Methods are described for producing optical elements, such as grating and lenses, in light of reduced temporal or spatial coherence. The preferred interferometer for producing fringes in light of low coherence is one formed from diffraction gratings. Considerable more noise reduction is achieved.

We propose two kinds of the aplanatic micro grating lens; the double grating lens and the plano-concave grating lens. We show the analytical procedure for designing these lenses and present the numerical examples. The study has shown that the micro grating lenses proposed have the aplanatism.

Highly efficient and good quality blazed diffraction gratings are required to achieve low insertion losses of wavelength division multiplexer/demultiplexer in multichannel multiplex systems. This paper presents a method and describes the technology for fabrication of diffraction gratings on glass using an ion etching technique. In contrast to other methods, ion etching technique allows not only the fabrication of arbitrary blaze angles but also different blaze angles can be realized on a single glass sample. The process is low in cost, uses readily available materials and has mass production capability.

This paper reviews the present status of diffraction grating based wavelength division multiplexer/demultiplexers (WDM). A comparison is made of WDM's currently in commercial use with both monomode and multimode fibres. Devices are described ranging from an industrial system multiplexing and demultiplexing 49 channels to a 12-channel monomode demultiplexer. The discussion includes multi-multiplexers in which several multiplexers share a common optical element.

A theoretical optimization of the efficiency of gold echelette gratings on silicon substrate is achieved, in order to obtain wavelength demultiplexers with a high efficiency in the ranges 0.78 μm- 0.9 μm or 1.2 μm - 1.35 μm. The experimental results confirm the theoretical predictions.

Parametric and scaling equations for a generalized grating spectrometer configuration are presented; these equations specify noise equivalent radiance in terms of instrument optical design parameters. Optical design criteria are derived from these equations for a multi-channel IR grating spectrometer for use as an advanced atmospheric sounder.

Dual detectors, a servoed grating positioning system and a computer controlled wave-length calibration technique are incorporated into a unique optical waveguide spectrophotometer used for remote monitoring.

A spectrometer system, based on the Multi-Echelle Grating Arrangement (MEGA) (1) has been developed. Through series diffraction in an even number of echelle gratings, high dispersion and spectral resolutions are obtained. It can be shown (1) that with n gratings of width W, utilized in a MEGA-spectrometer of focal length f, the same resolution and dispersion is obtained as in a conventional spectrometer with a grating width nW and a focal length nf.

Diffraction gratings are known to exhibit anomalous behavior at certain critical wavelengths or incident angles. Previously reported 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. This paper reports experimental observations indicating a diffraction grating anomaly in the angular position of certain diffracted orders, which appears to violate the grating equation. Efforts to trace this behavior to experimental error failed and physical causes were sought. Experimental data for several grating profiles and measurement geometries are presented and compared to the results of an analysis of the effect of finite beam size upon the centroid location of diffraction grating orders.

A direct reading spectrometer utilizing two concave holographic gratings is able to analyze as many as 40 elements simultaneously over the spectral range 170-900nm. This paper provides a discussion of the basic concepts, problems, and solutions involved in spectrometer optimization and aberration corrected grating design.

Infrared gas monitoring instruments have mainly been constructed around various filter arrangements, some of which are suffering from spectral interferences due to large optical bandwidths and temperature sensitivity. It is the purpose of this paper to describe the use of concave, aberration corrected holographic gratings as wavelength selective elements in these applications in order to reduce interferences and gain higher wavelength stability. The wavelength range discussed is about 2-10 micron. An example of a novel two element gas monitor is presented.

A new optical ray-tracing program is presented and some applications discussed. A Monte-Carlo modelling of several types of sources is implemented, and in particular the Synchrotron Radiation source is modelled exactly. The program is written specifically for grazing optics, although gaussian optics can be treated as well. Diffraction from gratings, both ruled and holographic, is included as well as Bragg diffraction from crystals. The reflectivity of mirror surfaces and transmission of filters is treated exactly and locally, solving the Fresnel equations for each ray. The interactive nature of the program and its fast execution time allow the simulation of real-life situations quickly and efficiently. Applications to the Toroidal Grating Monochromator (TMG), Grating Crystal Monochromator (GCM), and Extended Range Grasshopper (ERG) are presented.

The concave grating provides both focusing and dispersion in one component, thus reducing the number of reflecting surfaces in a VUV spectroscope and thereby conserving radiation. Most concave grating spectroscopes use well known grating mountings, such as the Rowland circle, Wadsworth, Abney, etc. However, requirements imposed by spectroscopy in space and the use of synchrotron radiation have resulted in special types of mountings to accomodate the conditions peculiar to each of these two branches of research and that are not found in the usual laboratory radiation sources. Some of these special mountings are not new, having first been discovered three decades ago and since rediscovered.

Variable line spaced gratings have been reported with high diffraction efficiencies at EUV and soft Xray wavelengths. Their availability makes it possible to consider new designs of spectroscopes. A solar spectrograph design is presented, which uses a holographic grating to correct system aberrations and produce a flat image field, perpendicular to the principal ray, over an extended wavelength range.

An ion-etching technique for fabrication of X-ray and VUV gratings will be presented. A photoresist grating, made holographically, is bombarded by Ar-ions and the grating profile is transfered into the substrate. By using a theoretical formalism based on the Rayleigh theory the profile that gives the highest efficiency for a given mounting can be calculated. We will discuss how to design the photoresist grating and the etch process in order to obtain the optimal profile. Measured efficiency curves at λ=44 Å will be presented.

As part of an ongoing effort to develop sensitive, high resolution spectrographs for the EUV and Soft X-rays we have been performing laboratory evaluation of novel spectrograph designs. We will discuss the measured performance levels of three systems: 1) A "hybrid" grazing incidence echelle spectrograph; 2) a Radial-Groove Grating Spectrograph; and 3) An Objective Reflection Grating Spectrograph for X-ray Astronomy. These systems show the great potential that conical diffraction spectrographs hold for the future.

Recent work in the design of soft X-ray and extreme UV spectrographs has identified a new class of reflection gratings whose aberrations do not increase at grazing incidence. To achieve this characteristic, the groove spacings are varied in a continuous manner across a plano grating aperture. Ray traces of the concentric groove grating, the oriental fan grating and variations illustrate their potential for space astronomy and laboratory applications in the wavelength range of approximately λλ10-1000 Å. Both straight-groove and concentric-groove patterns have been successfully fabricated with varied line spacings through mechanical ruling techniques. A concave varied line-space grating has been measured to achieve 70% of its theoretical efficiency in the extreme UV. An interferometric method of fabrication is also discussed, in which the recording wavelength is scaled-up into the far UV or even visible region of the spectrum. This holographic grating is designated "Type V." Two interferometers capable of recording grating wavefront aberrations in the extreme UV and soft X-ray are proposed.

A grazing incidence monochromator to scan the 5 - 100 Å wavelength range of synchrotron radiation is designed by taking advantage of the focusing property of a varied-space plane grating ruled with a numerically controlled ruling engine. The plane grating monochromator uses only two plane surfaces for reflection optics so that high throughput in the soft x-ray region is expected.

In the photographic industry, two dimensional periodic arrays, or hole patterns, that have a periodicity on the order of one to several micrometers, can have many significant applications. One use of such an array is the regular positioning of photosensitive elements, including, for example, photographic emulsion grains, into film systems of exceptionally low noise. A method is described for producing the array patterns using the technique of multiple beam interferometry applied to the already well known techniques of holographic grating formation. In the first process a square hole pattern is formed using two sequential two beam interference exposures in a thick layer of positive photoresist. Upon development an array of hills and valleys is formed, with the valleys corresponding to the holes and occupying about half of the available surface area. In the second process a hexagonal close packed hole pattern (honeycomb array) is formed using a single simultaneous three-beam coherent exposure of the photoresist. In the third process a square close packed hole pattern (egg-crate array) is formed using a single simultaneous four-beam exposure. The second and third processes produce surface depressions in the photoresist layer that occupy practically all of the available surface area. Because the periodic arrays are required in large quantities, the patterns formed in photoresist must be replicated. A nickel master is made from the original photoresist by electroplating, and this master is then used to repeatedly emboss the pattern into long plastic sheets. A description is given of the special industrial requirements for making high quality embossed patterns in this way on a large scale.

This paper relates the performances of an interferometry based upon a bidimensional grating taken as a reference. This interferometry permits to position the X-Y stage of a wafer stepper with a resolution comparable with a laser interferometer. The principle and the performances of an X-Y table controlled by this interferometer are presented.

This paper describes a compact, high-resolution laser scale interferometer measuring only 40 x 68 x 28 mm, with a scale -- a holographically-produced diffraction grating --of pitch 0.83 μm and 108 mm long. A collimated vertical light beam from a diode laser is diffracted from the horizontal diffraction grating and split into two beams; the beams are reflected so that they impinge symmetrically on opposite sides of a half-silvered mirror which acts as both interferometer and optical phase shifter. Scale movement generates sinusoidal quadrature optical signals. A zero-crossing detector circuit generates four pulses per cycle (one pulse per 0.1 μm movement) from the quadrature outputs, and an A/D converter and microprocessor are used for precision analog interpolation and linearization. To normalize the quadrature optical signals (to eliminate the effects of light amplitude variation) ±√ ((sin)2 + (cos)2) --the square root of the sum of the squares of the quadrature signals -- is used as the A/D converter reference signal. Linearity of ±0.1 μm and 1 nm resolution were obtained.

Recent advances in high sensitivity moire interferometry are described. In-plane displacement fields are shown for very challenging problem areas: adhesive joints in tension and in bending; flexure of quasi-isotropic composite laminates; and fatigue cracks in aluminum. Reference gratings with 2400 lines/mm (60,960 ℓ/in.) were used, providing a sensitivity of 0.417 μm/fringe order (16.4 μin./fringe order). Excellent fringe contrast was obtained in all cases, even for gradients of 64 fringes/mm (1600 fringes/in.). A 4-beam optical system to produce two orthogonal virtual reference gratings was employed. The question of unknown relative displacements in two-body problems was answered by use of a soft bridge between the bodies to provide a continuous path for the fringe count.

A new technique is presented in this paper for gaging curvatures of industrial parts such as the panels of automobile bodies. This non-contact technique utilizes the projection of a grating upon the surface to be gaged. Implementation of the proposed technique is carried out with a digital image processor. Experimental results of applying the technique are presented.

In this paper we have studied the moire contour fringes of the skull and femur knee joint of Nycticebus coucany and obtained the following results: 1. The skull's value K is very useful for comparative study with the different kinds of Primate. 2. The moire contour fringes of the tibia facies of knee joint is convex on one side while the other side is concave. 3. At the same condition the grade of the first moire contour fringe of connection on the femur knee joint between the two condyles and its angle β are smaller than Hylobates concolor leucongeuys. This study is significant, because: 1. The evolution of skull may be related with the increased value K. 2. The moire contour fringes of the Nycticebus coucany's tibia and femur knee joint have lower range of activity. 3. From the moire contour fringes of knee, the Nycticebus coucany and. Hylobates concolor leucongeuys are of one kind. But the moire contour Nycticebus of tibia is different form.

In the resonance domain (i.e. when the grating spacing d and the wavelength λ are of the same order of magnitude), the efficiencies of gratings can be determined from Maxwell's equations using integral or differential methods provided that the groove deep h is not too large (h/d is less than 0.5 for most of the gratings used in spectroscopy). However, for both practical applications (Z.O.D. systems, color separation, selective absorbers) and theoretical purposes, there is a need for the study of very deep gratings (h/d >> 1). This is why a new method has been proposed by an australian research group for the theoretical study of deep and very deep lamellar (or even multistep lamellar) gratings. The australian authors (A.A.) reported that their method works as well for dielectric as for lossy dielectric or metallic gratings.

Due to various recent technological developments in the fields of synchrotron radiation and microfabrication technology, the field of soft x-ray optics is experiencing a vital re-growth in several associated areas. The topic of this paper will be specifically the area of transmission diffraction systems, relevant examples of which include transmission gratings and zone plates - two devices that have been fabricated as free-standing ultrafine structures and tested by various experimenters in the soft x-ray range in recent years. In this paper we will describe a general design procedure for such systems which is guaranteed to generate the optimum diffraction structure geometries for arbitrarily specified systems composed of materials of arbitrary indices of refraction n. The systemic approach we employ first identifies a desired system function which is formally a functional of the diffraction system geometry, and then variationally derives the optimum geometries that maximize it. Two important system transfer functions on which the specific treatments in this paper are based are and I(1)/IIN and I(1)/IOUT the through-put and output diffraction efficiences, where I(1) is the total power diffracted into the first order, and IIN and IOUT are the total input and output powers impinging on the system. The results will be seen to unify all previously disclosed results in the area of zone plate theory, and will provide a sound basis on which to implement current experimental/developmental programs concerned either with fabricating more exotic diffraction structures or with maximizing or minimizing other classes of system functions in the soft x-ray range.

Many different formalisms treating diffraction efficiency of gratings have been developed. They are mainly designed to treat the problem in the 'resonance region', wavelength-to-period ratio approximately 1. The low value of this ratio for gratings in the X-ray region might give the impression that scalar diffraction theory would be able to predict grating efficiencies with a good agreement with experimentally measured values. However, this is not the case. The reason for this is the poor normal reflectivity of all materials in the X-ray region which makes it necessary to use grazing incidence mountings. Although polarization effects become less important as the angle of incidence tends towards grazing incidence, scalar theory does not give correct results for large angles of incidence. The performance of different theories: integral formalism, differential formalism, Rayleigh theory and the Beckmann theory, in the soft X-ray region will be presented. Both theoretical and computational aspects will be treated. Mainly, gratings having a sinusoidal profile are studied, but results for lamellar and echelette gratings will also be discussed.

Surface plasmon scattering from 4 holographic and 5 ruled gratings, illuminated with a 458nm laser beam was recorded on photographic paper in a cylindrical configuration. Elementary plasmon theory is reviewed and compared with the experimental recordings. Significant differences in behavior are noted between gratings of different modulations, although the basic patterns conform closely to theory.

In infrared technology, most of transmission gratings are used in the resonance domain (their spacing is of the same order that the wavelength of the incident light). Under such circumstances, the polarization takes a prominent part in the determination of the efficiencies. We have to take into account the vectorial character of light and therefore we must abandon the scalar theories of Optics to use electromagnetic theories derived from Maxwell equations. In other words, there is a need for efficient numerical techniques capable of solving rigorously the problem of perfectly conducting wire gratings. The approximate methods proposed by Marcuwitz in the Waveguide Handbook (Mac Graw Hill, New York, 1951) seem now unable to answer all the questions the experimenters asked for. In this paper we report on two completely different methods called H.M. (Hamiltonian method) and B.F.M. (Bessel function method) that we have recently implemented on a IBM 3081 computer.

A scalar grating efficiency model is developed primarily for use with Echelle gratings when the incident beam does not directly illuminate the antiblaze facet. Relative field intensities are calculated as the square of the vector sum of the direct diffraction field from the blaze facet and the reflected diffraction field from the antiblaze facet. Relative grating efficiency is the ratio of the relative intensity in the desired order to the summation of the relative intensities in all possible orders. Calculated efficiencies are compared with measured efficiencies for Echelle gratings.

Absorption of 633-nm photons in silver-coated diffraction gratings was studied by a photoacoustic method. The measurements were made as a function of the ruling orientation relative to the plane of photon incidence, and special attention was paid to plasmon resonance absorption in conical diffraction geometries. The results obtained were compared with predictions from perturbation theory.

A new theory to study the behavior of a grating ruled on a Kerr nonlinear medium and lighted by a high energy laser is presented. It is shown that the use of a suitable electromagnetic resonance, namely the guided wave resonance which can be supported by a dielectric coated grating or a corrugated waveguide, can lead to a very high enhancement of the local field and of he, nonlinearities of the medium. Under such conditions, the new nonlinear electromagnetic theory we have developed shows that, in a particular range of incidence, such a device has two possible values for its zero order (reflected) efficiency and determines the critical incident power to achieve bistability. The interest of such a bistable component is its low switching time and threshold. The grating coupler component has, contrary to the prism coupler device, the advantage of its planar geometry.

In 1977, we published two papers on the diffraction of electromagnetic waves at a locally deformed flat boundary surface and at a locally deformed plane wave-guide. Since this time, an important theoretical and numerical study of locally deformed stratified media has been carried out in our lab. This study has been summarized three years ago in the J.O.S.A. and it has been presented last year as a thesis dissertation. But both the J.O.S.A. paper and the thesis are difficult to read for non specialists because the involved mathematics are rather subtle and, at least, tedious for experimenters. In other words, an important work has been done, which seems to be unknown to most of "practical people". We thought that a SPIE meeting is a good opportunity to cure this regrettable situation. A computer program is now available which probably might be very useful for those working on rough dielectric surfaces and on guided wave devices with corrugated boundaries. We would like to present to engineers the possibilities and the limits of this big computer code called hereafter Program (P)

A theoretical and experimental study of the diffraction of an electromagnetic wave by a plane metallic crossed grating of hemispherical cavities is presented here. The cavities with radius R are periodically hollowed along two perpendicular directions x'x and z'z; the periods are A and B respectively. This crossed grating is illuminated at arbitrary incidence by a linearly polarized harmonic plane wave with wavelength λ. To solve this problem theoretically we use a modal method. Within the cavities the field is expanded in terms of spherical wave functions and above the grating surface the total field is written as the sum of the incident field and of the diffracted one (which is expressed as a Rayleigh expansion). Two types of boundary conditions are then considered. Firstly, on the metallic surface the tangential components of the electric field cancel. Secondly, on the plane circular surface limiting the hemispherical cavity from the free-space the fields on both sides are matched. Thus, we obtain a set of algebraic equations which are then resolved by means of a least squares method. The numerical results concern the particular case of normal incidence which leads to simpler calculus. We show that the efficiency in the (0,0) order (noted ε(0,0)) is widely dependent on the ratio R/λ and with appropriate values of R/λ and A/λ very low values of ε(0,0) can be obtained. An experimental study is carried out in the microwave range (λ ≈ 8.6 mm) with two metallic crossed gratings having the same periods A E B = 13 mm and radii R1 = 4 mm and R2 = 6 mm. The experiments concern the variations of ε(0,0) versus the angle of incidence and the two cases of polarization (T.E. and T.M.) are investigated.

An exact method of analyzing the dielectric gratings with rectangular grooves is presented. The most common of rigorous approaches are the expansion-methods such as coupled-wave approaches and modal approaches, which expand the fields in terms of space harmonics based on the Floquet's theorem. However, these methods are not rigorous in the strict sence for the numerical analysis of dielectric gratings with rectangular grooves, since in the case of rectangular shapes the Fourier series sometimes fails to converge with the increase of the number of order in the expansion. In this paper, a rigorous numerical method for rectangular-groove gratings is presented by using modal expansion in terms of modal functions consisting of the Bloch waves inside the periodic stratified media. The convergence of the solutions in this method is very rapid with the increase of the truncation size retained in the calculation, moreover the accuracy of the solutions can be checked by the energy-conservation and the square-errors of the electromagnetic fields on the boundaries. The scattering problems for both E-mode and H-mode polarizations are treated.