Unpolarized X-ray Research Articles

A conceptual polarimetry applied in X-ray polarization in the energy range of 10–30 keV

The lower energy part of the hard X-ray band, 10–30 keV, still remains unexplored for X-ray polarimetry. A photo-electric polarimetry based on a CMOS imaging sensor typed GMAX0505 was proven to be a candidate polarimeter applied in this energy band, the pixel size is 2.5 μm and X-ray detection depth is around 5 μm. Due to a limitation of its pixel shape, the sensors can not give the polarization angle of incoming X-rays directly, but predict the angle by utilizing the asymmetric response at different polarization angle of X-rays. In this study, we construct a simplified sensor based on the structure of the GMAX0505, utilizing the GEANT4 toolkit. The variation trend of modulation factor in the simulation is similar with those measured in the reference at 12.4-keV and 24.8-keV X-rays. Based on the simulation framework, we change the pixel shape from square to hexagon with the same pixel pitch of 2.5 μm and define three directions along the symmetry axis of a pixel. Comparing the modulation curves obtained by solving the modulation curve function with three parameters, the modulation factor is around 10% and 23% at 12.4 keV and 24.8 keV in response to X-rays with different polarization angle and 100% linear polarization, the difference between predicted and incident polarization angle is less than 2.5° which is an estimate of the systematic error. Meanwhile, the degree of modulation is less than 1% in response to unpolarized X-rays. This study shows that similar sensors with a hexagonal pixel shape can give the modulation curve and directly predict the polarization angle of an X-ray source. It also provides a conceptual design for next photo-electric X-ray polarimetry in the energy band. In addition, the performance characterized by quality factor (QF) was compared for the sensors with different pixel pitch and the same pixel gap, the results show the QF is sensitive to a pixel pitch with different value and the value of the QF is maximum as a pixel pitch of the sensors is 0.75 μm under the same condition of pixel gap of 0.2 μm.

Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

Analytical formalism for calculations of parameters needed for quantitative analysis by X-ray photoelectron spectroscopy

Universal analytical formula for the emission depth distribution function for photoelectrons with kinetic energies up to 5000 eV

Numerous parameters needed for quantification of X-ray photoelectron spectroscopy can be derived from the emission depth distribution function (EMDDF) known for a given photoelectron line, an experimental configuration, and a solid. This function describes the probability that a photoelectron emitted at a certain depth enters an analyzer without energy loss. The EMDDF turns out to be distinctly affected by photoelectron elastic scattering effects. A useful measure of influence of elastic scattering is a closely related function named the correction factor (CF). This function is a useful tool for correcting the in-depth concentration profiles obtained from the procedure of non-destructive depth profiling. Due of complexity of the theoretical models describing transport of photoelectrons emitted by unpolarized X-rays in the surface region of solids, a typical computational approach involves Monte Carlo algorithms with different simulation strategies. However, convenient sources of EMDDFs (and CF functions) are analytical formulas that can be implemented in the software dedicated for practical surface analysis. The present report evaluates accuracy of different analytical formulae. A new expression is proposed which can be considered as a predictive formula, i.e., a simple analytical expression of reasonable accuracy for typical measurement conditions. This formula is applicable to photoelectrons emitted by unpolarized or circularly polarized X-rays. Furthermore, stress is put on the influence of non-dipolar parameters that define a high-energy photoemission cross section on the EMDDF for photoelectrons with kinetic energies exceeding 1500 eV. Eventually, a photoelectron kinetic energy of 5 keV was established as an upper limit of applicability of the presented formalism. Finally, applicability of the analytical formalism, derived for unpolarized X-rays, to photoelectrons emitted by linearly polarized radiation is analyzed. Due to the considerable influence of the position of the polarization vector on the photoelectron signal, the analytical formalism developed for unpolarized radiation cannot be recommended for use if the of X-ray beam is linearly polarized or has partial polarization.

A note on calculations of photoelectron partial intensities for energies reaching 4000 eV

A very simple method for determining the photoelectron partial intensities and reduced partial intensities for HAXPES photoelectrons is proposed. For these calculations, it is sufficient to know a formalism expressing the photoelectron signal intensity as a function of the inelastic mean free path. The only computational problem is due to required procedure of multiple numerical differentiation, although one can use published programs for that purpose. The proposed method was designed to photoemission emitted by unpolarized X-rays and for planar samples. A wide range of photoelectron energies was considered: from 500 eV to 4000 eV. Evaluation of accuracy was performed by comparison with partial intensities obtained from accompanying Monte Carlo simulations of photoelectron trajectories in the same analytical conditions. The proposed method was found to provide up to eight partial intensities with reasonable accuracy. Depending on element, photoelectron line, and kinetic energy, the mean percentage deviation varied in the range from 0.95% to 3.11%. Similar agreement was observed in comparisons with published partial intensities obtained from Monte Carlo simulations, and with partial intensities obtained from the database SESSA (NIST Database for the Simulation of Electron Spectra for Surface Analysis, Version 2.1.1).

Polarized x-ray excitation for scatter reduction in x-ray fluorescence computed tomography.

X-ray fluorescence computer tomography (XFCT) is a new molecular imaging modality which uses x-ray excitation to stimulate the emission of fluorescent photons in high atomic number contrast agents. Scatter contamination is one of the main challenges in XFCT imaging which limits the molecular sensitivity. When polarized x rays are used, it is possible to reduce the scatter contamination significantly by placing detectors perpendicular to the polarization direction. This study quantifies scatter contamination for polarized and unpolarized x-ray excitation and determines the advantages of scatter reduction. The amount of scatter in preclinical XFCT is quantified in Monte Carlo simulations. The fluorescent x rays are emitted isotropically, while scattered x rays propagate in polarization direction. The magnitude of scatter contamination is studied in XFCT simulations of a mouse phantom. In this study, the contrast agent gold is examined as an example, but a scatter reduction from polarized excitation is also expected for other elements. The scatter reduction capability is examined for different polarization intensities with a monoenergetic x-ray excitation energy of 82keV. The study evaluates two different geometrical shapes of CZT detectors which are modeled with an energy resolution of 1keV FWHM at an x-ray energy of 80keV. Benefits of a detector placement perpendicular to the polarization direction are shown in iterative and analytic image reconstruction including scatter correction. The contrast to noise ratio (CNR) and the normalized mean square error (NMSE) are analyzed and compared for the reconstructed images. A substantial scatter reduction for common detector sizes was achieved for 100% and 80% linear polarization while lower polarization intensities provide a decreased scatter reduction. By placing the detector perpendicular to the polarization direction, a scatter reduction by factor up to 5.5 can be achieved for common detector sizes. The image reconstruction showed that for a scatter magnitude decrease by a factor of 2.4, the molecular sensitivity could almost be doubled. Scatter reduction lowers the amount of noise in the projection datasets and reconstructed images which enhance molecular sensitivity at equal dose. The results support the use of linear polarized x rays to reduce scatter in XFCT imaging.

Development of the GEM-TPC X-ray Polarimeter with the Scalable Readout System

We have developed a gaseous Time Projection Chamber (TPC) containing a single-layered foil of a gas electron multiplier (GEM) to open up a new window on cosmic X-ray polarimetry in the 2–10 keV band. The micro-pattern TPC polarimeter in combination with the Scalable Readout System produced by the RD51 collaboration has been built as an engineering model to optimize detector parameters and improve polarimeter sensitivity. The polarimeter was characterized with unpolarized X-rays from an X-ray generator in a laboratory and polarized X-rays on the BL32B2 beamline at the SPring-8 synchrotron radiation facility. Preliminary results show that the polarimeter has a comparable modulation factor to a prototype of the flight one.

Performance of the PRAXyS X-ray polarimeter

The performance of the Time Projection Chamber (TPC) polarimeter for the Polarimeter for Relativistic Astrophysical X-ray Sources (PRAXyS) Small Explorer was evaluated using polarized and unpolarized X-ray sources. The PRAXyS mission will enable exploration of the universe through X-ray polarimetry in the 2–10keV energy band. We carried out performance tests of the polarimeter at the Brookhaven National Laboratory, National Synchrotron Light Source (BNL-NSLS) and at NASA's Goddard Space Flight Center. The polarimeter was tested with linearly polarized, monochromatic X-rays at 11 different energies between 2.5 and 8.0keV. At maximum sensitivity, the measured modulation factors at 2.7, 4.5 and 8.0keV are 27%, 43% and 59%, respectively and the measured angle of polarization is consistent with the expected value at all energies. Measurements with a broadband, unpolarized X-ray source placed a limit of less than 1% on false polarization in the PRAXyS polarimeter.

Parameterization of HAXPES photoelectrons with kinetic energies up to 10 keV

An algorithm for modeling transport of photoelectrons with kinetic energies up to 10keV has been developed. Calculations were performed for photoelectrons emitted by the unpolarized (or circularly polarized) X-ray radiation. In the theoretical model used, different approximations for the photoemission cross section were used: the cross sections derived within the dipole approximation or the cross sections corrected for the nondipolar effects. It turned out that the photoelectron signal intensity can be considerably affected in the high energy range by the neglect of the first order correction. The percentage deviations may reach 40%. On the other hand, the influence of the second order correction is less pronounced; the difference between both corrections is below 6%. On the other hand, the parameters needed for quantification of XPS (or HAXPES), the mean escape depth and the effective attenuation length, were found to be practically independent of the photoelectron cross section used in calculations in wide range of the experimental configurations. An attempt has been made to elucidate this unexpected result. A criterion has been proposed that allows prediction of systems and experimental geometries in which the above parameters are insensitive to the photoemission cross sections.

Effective attenuation lengths for photoelectrons emitted by high-energy laboratory X-ray sources

We report calculations of effective attenuation lengths (EALs) for Si 2s1/2, Cu 2p3/2, Ag 3d5/2, and Au 4f7/2 photoelectrons excited by Mg Kα, Al Kα, Zr Lα, and Ti Kα X-rays, where the photoelectron energies ranged from 321eV to 4.426keV. These EALs, appropriate for determining overlayer-film thicknesses, were calculated from the transport-approximation formalism and from Monte Carlo simulations using photoionization cross sections from the dipole and non-dipole approximations. Satisfactory consistency was found between EALs determined from the TA formalism and from MC simulations, while differences between EALs for Au 4f7/2 photoelectrons from the dipole and non-dipole approximations were between 1% (for Mg and Al Kα X-rays) and 2.5% (for Ti Kα X-rays) for photoelectron emission angles less than 50°. As in past work for electron energies less than 2keV, we found a simple linear relation between the ratio of the average EAL (for emission angles less than 50°) to the inelastic mean free path (IMFP) and the single-scattering albedo, a function of the IMFP and the transport mean free path. The root-mean-square difference between our average EALs and those from the linear expression was 1.44%. This expression should be useful in determinations of film thicknesses by XPS with unpolarized X-rays for photoelectron energies up to about 5keV.

X-ray polarization splitting by a single crystal evaluated with synchrotron x-rays.

In hexagonal crystals such as quartz, an asymmetric Bragg reflection from two equivalent internal crystal planes can separate unpolarized x-rays into two linearly polarized components. The perfectly polarized and tunable x-rays from a synchrotron are ideal to evaluate polarization spitting in detail. One unanticipated feature is that additional reflections from the crystal affect the diffraction intensity of the two polarized components, an effect that is unlikely to matter in polarization spectroscopy of radiating plasmas for which the crystal is intended.

Re-testing the JET-X Flight Module No. 2 at the PANTER facility

The Joint European X-ray Telescope (JET-X) was the core instrument of the Russian Spectrum-X-gamma space observatory. It consisted of two identical soft X-ray (0.3 - 10 keV) telescopes with focusing optical modules having a measured angular resolution of nearly 15 arcsec. Soon after the payload completion, the mission was cancelled and the two optical flight modules (FM) were brought to the Brera Astronomical Observatory where they had been manufactured. After 16 years of storage, we have utilized the JET-X FM2 to test at the PANTER X-ray facility a prototype of a novel X-ray polarimetric telescope, using a Gas Pixel Detector (GPD) with polarimetric capabilities in the focal plane of the FM2. The GPD was developed by a collaboration between INFN-Pisa and INAF-IAPS. In the first phase of the test campaign, we have re-tested the FM2 at PANTER to have an up-to-date characterization in terms of angular resolution and effective area, while in the second part of the test the GPD has been placed in the focal plane of the FM2. In this paper we report the results of the tests of the sole FM2, using an unpolarized X-ray source, comparing the results with the calibration done in 1996.

A Monte Carlo study of the primary absorbed energy redistribution in X-ray lithography

The minimum feature size producible by LIGA X-ray lithography is fundamentally limited by the redistribution of primary doses via photoelectrons and the influence of the resulting dose distribution on resist development. Secondary radiation from mask and substrate are well known as source for pattern distortion in deep X-ray lithography. Numerical simulations by means of Monte Carlo simulations using PENELOPE (Salvat et al. in PENELOPE-2008: a code system for Monte Carlo simulation of electron and photon transport. http://www.nea.fr/html/dbprog/penelope-2008.pdf , 2008) are applied to quantify these additional dose values in the resist/substrate interface and the irradiated/shadowed interface. A significant reduction of the additional dose by secondary radiation from the plating base is not observed for Au and Ti layers thicker than 10 nm. The influence of polarized or unpolarized X-rays might be neglected for structure dimensions larger than a few 10 nm. As an example of critical dimension, simulations were used to predict the structure quality of grating structures with a period of 2.4 μm and duty cycle 0.5 in a resist layer of 300 μm.

Optimization of the design of the hard X-ray polarimeter X-Calibur

We report on the optimization of the hard X-ray polarimeter X-Calibur for a high-altitude balloon-flight in the focal plane of the InFOCμS X-ray telescope from Fort Sumner (NM) in Fall 2013. X-Calibur combines a low-Z scintillator slab to Compton-scatter photons with a high-Z Cadmium Zinc Telluride (CZT) detector assembly to photo-absorb the scattered photons. The detector makes use of the fact that polarized photons Compton scatter preferentially perpendicular to the electric field orientation. X-Calibur achieves a high detection efficiency of order unity and reaches a sensitivity close to the best theoretically possible. In this paper, we discuss the optimization of the design of the instrument based on Monte Carlo simulations of polarized and unpolarized X-ray beams and of the most important background components. We calculate the sensitivity of the polarimeter for the upcoming balloon flight from Fort Sumner and for additional longer balloon flights with higher throughput mirrors. We conclude by emphasizing that Compton polarimeters on satellite borne missions can be used down to energies of a few keV.

Resonant Raman scattering of polarized and unpolarized x-ray radiation from Mg, Al, and Si

The x-ray resonant Raman scattering (RRS) effect of polarized and unpolarized radiation in the vicinity of the $1s$ absorption threshold of low-$Z$ elements such as magnesium, aluminum, and silicon is investigated. For the polarized and tunable exciting x-ray radiation the plane grating monochromator (PGM) beam line at the PTB laboratory in the BESSY II synchrotron radiation facility was employed, while unpolarized x-ray beams were induced by 1-MeV proton beam irradiation on various pure thick targets. For the latter case, a novel proton-induced x-ray fluorescence scattering chamber was designed and installed at the Tandem accelerator laboratory of the Institute of Nuclear Physics at N.C.S.R. ``Demokritos.'' The total RRS cross sections deduced from both independent excitation modes were found to be in a good agreement, within the experimental uncertainties. The predictions of the existing theory with respect to the dependence of the RRS to the incident beam polarization state is calculated and discussed with respect to the experimental results.

Breakdown of spatial inversion symmetry in core-level photoemission of Pt(001)

We have measured the spin polarization of the $4d$ and $4f$ core-level photoelectrons from Pt(001) by using unpolarized laboratory x-ray sources under a highly bulk sensitive condition. The $4d$ and $4f$ photoelectrons are highly spin polarized perpendicular to the reaction plane as defined by the incident photons and the outgoing electrons. The measured spin polarization and a close look at the core-level photoemission process demonstrate that the bulk core-level photoemission with unpolarized light contributes to the measured spin polarization. This result is in contrast to the valence band photoemission from nonmagnetic solids, wherein the bulk cannot contribute to the measured spin polarization due to the existence of spatial inversion symmetry. Thus, the argument based on spatial inversion symmetry does not apply to the core-level photoemission. The measured spin polarization is in good agreement with an atomic model.

Gas Pixel Detectors for low energy X-ray polarimetry

Gas Pixel Detectors are position-sensitive proportional counters in which a complete integration between the gas amplification structure and the read-out electronics has been reached. Various generation of Application-Specific Integrated Circuit (ASIC) have been designed in deep submicron CMOS technology to realize a monolithic device which is at the same time the charge collecting electrode and the analog amplifying and charge measuring front-end electronics. The experimental response of a detector with 22060 pixels at 80 μ m pitch to polarized and un-polarized X-ray radiation is shown and the application of this device for Astronomical X-ray Polarimetry discussed.

Direct reading of charge multipliers with a self-triggering CMOS analog chip with 105 k pixels at 50 μm pitch

We report on a large area (15×15 mm 2), high channel density (470 pixel/mm 2), self-triggering CMOS analog chip that we have developed as a pixelized charge collecting electrode of a Micropattern Gas Detector. This device represents a big step forward both in terms of size and performance, and is in fact the last version of three generations of custom ASICs of increasing complexity. The top metal layer of the CMOS pixel array is patterned in a matrix of 105,600 hexagonal pixels with a 50 μm pitch. Each pixel is directly connected to the underlying full electronics chain which has been realized in the remaining five metal and single poly-silicon layers of a 0.18 μm VLSI technology. The chip, which has customizable self-triggering capabilities, also includes a signal pre-processing function for the automatic localization of the event coordinates. Thanks to these advances it is possible to significantly reduce the read-out time and the data volume by limiting the signal output only to those pixels belonging to the region of interest. In addition to the reduced read-out time and data volume, the very small pixel area and the use of a deep sub-micron CMOS technology has allowed bringing the noise down to 50 electrons ENC. Results from in depth tests of this device when coupled to a fine pitch (50 μm on a triangular pattern) Gas Electron Multiplier are presented. It was found that matching the read-out and gas amplification pitch allows getting optimal results. The experimental detector response to polarized and unpolarized X-ray radiation when working with two gas mixtures and two different photon energies is shown and the application of this detector for Astronomical X-ray Polarimetry is discussed. Results from a full Monte-Carlo simulation for several galactic and extragalactic astronomical sources are also reported.

Gas pixel detectors for X-ray polarimetry applications

We discuss a new class of micro pattern gas detectors, the gas pixel detector (GPD), in which a complete integration between the gas amplification structure and the read-out electronics has been reached. An application-specific integrated circuit (ASIC) built in deep sub-micron technology has been developed to realize a monolithic device that is, at the same time, the pixelized charge collecting electrode and the amplifying, shaping and charge measuring front-end electronics. The CMOS chip has the top metal layer patterned in a matrix of 80 μm pitch hexagonal pixels, each of them directly connected to the underneath electronics chain which has been realized in the remaining five layers of the 0.35 μm VLSI technology. Results from tests of a first prototype of such detector with 2 k pixels and a full scale version with 22 k pixels are presented. The application of this device for Astronomical X-ray Polarimetry is discussed. The experimental detector response to polarized and unpolarized X-ray radiation is shown. Results from a full MonteCarlo simulation for two astronomical sources, the Crab Nebula and the Hercules X1, are also reported.

Elastic scattering and the associated anomalous dispersion in the energy range 8.63E42.75 keV from heavy atoms

Elastic scattering cross-sections for Pt, Au and Pb were measured using nearly monoenergetic unpolarized Kα x-ray photons in the energy range 8.63⩽E⩽42.75 keV at an angle of 90°. The experimental results were compared with theoretical elastic scattering cross-sections calculated using relativistic form factors (RFFs), relativistic modified form factors (RMFs), a combination of RFFs, RMFs with angle-independent anomalous scattering factors (ASFs) and relativistic numerical calculations based on the multipole expansion of the second-order S-matrix approach. The experimental results were in reasonable agreement with the S-matrix values and values based on an RMF+ASF approach compared with an RFF+ASF approach. © 1988 John Wiley & Sons, Ltd.

MAGNETIC DICHROISM UNDER EXCITATION BY UNPOLARIZED RADIATION

Magnetic dichroism has been observed in the angular distribution of p-core level photoemission spectra excited from crystalline ferromagnets by unpolarized X-rays. The angular dependence of the angular and energy-resolved photoemission intensity was recorded as a function of the emission direction with respect to the crystal, revealing a strong variation of the magnetic dichroism with emission angle due to photoelectron diffraction. This variation is particularly strong around the forward scattering peaks, including sign reversals close to these directions. The results demonstrate that any standard X-ray photoelectron spectroscopy apparatus possesses the potential for combined analysis of surface magnetic structure and geometric structure in a chemically specific way.