Extended depth of focus as a process of pupil manipulation

Abstract

During the last few years, the understanding of pupil plane manipulation capabilities to achieve an enhanced image formation process and its theoretical limitations becomes more and more important. Particularly the increased potential of computer calculations and digital signal detection makes it possible to simulate this kind of manipulations very fast and efficient. At the same time there is the opportunity to change the optical system such, that a digital reconstruction of the image gives a higher amount of information. An analysis of the optical transfer function as an important parameter of imaging quality with special interest in extended depth of focus is presented. The performance of different pupil plane masks is illustrated in comparison with standard optical systems. This means the basic features like depth of focus, resolution and contrast were derived and the limitations are shown. The mathematical principle of extended depth of focus with pupil manipulation is described and demonstrated with exemplary calculations. Furthermore, the relation between a given optical transfer function and the matching pupil function is shown. A robust and iterative algorithm is presented to calculate a pupil mask for a desired optical transfer function.