0000000000082747
AUTHOR
Tomasz Cichocki
Binarization of a super-resolving graytone pupil filter by digital halftoning
— Six digital-halftoning procedures, including one algorithm proposed by us, are compared to determine which one is best suited to binarization of a parabolic super-resolving pupil filter. The procedures we deal with include iterative, error-diffusion, error-convergence, and 1-pixel algorithms. We carry out a numerically simulated experiment in which an object that consists of either one point source or two coherent point sources is imaged in a 4f imaging system with either a continuous super-resolving parabolic filter or one of its six different binary versions. The performance of binary filters is examined in terms of two parameters: the resemblance of their amplitude impulse response (AI…
Annular binary filters for controlling the axial behaviour of optical systems
The one-dimensional (1D) version of the iterative Fourier transform algorithm (IFTA) and a modified error diffusion algorithm are proposed for binarizing rotationally symmetric pupil filters designed to shape the axial impulse response of optical system. The resulting binary masks consist of a set of transparent and opaque annular zones of equal area or equal width. A numerical experiment in which we examine the performance of the binarization methods is carried out. In this experiment the resemblance between the axial diffractive behaviour of the binary version of an axially superresolving pupil filter, and that of the original continuous-tone filter is evaluated. It is shown that the perf…
One-dimensional iterative algorithm for three-dimensional point-spread function engineering.
We present a new method with which to binarize pupil filters designed to control the three-dimensional irradiance distribution in the focal volume of an optical system. The method is based on a one-dimensional iterative algorithm, which results in efficient use of computation time and in simple, easy to fabricate binary filters. An acceptable degree of resemblance between the point-spread function of the annular binary filter and that of its gray-tone counterpart is obtained.
Sampling expansions for three-dimensional light amplitude distribution in the vicinity of an axial image point: comment.
Landgrave and Berriel-Valdos presented axial and radial sampling expansions for three-dimensional light amplitude distribution around the Gaussian focal point. [J. Opt. Soc. Am. A 14, 2962 (1997)]. The expansions were obtained under the assumption that the pupil function was rotationally symmetric. We present a new derivation of the axial expansion that does not make use of arbitrary formal assumptions used by Landgrave and Berriel-Valdos and eliminates some faults of the derivation given by Arsenault and Boivin, who published this expansion in 1967 [J. Appl. Phys. 38, 3988 (1967)]. We also discuss generalizations of the axial expansion to the case of pupils that exhibit no symmetry with re…
One-dimensional error-diffusion technique adapted for binarization of rotationally symmetric pupil filters
Abstract Two novel algorithms for the binarization of continuous rotationally symmetric real and positive pupil filters are presented. Both algorithms are based on the one-dimensional error diffusion concept. In our numerical experiment an original gray-tone apodizer is substituted by a set of transparent and opaque concentric annular zones. Depending on the algorithm the resulting binary mask consists of either equal width or equal area zones. The diffractive behavior of binary filters is evaluated. It is shown that the filter with equal width zones gives Fraunhofer diffraction pattern more similar to that of the original gray-tone apodizer than that with equal area zones, assuming in both…