[en] Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched

[en] The observation results of the spatial spectrum harmonic height are given. It was experimentally shown that the limitation associated with the final aperture and the parabolic approximation in the Fresnel integral does not interfere with the confident observation of the high harmonics reaching the fortieth. (paper)

[en] A review article about phase retrieval problem in X-ray phase contrast imaging is presented. A simple theoretical framework of Fresnel diffraction imaging by X-rays is introduced. A review of the most important methods for phase retrieval in free-propagation-based X-ray imaging and a new method developed by our collaboration are shown. The proposed algorithm, Combined Mixed Approach (CMA) is based on a mixed transfer function and transport of intensity approach, and it requires at most an initial approximate estimate of the average phase shift introduced by the object as prior knowledge. The accuracy with which this initial estimate is known determines the convenience speed of algorithm. The new proposed algorithm is based on the retrieval of both the object phase and its complex conjugate. The results obtained by the algorithm on simulated data have shown that the obtained reconstructed phase maps are characterized by particularly low normalized mean square errors. The algorithm was also tested on noisy experimental phase contrast data, showing a good efficiency in recovering phase information and enhancing the visibility of details inside soft tissues.

[en] The diffraction character is redefined based on Fresnel number. This new definition is extended to focusing or diffusing optical path. The sign of the new diffraction character is defined for each optical element in a laser system. According to these definitions and extending, the effect of phase aberration on near-field modulation and the effect of linear diffraction on FM-to-AM are studied. The linear diffraction effect on high power laser facility can be evaluated by the combination of the new diffraction character and the energy fluence. (authors)

[en] It is shown experimentally that by placing a flat screen with an axial hole in a diffraction field formed by the first open Fresnel zone upon diffraction of a plane electromagnetic wave from a parallel screen with a hole of a larger diameter, one can observe diffraction multifocal focusing of radiation in the near-field zone of the first screen. The diffraction pattern in the near-field zone of the first screen in focal planes represents circular nonlocalised Fresnel bands with a bright narrow peak at the centre, whose intensity is 6 - 10 greater than that of the incident wave. (nonlinear optical phenomena)

No abstract available

[en] The loss permutations of Fabry - Perot resonator modes caused by the harmonic spatial perturbation of the radiation phase on one of the mirrors are studied numerically. The periods and amplitudes of perturbations are found at which the second or third mode in the eigenvalue modulus becomes the first mode. It is shown that in the case of perturbations with the period l₀, at which the Talbot length is equal to the double resonator length, the permutations are caused by an increase in the losses of the fundamental mode. It is also shown that the perturbation amplitudes with the period l₀, which equalise losses of the modes, depend linearly on the inverse Fresnel number F_-1. (resonators. modes)

[en] Expressions for the phase of a spherical wave in the near, middle, and far zones of observation are obtained. It is proved that in the Fresnel approximation a spherical wave is approximated by a paraboloidal wave, which, in turn, is approximated by a plane wave in the Fraunhofer approximation. Based on this, the problem of describing a wave field generated by a system of many coherently emitting point sources is considered. An expression is obtained for the intensity distribution in the interference problem for the near field approximation. It is shown that the distribution of intensity maxima is determined by solving a cubic equation, which, in the Fresnel approximation, transforms into a linear equation expressing the classical result on a uniform distribution of intensity maxima

[en] Using the conventional Young's experiment with two pinholes, we observe the shift effect of the Fresnel's phase on the interference patterns, by measuring its intensity on the optical axis. It allows us to propose a criterion for distinguishing between Fraunhofer and Fresnel diffraction. Indeed, in the Fraunhofer domain the Young's patterns will be centered on the optical axis. As a consequence, only constructive interference will occur at this point. But in the Fresnel domain, the Young's patterns will be laterally shifted in such a way that constructive and destructive interference will occur alternatively on the optical axis, and the intensity of the diffraction pattern at this point will oscillate. Extended diffracting apertures can be analyzed as ensembles of Young's pairs of wavelet sources. From this point of view, the intensity distribution they produce on the detector plane results from the superposition of all their interference patterns. (author)

[en] In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from |φ> to F^†_r,s|φ>, except for variation within the family of dilations and translations. The Parseval's equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented. (general)