Walsh filters for tailoring of resolution in microscopic imaging

Walsh functions form a complete set of normal orthogonal functions that take on values either +1 or -1 over a prespecified domain. Corresponding filters can be synthesized as phase filters that take on values either 0 or pi phase. This paper presents different types of Walsh functions in one and two dimensions to demonstrate that a large class of pupil filters can be synthesized from them to cater to the various needs of diffraction pattern for tailoring transverse and/or axial resolution in microscopic applications. Illustrative numerical results are presented.