Cross Dispersion Research Articles

Anomalous diffusion of particles driven by correlated noise

We study the effect of an arbitrary stationary random force on the motion of damped particles. Using a Langevin description, we derive exact expressions for the dispersion of the particle position, of the particle velocity, and their cross dispersion. The particles can exhibit anomalous diffusion, and the connection between this behavior and the functional form of the noise correlations is investigated in detail. We also study anomalous diffusion for the special cases of overdamped and undamped particles.

Asymmetric white-pupil collimators for high-resolution spectrographs

We present the optical principle of a white-pupil collimator made up of two mirrors with unequal focal lengths. Analytic formulas for third-order aberrations are derived and compared with the results of ray-tracing experiments. It is shown that the image quality is good if the second mirror has a suitable conic coefficient and the F ratio is not too small. Furthermore, third-order coma and astigmatism can be zeroed simultaneously if the angles are also appropriately selected. When implemented in high-resolution echelle spectrographs, this design permits smaller cross dispersers and cameras, with considerable savings in cost.

A TREATMENT FOR THE BACKGROUND CORRECTION ON THE HAMILTON ECHELLE SPECTROGRAPH

ABSTRACT A method for background illumination correction for the Hamilton Echelle Spectrograph is presented. The background is parameterized as (1) a global two dimensional polynomial of scattered light, and (2) a local contamination of spectral features from adjacent orders modeled as a power law in the cross dispersion. The latter component corrects the overlap of closely packed adjacent orders. The significance of the local component is verified by statistical tests and interorder inspection. A software tool useful with the Image Reduction Analysis Facility has been made publicly available.

Zeeman Doppler Imaging

AbstractStellar rotation maps the surface of a star into its line spectrum and gives a dimension to a point on the star - the Doppler dimension. This is of great importance for the detection of Zeeman polarization especially in certain cases. Typically a magnetic configuration will exhibit both polarities, thus the polarization signals of oposite signs may superpose and cancel. The Doppler coordinate will be in general different for parts of the stars having different polarities and therefore the polarization signals will also appear at different wavelengths and will not cancel. Moreover, the time variations plus the Doppler coordinate constitutes two variables that may allow the reconstruction of two dimensional map of the magnetic field over the star surface.Attention will be given to the set-up that allows spectropolarimetry with high spectral resolution and high S/N ratio. The use of cross dispersion spectrographs allows one to observe several tens of spectral lines. The method of adding signals to increase S/N ratio will be indicated.

Erratum: Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials

Previous article Full AccessErratum: Generalized Jacobi Weights, Christoffel Functions, and Jacobi PolynomialsTamás Erdélyi, Alphonse P. Magnus, and Paul NevaiTamás Erdélyi, Alphonse P. Magnus, and Paul Nevaihttps://doi.org/10.1137/0525082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Erratum: Generalized Jacobi Weights, Christoffel Functions, and Jacobi Polynomials." SIAM Journal on Mathematical Analysis, 25(5), p. 1461[1] Paul Nevai, , Tamás Erdélyi and , Alphonse P. Magnus, Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal., 25 (1994), 602–614 10.1137/S0036141092236863 95f:33011a 0805.33013 LinkISIGoogle Scholar Previous article FiguresRelatedReferencesCited byDetails ASYMPTOTIC LINEAR PROGRAMMING LOWER BOUNDS FOR THE ENERGY OF MINIMIZING RIESZ AND GAUSS CONFIGURATIONS27 September 2018 | Mathematika, Vol. 65, No. 1 Cross Ref Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operatorAdvances in Mathematics, Vol. 333 Cross Ref Fractional Pearson diffusionsJournal of Mathematical Analysis and Applications, Vol. 403, No. 2 Cross Ref Decomposition of spaces of distributions induced by tensor product basesJournal of Functional Analysis, Vol. 263, No. 5 Cross Ref A Cohen type inequality for Fourier expansions of orthogonal polynomials with a non-discrete Gegenbauer-Sobolev inner product12 January 2011 | Mathematische Nachrichten, Vol. 284, No. 2-3 Cross Ref An upper bound on Jacobi polynomialsJournal of Approximation Theory, Vol. 149, No. 2 Cross Ref Inequalities for orthonormal Laguerre polynomialsJournal of Approximation Theory, Vol. 144, No. 1 Cross Ref On the maximum value of Jacobi polynomialsJournal of Approximation Theory, Vol. 136, No. 1 Cross Ref Inequalities for real-root polynomials and entire functionsAdvances in Applied Mathematics, Vol. 29, No. 1 Cross Ref Large Sieve Estimates on Arcs of a CircleJournal of Number Theory, Vol. 91, No. 2 Cross Ref A new bound for the Laguerre polynomialsJournal of Computational and Applied Mathematics, Vol. 133, No. 1-2 Cross Ref New Bounds for Hahn and Krawtchouk PolynomialsHolger Dette17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 26, No. 6AbstractPDF (1173 KB) Volume 25, Issue 5| 1994SIAM Journal on Mathematical Analysis History Submitted:13 April 1994Accepted:14 April 1994Published online:17 July 2006 InformationCopyright © 1994 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0525082Article page range:pp. 1461-1461ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics

X-ray optics 2: A technique for high resolution spectroscopy

A novel combination of optical elements and properties is combined to achieve high spectral resolution using grazing incidence optics of modest quality. We show through analysis and ray tracing of examples that using radial groove gratings at high blaze angles in the manner of an echelle spectrograph can provide high spectral resolution. We compare this arrangement to the conventional in-plane designs and show the off-plane to be superior in nearly every respect. Cross dispersion can be provided by the energy resolution of a CCD detector. Then, we show how additional resolution can be squeezed from the system by strategic placement of gratings to take advantage of the azimuthal response of a Wolter x-ray optic. With a telescope that has only 30-sec of arc imaging we are able to support resolution lambda/deltalambda of 3000, while a conventional design at the same graze angle supports resolution of only 200.

ＩＣＰ発光分光分析における高分解能エシェル分光器のスリット条件の選択

A limiting noise in inductively coupled plasma atomic emission spectrometry and relations between slit conditions and detection limits were investigated with an echelle spectrometer using a prism as a cross disperser. A Hamamatsu R-955 multialkali PMT was used as a detector. Since the net background signal was considerably law in the u.v. region, the shot noise contribution in the relative standard deviation (RSD) of the background signal was found to be extremely large (50% under a slit condition, width 100 pm and slit height 1000 μm at 200 nm). In order to obtain a RSD value comparable to that with a conventional grating spectrometer, it was necessary that the slit width was larger than or equal to 200 μm. The use of a slit width of 200 μm, however, provides nearly the same resolving power as that with the conventional spectrometer.

Extracting mu /sub r/ and epsilon /sub r/ of solids from one-port phasor network analyzer measurements

A method for simultaneously and rapidly extracting permittivity, epsilon , and permeability, mu , of nonmetallic solids over a wide range of frequencies, based on one-port reflection measurements made by an automatic network analyzer (ANA), is described. Reflection measurements are taken of a short, an offset short-circuited air line of length l, and two short-circuited samples of lengths land nl, where n is any integer >1. The information contained in these four measurements is sufficient to extract epsilon and mu without recourse to any a priori knowledge of the waveguide's cross section, dispersion, or loss. This method is particularly convenient for measuring epsilon and mu at temperatures significantly different from ambient and in waveguide cross sections whose dispersion and loss are not well known. The presence of higher order modes and of sample inhomogeneities can be detected from an additional measurement of an offset short-circuited air line of length nl. Measurements at Ka-band on polystyrene agree with those of other investigators. A number of practical considerations for successfully implementing the method discussed above, relating to sample length, time-domain gating, mode suppression, and sample fabrication, are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

THE EXTRACTION OF HIGHLY DISTORTED SPECTRA

ABSTRACT Digital spectra of point sources can be extracted with maximum signal-to-noise ratio by applying appropriate weights across the profile of the object. The first stage in computing these weights involves determination of the fraction of the flux of the object which falls into each pixel. The published methods differ at this stage, and none can cope with some commonly available types of data. An improved method for fitting the object profile is presented, which is particularly suited to the extraction of tilted and distorted spectra, as produced by data taken with cross dispersers and image tubes.

The Lick Observatory Hamilton Echelle Spectrometer

The Hamilton Echelle Spectrometer, recently installed at the coudé focus of the Shane 3-m telescope, is a high dispersion spectrograph optimized for use with large format CCD's. It was designed primarily for high resolution (R=50,000) wide bandpass spectroscopy of point-like sources down to a limiting magnitude of about V=16.5, over the 0.34 μm to 1.1 μm spectral region. Its design features a relatively large collimated beam size, the use of prisms rather than gratings for cross dispersion, minimum order separation, the use of protected silver mirror coatings throughout the system, and a fast (f/1.67) folded Schmidt camera with a flat external focal plane. Together, these features yield a very powerful spectrometer for high resolution stellar spectroscopy. This paper gives a brief description of the Hamilton spectrometer and gives several examples of its performance on astronomical objects.

Progress toward a multiobject radial-velocity spectrometer

view Abstract Citations References (18) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Progress toward a multiobject radial-velocity spectrometer. Lutz, Thomas E. ; Ingerson, Thomas ; Weller, William G. Abstract It is shown that it is possible to obtain stellar radial velocities of high accuracy using a fiber-fed echelle spectrograph with no cross disperser. Although the resulting spectrum contains many overlapping orders, the radial-velocity information is still present. Velocities may be obtained by cross correlation with reference data obtained with the same instrument. The accuracy is a function of the signal-to-noise ratio, and ranges from + or - 4 km/s to + or - 1 km/s. Velocities are obtained with exposure times just sufficient to obtain the barest trace of a spectrum using the same spectrograph and CCD detector with a cross disperser. Thus, it appears possible to obtain precision similar to that obtained with an order separator, but with considerably better sensitivity, due to a multiplexing gain. Moreover, the overlapping orders of the stellar spectrum only occupy a few rows of the CCD. Using a multiple-fiber-feed device, many such spectra could be fit on the CCD. This leads to the expectation of obtaining many radial velocities simultaneously using a multiobject spectrometer now under construction at Cerro Tololo. Publication: The Astronomical Journal Pub Date: December 1987 DOI: 10.1086/114603 Bibcode: 1987AJ.....94.1686L Keywords: Fiber Optics; Radial Velocity; Research And Development; Spectrometers; Stellar Spectra; Cross Correlation; Spectrum Analysis; Stellar Magnitude; Stellar Spectrophotometry; Instrumentation and Photography full text sources ADS | data products SIMBAD (17)

THE LICK OBSERVATORY HAMILTON ECHELLE SPECTROMETER.

ABSTRACT The Hamilton Echelle Spectrometer, installed at the coude focus of the Shane 3-m telescope, is a high-dispersion spectrograph optimized for use with today's largest available CCDs, and for the even larger CCDs expected in the future. It was designed primarily for high-resolution (R = 30,000 to 60,000) wide-bandpass spectroscopy of point-like sources down to a limiting magnitude of about V = 16.5, over the 0.34- to 1.1 -micron spectral region. Its design differs from many conventional echelle spectrographs in several areas. The most important differences are its relatively large collimated beam size, the use of prisms rather than gratings for cross dispersion, minimum order separation, the use of protected silver mirror coatings throughout the system, and a fast (f/1.67) folder Schmidt camera with a flat external focal plane. Together, these features yield a very powerful spectrometer for high-resolution stellar spectroscopy. This paper describes the Hamilton spectrograph and discusses the philosophy behind its design. Several examples of the performance of the system are given.

Condition Estimates

Condition Estimates

Some Properties of Small Gas Molecules Determined by Refractive Index Measurements

AbstractThe dispersion of the refractive index of the gases He, Ne, Ar, H2, N2, O2, CH4, and C(CH3)4 at low densities is determined in the visible wave length range 400 nm ≦ λ ≦ 700 nm by means of scanning‐wavelength interferometry. The measurements are fitted by one‐term Kramers‐Heisenberg dispersion relations and used to calculate some macroscopic and molecular properties like mean polarizabilities, effective eigenenergies and oscillator strengths, oscillator strength sums, Verdet and related constants, Rayleigh scattering cross sections and dispersion force constants. The theoretical background as well as the significance of the different relations between refractive index and these properties is presented and discussed briefly.

Nonparametric Identification of Continuous Nonlinear Systems Using Rajbman's Dispersional Method

The paper deals with a nonparametric, (statistical) identification model of continuous nonlinear dynamic system, especially with the identification of continuous Hammerstein systems with white noise input applying the dispersional method. It discusses how the Rajbman's cross dispersion function plays an analog role in the identification problem of continuous Hammerstein systems to that played by the cross correlation function in the case of the "active" identification of linear systems. The method introduced can ensure an optimal estimation of the nonlinear static and linear dynamic part of the Hammerstein system according to the mean square error. The paper gives results obtained by computer simulation as well as identification model applications.

Statistical (Dispersional) Identification of Hammerstein Systems With Weakly Correlated Input Process

By using the Rajbman dispersion method the statistical identification of Hammerstein systems with "white" noise (weakly correlated) input process, can be effected. From the obtained results we prove that the identification of Hammerstein systems with the help of regression function and cross dispersion function (correlation ratio) is optimally defined by the means square error criterion for "white" noise process. This gives a possibility to use this statistical characteristics as a good approximation for weakly correlated input processes, too.

A HIGH-RESOLUTION ECHELLE SPECTROGRAPH SUITABLE FOR ASTRONOMICAL USE AT BOTH FAR ULTRAVIOLET AND VISIBLE WAVELENGTHS.

ABSTRACT A high-resolution far-ultraviolet echelle spectrograph using a LiF prsims cross disperser has been designed and constructed at The Johns Hopkins University. The instrument has been adapted for use in the visible by a simple interchanging of gratings and of cross dispersers. and has been used at the Cassegrain focus of the 0.9-m telescope at the Goddard Space Flight Center. The performance of the instrument is described in detail. Preliminary observations of a Boo (K2 IIIp) are compared with published data obtained with conventional coudé spectrographs.

High-dispersion astronomical spectroscopy with holographic and ruled diffraction gratings

Holographic gratings cause much less stray light and spectral degradation than classically ruled gratings. Their high groove densities enable high dispersion in first diffraction order and a high spectrograph through-put comparable to the best echelles. Their lower reflective efficiency is compensated by the avoidance of cross dispersers, enabling efficient high-fidelity spectroscopy with single-pass spectrographs. Instrumental profiles of the ESO coudé spectrograph with large holographic and ruled gratings have been studied in detail, and their effects on astronomical spectra are discussed and compared to those of other instruments.

Collisions of fast electrons with helium. I. Various forms of the second Born approximation

Various forms of the second Born approximation are applied to electron collisions with helium in the energy range 200 to 500 eV. In each case all intermediate states up to 31P are included explicitly, and a closure approximation used for higher states, the energy parameter being chosen to fit the total cross section and dispersion relation values for Re f(0) and Imf(0). Calculations are carried out with and without V4 terms, and in a (1,1)-Pade approximation for the 12S to 11S, 21S and 21P transitions. Results are compared with experiment and with those of other calculations. The present results cast doubt upon the practice of normalizing experiment to the first Born approximation at intermediate energies.

DESIGN CONSIDERATIONS FOR ASTRONOMICAL ECHELLE SPECTROGRAPHS

ABSTRACT Principles common to the design of all spectrographs using echelles as the main dispersing element and gratings for the cross dispersion are discussed. Consideration is given to the possibilities of a Cassegrain echelle spectrograph for an f/8 beam, and a comparison of its features with those of conventional grating spectrographs. Results are presented in a form which makes them useful for echelle spectrograph design for any telescope.