Abstract
In a recent communication we reported the self-similarity in radial Walsh filters. The set of radial Walsh filters have been classified into distinct self-similar groups, where members of each group possess self-similar structures or phase sequences. It has been observed that, the axial intensity distributions in the farfield diffraction pattern of these self-similar radial Walsh filters are also self-similar. In this paper we report the self-similarity in the intensity distributions on a transverse plane in the farfield diffraction patterns of the self-similar radial Walsh filters.
Highlights
A self-similar object is exactly or approximately similar to a part of itself; that is, the whole has the same shape or structure as one or more of the parts
Derived from radial Walsh functions [2–4], radial Walsh filters form a set of orthogonal phase filters that take on values either 0 or π phase, corresponding to +1 or −1 value of the radial Walsh functions over the prespecified annular regions of the circular filter
It has been shown that the axial intensity distributions in the farfield diffraction pattern of a pupil with these self-similar groups of filters are self-similar [16]
Summary
A self-similar object is exactly or approximately similar to a part of itself; that is, the whole has the same shape or structure as one or more of the parts. Derived from radial Walsh functions [2–4], radial Walsh filters form a set of orthogonal phase filters that take on values either 0 or π phase, corresponding to +1 or −1 value of the radial Walsh functions over the prespecified annular regions of the circular filter They may be considered as binary zone plates [5, 6] and have wide range of applications [7–15]. It has been shown that the axial intensity distributions in the farfield diffraction pattern of a pupil with these self-similar groups of filters are self-similar [16]. It is noted that the transverse intensity distributions exhibited by the self-similar groups of radial Walsh filters are self-similar.
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