A. Guha

Bio: A. Guha is an academic researcher from University of Calcutta. The author has contributed to research in topics: Orthogonal functions & Finite set. The author has an hindex of 1, co-authored 1 publications receiving 22 citations.

Far-field diffraction properties of radial Walsh filters

Abstract: Radial Walsh functions form a closed set of orthogonal functions over a given finite interval, each function taking merely one constant value (either +1 or −1) in each of a finite number of subintervals into which the entire interval is divided. This set provides a remarkable set of orthogonal radial filters for the pupil of an imaging system. We report analytical expressions for members of the set and their Hankel transforms of order zero. Far-field diffraction characteristics, namely, the far-field amplitude distribution and the optical transfer functions, are presented for the first eight members of the set.

Tuning field depth at high resolution by pupil engineering

Abstract: We present a simple comprehensive treatment on the use of free-form optical elements, and of nonuniform optical windows, either for increasing focal depth [by regulating the width of the axial point spread function (PSF)] or for tuning the depth of field [by controlling the influence of focus error on the modulation transfer function (MTF)]. We employ the rising notation of pupil engineering, which incorporates techniques for controlling the spread of the axial PSF, as well as methods for governing the impact of focus errors on the MTF. Our discussion also includes the use of vortex lenses for designing nonconventional optical systems.

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

Abstract: 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.

Influence of nonuniform amplitude on the optical transfer function.

Abstract: The purpose of this work was to develop formulas and accurate numerical techniques for computation of the optical transfer function (OTF) in the general case of unrestricted aberration and with the following different forms of nonuniform real amplitude: (1) when the real amplitude is described by a polynomial, (2) a Gaussian distribution of real amplitude, and (3) a pupil with a central obstruction. The resulting computer program has been carefully tested and used to study the influence of nonuniform amplitude on the OTF in typical cases, for which detailed numerical results are given.

Far-field Diffraction Properties of Annular Walsh Filters

Abstract: Annular Walsh filters are derived from the rotationally symmetric annular Walsh functions which form a complete set of orthogonal functions that take on values either