After presenting various grating problems which arise nowadays in modern physics, a review of the basic ideas of the main electromagnetic theories of gratings is given, pointing out their specific domains of validity, advantages and shortcomings. A user guide is given to help researchers and engineers to select the most appropriate theory to resolve their specific grating problem.

Soft x-ray emission spectroscopy is a well established technique which has seen increased interest in recent years due to the development of high brilliance synchronization radiation facilities. Emission spectra are obtained when a hole is created by impinging photons and an electron from the valence band decays into the core hole emitting its excess energy radiatively. The fluorescence yield is intrinsically low in the range of soft x-rays, usually less than about 0.5%, since most of the incoming photon energy is lost to radiationless decay channels like Coster Kronig and Auger processes. Emission is over all space, but only a restricted solid angle can be collected and this further reduces the efficiency of the instrumentation. Moreover, the emitted photons must be energy selected, and this involves the use of soft x-ray monochromators with good resolving power. In this work, we report the design and comparison of two different spectrometers both based on variable line space (VLS) gratings. The main constraints are the requirements of a compact instrument, good resolving power, high efficiency, and high angular acceptance. In the first case, a solution with two spherical gratings with variable groove density were utilized. The grating is fixed and the photon detector scans the energy by means of a small translation to cover all the energies from 40 to 1000 eV. In the second case the detector is fixed and a plane grating, with variable line density, moves parallel to its surface. By coupling the diffractive and focusing properties of a VLS plane grating with a single movement one can always focus the radiation at the selected energy on a fixed detector. This grating is also always in the blaze condition, thus one has very good efficiency and good resolving power in the whole range of energy of interest.

Variable line space (VLS) diffraction gratings present interesting solutions to design high resolution monochromators for synchrotrons. The problem is to be able to record holographically the desired grooves distribution in order to take advantage of the holographic recording and ion etching process: low stray light, absence of ghosts and second order reduction. We will review the method of calculation of VLS diffraction gratings recorded holographically by using spherical and aspherical laser wavefronts. Then the manufacture of these gratings (accuracy of recording and ion etching process) will be described. We will give an example. And finally, the theory and the accuracy of a checking method will be presented.

We have developed a LURE a code to predict the efficiency of gratings. The code is based on differential theory and uses a simplified R-matrix propagation algorithm to obtain numerical stability on the whole range from visible to hard x-rays. Experimental and numerical studies have been performed on some test cases at a synchrotron source. A good agreement between numerical prediction and measurements has been found. The code is a rigorous application of electromagnetic theory and gives exact results as long as accurate optical constants can be attributed to grating materials. Such rigorous calculations provide an important tool for the optical engineering of modern synchrotron monochromator gratings. We give an example of application of this code to the engineering of a modern beam line and for the optimization of harmonic rejection.

A new type of translation-rotation encoder using diffraction gratings is proposed and its advantages upon previously developed ones are pointed out. It makes use of two transparent dielectric gratings with the same groove spacing, each of them being joint to each of the moving parts whose relative displacement has to be detected and measured. The first grating is lighted under -1 order Littrow incidence, and the wavelength-to-groove spacing ratio is chosen in such a way that only 2 diffracted orders propagate both in reflection and transmission. The two transmitted orders fall on the second grating, and it is shown that they produce interference fringes with highest possible visibility in a large range of groove profile parameters and other experimental conditions. Thus this mounting allows producing high accuracy encoders by using cheap photoresist or plastic gratings, which opens the way to industrial applications in high-precision mechanics, information processing, etc.

The fabrication process of blazed diffraction gratings and grisms utilizing anisotropic etching of single crystal silicon is described. Grating patterns are formed either holographically or mechanically on the resist film coated onto the dioxide surface of the silicon substrate. Triangularly shaped grating grooves are formed by etching the substrate using KOH based solvent. The grooves are with the specific orientation of the single crystal so that accurate and ultra-smooth groove facets can be obtained especially for infrared gratings and shallow groove grisms.

The conceptual framework for the characterization of systems of gratings and mirrors is reviewed, based on the methods of Lie optics, which represents each optical element by a mapping that transforms a ray in object space into a ray in image space. The mathematical tools of Lie optics are presented, the complete transformation for a single grating is given in terms of its elementary transformations, and imaging equations are derived using this transformation that correspond with well-known expressions for aberration coefficients. Lie algebraic techniques have certain significant advantages over the more commonly used wavefront aberration theory, which will become apparent when the imaging properties of multi-element systems are considered in Part II of this work.

In the context of the NASA Far Ultraviolet Spectroscopic Explorer (FUSE) mission, the Laboratoire d'Astronomie Spatiale (LAS) has been in charge of designing and testing the six flight gratings of the spectrograph. The FUSE experiment is dedicated to the spectroscopic study of the 900 - 1200 angstroms range with a 100 cm² equivalent surface and a resolution power of 30,000. These requirements yielded to especially challenging gratings with both very high groove density (6000 g/mm) and large size (300*300 mm²). The aberrations have been corrected using a new recording geometry proposed by LAS. After recalling this new recording setup, we will describe the optical performances (resolution, efficiency, stray light) of the six flight gratings manufactured by Jobin-Yvon company. In particular, we will show that the groove efficiency has reached a value of 38% at 1048 angstroms that is 80% of the theoretical value. Efficiency improvement is still possible using ion- etching technique to modify the groove profile.

The imaging properties of varied line-space diffraction gratings are presented for cases in which the underlying grating substrate is bent to form a weak cylinder. Bending the flat grating substrate affects its imaging in two ways: it provides focal properties due to the non-zero substrate curvature, and it changes the local groove spacing across the surface of the grating. Aberration coefficients for such a grating are derived, and a numerical example is presented.

The general theory of diffraction grating was developed in 1974. Although this theory is in wide use, not all the problems associated with the theory have been resolved. We began our work from the particular solution of the problem, which allows us to compensate four aberrations instead of three. For recording of the grating with the compensation of the four aberrations it is necessary to use beams from opposite sides of the blanks. One of the recording beams, going from the back side of the grating blank should be convergent. To form this convergent beam some objective should be used. This objective should not introduce additional aberrations into the system. We suggest to produce objective holographically, like another diffraction grating, made in traditional mounting of recording. This two-steps recording system has six free parameters instead of three in the traditional one. Theoretically it allows to compensate more than four aberrations. Another advantage of this method of recording is in improving of the energetic characteristics since grating have the triangular form of the grooves.

The present paper deals with an investigation of the image formation properties of As₄₀Se₆₀ thin layers and their application for the production of diffractive optical elements. Thin layers (0.5 - 5 micrometers ) were deposited by the vacuum thermal evaporation and exposed by a Xe-lamp or annealed at 150 degree(s)C. The spectral dependence of the index of refraction, n, of variously treated samples was obtained using Swanepoel method and the single-oscillator model parameters ((epsilon) , E_o, E_d) were estimated. Photo- and thermally induced changes of n, (epsilon) , E_o and E_d induced by exposure or by annealing are discussed on the basis of photo- and thermally induced structural changes, which were directly confirmed by Raman spectroscopy. Such photostructural changes provide good etching selectivity of unexposed and exposed parts of As₄₀Se₆₀ layers in amine based solutions. This provides possibility for the fabrication of surface-relief patterns. The sensitivity of As₄₀Se₆₀ layers has been found to be approximately 10 cm²/J. Holographic diffraction gratings were produced by the Ar and/or HeNe laser exposure. Diffraction efficiency values of holographic gratings achieved approximately 90% for the polarized light. The results obtained show that As₄₀Se₆₀ inorganic resists can be used for the production of holographic diffraction gratings.

A new instrumentation program was decided in 1996 to renew LURE's aging beamline equipment, and also get some experience in view of a new French synchrotron source. For the VUV and soft X-ray domain which are covered by the low energy machine Super-ACO, three new beamlines were scheduled over a three year period with a clear goal toward resolution. Two soft X-ray beamlines are equipped with grazing incidence monochromators, a spherical grating monochromator (SGM) and a plane grating monochromator; a VUV beamline will use an off-plane Eagle normal incidence monochromator. The particular features of each beamline are described. Some emphasis is given to the design, construction and alignment principles which have been followed to the insure an optical quality. A status of the program advance is given. Results from the already commissioned SGM beamline are reported.

We consider the Lie transformation for a general multi- element optical system, and derive expressions for the primary imaging conditions. In order to reduce the computational complexity of the Lie method, which produces successively more complicated expressions after each elementary transformation, we propose a simplified transformation method that makes repeated use of the single- element transformations. The simplified method is applied to a two-element example (the Monk-Gillieson monochromator), and the way is shown for the extension of the method to three or more elements.