Pass Options to Export[]

I'm working with Options to change the look and feel of some generated Graphics by passing Options to several functions, one of them being Export[]. For example:

Options[myPlot] := {Resolution -> 325, Size -> 12, FileName -> "A", 
  PlotStyle -> Automatic};

myPlot[f_, opts : OptionsPattern[myPlot]] := Block[{fig},
(* ... some calculations here *)

fig = Plot[f[x], {x, -\[Pi], \[Pi]}, 
    Evaluate[FilterRules[{opts}, Options[Plot]]]];
fig = Show[fig, ImageSize -> OptionValue[Size]*72/2.54];+
Export[OptionValue[FileName] <> ".png", fig,  FilterRules[{opts}, Options[Export]]];
Print[fig];
]

And using f[x_] := x^2 use the function as

 myPlot[f, Resolution -> 120, PlotStyle -> Red]

The Option to plot the function in Red is passed correctly to Plot but Resolution is not passed to Export. This is of course due to the fact that Options[Export] = {}.

My question is:

How can I still pass Options to Export (i.e. how to determine, which are available, if they are not written in Options[Export]?

And closely related:

How to do that on your own, i.e. now I defined PlotStyle to be an Option of myPlot, though it's only passed on, how can I pass Options, that I haven't given myself, without getting the message

OptionValue::nodef: "Unknown option PlotStyle for ...

Answer

Extraction of Export options

To extract the options for specific image export formats automatically, I really don't know an easy way. What you can do is to use Trace in combination with ExportString to investigate what Mathematica is doing. To make the next thing work you have to call e.g. ExportString["test", "GIF"]; for every format at least once:

ExportString["test", #]; & /@ {"PNG", "GIF", "BMP", "JPEG"}

System`ConvertersDump`exportOptions /@ {"PNG", "GIF", "BMP", "JPEG"}
(*
{{"BitDepth", "ColorSpace", 
  "DataType"}, {"AnimationRepetitions", "Background", "FrameRate", 
  "TransitionEffect", "TransparentColor", 
  "UserInputFlag"}, {"BitDepth", "ColorSpace", "DataType", 
  "HorizontalResolution", "RLECompression", 

  "VerticalResolution"}, {"BitDepth", "ColorSpace"}}
*)

which is unfortunately very distinct from the documentation. For some exporters you find for instance such stuff

Options[System`ConvertersDump`exportGraphicsToGIFConverter]
(*
 {Background -> None, ImageResolution -> Automatic, 
 ImageSize -> Automatic, "ImageTopOrientation" -> Top, 
 "ColorReductionPalette" -> 256, "ColorReductionDither" -> True, 
 "GlobalColorMap" -> True}

*)

But how to find this automatically? I have no idea. Checkout this too

Options[System`ConvertersDump`exportToBitmapConverter]
Options[System`ConvertersDump`exportToColormappedBitmapConverter]

Setting up options for own functions

Say you want to setup a function which can take its own options, options of Plot and options of NMinimize. Furthermore, you want to specify some of the default option-values for Plot and NMinimize. You can set the function up and use it like follows:

Options[f] = {
   fopt1 -> Automatic,

   fopt2 -> True,
   PlotStyle -> Green,
   AccuracyGoal -> 1
   };


f[x_, opts : OptionsPattern[{f, Plot, NMinimize}]] := Module[{},
  Print["Given Options usable by f only:", 
   FilterRules[{opts}, Options[f]]];
  Print["Given Options usable by Plot only:", 

   FilterRules[{opts}, Options[Plot]]];
  Print["Given Options usable by NMinimize only:", 
   FilterRules[{opts}, Options[NMinimize]]];

  Print["Defaultvalue for not specified options:" ];
  Print[OptionValue[StepMonitor]];
  Print[OptionValue[PlotRange]];
  Print[OptionValue[fopt2]];
]

Test case

f[x, fopt1 -> Full, PlotStyle -> Yellow, AccuracyGoal -> 42]
(*
Given Options usable by f only:{fopt1->Full,PlotStyle->RGBColor[1,1,0],AccuracyGoal->42}
Given Options usable by Plot only:{PlotStyle->RGBColor[1,1,0]}
Given Options usable by NMinimize only:{AccuracyGoal->42}

Defaultvalue for not specified options:
None
{Full,Automatic}

True
*)

And now you can pass any other option of Plot or NMinimize without a warning. But be carful, something like Method is an option for many functions and would be passed to each approapriate.