Vector diffraction theory can he formulated along lines completely analogous to scalar theory by expressing the diffracted fields in terms of the Hertz potentials. We show that the diffracted fields can be regarded as superpositions of elementary dipole or quadrupole fields, starting with the familiar Rayleigh formulas for solutions to the scalar Helmholtz equation. An angular spectrum of vector plane waves is also derived, and the connection with the superposition integrals is explained. Finally, the application of Kirchhoff-type boundary conditions to either the Hertz potential or its normal derivative in the aperture plane is investigated. Applying boundary conditions directly to the potential instead of its derivative makes it simpler to use scalar theory techniques to treat problems involving incident waves with nonuniform amplitude and phase distributions, and therefore yields the most useful solutions.

Much is said in the literature about Gaussian beams. However, there is little in terms of a quantitative comparison between the propagation of uniform and Gaussian beams. Even when results for both types of beams are given, they appear in a normalized form in such a way that some of the quantitative difference between them is lost. In this paper, we consider an aberration-free annular beam and investigate the effect of Gaussian amplitude across the aperture on the focal-plane irradiance and encircled-power distributions. We also consider the problem of aberration balancing and compare the effects of primary aberrations on the two types of beams.

Diffraction gratings are known to exhibit anomalous behavior at certain critical wavelengths or incident angles. These traditional anomalies manifest themselves as abrupt variations in diffracted order efficiency or grating absorption while their angular position remains unchanged as predicted by the grating equation. Experimental observations were recently reported which indicated a diffraction grating anomaly in the angular position of certain diffracted orders that appeared to violate the grating equation. Several exotic physical mechanisms have been suggested as possible causes of this intriguing behavior. In this paper we attempt to show that this angular grating anomaly is the straightforward result of finite beam size upon wide-angle diffraction phenomena as described by simple scalar diffraction theory.

A technique for calculating the equivalent mesh impedances for a doubly periodic mesh which may contain small discrete loads is demonstrated. The mesh is modeled by a two port network. One port is shunted across a transmission line that carries the incoming and outgoing waves. The discrete load is placed across the second port. The equivalent port impedances are calculated without approximation using the method of moments. This technique allows predictions to be made of the performance of a mesh with arbitrary load since the port impedances are load independent. It also allows the design of variable meshes in which the lumped load is adjusted externally.

The propagation of a Gaussian beam through an asymmetric optical system results in a generally or "twisted"" astigmatic beam whose elliptical spot rotates as it propagates in free space. A general mathematical form for this beam is derived by applying the angular spectrum approach to the paraxialized wave equation. This result is compared to those derived by other researchers and it is found that the beam can be equivalently represented by a set of paraxial rays traced about the central beam ray. The application of general Gaussian beam propagation to the analysis of non-Gaussian beam propagation in arbitrary optical systems is also discussed.

The GEMASIS is an automated device for general characterization of diffraction and surface scatter. Samples can be measured for out-of-plane as well as for in-plane incidence conditions. In-plane characterization includes angle-resolved measurements of scatter and diffraction orders. The device is described and typical data are shown.

Recent and continuing developments in laser positional measurement interferometers and computer control make it possible to rule high quality,linear diffraction gratings of variable spacing. One application of such gratings is for testing cylindrical optics. A natural progression from this was the construction an interferometrically controlled rotary ruling engine for the production of precision circular, reflection gratings which may be used for testing optics that have axial symmetry. The construction and operation of this engine will be described, along with earlier practical results with cylindrical and prototype circular gratings.

With the increasing number of optical systems for use in the near- and middle-infrared spectral regions, the demand for optical elements that exhibit predetermined spectral and polarizing characteristics has increased also. Although continuous thin films are capable of producing a wide variety of optical characteristics, the use of metal meshes adds another dimension to spectral and polarization selectivity. Metal meshes are essentially amplitude diffraction gratings whose periodicity is less than the wavelength of the incident radiation. As such, only a single propagating mode exists, all others being evanescent. Diffractive structures of this type have been shown to produce spectral and polarizing properties that depend on the geometry of the mesh. Microlithographic techniques were used to fabricate diffractive patterns of aluminum and gold, with minimum feature sizes less than 0.25 p,m for use as mesh filters with near and middle-infrared.

Ultrahigh-resolution gratings are produced in GaAs crystals by using two interfering beams to initiate localized chemical reactions at the solid/liquid interface. Optical gratings with periods between 0.1 and 1 }im are produced with controllable and reproducible optical properties. This maskless technique has potential applications in the fabrication of distributed feedback lasers. Futhermore, a variety of groove profiles are made under different etching conditions. A novel aspect of the direct processing is that the grating growth can be monitored in real time by observing the diffraction of the writing beams, thus allowing a precise control over the grating depth and groove profiles. In addition, because the gratings have a very high resolution, the process of grating fabrication becomes a method of studying the micrometer-scale physical processes which influence the grating structure and growth.

The use of gratings as optical elements is proving to be a powerful technique in the metrology of unusual optical surfaces such as cylindrical X-ray optics, cone-shaped optics for laser ring resonators, and highly aspherized conventional optics. However, the tremendous flexibility for the optical designer is obtained at the cost of unusually tight tolerances in the areas of grating fabrication, interferometer alignment, and interferometer environment. In this paper, a review is given of the use of gratings in optical metrology, followed by derivations and discussion of these various tight tolerances.

A classically ruled diffraction grating consists of grooves which are equidistant, straight and parallel. Conversely the so-called "holographic" grating ( formed by the interfering waves of coherent visible light ) , although severely constrained by the recording wavelength and recording geometry, has grooves which are typically neither equidistant, straight nor parallel. In contrast a varied line-space (VLS) grating, in common nomenclature, is a design in which the groove positions are relatively unconstrained yet possess sufficient symmetry to permit mechanical ruling. Such seemingly exotic gratings are no longer only a theoretical curiosity, but have been ruled and used in a wide variety of applications. These include 1) aberration-corrected normal incidence concave gratings for Seya-Namioka monochromators and optical demultiplexers, 2) flat-field grazing incidence concave gratings for plasma diagnostics, 3) aberration-corrected grazing incidence plane gratings for space-borne spectrometers, 4) focusing grazing incidence plane grating for synchrotron radiation monochromators, and 5) wavefront generators for visible interferometry of optical surfaces (particularly aspheres). Future prospects of VLS gratings as dispersing elements, wavefront correctors and beamsplitters appear promising. I discuss the history of VLS gratings, their present applications and their potential in the future.

A 3-D holographic miniprojector on the basis of holographic optical element screens using for integrated circuits assembly and quality control is described. This is a compact, professional projection-type microscope using hybrid technique combing the advantages of both stereoscopy and holography. The optical principle of this miniprojector, recording scheme of holographic diffusing screen, improvement of chromatic dispersion of screen and relative parameters of projection system are discussed.

For points on and near the optical axis, asymptotic solutions to the Rayleigh-Sommerfeld diffraction integral are possible for annular apertures illuminated by plane waves of uniform intensity distribution containing rotationally symmetric Seidel aberrations (defocus and spherical aberration). Computer studies of these cases show excellent agreement with experiment. The amount of defocus and spherical aberration can be determined from shifts in positions of on-axis intensity extrema. An empirical study of the non-rotationally symmetric Seidel aberration astigmatism reveals a predictable change in the diffraction pattern allowing for the verification of the aberration to within .05 wavelengths.