}], ",", "mtf"}], "]"}], ")"}], "2"]}]]}], ";"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.442053246358774*^9, 3.442053412868203*^9}, { 3.442053455829979*^9, 3.44205347367564*^9}, {3.442053547912387*^9, 3.4420535579568305`*^9}, {3.4420535917053585`*^9, 3.4420536093607454`*^9}, 3.4420536549963665`*^9, {3.442053744334829*^9, 3.442053752366378*^9}, 3.4420740184575853`*^9}], Cell["\<\ In the following panel use the sliders to adjust mtf value to the MTF of the \ recording media of interest, then adjust the x and y sliders to the width and \ height of the recording media. The resolution estimate is plotted as a \ function of the f number, e.g. at the default values of mtf = 40 line pairs \ per mm, x = 100 mm and y = 200 mm, f/45 produces a MP equivalence of \ approximately 30 MP whereas at f/16 the resolution is approaching 50 MP.\ \>", "Text", CellChangeTimes->{{3.442074029403325*^9, 3.442074037044312*^9}, { 3.4420743339111853`*^9, 3.4420743518569903`*^9}, {3.4421404374692016`*^9, 3.4421404499371295`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"mp", "[", RowBox[{"f", ",", ".00055", ",", "mtf", ",", "x", ",", "y"}], "]"}], ",", RowBox[{"{", RowBox[{"f", ",", "1", ",", "64"}], "}"}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "250"}], "}"}]}], ",", RowBox[{"Filling", "\[Rule]", "Bottom"}], ",", RowBox[{"GridLines", " ", "\[Rule]", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ "2", ",", "2.8", ",", "4", ",", "5.6", ",", "8", ",", "11", ",", "16", ",", "22", 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100, 10}, {{ Hold[$CellContext`x$$], 100}, 24, 200, 1}, {{ Hold[$CellContext`y$$], 125}, 36, 250, 1}}, Typeset`size$$ = { 450., {148., 155.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`mtf$4664$$ = 0, $CellContext`x$4665$$ = 0, $CellContext`y$4666$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`mtf$$ = 40, $CellContext`x$$ = 100, $CellContext`y$$ = 125}, "ControllerVariables" :> { Hold[$CellContext`mtf$$, $CellContext`mtf$4664$$, 0], Hold[$CellContext`x$$, $CellContext`x$4665$$, 0], Hold[$CellContext`y$$, $CellContext`y$4666$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Plot[ $CellContext`mp[$CellContext`f, 0.00055, $CellContext`mtf$$, $CellContext`x$$, $CellContext`y$$], \ {$CellContext`f, 1, 64}, PlotRange -> {0, 250}, Filling -> Bottom, GridLines -> {{2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64}, Automatic}, AxesLabel -> { Style["f", 16], Style["MP", 16]}, Ticks -> {{5.6, 8, 11, 16, 22, 32, 45, 64}, Automatic}], "Specifications" :> {{{$CellContext`mtf$$, 40}, 10, 100, 10, Appearance -> "Labeled"}, {{$CellContext`x$$, 100}, 24, 200, 1, Appearance -> "Labeled"}, {{$CellContext`y$$, 125}, 36, 250, 1, Appearance -> "Labeled"}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{506., {237., 244.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`mp[ Pattern[$CellContext`f, Blank[]], Pattern[$CellContext`\[Lambda], Blank[]], Pattern[$CellContext`mtf, Blank[]], Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := ((4 $CellContext`x) $CellContext`y)/( 10^6 $CellContext`R[ $CellContext`rayleigh[$CellContext`f, $CellContext`\[Lambda]], \ $CellContext`mtf]^2), $CellContext`f[ Pattern[$CellContext`price1, Blank[]], Pattern[$CellContext`price2, Blank[]], Pattern[$CellContext`price3, Blank[]], Pattern[$CellContext`s1, Blank[]], Pattern[$CellContext`s2, Blank[]], Pattern[$CellContext`s3, Blank[]], Pattern[$CellContext`s4, Blank[]], Pattern[$CellContext`s5, Blank[]], Pattern[$CellContext`p1e1, Blank[]], Pattern[$CellContext`p1e2, Blank[]], Pattern[$CellContext`p1e3, Blank[]], Pattern[$CellContext`p1e4, Blank[]], Pattern[$CellContext`p1e5, Blank[]], Pattern[$CellContext`p2e1, Blank[]], Pattern[$CellContext`p2e2, Blank[]], Pattern[$CellContext`p2e3, Blank[]], Pattern[$CellContext`p2e4, Blank[]], Pattern[$CellContext`p2e5, Blank[]], Pattern[$CellContext`p3e1, Blank[]], Pattern[$CellContext`p3e2, Blank[]], Pattern[$CellContext`p3e3, Blank[]], Pattern[$CellContext`p3e4, Blank[]], Pattern[$CellContext`p3e5, Blank[]], Pattern[$CellContext`overhead, Blank[]], Pattern[$CellContext`e1hours, Blank[]], Pattern[$CellContext`e2hours, Blank[]], Pattern[$CellContext`e3hours, Blank[]], Pattern[$CellContext`e4hours, Blank[]], Pattern[$CellContext`e5hours, Blank[]], Pattern[$CellContext`p1capacity, Blank[]], Pattern[$CellContext`p2capacity, Blank[]], Pattern[$CellContext`p3capacity, Blank[]]] := Maximize[{$CellContext`p1 ($CellContext`price1 - ($CellContext`p1e1 \ $CellContext`s1 + $CellContext`p1e2 $CellContext`s2 + $CellContext`p1e3 \ $CellContext`s3 + $CellContext`p1e4 $CellContext`s4 + $CellContext`p1e5 \ $CellContext`s5)) + $CellContext`p2 ($CellContext`price2 - ($CellContext`p2e1 \ $CellContext`s1 + $CellContext`p2e2 $CellContext`s2 + $CellContext`p2e3 \ $CellContext`s3 + $CellContext`p2e4 $CellContext`s4 + $CellContext`p2e5 \ $CellContext`s5)) + $CellContext`p3 ($CellContext`price3 - ($CellContext`p3e1 \ $CellContext`s1 + $CellContext`p3e2 $CellContext`s2 + $CellContext`p3e3 \ $CellContext`s3 + $CellContext`p3e4 $CellContext`s4 + $CellContext`p3e5 \ $CellContext`s5)) - $CellContext`overhead, $CellContext`p1 $CellContext`p1e1 + \ $CellContext`p2 $CellContext`p2e1 + $CellContext`p3 $CellContext`p3e1 <= \ $CellContext`e1hours, $CellContext`p1 $CellContext`p1e2 + $CellContext`p2 \ $CellContext`p2e2 + $CellContext`p3 $CellContext`p2e3 <= \ $CellContext`e2hours, $CellContext`p1 $CellContext`p1e3 + $CellContext`p2 \ $CellContext`p2e3 + $CellContext`p3 $CellContext`p3e3 <= \ $CellContext`e3hours, $CellContext`p1 $CellContext`p1e4 + $CellContext`p2 \ $CellContext`p2e4 + $CellContext`p3 $CellContext`p3e4 <= \ $CellContext`e4hours, $CellContext`p1 $CellContext`p1e5 + $CellContext`p2 \ $CellContext`p2e5 + $CellContext`p3 $CellContext`p3e5 <= \ $CellContext`e5hours, $CellContext`p1 <= $CellContext`p1capacity, \ $CellContext`p2 <= $CellContext`p2capacity, $CellContext`p3 <= \ $CellContext`p3capacity, $CellContext`p1 >= 0, $CellContext`p2 >= 0, $CellContext`p3 >= 0}, {$CellContext`p1, $CellContext`p2, $CellContext`p3}], \ $CellContext`f[ Pattern[$CellContext`price1, Blank[]], Pattern[$CellContext`price2, Blank[]], Pattern[$CellContext`price3, Blank[]], Pattern[$CellContext`s1, Blank[]], Pattern[$CellContext`s2, Blank[]], Pattern[$CellContext`s3, Blank[]], Pattern[$CellContext`s4, Blank[]], Pattern[$CellContext`s5, Blank[]], Pattern[$CellContext`p1e1, Blank[]], Pattern[$CellContext`p1e2, Blank[]], Pattern[$CellContext`p1e3, Blank[]], Pattern[$CellContext`p1e4, Blank[]], Pattern[$CellContext`p1e5, Blank[]], Pattern[$CellContext`p2e1, Blank[]], Pattern[$CellContext`p2e2, Blank[]], Pattern[$CellContext`p2e3, Blank[]], Pattern[$CellContext`p2e4, Blank[]], Pattern[$CellContext`p2e5, Blank[]], Pattern[$CellContext`p3e1, Blank[]], Pattern[$CellContext`p3e2, Blank[]], Pattern[$CellContext`p3e3, Blank[]], Pattern[$CellContext`p3e4, Blank[]], Pattern[$CellContext`p3e5, Blank[]], Pattern[$CellContext`overhead, Blank[]], Pattern[$CellContext`e1hours, Blank[]], Pattern[$CellContext`e2hours, Blank[]], Pattern[$CellContext`e3hours, Blank[]], Pattern[$CellContext`e4hours, Blank[]], Pattern[$CellContext`e5hours, Blank[]], Pattern[$CellContext`p1capacity, Blank[]], Pattern[$CellContext`p2capacity, Blank[]], Pattern[$CellContext`p3capacity, Blank[]], Pattern[$CellContext`p1overhead, Blank[]], Pattern[$CellContext`p2overhead, Blank[]], Pattern[$CellContext`p3overhead, Blank[]]] := Maximize[{$CellContext`p1 ($CellContext`price1 - ($CellContext`p1e1 \ $CellContext`s1 + $CellContext`p1e2 $CellContext`s2 + $CellContext`p1e3 \ $CellContext`s3 + $CellContext`p1e4 $CellContext`s4 + $CellContext`p1e5 \ $CellContext`s5 + $CellContext`p1overhead)) + $CellContext`p2 \ ($CellContext`price2 - ($CellContext`p2e1 $CellContext`s1 + $CellContext`p2e2 \ $CellContext`s2 + $CellContext`p2e3 $CellContext`s3 + $CellContext`p2e4 \ $CellContext`s4 + $CellContext`p2e5 $CellContext`s5 + \ $CellContext`p2overhead)) + $CellContext`p3 ($CellContext`price3 - \ ($CellContext`p3e1 $CellContext`s1 + $CellContext`p3e2 $CellContext`s2 + \ $CellContext`p3e3 $CellContext`s3 + $CellContext`p3e4 $CellContext`s4 + \ $CellContext`p3e5 $CellContext`s5 + $CellContext`p3overhead)) - \ $CellContext`overhead, $CellContext`p1 $CellContext`p1e1 + $CellContext`p2 \ $CellContext`p2e1 + $CellContext`p3 $CellContext`p3e1 <= \ $CellContext`e1hours, $CellContext`p1 $CellContext`p1e2 + $CellContext`p2 \ $CellContext`p2e2 + $CellContext`p3 $CellContext`p2e3 <= \ $CellContext`e2hours, $CellContext`p1 $CellContext`p1e3 + $CellContext`p2 \ $CellContext`p2e3 + $CellContext`p3 $CellContext`p3e3 <= \ $CellContext`e3hours, $CellContext`p1 $CellContext`p1e4 + $CellContext`p2 \ $CellContext`p2e4 + $CellContext`p3 $CellContext`p3e4 <= \ $CellContext`e4hours, $CellContext`p1 $CellContext`p1e5 + $CellContext`p2 \ $CellContext`p2e5 + $CellContext`p3 $CellContext`p3e5 <= \ $CellContext`e5hours, $CellContext`p1 <= $CellContext`p1capacity, \ $CellContext`p2 <= $CellContext`p2capacity, $CellContext`p3 <= \ $CellContext`p3capacity, $CellContext`p1 >= 0, $CellContext`p2 >= 0, $CellContext`p3 >= 0, Plus[$CellContext`p1overhead] >= 0, Plus[$CellContext`p2overhead] >= 0, $CellContext`p3overhead >= 0}, {$CellContext`p1, $CellContext`p2, $CellContext`p3}], \ $CellContext`R[ Pattern[$CellContext`r1, Blank[]], Pattern[$CellContext`r2, Blank[]]] := 1/$CellContext`r1 + 1/$CellContext`r2, $CellContext`rayleigh[ Pattern[$CellContext`f, Blank[]], Pattern[$CellContext`\[Lambda], Blank[]]] := 1/((1.22 $CellContext`f) $CellContext`\[Lambda]), Attributes[PlotRange] = {ReadProtected}}; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.4421407945226192`*^9, 3.4421408502126975`*^9, {3.4421411187989054`*^9, 3.442141134781888*^9}, 3.442141430336875*^9, 3.442141523741184*^9, 3.442142719300314*^9, 3.4421429311950035`*^9, 3.442142972123856*^9, 3.442143338871213*^9, {3.442145237561395*^9, 3.44214525776044*^9}}] }, Open ]], Cell["\<\ 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