Axicons application in imaging systems for increasing depth of focus

The analysis of imaging abilities of axially symmetric optical elements within the limits of paraxial approach is executed. It is shown, that the optical elements which are not having square law dependence on radius, cannot form the precise image in one plane as it is doing by a lens, compensating propagation in free space. However the one lens imaging system is characterized by very short depth of focus which can be effectively extended by an additional optical element, for example, an axicon. Also it is possible to improve quality of the image using of additional phase optical elements with other dependence on radius, including fractional (fracxicon). Inserting an axicon in an objective plane of imaging system allows to compensate a little negative action of the obstacles located on optical axis.