Is there a simple way to estimate the contribution to the energy resolution of a Johansson cylindrically bent crystal analyzer given by the finite size of an x ray source ?
Taking into account a point source and perfectly diffracting element the outcome is a line (or point if focusing in the orthogonal direction s used).
Thus, for a first (geometrical) approximation for:
- a given distance between source and the diffracting element,
- a given distance between the diffraction element and the screen (detector)
- a given known source extension in space (size),
I would trace the edge rays from the source to the diffraction element and then to the screen accounting for minuscule changes in the incidence and diffracted angles. Assuming the single wavelength, or photon energy emitted, so there is no influence of the spectral components, the spread you get at the detector will be equal to your spectrograph resolution (from the geometrical point of view, what I understood from your question) and will account for both the geometry of your setup and the source size. You can of course do this like that, or use any other tracing software or Monte Carlo, but this is just the first rough approximation of what to expect. Best regards.
I agree with Przemyslaw Wachulak.
you can see the following:
1. https://books.google.iq/books?id=Ho3gCAAAQBAJ&pg=PA141&lpg=PA141&dq=The+energy+resolution+of+Johansson+cylindrically+bent+crystal+analyzer+for+a+hard+x-ray&source=bl&ots=UZWlRTZS_N&sig=ACfU3U2pVPhIEb3ScDaEotMRp-isCx0zWA&hl=ar&sa=X&ved=2ahUKEwjku-r2n5H1AhX88LsIHQrYCiIQ6AF6BAgkEAM#v=onepage&q=The%20energy%20resolution%20of%20Johansson%20cylindrically%20bent%20crystal%20analyzer%20for%20a%20hard%20x-ray&f=false
2. https://www.osti.gov/servlets/purl/1603648
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