Surveys of The Previous Literatures

1.3.1 Tables of Previous Literatures

Year Publication Provenance

1986 z Annular apodizers for low sensitivity to defocus and to spherical aberration

Opt. Lett

1988 z Axial behavior of pupil-plane filters J. Opt. A- Pure Appl. Opt 1995 z Extended depth of field through wave-front coding Appl. Opt.

1998 z Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function,

Appl. Opt.

z High focal depth with a pure-phase apodizer Appl. Opt.

2001

z Electronic imaging using a logarithmic asphere Opt. Lett.

2002 z Phase-shifting apodizers for increasing focal depth Appl. Opt.

z Combined amplitude and phase filters for increased tolerance to spherical aberration

J. Modern Opt.

z Computational imaging with the logarithmic asphere J. Opt. A- Pure Appl. Opt z Extended depth of field using a logarithmic asphere J. Opt. A- Pure Appl. Opt 2003

z Phase pupil functions for reduction of defocus and spherical aberrations

Opt. Lett.

z Symmetry properties with pupil phase-filters Opt. Express 2004

z Phase plate to extend the depth of field of incoherent hybrid imaging systems

Appl. Opt.

Table 1.1 Almanac -- Previous Publications for the Topic of Phase Pupil Filters

Year Publication Provenance

1988 z Axial superresolution with phase-only pupil filters Opt. Comm.

z Diffractive superresolution elements J. Opt. A- Pure Appl. Opt 1997

z Fundamental limits of optical superresolution Opt. Lett.

2000 z Superresolution in far-field imaging Opt. Lett.

2001 z New approach to superresolution Opt. Eng.

z Superresolution in far-field imaging J. Opt. A- Pure Appl. Opt 2002

z Theories for the design of diffractive superresolution elements and limits of optical superresolution

J. Opt. A- Pure Appl. Opt

z Design of superresolving continuous phase filters Opt. Lett.

z Design of Three-Dimensional Superresolution Filters and Limits of Axial Optical Superresolution

Appl. Opt.

z Theories for the design of a hybrid refractive-diffractive superresolution lens with high numerical aperture

J. Opt. A- Pure Appl. Opt 2003

z Transverse or axial superresolution in a 4Pi-confocal microscope by phase-only filters

J. Opt. A- Pure Appl. Opt

z Comparison of superresolution effects with annular phase and amplitude filters

Appl. Opt.

z Design and comparison of amplitude-type and phase-only transverse super-resolving pupil filters

Opt. Comm.

z Simple expressions for performance parameters of complex filters, with applications to super-Gaussian phase filters

Opt. Lett.

z Superresolution in compensated telescopes Opt. Lett.

2004

z Three-dimensional control of the focal light intensity distribution by analytically designed phase masks

Opt. Comm.

z Design theories and performance limits of diffractive superresolution elements with the highest sidelobe suppressed

J. Opt. A- Pure Appl. Opt 2005

z Three-dimensional superresolution by three-zone complex pupil filters

J. Opt. A- Pure Appl. Opt

Table 1.2 Almanac -- Previous Publications for the Topic of Super-resolution

1.3.2 A Brief Summary of The Previous Literatures

z For the Topic of Phase Pupil Filters:

In 1986, J. Ojeda-Castaneta and P. Andres proposed some heuristic arguments for suggesting the use of annular apodizers with the purpose of increasing focal depth and decreasing the influence of spherical aberration. They showed that some annular apodizers can be expected to produce low sensitivity to defocus and to spherical aberration. Later on, in 1988, C. J. R. Sheppard and Z. S. Hegedus presented the relationship between the transverse and the on-axis behaviors of various pupil-plane filters. And expressions for general energy constraints associated with these filters were also derived. Then in the following years, several types of pupil filters, mainly based on amplitude modulation, were being proposed to help control the 3-D response of the optical system. But, because of the intensity loss issue, major works were soon being shifted to the design of phase-only filters. Several methods for obtaining phase-type pupil filters, providing optimization of the axial intensity distribution, and giving rise to an increase of the image focal depth, were proposed.

In 2003, Mezouari and Harvey presented a succinct way to design a phase filter with application of stationary phase approximation. By essentially developed a differential equation of wavefront error coefficients, it leads to the phase pupil function for the desired filter. And also in the same year, J. Campos, J. C. Escalera and M. J. Yzuel published their study of different pupil symmetries which would produce a predictable image behavior. They showed that different pupil-filters, satisfying certain symmetry conditions, could produce axial responses which were either identical or mirror reflected. Differences in the symmetry properties between

amplitude-only filters and phase-only filters had also been established.

z For the Topic of Superresolution:

Superresolution, being able to overcome the limits of resolution, has aroused considerable interest. The study of the fundamental limits imposed on the performance of the superresolution strategy has been given by Sales and Morris in 1997. Later on, several methods have been proposed to the design of superresolving pupil filters. For instance, the diffractive superresolution elements (DSEs) with binary and multiple-phase structures were proposed by Sales and Morris; the three-zone binary phase filters were reported by Wang and Gan; and the superresolving continuous smoothly varying phase-only filters, defined to describe the effect of general complex pupil functions, were proposed by Liu, and Sun. The comparison of the performance between those proposed pupil filters has also been studied. In 2003, Ding, Li and Zhou discussed and compared the super-resolving characters of the amplitude-type and phase-type of filters. Later on, Luo and Zhou reported a comparison of the characteristics of annular amplitude and phase filters.

They carefully analyzed he behavior of two-zone phase and amplitude filters.

Notice that the sidelobe effect is still one of the tough issues in the design of superresolving filters. Recently, Liu and Yan presented a theory which could be used to design a diffractive superresolution element (DSE) with the highest sidelobe suppressed.