Grazing-incidence telescope-spectrograph for space solar-imaging spectroscopy

The design of a stigmatic grazing-incidence instrument for space applications to solar-imaging spectroscopy is presented. It consists of a double telescope and a spectrograph: Telescope I consists of a single cylindrical mirror with parabolic section, focusing the radiation on the entrance slit of the spectrograph in the spectral dispersion plane; telescope II consists of two cylindrical mirrors with aspherical section in a Wolter configuration, focusing the radiation on the spectrograph focal plane in the direction perpendicular to the spectral dispersion plane. The spectrograph consists of a grazing-incidence spherical variable-line-spaced grating with flat-field properties. Telescope II is crossed with respect to the grating and telescope I; i.e., it is mounted with its tangential planes coincident with the grating equatorial plane. The spectrum is acquired by a detector mounted at near-normal incidence with respect to the direction of the exit beam. The spectral resolution is also preserved for off-axis angles. The effective collecting area of the instrument can be preserved by adoption of a nested configuration for telescope II without degradation of the spectral resolution.     

High-resolution tunable spectrograph for x-ray laser linewidth measurements with a plane varied-line-spacing grating

We describe a spectrograph for x-ray laser linewidth measurements in the range 100-220 A. The design employs a plane varied-line-spacing grating operating in the convergent light produced by imaging of the entrance slit with a concave spherical mirror. By the appropriate choice of the linear term in the grating-spacing variation, two separate wavelengths can be focused at the same image distance. As a result all wavelengths within the range of interest are focused at or near the same distance. The spectrograph can be tuned by rotation of the grating to bring any wavelength within the range to the center of the focal plane, and the spectra are dispersed on a surface that is erect or practically flat and perpendicular to the principal ray. This allows the use of a planar detector. With a streak camera used as a detector, the instrument obtained time-resolved linewidth data on x-ray lasers with a resolving power of 1 x 10(4) to 2 x 10(4). This paper presents the design methods used to optimize the varied-line-spacing grating, the design of the tunable spectrograph, and the results from the instrument in operation.     

Sub-diffraction-limited multilayer coatings for the 0.3 numerical aperture micro-exposure tool for extreme ultraviolet lithography

Multilayer coating results are discussed for the primary and secondary mirrors of the micro-exposure tool (MET): a 0.30 NA lithographic imaging system with a 200 microm x 600 microm field of view at the wafer plane, operating in the extreme ultraviolet (EUV) region at an illumination wavelength around 13.4 nm. Mo/Si multilayers were deposited by DC-magnetron sputtering on large-area, curved MET camera substrates. A velocity modulation technique was implemented to consistently achieve multilayer thickness profiles with added figure errors below 0.1 nm rms demonstrating sub-diffraction-limited performance, as defined by the classical diffraction limit of Rayleigh (0.25 waves peak to valley) or Marechal (0.07 waves rms). This work is an experimental demonstration of sub-diffraction- limited multilayer coatings for high-NA EUV imaging systems, which resulted in the highest resolution microfield EUV images to date.     

Single-element imaging spectrograph

A spectrograph concept designed for both high wavelength and high spatial resolution (in one dimension) is briefly described. This design is referred to as a single-element imaging spectrograph (SEIS). It is a one-bounce diffractive system that combines the spectral properties of a Rowland mount spectrograph with the imaging (spatial resolution) properties of a Wadsworth mount spectrograph through the use of a toroidal diffraction grating. No primary optics are necessary, making the system especially attractive for use in the extreme and far ultraviolet, where low reflectivity of common optical coatings can severely limit instrument sensitivity.     

Two-channel tunable monochromatic illuminator with a concave diffraction grating and an original scanning system

A two-channel monochromatic illuminator with only one diffraction grating and an original scanning system has been designed for multiple applications. This scanning system consists of two rotational plane mirrors that reflect light diffracted by a concave diffraction grating to the ?1 orders of the spectrum. The light reflected by the mirrors goes to two exit slits that correspond to two channels of the device. The positions of the centers of rotation of the mirrors are selected to produce minimal deviation of the direction of the light reflected during the scanning. The aberration characteristics of some variations in the optical mounting of the device made by use of spherical and toroidal holographic diffraction gratings recorded in stigmatic and astigmatic beams, the possibilities for application of the device for measuring the color sensitivity of the human eye, and the possibilities for measuring the efficiency of concave diffraction gratings, are also discussed.     

Some comments on the dynamic properties of anisotropic and strongly anisotropic pre-stressed elastic solids

The effect of pre-stress on the propagation of small amplitude waves in an incompressible, transversely isotropic elastic solid is discussed in respect of the most general appropriate strain energy function. A simple set of sufficient conditions is noted which ensures that two real wave speeds exist for all directions of propagation. In the case of bi-axial primary deformations, and for propagation within each principal plane of the homogeneous primary deformation, the propagation condition is factorised and conditions which are both necessary and sufficient to ensure the existence of two real wave speeds are established. The paper also includes some graphical illustrations of the associated slowness and wave surfaces and discussion of the strongly anisotropic case, for which the extensional modulus along the preferred fibre direction is much larger than other material parameters.     

大型平行光管像质实时监测的可行性论证

针对目前大型平行光管成像质量监测的现状,本文提出了一种对平行光管进行实时监测的新方法,验证了这种监测方法的可行性.该方法根据光管自准检测原理,采用小平面镜对光管像质进行实时监测,计算了在一个焦深范围内小平面镜转角误差大小.实验结果证明在一个焦深范围内用精度0.02"的自准直仪,可将小平面镜转角误差控制在0.2"以内,对大型平行光管起到了进行实时监测的作用.大型平行光管在空间遥感设备中运用广泛,此检测光管像质的方法在工程上将起到积极的作用.     

Planes of Continuous-Wave Oscillations From an Electron Nanocontact Spin-Transfer Device

We have found that the frequencies of continuous-wave (CW) microwave oscillations in nanocontact spin-transfer (ST) devices occur in well-defined planes of frequencies, as a function of the dc current bias, the direction of the magnetic field, and the magnitude of the magnetic field. The frequency, f, of these technologically significant peaks for each magnetic field direction is described empirically by the equation of a plane, f=a|Boarr|+bI+c, where |Boarr| is the magnitude of the magnetic field, I is the dc bias current, and a, b, and c are constants of the plane. The primary frequency plane described by this equation is accompanied by a smaller secondary plane. The empirical equation describing the primary plane serves as a guide for efficiently locating CW oscillations within the independent variable space     

Off-plane anastigmatic imaging in Offner spectrometers

In this paper, the imaging performance of an Offner concentric imaging spectrometer is analyzed when the spectrometer entrance slit is disposed arbitrarily on the plane that is parallel to the grating grooves and contains the common center of curvature. Astigmatism-corrected designs are obtained for off-plane incidence on the grating if one point on the slit is located on the Rowland circle of the primary mirror. In this case, the combined system of primary mirror plus diffraction grating provides two astigmatic line images oriented parallel and orthogonal to the plane of diffraction, with the former located on the same plane as the slit. Consequently, these images can be brought to a single focus on this plane by the tertiary mirror if its radius of curvature is chosen properly. In addition, coma aberration is simultaneously removed. These results can be applied to the design of two-mirror or three-mirror spectrometers, generalizing the concept of the best imaging circle and providing solutions to get anastigmatic imaging for two object points and two wavelengths.     

Quantitative imaging through a spectrograph. 1. Principles and theory

Laser-based optical diagnostics, such as planar laser-induced fluorescence and, especially, Raman imaging, often require selective spectral filtering. We advocate the use of an imaging spectrograph with a broad entrance slit as a spectral filter for two-dimensional imaging. A spectrograph in this mode of operation produces output that is a convolution of the spatial and spectral information that is present in the incident light. We describe an analytical deconvolution procedure, based on Bayesian statistics, that retrieves the spatial information while it avoids excessive noise blowup. The method permits direct imaging through a spectrograph, even under broadband illumination. We introduce the formalism and discuss the underlying assumptions. The performance of the procedure is demonstrated on an artificial but pathological example. In a companion paper [Appl. Opt. 43, 5682-5690 (2004)] the method is applied to the practical case of fuel equivalence ratio Raman imaging in a combustible methane-air mixture.     

Optimization of the output beam homogeneity of short-pulse KrF amplifiers

The output beam of short-pulse excimer amplifiers exhibits an inhomogeneous spatial intensity distribution caused by diffraction effects at laser windows and mirrors. Theoretical and experimental studies show that the amplification parameters of a KrF amplifier can be optimized with respect to the output beam homogeneity by proper choice of the energy density in the amplifier. The homogenized intensity distribution is obtained at the plane of the output window of the amplifier and can be transferred by optical imaging onto a target plane. It is shown that the amplification parameters for the best output homogeneity are close to the ones previously found for optimal energy extraction efficiency.     

Novel moving cat's-eye-pair interferometer

A novel type of cat's-eye interferometer, the novel moving cat's-eye-pair interferometer, is presented. It has neither tilt nor shearing problems. It consists of one moving cat's-eye-pair (MCEP), i.e. two identical cat's-eye retro-reflectors fixed together back to back in a rigid structure as a single moving element, four fixed plane mirrors and one beam-splitter. The optical path difference (OPD) is created by the straight reciprocating motion of the MCEP, and the OPD value is eight times the displacement of the MCEP. The new interferometer is suitable for very-high resolution Fourier transform spectrometers for any wave-number region from the far infrared down to the visible if the cat's-eye retro-reflector comprises a parabolic primary and a spherical secondary.     

Reflection and refraction of an arbitrary electromagnetic wave at a plane interface separating an isotropic and a biaxial medium.

Exact solutions are obtained for the reflected and transmitted fields resulting when an arbitrary electromagnetic field is incident on a plane interface separating an isotropic medium and a biaxially anisotropic medium in which one of the principal axes is along the interface normal. From our exact solutions for the reflected fields resulting when a plane TE or TM wave is incident on the plane interface, it can be inferred that the reflected field contains both a TE and a TM component. This gives a change in polarization that can be utilized to determine the properties of the biaxial medium. The time-harmonic solution for the reflected field is in the form of two quadruple integrals, one of which is a superposition of plane waves polarized perpendicular to the plane of incidence and the other a superposition of plane waves polarized parallel to the plane of incidence. The time-harmonic solution for the transmitted field is also in the form of two quadruple integrals. Each of these is a superposition of extraordinary plane waves with displacement vectors that are perpendicular to the direction of phase propagation.     

Methodology for third-order astigmatism compensation in off-axis spherical reflective systems

The main constraint of classical off-axis reflecting systems is the primary astigmatism that has long been a research topic of interest. This astigmatism in off-axis spherical reflective imaging systems can be eliminated by using the proper configuration. These configurations could be derived from the marginal ray fans equation, and they are valid for small angles of incidence. The conditions for the astigmatism compensation in configurations with two and three off-axis mirrors have been derived and analyzed, which have not been reported previously. The expression that defines the conditions for primary astigmatism compensation in a four-mirror system is presented. This shows that the marginal ray fan equation can be used to obtain the condition for astigmatism compensation of a reflective system with any number of mirrors. The developed methodology is verified by ray-tracing analysis of some examples.     

Theoretical basis for the scheme of an electrostatic energy- and angle-resolved spectrograph

The results of the studies in which a formalism relevant for solving the problem of focal line straightening in an energy analyzer composed of electrostatic two-dimensional or cylindrical mirrors have been systematized. The scheme for an energy-angle resolved spectrograph which provides high-quality angular focusing of beams of various energies along the focal surface shaped as a right circular cone has been theoretically substantiated.     

Phase unwrapping method for three-dimensional stress analysis by scattered-light photoelasticity with unpolarized light

In scattered-light photoelasticity with unpolarized light, the secondary principal stress direction psi and the relative phase retardation rho in a three-dimensional stressed model with rotation of the principal stress axes can be obtained by use of Stokes parameters. For completely automated stress analysis, measurements of the total relative phase retardation and the secondary principal stress direction over the entire field are required, and it is necessary to unwrap psi and rho. A phase unwrapping method is thus proposed for the determination of these values based on scattered-light photoelasticity. The values are easily obtained via an arctangent function, overcoming the error associated with the quarter-wave plate by employing an incident light of different wavelengths. The proposed technique provides automated and nondestructive determination of the total relative phase retardation and the secondary principal stress direction in a model exhibiting rotation of the principal stress axes.     

平面镜多次反射的二维高精度小角度偏转测量

介绍了利用平面镜多次反射系统实现二维高精度小角度偏转测量的光学测量方法,构建了实验系统,针对系统的测量精度和测量范围与激光束在平面镜系统中反射次数的关系进行了研究,最后根据应用实例给出了具体的计算分析,研究结果表明,该方法具有结构简单、测量精度高的特点,当反射次数达到10次以上时,系统的测量精度将达到0.01",为亚角秒级高精度动态测量提供了一种新的研究方法.     

Spin-up and spin-down of a viscous fluid over a heated disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force

Summary The hydromagnetic spin-up and spin-down of an incompressible electrically conducting fluid on a heated infinite disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force have been studied. The flow is non-axisymmetric due to the imposition of the buoyancy force. We have considered the situation where there is an initial steady state which is perturbed by suddenly changing the angular velocity of the disk. By using suitable transformations the Navier-Stokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (,t ^*). Also, these transformations uncouple the momentum and energy equations, resulting in a primary axisymmetric flow with an axial magnetic field, in an energy equation dependent on the primary flow and in a buoyancy induced secondary cross flow dependent on both primary flow and energy.The results indicate that the effect of the step-change in the angular velocity of the disk is more pronounced on the primary flow than on the secondary flow and the temperature field. For both spin-up and spin-down cases the surface shear stress in the non-axial direction normal to gravity for the primary flow and the surface shear stresses for the secondary flow increase with the magnetic parameter, whilst the surface shear stress in the vertical direction and the heat transfer at the surface decrease as the magnetic parameter increases. Also, the secondary flow near the disk dominates the primary flow. We have also developed an asymptotic analysis for large magnetic parameters which complements well the numerical results obtained in the lower magnetic parameter range.     

Simultaneous measurement of foveal spectral reflectance and cone-photoreceptor directionality

An instrument for simultaneous measurement of foveal spectral reflectance and cone-photoreceptor directionality is described. The key element is an imaging spectrograph (spectral range of 420-790 nm) with its entrance slit conjugate to the pupil plane of a human eye. A 1.9-deg spot on the retina is sampled in 1 s. Video observation of the retina and the pupil facilitates proper alignment. Measurements were performed on 21 healthy subjects. Model analysis of the spectra provided densities of photostable ocular absorbers. As an example, macular pigment and melanin are discussed in more detail. Spatial profiles exhibited the optical Stiles-Crawford effect, reflecting cone-photoreceptor directionality.