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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 2 — Feb. 1, 2014
  • pp: 379–387

Self-similarity in radial Walsh filters and axial intensity distributions in the far-field diffraction pattern

P. Mukherjee and L. N. Hazra  »View Author Affiliations

JOSA A, Vol. 31, Issue 2, pp. 379-387 (2014)

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Pupil plane filtering by radial Walsh filters is a convenient technique for tailoring the axial intensity distribution near the focal plane of a rotationally symmetric imaging system. Radial Walsh filters, derived from radial Walsh functions, form a set of orthogonal phase filters that take on values either 0 or π phase, corresponding to +1 or 1 values of the radial Walsh functions over prespecified annular regions of the circular filter. Order of these filters is given by the number of zero-crossings, or equivalently phase transitions within the domain over which the set is defined. In general, radial Walsh filters are binary phase zone plates, each of them demonstrating distinct focusing characteristics. The set of radial Walsh filters can be classified into distinct groups, where the members of each group possess self-similar structures. Self-similarity can also be observed in the corresponding axial intensity distributions. These observations provide valuable clues in tackling the inverse problem of synthesis of phase filter in accordance with prespecified axial intensity distributions. This paper reports our observations on self-similarity in radial Walsh filters of various orders and corresponding axial intensity distributions.

© 2014 Optical Society of America

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(050.1970) Diffraction and gratings : Diffractive optics
(100.5090) Image processing : Phase-only filters

ToC Category:
Diffraction and Gratings

Original Manuscript: October 18, 2013
Manuscript Accepted: December 11, 2013
Published: January 23, 2014

P. Mukherjee and L. N. Hazra, "Self-similarity in radial Walsh filters and axial intensity distributions in the far-field diffraction pattern," J. Opt. Soc. Am. A 31, 379-387 (2014)

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