Cross Dispersion Research Articles

Reactive ion plasma etched surface relief gratings for low/medium/high resolution spectroscopy in astronomy

We report the fabrication of a binary-phase proof-of-concept astronomical diffraction grating embedded in a quartz substrate via reactive ion plasma etching. This grating operates at the first diffraction order within the 450 to 750 nm wavelength band. It features 1400-nm-deep, 188-nm-wide binary grooves at a 566-nm pitch, or 1767 lines/mm groove density, over a 25.4 × 25.4 mm2 area. A high depth-to-width ratio ( ∼ 8 ∶ 1 in this case) is one of the keys to near-theoretical diffraction efficiency being attained by the fabricated grating (94% at center wavelength and 70% at band edges) over a broad bandpass (>200 nm). This performance is also attributed to high-resolution micro-lithographic electron-beam patterning and anisotropic reactive ion etching process fabrication techniques. These types of binary gratings can potentially be high-throughput alternatives to Volume-Phase Holographic Gratings (VPHGs) for general spectroscopic applications. When scaled to appropriate sizes for astronomy, such gratings can serve as main or cross dispersion elements in low-, medium-, and high-resolution spectrographs not only in ground-based telescopes but also in those subject to challenging environmental conditions such as in space observatories.

Cross‐dispersion effect on magnetohydrodynamic dissipative Casson fluid flow via curved sheet

AbstractWe examine the heat and mass transfer on magnetohydrodynamic Casson fluid motion via a curved sheet. The fluid flow is assumed to be along a stretched curved sheet. The effects of Soret (“viscous dissipation”) and Dufour (“cross dispersion”) are taken into account. The governing partial differential equations have been transformed into ordinary differential equations by using relevant similarity transformations. These converted equations are solved using a combination of Runge–Kutta–Fehlberg along with the shooting technique algorithm. We find out the various physical parameter behavior of , , and . We found that the (“temperature profile”) enhances while opposite behavior of (“concentration profile”) with enlarge values of and . Also, we get a good agreement with the present results when compared with the previous study.

MGDMD: Multi-variate generalized dispersive mode decomposition

In this paper, we propose a multi-variate extension of the recently proposed generalized dispersive mode decomposition (GDMD) which can accurately estimate cross group delays and extract overlapped dispersive modes. We propose a joint dispersion optimization solution for multi-channel dispersive signals which can extract all high-quality overlapped dispersive modes with very few cross dispersion effects. Simulation results on multi-channel synthetic dispersive signals and real-life signals taken from four publicly available datasets depict the superiority of the proposed multi-variate GDMD (MGDMD) as compared to existing decomposition techniques.

The Covariance Structure between Liquid and Illiquid Assets

The traditional methods of estimating investment risk based on the observed variation of asset prices falter on sparsely traded assets owing to the lack of price quotes. The price variance of illiquid assets such as private equity, loans, or real estate is, if calculable at all, not meaningful. Nor does the observed covariance between illiquid assets indicate a degree of proximity in the price behavior. The author proposes a cross-sectional approach instead, taking the price dispersion across assets as an estimate of variance and using the so-called cross dispersion of covariance. The covariance matrix computed in this way over traded and nontraded assets seems coherent with the (sub)matrix computed over time on traded assets. The cross-sectional matrix sets a universal framework for managing portfolios invested in traded and nontraded assets, making all-encompassing risk assessments possible.

NEREA (Near Earths and high-Res Exoplanet Atmospheres), a red/near-IR spectrograph concept for the Gran Telescopio Canarias

NEREA (Near Earths and high-Res Exoplanet Atmospheres) is a stable, compact, high-resolution spectrometer concept for the Gran Telescopio Canarias (GTC). The spectrograph is designed to be a common user instrument; however, its specifications are governed by two main science goals. (1) The discovery and characterization of planets around late-M type stars. Using the GTC’s large 10 m collecting area, NEREA would be capable of reaching out for planets around cooler, smaller, and dimmer stars than current facilities, contributing to completing the census of small planets in our stellar neighborhood (<30 pc); (2) The characterization of planetary atmospheres from Hot-Jupiters to Super-Earths. NEREA would be capable of detecting species including H2O, CH4, CO2, and ionized metals in planetary atmospheres; as well as detecting and resolving individual Na I, Hα, and He I line profiles, improving our understanding of the physical and chemical evolution of planetary atmospheres. Owing to the GTC’s collecting area, the current planetary sample size can be expected to increase by ∼40 times. The spectrometer preliminary design follows a single-pass echelle layout and is fiber-fed with both a rectangular 22 μm × 198 μm science fiber and a 29 μm calibration fiber. The system is designed to achieve a resolving power of 100,000 in the red-NIR regime (0.7 to 1.7 μm). The device footprint is ∼0.25 m × 1 m × 0.75 m, allowing the system to be temperature and pressure stabilized (<50 cm / s) in a small, compact container. The concept applies a 320 mm × 90 mm, R4 blazed, diffraction grating as the disperser and a 60.6-deg P-SF67 prism as the cross disperser. A 325 mm focal length, off-axis, parabolic mirror is employed as the collimator and the camera consists of a custom designed 325 mm refocusing lens. The instrument is designed to efficiently couple to the GTC AO system, for which we assume moderate performance of 0.3″ in our wavelength range. The spectrometer would also be able to perform efficiently without adaptive optics at a resolving power of 40,000 or, with losses, at a resolving power of 70,000 to 100,000.

First Radial Velocity Results From the MINiature Exoplanet Radial Velocity Array (MINERVA)

The MINiature Exoplanet Radial Velocity Array (MINERVA) is a dedicated observatory of four 0.7 m robotic telescopes fiber-fed to a KiwiSpec spectrograph. The MINERVA mission is to discover super-Earths in the habitable zones of nearby stars. This can be accomplished with MINERVA’s unique combination of high precision and high cadence over long time periods. In this work, we detail changes to the MINERVA facility that have occurred since our previous paper. We then describe MINERVA’s robotic control software, the process by which we perform 1D spectral extraction, and our forward modeling Doppler pipeline. In the process of improving our forward modeling procedure, we found that our spectrograph’s intrinsic instrumental profile is stable for at least nine months. Because of that, we characterized our instrumental profile with a time-independent, cubic spline function based on the profile in the cross dispersion direction, with which we achieved a radial velocity precision similar to using a conventional “sum-of-Gaussians” instrumental profile: 1.8 m s−1 over 1.5 months on the RV standard star HD 122064. Therefore, we conclude that the instrumental profile need not be perfectly accurate as long as it is stable. In addition, we observed 51 Peg and our results are consistent with the literature, confirming our spectrograph and Doppler pipeline are producing accurate and precise radial velocities.

Compton scattering off pions and electromagnetic polarizabilities

The electric [Formula: see text] and magnetic [Formula: see text] Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the [Formula: see text] Compton scattering angular distribution at back scattering angles and [Formula: see text] absolute cross sections. Theory derivations are given for the [Formula: see text] Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The [Formula: see text] polarizabilities were deduced from DESY Crystal Ball [Formula: see text] data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering [Formula: see text] at CERN COMPASS, (2) two-photon pion pair production [Formula: see text] at SLAC Mark II, and (3) radiative pion photoproduction [Formula: see text] from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value [Formula: see text] agrees well with the two-loop ChPT prediction [Formula: see text], strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.

PEPSI deep spectra

Context. Full-disk solar flux spectra can be directly compared to stellar spectra and thereby serve as our most important reference source for, for example stellar chemical abundances, magnetic activity phenomena, radial-velocity signatures or global pulsations. Aim. As part of the first Potsdam Echelle Polarimetric and Spectroscopic Instrument (PEPSI) key-science project, we aim to provide well-exposed and average-combined (viz. deep) high-resolution spectra of representative stellar targets. Such deep spectra contain an overwhelming amount of information, typically much more than what could be analyzed and discussed within a single publication. Therefore, these spectra will be made available in form of (electronic) atlases. The first star in this series of papers is our Sun. It also acts as a system-performance cornerstone. Methods. The Sun was monitored with PEPSI at the Large Binocular Telescope (LBT). Instead of the LBT we used a small robotic solar disk integration (SDI) telescope. The deep spectra in this paper are the results of combining up to ≈100 consecutive exposures per wavelength setting and are compared with other solar flux atlases. Results. Our software for the optimal data extraction and reduction of PEPSI spectra is described and verified with the solar data. Three deep solar flux spectra with a spectral resolution of up to 270 000, a continuous wavelength coverage from 383 nm to 914 nm, and a photon signal to noise ratio (S/N) of between 2000–8000:1 depending on wavelength are presented. Additionally, a time-series of 996 high-cadence spectra in one cross disperser is used to search for intrinsic solar modulations. The wavelength calibration based on Th-Ar exposures and simultaneous Fabry–Pérot combs enables an absolute wavelength solution within 10 m s−1 (rms) with respect to the HARPS laser-comb solar atlas and a relative rms of 1.2 m s−1 for one day. For science demonstration, we redetermined the disk-average solar Li abundance to 1.09 ± 0.04 dex on the basis of 3D NLTE model atmospheres. We detected disk-averaged p-mode RV oscillations with a full amplitude of 47 cm s−1 at 5.5 min. Conclusions. Comparisons with two solar FTS atlases, as well as with the HARPS solar atlas, validate the PEPSI data product. Now, PEPSI/SDI solar-flux spectra are being taken with a sampling of one deep spectrum per day, and are supposed to continue a full magnetic cycle of the Sun.

A thermodynamic model for strong aqueous electrolytes based on the eSAFT-VR Mie equation of state

The latest formulation of the SAFT-VR Mie equation of state (EoS) is extended to solutions of salts which are assumed to be strongly dissociating in water – through the addition of a Born term for accurate representation of the Gibbs energy of solvation, and a Debye-Hückel term for long-range, electrostatic interactions. Two adjustable parameters are assigned to each ionic species, the ion-solvent (here water) cross dispersion energy parameter and the ion segment diameter, which are optimized against experimental data for electrolyte solution densities and mean ionic activity coefficients. Model correlations for the activity coefficients and liquid densities, as well as predictions for vapor pressure and osmotic coefficients, show that the developed model performs accurately and, in many cases, is more accurate than other recent formulations for electrolyte solutions. Finally, a methodology for equation of state parameterization is presented to capture the non-monotonic temperature dependence of activity coefficient isotherms at low temperatures.

PEPSI: The high‐resolution échelle spectrograph and polarimeter for the Large Binocular Telescope

AbstractPEPSI is the bench‐mounted, two‐arm, fibre‐fed and stabilized Potsdam Echelle Polarimetric and Spectroscopic Instrument for the 2×8.4 m Large Binocular Telescope (LBT). Three spectral resolutions of either 43 000, 120 000 or 270 000 can cover the entire optical/red wavelength range from 383 to 907 nm in three exposures. Two 10.3k×10.3k CCDs with 9‐µm pixels and peak quantum efficiencies of 94–96 % record a total of 92 échelle orders. We introduce a new variant of a wave‐guide image slicer with 3, 5, and 7 slices and peak efficiencies between 92–96 %. A total of six cross dispersers cover the six wavelength settings of the spectrograph, two of them always simultaneously. These are made of a VPH‐grating sandwiched by two prisms. The peak efficiency of the system, including the telescope, is 15 % at 650 nm, and still 11 % and 10 % at 390 nm and 900 nm, respectively. In combination with the 110 m2 light‐collecting capability of the LBT, we expect a limiting magnitude of ≈20th mag in V in the low‐resolution mode. The R = 120 000 mode can also be used with two, dual‐beam Stokes IQUV polarimeters. The 270 000‐mode is made possible with the 7‐slice image slicer and a 100‐µm fibre through a projected sky aperture of 0.74″, comparable to the median seeing of the LBT site. The 43 000‐mode with 12‐pixel sampling per resolution element is our bad seeing or faint‐object mode. Any of the three resolution modes can either be used with sky fibers for simultaneous sky exposures or with light from a stabilized Fabry‐Pérot étalon for ultra‐precise radial velocities. CCD‐image processing is performed with the dedicated data‐reduction and analysis package PEPSI‐S4S. Its full error propagation through all image‐processing steps allows an adaptive selection of parameters by using statistical inferences and robust estimators. A solar feed makes use of PEPSI during day time and a 500‐m feed from the 1.8 m VATT can be used when the LBT is busy otherwise. In this paper, we present the basic instrument design, its realization, and its characteristics. Some pre‐commissioning first‐light spectra shall demonstrate the basic functionality. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Fully programmable two-dimensional pulse shaper for broadband line-by-line amplitude and phase control

We introduce a fully programmable two-dimensional (2D) pulse shaper, able to simultaneously control the amplitude and phase of very fine spectral components over a broad bandwidth. This is achieved by aligning two types of spectral dispersers in a cross dispersion setup: a virtually imaged phased array for accessing fine resolution and a transmission grating for achieving broad bandwidth. We take advantage of the resultant 2D dispersion profile as well as introduce programmability by adding a 2D liquid crystal on silicon spatial light modulator at the masking plane. Our shaper has a resolution of ~3 GHz operating over the entire 'C' band of >5.8 THz. Experimental evidence is provided that highlights the full programmability, fine spectral control, and broad bandwidth operation (limited currently by the bandwidth of the input light). We also show line-by-line manipulation of record 836 comb lines over the C-band.

Changes of collagen in sea cucumber (Stichopus japonicas) during cooking

Changes of the collagen in sea cucumber (Stichopus japonicas) during cooking were investigated. Crude collagen fibers (CCF) is more sensitive to heat than pepsin-solubilized collagen (PSC), absorbance at 226–232 nm increased from 60 to 100°C. PSC nearly completely degraded after cooking for 8–10 h, 4–6 h, 1–1.5 h, 40–50 min, and 10–20 min at 60, 70, 80, 90, and 100°C, respectively. Collagen fiber shrinkage, disappearance of periodic cross striation, complete denaturation, and dispersion of denatured fibers at 40, 60, 80 and 100°C, respectively, were demonstrated by transmission electron microscope (TEM). Above results might be instructional for sea cucumber processing and collagen usage.

Thermometry for turbulent flames by coherent anti-Stokes Raman spectroscopy with simultaneous referencing to the modeless excitation profile

An optimal system for temperature measurements by coherent anti-Stokes Raman spectroscopy (CARS) in turbulent flames and flows is presented. In addition to a single-mode pump laser and a modeless dye laser, an echelle spectrometer with a cross disperser is used. This system permits simultaneous measurement of the N2 CARS spectrum and the broadband dye laser profile. A procedure is developed to use software to transform this profile into the excitation profile by which the spectrum is referenced. Simultaneous shot-to-shot referencing is compared to sequential averaged referencing for data obtained in flat flames and in room air. At flame temperatures, the resultant 1.5% imprecision is limited by flame fluctuations, indicating that the system may have a single-shot imprecision below 1%. At room temperature, the 3.8% single-shot imprecision is of the same order as the best values reported for dual-broadband pure-rotational CARS. Using the unique shot-to-shot excitation profiles, simultaneous referencing eliminates systematic errors. At 2000 and 300 K, the 95% confidence intervals are estimated to be +/- 20 and +/- 10 K, respectively.

Multivariate Optimization of an Axially‐Viewed Inductively Coupled Plasma Multichannel‐Based Emission Spectrometer for the Analysis of Environmental Samples

An experimental design procedure was applied to optimize the operating conditions of an axially-viewed inductively coupled plasma emission spectrometer instruments equipped with echelle optics with cross dispersion and charge transfer device. The multivariate effect of carrier gas flow rate and r.f. power on several analytical figures was investigated and discussed. Both ultrasonic and pneumatic nebulization were used. For the final choice of the optimum, different criteria were taken into account, mainly plasma robustness, instrumental precision, analyte and background net emission, detection limits and signal-to-background ratios. It was found that the use of moderate power (1100W) and mean carrier gas flow rate (0.75 L/min) allows to obtain sufficient plasma robustness, satisfactory precision, and excellent signal-to-background ratios and limits of detection, favorable for ultratrace element determinations in environmental matrices.

Automated determination of stellar parameters from simulated dispersed images for DIVA

We have assessed how well stellar parameters (T e f f , log g and [M/H]) can be retrieved from low-resolution dispersed images to be obtained by the DIVA satellite. Although DIVA is primarily an all-sky astrometric mission, it will also obtain spectrophotometric information for about 13 million stars (operational limiting magnitude V ≃ 13.5 mag). Constructional studies foresee a grating system yielding a dispersion of ≃ 200 nm/mm on the focal plane (first spectral order). For astrometric reasons there will be no cross dispersion which results in the overlapping of the first to third diffraction orders. The one-dimensional, position related intensity function is called a DISPI (DISPersed Intensity). We simulated DISPIS from synthetic spectra taken from Lejeune et al. (1997) and Lejeune et al. (1998) but for a limited range of metallicites, i.e. our results are for [M/H] in the range -0.3 to 1 dex. We show that there is no need to deconvolve these low resolution signals in order to obtain basic stellar parameters. Using neural network methods and by including simulated data of DIVA's UV telescope, we can determine T e f f . to an average accuracy of about 2% for DISPIS from stars with 2000 K ≤ T e f f < 20000 K and visual magnitudes of V = 13 mag (end of mission data). log g can be determined for all temperatures with an accuracy better than 0.25 dex for magnitudes brighter than V = 12 mag. For low temperature stars with 2000 K ≤ T e f f < 5000 K and for metallicities in the range -0.3 to +1 dex a determination of [M/H] is possible (to better than 0.2 dex) for these magnitudes. For higher temperatures, the metallicity signatures are exceedingly weak at DISPI resolutions so that the determination of [M/H] is there not possible. Additionally we examined the effects of extinction E(B - V) on DISPIS and found that it can be determined to better than 0.07 mag for magnitudes brighter than V = 14 mag if the UV information is included.

X-ray emission line gas in the LINER galaxy M 81

We present the soft X-ray spectrum of the LINER galaxy M 81 derived from a long observation with the XMM- Newton RGS. The spectrum is dominated by continuum emission from the active nucleus, but also contains emission lines from Fe L, and H-like and He-like N, O, and Ne. The emission lines are significantly broader than the RGS point-source spectral resolution; in the cross dispersion direction the emission lines are detected adjacent to, as well as coincident with, the active nucleus. This implies that they originate in a region of a few arcminutes spatial extent (1 arcmin ∼ 1 kpc in M 81). The flux ratios of the O VII triplet suggest that collisional processes are responsible for the line emission. A good fit to the whole RGS spectrum is obtained using a model consisting of an absorbed power law from the active nucleus and a 3 temperature optically thin thermal plasma. Two of the thermal plasma components have temperatures of 0.18 ± 0.04 keV and 0.64 ± 0.04 keV, characteristic of the hot interstellar medium produced by supernovae; the combined luminosity of the plasma at these two temperatures accounts for all the unresolved bulge X-ray emission seen in the Chandra observation by Tennant et al. (2001). The third component has a higher temperature (1.7 +2.1 −0.5 keV), and we argue that this, along with some of the 0.64 keV emission, comes from X-ray binaries in the bulge of M 81.

HiTIES: A High Throughput Imaging Echelle Spectrogragh for ground‐based visible airglow and auroral studies

We describe an imaging spectrograph with high spectral resolution (0.3 Å) that uses an echelle grating without the conventional cross disperser. The spectrograph covers the entire visible region. However, only 5 – 20 wavelength regions can be observed simultaneously. The total wavelength coverage is limited by the number of available pixels on the detector and for a 1024 × 1024 pixels detector is ∼ 100 – 300 Å. Order separation is achieved by a mosaic of interference filters located at the image plane.

The Coudé Echelle Spectrograph for the Xinglong 2.16-m Telescope

A brief description of the NAO coude echelle spectrograph mounted on the 2.16m telescope at Xinglong station is given. This echelle spectrograph is located at the coude focus with a prism cross disperser. The echelle image covers the spectral region from 330 to 1100nm displayed in 80 spectral orders in one exposure through two light beams. With a slit height of 2mm, spectral orders are separated by 15 to 23 pixels in blue region and by 7 to 19 pixels in red region. Alternatively, two additional resolution modes corresponding to dierent focal length cameras with resolving power R = 16000, 170000 in the blue beam and R = 13000, 170000 in the red beam could be provided by this spectrograph. The bias, dark, wavelength calibration, flat field and science exposure are described in details. The limiting magnitude for 1 hour exposure with an S/N ratio of 100 scales to V = 9.5 in the red path and to V = 7.2 in the blue path.

On-chip integration of sequential ion-sensing system based on intermittent reagent pumping and formation of two-layer flow.

A sequential ion-sensing system using a single microchip was successfully realized. The system developed here involves intermittent pumping of plural organic phases into a microchannel, followed by contact with a single aqueous phase to form a stable organic-aqueous two-layer flow inside the microchannel. Because the plural organic phases created by intermittent flow contain the same lipophilic pH indicator dye but different ion-selective neutral ionophores, different ions can be sequentially and selectively extracted into the different organic phases, where they can be determined by thermal lens microscopy (TLM). We used KD-A3 as the lipophilic pH indicator dye and valinomycin and DD16C5 as neutral ionophores to demonstrate sequential ion sensing of potassium and sodium ions by measuring the deprotonated dye caused by the ion extraction. The integrated microfluidic system proposed here allows multi-ion sensing, which is not easily demonstrated by conventional ion sensor technology using a solvent polymeric membrane. The minimum volume of single organic phase needed to obtain an equilibrium response without dilution by cross dispersion of two organic phases was ca. 500 nL in our system, indicating that the required amounts of expensive reagents in one measurement could be reduced to 1.7 ng and 2.8 ng for the dye and ionophore molecules, respectively.

Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch–Zernike polynomials

Recording methods for making aberration-corrected holographic gratings are greatly simplified by use of a plane multimode deformable mirror (MDM) upon one of the two recording beams. It is shown that MDM compensators easily provide the superposition of many interesting active optics modes, which we have named Clebsch-Zernike modes. When we apply only a uniform loading or no loading at all onto the rear side of the MDM clear aperture, the available Clebsch-Zernike modes are made to belong to a subclass of the Zernike modes that includes the three modes of the third-order aberration theory as well as a well-defined part of the Zernike higher-order modes. Such a recording method is considered to be universal, since it does not require the use of a sophisticated optical system such as a compensator. Active optics 12-arm MDM's in the vase form have been designed from the elasticity theory. The design of six-arm MDM's is currently carried out with theoretical results. As an example of the method, the recording of three holographic gratings of the Hubble Space Telescope Cosmic Origins Spectrograph has been investigated. Substantial improvements in image quality have been found by use of a six-arm MDM as recording compensator. The result is that aberrations of much higher order can simultaneously be corrected so that the residual blur images of the spectra occupy areas approximately 10 (direction of dispersion) x 3 (cross dispersion) = 30 times smaller--also in terms of pixel number--than those obtained by our American colleagues. Therefore the active optics recording method appears to provide substantial gains in resolving power and in sensitivity: (i) For all three gratings the spectral resolution would be increased by a factor of 10, and (ii), in addition, for the two higher dispersion gratings, the limiting magnitude on the sky appears to be increased by a magnitude of approximately 1-1.2.