Axial resolution performances of Gaussian beam with pupil filters

Pupil filters designed to overcome the resolution limits imposed by diffraction imaging systems have been the aim of many research efforts. A great number of previous efforts have been chiefly focused on improving the resolving capacity of imaging systems such as optical pickups and laser printers in the transverse direction while a low number of publications have been addressed to achieve super-resolution along the axial direction. However, when dealing with imaging systems in which optical sectioning is important there is of great interest to improve the axial resolution. The high depth-discrimination feature allows the formation of three-dimensional images by sectioning only a thin slice of a sample at a time. Presently, most super-resolution performances based on the pupil filters are analyzed by the assumpran that the incident beam of the imaging system is Uniform amplitude beam. However, from a practical perspective, the incident beam from a laser is a Gaussian beam with a Gaussian field amplitude distribution. The focusing lens cannot be overfilled and the spot size will tend to be larger. Therefore, it is necessary to research the axial resolution performances of Gaussian beam. In this work, we assume the incident beam of the imaging system is Gaussian beam and theoretically investigate the axial intensity point spread function (PSF) of Gaussian beam with the specified pupil filters. As our previous work, several parameters such as the Strehl ratio, the axial super-resolving gain and side-lobe to peak intensity ratio are introduced to describe the super-resolution performance. The Strehl ratio S is a relevant parameter for analyzing image quality and is defined as the ratio of the intensity at the focal point to that corresponding to an unobstructed pupil. The axial super-resolving gain G_A gives a measure of the super-resolution performance in the axial direction and is defined as the ratio between the first minimum of the super-resolution pattern- - and the first minimum of the clear pupil pattern. In a particular direction, a filter is super-resolving when the corresponding gain is greater than unity and it is an apodizer when the corresponding gain is lower than unity. The side-lobe to peak intensity ratio M is to evaluate the impact of the side-lobe on the central-lobe and is given by the maximum intensity of side-lobes to the intensity of central peak.