Chanh Q. Tran

X-ray phase imaging: Demonstration of extended conditions with homogeneous objects

We discuss contrast formation in a propagating x-ray beam. We consider the validity conditions for linear relations based on the transport-of-intensity equation (TIE) and on contrast transfer functions (CTFs). From a single diffracted image, we recover the thickness of a homogeneous object which has substantial absorption and a phase-shift of --0.37 radian.

Observation of an x-ray vortex

Phase singularities are a ubiquitous feature of waves of all forms and represent a fundamental aspect of wave topology. An optical vortex phase singularity occurs when there is a spiral phase ramp about a point phase singularity. We report an experimental observation of an optical vortex in a field consisting of 9-keV x-ray photons. The vortex is created with an x-ray optical structure that imparts a spiral phase distribution to the incident wave field and is observed by use of diffraction about a wire to create a division-of-wave-front interferometer.

Extracting coherent modes from partially coherent wavefields

A method for numerically recovering the coherent modes and their occupancies from a known mutual optical intensity function is described. As an example, the technique is applied to previously published experimental data from an x-ray undulator source. The data are found to be described by three coherent modes, and the functional forms and relative occupancies of these modes are recovered.

X-ray extended-range technique for precision measurement of the X-ray mass attenuation coefficient and Im (f ) for copper using synchrotron radiation

We reconsider the long-standing problem of accurate measurement of atomic form factors for fundamental and applied problems. We discuss the X-ray extended-range technique for accurate measurement of the mass attenuation coefficient and the imaginary component of the atomic form factor. Novelties of this approach include the use of a synchrotron with detector normalisation, the direct calibration of dominant systematics using multiple thicknesses, and measurement over wide energy ranges with a resulting improvement of accuracies by an order of magnitude. This new technique achieves accuracies of 0.27– 0.5% and reproducibility of 0.02% for attenuation of copper from 8.84 to 20 keV, compared to accuracies of 10% using atomic vapours. This precision challenges available theoretical calculations. Discrepancies of 10% between current theory and experiments can now be addressed.  2001 Elsevier Science B.V. All rights reserved.

Measurement of the x-ray mass attenuation coefficient of silver using the x-ray-extended range technique

We used the x-ray-extended range technique to measure the x-ray mass attenuation coefficients of silver in the 15–50 keV energy range with a level of uncertainty between 0.27% and 0.4% away from the K-edge. The imaginary part of the atomic form factor of silver was derived by subtracting the scattering component from the measured total mass attenuation coefficients. Discrepancies between the measured mass attenuation coefficients and alternative theoretical predictions are discussed.

X-ray imaging : a generalized approach using phase-space tomography.

We discuss the role of coherence in x-ray imaging and consider how phase-space tomography can be used to extract information about partial coherence. We describe the application of phase-space tomography to x-ray imaging and recover the spatial coherence properties of a one-dimensional soft (1.5 keV) x-ray beam from a synchrotron undulator source. We present phase-space information from a Youngs experiment and observe negative regions in the quasi-probability distribution. We show that, given knowledge of the coherence of the beam, we can use partially coherent diffraction data to recover fully coherent information, and we present some simple experimental demonstrations of this capability.

Absolute determination of the effect of scattering and fluorescence on x-ray attenuation measurements

We investigate the effect of x-ray scattering and fluorescence upon measurements of the x-ray mass attenuation coefficient. Measurements of scattering and fluorescence are obtained from a comparison of attenuation measurements using different sized apertures to admit varying amounts of the scattering and fluorescence into the detectors. The result of such a comparison is found to be in good agreement with a theoretical calculation of the fluorescent and scattered photons reaching the ion chambers and, under our experimental conditions, decreases the measured attenuation coefficients of silver by up to 0.2%.

Precision X-ray optics for fundamental interactions in atomic physics, resolving discrepancies in the X-ray regime

Reliable knowledge of the complex X-ray form factor (Re(f) and f″) is required for many fields including crystallography, medical diagnosis and XAFS studies. However, there are discrepancies between theory and theory, experiment and experiment and theory and experiment of 10% and more, over central X-ray energies. Discrepancies exist for most elements, despite claimed experimental accuracies of 1%. This paper summarises the current variation between experimental and theoretical results, and outlines key issues for obtaining experimental accuracies of 1% in critical wavelength ranges for selected elements to address these issues. This paper critically surveys available experimental data for attenuation coefficients and suggests a procedure for obtaining significantly higher accuracy measurements in the future.

Synchrotron beam coherence: a spatially resolved measurement

We report a precise and spatially resolved measurement of the complex degree of coherence of a one-dimensional 1.5-keV beam produced by a third-generation synchrotron source. The method of phase-space tomography is used, which requires only measurements of the x-ray intensity. We find that the field is statistically stationary to within experimental error, the correlations are very well approximated by a Gaussian distribution, and the measured coherence length is in excellent agreement with expectations.

Measurement of the x-ray mass-attenuation coefficients of gold, derived quantities between 14 keV and 21 keV and determination of the bond lengths of gold

The x-ray mass-attenuation coefficients of gold are measured at 91 energies between 14 keV and 21 keV using synchrotron radiation. The measurements are accurate to between 0.08% and 0.1%. The photoelectric mass-absorption coefficients and the imaginary component of the form factors of gold are also determined. The results include the LI edge and are the most accurate and extensive gold dataset available in this energy range. An analysis of the LI edge XAFS showed excellent agreement between the measured and simulated XAFS and yielded highly accurate values of the bond lengths of gold. When our results are compared with earlier measurements and with predictions of major theoretical tabulations, significant discrepancies are noted. The comparison raises questions about the nature of discrepancies between experimental and theoretical values of mass-attenuation coefficients.