diffraction

Modeling extensive air showers and obtaining high-energy cosmic rays' origin information depends on the description of hadronic interactions (in the energy range of LHC collisions and more). Diffraction events in hadronic interactions are expected to be well-effective in observables of extensive air showers and affect shower characteristics profile since it provides a different way of transferring energy to the atmosphere. In particular, in this research, the maximum depth and the maximum number of secondary particles of extensive air showers with diffractive events have been measured. The results obtained from this article, predicts slower shower distribution, an increase in the maximum depth and a decrease in the maximum number of particles in the presence of diffractive interactions.

- In this paper, we introduce a novel diffraction element for generating any desired arrays of the vortex and perfect vortex beam. The method is based on combining radially phase shifted spiral zone plate with different gratings. We show that the element has a great potential in generating a variety of arrays with desired vortex ring radius and topological charges. We can assemble various vortex and perfect vortex beams not only in a lattice array but also in a tilted lattice or circular arrays. Reported vortex arrays are in the group of vortices having the same topological charge p so the total topological charge of MP which M the number of elements. The experimental results are in good agreement with the simulation predictions.

In this paper, we report on the design and fabrication of a low-cost phase shifter for application in phase shifting interferometry. Phase shifting interferometry is a powerful method for surface characterization. It uses interference data recorded during a series of predetermined phase shifts to recover the induced phase by the object surface. These controlled phase shifts are typically performed by putting a piezo-electric ceramic behind one of interferometer mirrors. Applying the controlled voltage to this ceramic provides the desired phase shifts. The piezo-electric positioners are very expensive. Phase shifting interferometry has different algorithms. One of the most effective algorithms is the four step phase shifting interferometry. In this algorithm, four interferograms are taken; then the unknown phase term due to surface is extracted by combining these interferograms. Here, we have proposed a low-cost alternative for piezo-electric positioners. Firstly, using the Fresnel diffraction from the phase step, we have measured etch rate of glass by HF acid. Then, a phase step with a quarter wavelength phase shift has been fabricated on a glass plate. The step height has been measured using Fresnel diffraction (phase step diffractometer) and interferometry. Then a stepwise structure has been fabricated on glass, providing phase shifts needed in the four step phase shifting interferometry.

X-ray diffraction is a very practical and useful method for characterizing crystals, viruses, including influenza viruses, microscopic particles in biological sciences etc. So, X-ray diffraction is simulated and analyzed in the paper. The calculations are performed using the Green's function by written FORTRAN codes. Also, atoms in a crystal are proposed to be the same as circular apertures and diffraction patterns of square and triangular arrays are studied. In this approach the apertures represent the core of the crystal atoms, and the X-ray diffraction pattern is simulated by passing electromagnetic waves from these apertures. The results show that the general diffraction patterns are independent of the number of crystal atoms, so they can be used as a fingerprint to examine a variety of crystal structures. Also, the increase in the atoms sizes (atomic radius) leads to raise the intensity of the diffraction pattern. The increase in the crystal lattice constant reduces divergence and higher order diffraction patterns appear.