One thing that I suggest you to take into account is the color profile with which your image is encoded. For the applications in physics it is crucial whether the color intensity values of your image are proportional to the actual light intensities recorded by your photoelectronic device or they are transformed into a "gamma-corrected" and hence non-additive derivatives. With non-additive values any interpolation scheme produces misleading results.

Sorry for the lack of labels.... "a" is the angle of the line, "w" is the width (in degrees) of the section of the image. If you modify the parameters in the Manipulate, you will see immediately how they relate to the radial section of the image.

The curves are: Min, Max, and Mean of the data, summed over the angular width w, for each radius (from 0 to 500 here). The bottom curve (in red) is the Standard Deviation of the data for each radius.

The idea was to demonstrate that once the image is transformed in polar coordinates, you can compute a lot of useful radial information in real time.

Dear Alexey, All solutions are good. If you allow me I would like to add one more requirement. I have tried, but my knowledge is still not enough to solve it in a short time. It would be interesting if it were possible to use the image center (prior calculation of the centroid). Also interesting would finish line profile in a circle of radius r. I have tried adapt a small routine in attachment without success until now. Thank you anyway

Antonio

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Hi Antonio,

Here is one approach:

\[Alpha] = Pi/3;
id = ImageDimensions[img];
pr = {0, #} & /@ id;
center = Mean /@ pr;
gr = Graphics[{White, AbsoluteThickness[1], 
    Line[{center, AngleVector[center, {Norm[id], \[Alpha]}]}]}, Background -> Black, 
   PlotRangePadding -> None, ImageSize -> id, PlotRange -> pr, AspectRatio -> Automatic];
mask = Binarize@Rasterize[Style[gr, Antialiasing -> False], "Image"];
radialProfile = 
  PixelValue[img, SortBy[PixelValuePositions[mask, 1], N@EuclideanDistance[center, #] &]];
Row[{ListLinePlot[radialProfile, ImageSize -> Medium], Show[img, gr /. White -> Red]}]

I also attach updated version of your Notebook to this post.

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