In diffraction process, how to describe the edge in the sense of particle-wave duality? In diffraction experiments photons show behind an edge intensity distributions in the form of fringes. It seems to be without doubt that the edge is a part of the game. My question is, how to describe the edge in the sense of particle-wave duality?
 A: The edge provides a boundary condition that the EM field must satisfy.  The total EM field is "aware" of the boundary.  "Photons", being quantized excitations of the EM field, are created (emitted) and destroyed (hit a screen) only where the EM field exists.  If you are trying to think of photons as particles, forget it.  You'll end up with all sorts of questions that can't be answered.
Addendum, as requested in comments
The question was: 

Is there an influence between the edge (may be better the surface electrons of the edge) and the photon? If yes, how to describe the common field?

Yes there is. The electrons at the surface of the edge move, either a little (polarize) or a lot (currents near the surface). The combined microscopic field of the incident radiation, the electrons, and the ion cores of the solid is very complicated, and not at all smooth. However, one can make approximations that work extremely well by averaging all of the quantities over volumes that are large compared to the size of an atom, but small compared to the wavelength of the radiation. What one obtains is the "classical" theory of macroscopic fields and idealized conductors and dielectrics.
A: never try to apply both particle and wave nature of the photons at once. because in dual nature, photons 'sometimes' show wave nature (expecially in travelling ie. propogation) , and other times particle nature(when interacting with other particles).
not both 'simultaneously'. and in your question, due to wave nature ,diffraction is observed because,of smaller(comparable with wavelength of photons) sizeof sharp edges.
A: There is no doubt that the edge is a part of the game. The fringe intensity distribution or the fringe pattern is directly related to the edges. You don't need duality to explain this. You don't even need waves to explain this. Any fringe pattern can be calculated with basic math based on a particle (photon) theory alone. A single edge produces a unique fringe pattern with spacing's that are not equal and in fact diminish the farther away from the edge they get. Each one of these bright and dark fringes can be calculated easily just by using Pythagorean theorem.  All you need is the distance (L) from edge to screen and the wavelength of light. I clearly explain this in my paper "Single Edge Certainty" found on my website at the top of my page.  Starting on page seven I show how to derive any fringe pattern. 
