Dear Kiranjot Dhaliwal , what is 'vertical coherence'. I assume you mean polarization.

In fact the x-ray reflectivity depends on the state of polarization, but differences only show up in the quite low x-ray photon energy range.

Please have a look for example at the following link:

http://henke.lbl.gov/optical_constants/layer2.html or

http://henke.lbl.gov/optical_constants/

Here the state of polarization is asked as input parameter.

You may play around....

Good luck

Dear Gerhard Martens , thanks for your response. I apologize for not being clear in the question. By vertical coherence, I meant the incident beam has transverse coherence. For this incident beam, whether the reflectivity pattern will be modified from the one obtained using incoherent beam< If yes, then how?

Dear Kiranjot,

if 2 beams superimpose, their phaseshift phi decides the resulting intensity. For coherent beams, the phaseshift is constant and you can exact calculate the resulting intensity I:

I = I1 +I2 + 2*(I1*I2)0,5*cos(phi)

Whether the phaseshift is equal to zero or 180° depends on the refractive indize's of incident n1 and refractive n2 medium.

For n2 > n1 you have phi = 0, otherwise phi = 180 °. That means, cos( phi) = 1 or cos( phi) = -1 (stitch like at a mirror). The intensities add geometrically (the field strength arithmetically)

For incoherent radiation the cos(phi) is zero and the intensities add arithmetically.

I add some lecture notes (sorry in german), but it can help to clarify.

With Regard

R. Mitdank