Peak deconvolution - How much information can I get from these peaks?

[blonk]

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!

 

[mfb]

Some questions about your setup:
- your distribution is 1-dimensional, or at least you are interested in the 1-dimensional projection only?
- both A and B do not "fill" the space, so their concentration can be anything from 0 to whatever?
- do you expect that B behaves similar to A (FWHM of 0.55 in a pure sample of B)?
- how does your mixing occur? And which parameter do you want to extract?
- do you expect that the distribution of B is a convolution of the "B only distribution" and some "mixing distribution"? If yes, and both are gaussian (or some other nice function), FWHM is proportional to the square of the variance, and that variance is the sum of the individual values. This allows to calculate a "mixing distribution".