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In addition to the optical aberrations, the magnitude of the optical cells of detectors is one of the most important parameters, which restricts the resolution of detectors. Adaptive optic and the methods of reducing the aberrations are often used to increase the resolution of optical systems. In the best situation the image structures, which are larger than the magnitude of the cells, are detected and the finer structures are removed. In this paper, a new method for increasing the resolution of images is presented. In this method, the cells will scan the images by a piezoelectric crystal. The piezoelectric crystal moves the cells in n identical steps. In each step, cells move 1/n of the cell magnitude and the data are recorded. Finally, data are analyzed and the structure of images is reconstructed. In this method, the structure of images is n times finer than the cells magnitude.

Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative system. Here, as an application of this formalism, we consider a dissipative system of charged particles interacting with an external time dependent electric field. Such a system has been investigating by Buch and Denman, and two solutions with completely different structure have been obtained for Schr\"{o}dinger's equation in two different gauges. We demonstrate how both gauges lead to the same conductivity by generalizing the gauge transformations to the phase space and using the extended phase space technique., Comment: 6 pages

Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative systems. Here, as a further application of this formalism, we consider a dissipative system of charged particles interacting with an external time dependent electric field. Such a system has been investigated by Buch and Denman, and two distinct solutions with completely different structure have been obtained for Schr\"odinger's equation in two different gauges. However, by generalizing the gauge transformations to the phase space and using the extended phase space technique to study the same system, we demonstrate how both gauges lead to the same conductivity, suggesting the recovery of gauge invariance for this physical quantity within the extended phase space approach., Comment: 14 pages

A generalized quantum distribution function is introduced. The corresponding ordering rule for non-commuting operators is given in terms of a single parameter. The origin of this parameter is in the extended canonical transformations that guarantees the equivalence of different distribution functions obtained by assuming appropriate values for this parameter., Comment: 6 pages