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

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.

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.

Extra-axial stigmatic imagery with a thick planar kinoform.

A kinoform lens and its substrate are usually treated as two distinct components with a common interface. Thick kinoform lenses treat the relief profile and the substrate as an integrated component. An analytical approach for the design of higher-order thick kinoform lenses for stigmatic imaging between extra-axial conjugate points is presented. An illustrative example is given.

Curved kinoform lenses for stigmatic imaging of axial objects.

We present a generalized approach for determination of the location of full-period zones and the surface-relief profile of a spherically curved kinoform lens that provides stigmatic imaging between any two prespecified points on axis. A common framework is provided for the treatment of both converging and diverging kinoform lenses. Some illustrative numerical results demonstrate the convenient amenability of our method in practical applications.

Numerical evaluation of a class of integrals for image assessment.

The calculation of image assessment critiera, e.g., the Strehl ratio, the point spread function, or the optical transfer function, involves the evaluation of an itegral where the integrand is highly oscillatory over a large range of integration. Prefaced with a brief description of the well-known numerical quadrature methods apopted for the purpose, this paper presents a new quadrature technique that obviates the need for knowledge of derivatives of the argument of the exponential integrand. Some illustrative numerical results are presented.