High-dispersion spherical holographic gratings in a modified rowland mounting

For holographic gratings requiring an extreme dispersion, I consider a modified Rowland mounting, in which the recording laser sources are moved away from the grating, to reduce the uncorrected higher-order aberrations. In addition, I choose the geometric parameters such that first-type coma is corrected. Then a plane multimode deformable mirror (MDM) or two auxiliary spherical holographic gratings (R3 device) are used to aberrate the grating's recording sources; correction up to the fourth order is sufficient to obtain high image quality. Applied to the FUSE-Lyman (FUSE is Far Ultraviolet Spectroscopic Explorer) grating, with a groove density as high as 5767 grooves/mm, these recording devices produce a resolution (chromatic resolving power) as great as 611,000 with the MDM and 3,030,000 with the R3 device. These results far exceed the specified performance of 30,000. Since diffraction limits the resolution to 482,000, the images are diffraction limited with both devices.     

Aberration compensation in a grating interferometer

The transfer function of a grating interferometer with aberrated gratings is discussed. A geometrical configuration is developed that minimizes the aberrations of the output fringes in the interferometer, which is constructed with three hyperbolic gratings. Theoretical and experimental investigations show that it is possible to compensate for first-order aberrations of the interferometer and obtain straight output fringes if a suitable geometric configuration is used for both the recording of the grating components and the interferometer itself.     

Broadband FUV imaging spectrometer: advanced design with a single toroidal uniform-line-space grating

Performances of a far-ultraviolet (FUV) imaging spectrometer in an advanced design are presented with a toroidal uniform-line-space (TULS) grating. It provides high spatial resolution and spectral resolution for a broadband and a wide field of view. A particular analysis for the grating aberrations, including all the high-order coefficients neglected by previous existing designs, was generated for indicating their significance. The analysis indicates that these high-order off-axis aberrations would have a remarkable influence on the design results. The transcendental equations composed of these aberration coefficients do not have analytic solutions in algebra. To solve the problem, the past designs always do some simplified calculation which only suits a narrow field of view and waveband. Thus, the optimization of the genetic algorithm is introduced to propose reasonable ranges of optical parameters. Then ZEMAX software is used to obtain the final optical system from these ranges. By comparing different design results of the same example, our advanced TULS design performs better than conventional TULS design and spherical varied-line-space grating design, and as well as the toroidal varied-line-space design. It is demonstrated that aberrations are minimized when the TULS design is operated by our method. The advanced design is low-cost, easy to fabricate, and more suitable for FUV observations.     

Holographic Grating Aberration Correction for a Rowland Circle Mount I

The aberration coefficients of a concave holographic diffraction grating, derived using Fermat's principle, are used to correct the aberrations of a Rowland circle spectrograph when the slit and grating recording sources lie on the Rowland circle. The correction at two wavelengths of primary astigmatism or primary coma is demonstrated under this constraint.     

Design for an aberration-corrected concave grating for a mid-infrared long-slit spectrometer

A new design for an aberration-corrected concave grating for the spectral region near 10 mum is presented. It was designed for use in the ground-based astronomical medium-resolution (lambda/Dlambda ~ 100) Mid-Infrared Camera and Spectrometer (MICS). It provides a flat focal plane for a wide spectral range (7.5-13.5 mum) with small aberrations, permitting efficient long-slit observations in the mid-infrared region. It permits a simple design of the spectrometer without collimator and camera mirrors, which is quite advantageous for cryogenic instruments. The grating has variable spacing grooves to reduce aberrations. In addition, the grating surface figure is designed to be toroidal and in the direction perpendicular to the grooves, aspherical, to suppress the aberrations further over a wide spectral range. The angle of the grooves is also varied to yield better efficiency near the blaze angle. The grating was fabricated by high-quality ultraprecision machining, which made these features possible. Test observations confirmed that the designed spectral resolution was achieved.     

Comparison of mechanically ruled versus holographically varied line-spacing gratings for a soft-x-ray flat-field spectrograph

Recent progress in the design of aspheric wave-front recording systems has permitted the manufacture of holographic gratings with highly variable groove densities that are suitable for flat-field spectrographs. A holographic grating thus recorded was processed to produce a laminar profile by use of reactive-ion etching. Measurements are reported of the absolute diffraction efficiency of this grating and of a comparable mechanically ruled grating. It is found that the holographic grating is much more effective in suppressing the higher orders. The spectral resolution was determined by use of a carbon Kalpha x-ray generator and a spectrograph with an imaging detector. The spectral resolution of the holographic grating was approximately 3 times worse than that of the ruled grating.     

Computer-originated planar holographic optical elements

We present novel, to our knowledge, methods for the analytical design and recording of planar holographic optical elements in thick materials. The recording of each planar holographic element is done by interference of two aspherical waves that are derived from appropriately designed computer-generated holograms such that the element has the desired grating function for minimizing aberrations and closely fulfills the Bragg condition over its entire area. The design and recording methods are described, along with calculated results of representative elements.     

Aberration measurement from specific photolithographic images: a different approach

Techniques for measurement of higher-order aberrations of a projection optical system in photolithographic exposure tools have been established. Even-type and odd-type aberrations are independently obtained from printed grating patterns on a wafer by three-beam interference under highly coherent illumination. Even-type aberrations, i.e., spherical aberration and astigmatism, are derived from the best focus positions of vertical, horizontal, and oblique grating patterns by an optical microscope. Odd-type aberrations, i.e., coma and three-foil, are obtained by detection of relative shifts of a fine grating pattern to a large pattern by an overlay inspection tool. Quantitative diagnosis of lens aberrations with a krypton fluoride (KrF) excimer laser scanner is demonstrated.     

Hyperbolic holographic gratings: analysis and interferometric tests

The aberrations of hyperbolic diffraction gratings produced with two spherical waves are analyzed theoretically and experimentally. The behavior of these gratings in collimated illumination indicates that for a grating of a given size there is a critical spatial frequency above which the aberration remains constant for all spatial frequencies. Aberrations associated with geometrical errors in the recording geometry are derived. With simple interferometric tests, misalignments in the recording process can be identified easily.     

Third-generation holographic Rowland mounting: fourth-order theory

The third-generation holographic Rowland mount consists of a Rowland-mounted, optimally recorded holographic spherical grating, referred to as an optimized Rowland grating (ORG), whose recording sources are aberrated by two auxiliary ORG's. The main purpose of this mount is to avoid any aspherical surface while providing control over all the parameters needed to correct the aberrations up to and including the fourth order. Earlier [Appl. Opt. 30, 4019-4025 (1991)], we considered the case of a moderate coma c2. We now give the fourth-order theory, apply it to the high-dispersion (4600 grooves/mm) grating considered previously, and obtain for it diffraction-limited images.     

Aberrations from a prism and a grating

Formulas for the wave aberrations introduced into a beam by a prism or a plane grating are derived from the theory of plane symmetric systems. Emphasis is made on the field-dependent aberrations.     

Wavelength Mismatch Correcting Elements for Volume Holograms Written on a Laser Pattern Generator

Abstract

Holographic optical lenses based on volume gratings commonly suffer from severe aberrations due to wavelength mismatch between recording (blue-sensitive material) and application (often employing diode lasers). Here, methods are described for the precompensation of the aberrations at the recording. Both, aberrations in the phase of the reconstructed wave from the desired wave (‘wave aberration’), as well as aberrations in intensity resulting from deviations from the Bragg condition during reconstruction (‘Bragg aberration’) need to be compensated for. The design method for generating the computer generated holograms is described which are used as precompensating elements in the recording step of the interferometrically produced holographic optical elements. The computer generated holograms are written on a laser pattern generator. Test results of our laser pattern generator are shown to demonstrate its capability for this process. The measurement of the aberrations at the design wavelength in the near infrared is a very important step because it allows to eliminate in a second recording process misadjustment errors which will occur during the first recording step. By modification of at least one of the computer generated holograms the convergence of the procedure can be achieved.     

Aberrations of diffracted wave fields. II. Diffraction gratings

The Rayleigh-Sommerfeld theory is applied to diffraction of a spherical wave by a grating. The grating equation is obtained from the aberration-free diffraction pattern, and its aberrations are shown to be the same as the conventional aberrations obtained by using Fermat's principle. These aberrations are shown to be not associated with the diffraction process. Moreover, it is shown that the irradiance distribution of a certain diffraction order is the Fraunhofer diffraction pattern of the grating aperture as a whole aberrated by the aberration of that order.     

Control of spectral aberrations in a monochromator using a plane holographic chirped grating

A method aimed to minimize the impact of spectral aberrations in a monochromator is proposed in which the spectrum of the source of radiation under study is scanned by the rectilinear translation of a plane chirped grating. The chirped grating, which has a spatially variable groove spacing, is used to diffract and to spectrally focus the radiation. Imaging properties of the chirped grating were analyzed in order to develop the expression of the aberration coefficients of the system and the expression of the width of the instrument line shape due to aberrations. The optimal rectilinear trajectory required to operate the monochromator without significant spectral aberrations in measurements has been obtained numerically and tested in the laboratory. Experimental measurements of the emission spectrum of a seven-wavelength helium-neon laser are presented, as well as the sensitivity of the monochromator performance to different geometrical parameters.     

Geometric theory of the ellipsoidal grating

A third-order geometric aberration theory of the ellipsoidal grating has been developed by analytically following an exact ray-tracing formalism with the aid of power series expansions. The theory takes into account all the possible aberrations up to third order and provides analytic formulas for the spot diagram of a spectral image formed by a modified or a nonmodified ellipsoidal grating with any of the groove patterns producible by means of mechanical ruling or conventional holographic recording. The present analytic formulas and other analytic ray-deviation formulas used in designing grating instruments have been evaluated in comparison with exact ray tracing. The results show the validity of the present theory and the limitation of the ray-deviation formulas based on the light path function and wave-frontaberration theory.     

Generalized groove density equation concerning bending-grating-related imaging properties

Varied-line-spacing gratings are used in soft-x-ray monochromators and spectrometers because of their ability to correct various aberrations by varying the groove density. A curved grating blank in a Rowland circle mounting could eliminate primary aberrations. Bending a plane constant-groove-density grating into a desirable surface can eliminate higher-order aberrations as a result of the change in surface profile and groove density. This provides a simple means for improving the imaging properties. When used in a monochromator, the grating can be bent to different degrees to minimize aberrations at all wavelengths. General formulas concerning the transformations of groove function, groove density, and groove spacing are presented for the bending grating. Analytic results with a numerical example show the significant properties of the system.     

Spherical-grating monochromator with a variable-line-spaced grating for synchrotron radiation

An optical design for spherical-grating monochromators for application to synchrotron radiation is presented. High spectral and spatial performance is obtained with a spherical variable-line-spaced grating coupled to a spherical mirror with its tangential plane coincident with the grating's equatorial plane. The monochromator works without an entrance slit in an off-Rowland configuration with a fixed entrance arm and demagnification on the exit slit. The law for groove-space variation of the grating compensates for the main spectral aberrations; spectral focusing in an extended energy range is ensured by a slight change in the exit arm with translations of the order of a few tens of millimeters. The inclusion of a spherical mirror ensures focusing on a plane perpendicular to the plane of spectral dispersion. The ultimate resolution is limited by the slope errors of a single spherical surface. The layout is applied to the design of a high-resolution monochromator for the 1000-250-eV region.     

Fourth-order optical aberrations and phase-space transformation for reflection and diffraction optics

One can derive fourth-order optical ray deviations for a mirror or grating from the optical path function by using the analytical code REDUCE. Some of the aberrations are discussed for normal-incidence and grazing-incidence monochromators. The nonlinear transformation of light from the source to the image plane of a mirror or grating is represented by a transformation matrix. The optical properties of a combination of several optical elements are given by the product of the matrices of the individual optical elements. The matrix elements can be interpreted as optical aberrations. A program has been written that optimizes a complete beam line with respect to various optical aberrations by minimizing an appropriate cost function that is built from a weighted sum of the matrix elements.     

Rainbow holographic aberrations and the bandwidth requirements

Rainbow holographic image resolution, primary aberrations, and bandwidth requirements are presented. The results obtained for the rainbow holographic process are rather general, for which the conventional holographic image resolution, aberrations, and bandwidth requirements, can be derived. The conditions for the elimination of the five primary rainbow holographic aberrations are also given. These conditions may be useful for the application of obtaining a high-quality rainbow hologram image. In terms of bandwidth requirements, we have shown that the bandwidth requirement for a rainbow holographic construction is usually several orders lower than that of a conventional holographic process. Therefore, a lower-resolution recording medium can generally be used for most of the rainbow holographic constructions.