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I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample.

The two materials mix quite well, but not perfectly, so on my image I can see that some areas are mostly material A, some are mostly material B, and most of the areas are a mix between.

I also took an image of a sample consisting only of material A.

On my images material A will look white, and material B will look black.

If I make a histogram of the image of material A (and only A) it has the center around 6 [A.U] which fits my theory. The histogram also has a FWHM of 0.55 [A.U.]

The same histogram of material A & B is centered around 7 [A.U] which also fit my theory since it's a 50:50 mix of A & B and A is centered at 6 [A.U] and B should be centered at 8 [A.U]. The FWHM of this peak 0.64 [A.U] - thus only slightly larger than the image with pure A.

Here's my problem, since the peak with the mix only is slightly wider than the peak for the pure material it means that my resolution i not good enough to distinguish the two materials from each other (if I could see areas with pure material A or B it would be a camel/double-peak, if I could see areas with mostly material A or B I would have a very wide peak - here I only have a slightly wider peak). However, it is still wider, so there must be some kind of information I can subtract.

I'm not really sure what - if any.

EDIT: If anything is unclear, please ask!

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closed as off topic by Qmechanic, Sklivvz, Manishearth Dec 29 '12 at 15:57

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To avoid confusion what is A.U.? – user11547 Oct 22 '12 at 11:30
Arbitrary Units :) – Marcus Oct 22 '12 at 11:41
With 10 rep under your belt you are now able to post images. Exhibiting the histograms would help a lot. There is a certain amount of art to this business. – dmckee Oct 22 '12 at 15:48

Deconvolution of image histograms obviously is an art, particularly blind convolution. One option is to do similar trial and error with inverse noise functions and see if you can introduce additional contrast into the image.

If you want here is a decent article that covers inverse Gaussian deconvolution that also might help.

It sounds that your issue is that there is no indication of bimodalism in the mixed material. An interesting article is one regarding how bimodalism arises in statistical data regarding height distribution in populations. It turns out that opposite rounding conventions (floor vs ceiling functions) can induce slight bimodalism in samples.

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