A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Using a high-efficiency grating interferometer for hard X rays (10-30 keV) and a phase-stepping technique, separate radiographs of the phase and absorption profiles of bulk samples can be obtained from a single set of measurements. Tomographic reconstruction yields quantitative three-dimensional maps of the X-ray refractive index, with a spatial resolution down to a few microns. The method is mechanically robust, requires little spatial coherence and monochromaticity, and can be scaled up to large fields of view, with a detector of correspondingly moderate spatial resolution. These are important prerequisites for use with laboratory X-ray sources.

/pdf/x-ray-phase-imaging-with-a-grating-interferometer-4px897qwex.pdf

X-ray phase imaging with a grating interferometer.

The development of wave optics for light brought many new insights into our understanding of physics, driven by fundamental experiments like the ones by Young, Fizeau, Michelson-Morley and others. Quantum mechanics, and especially the de Broglie’s postulate relating the momentum p of a particle to the wave vector k of an matter wave: k = 2 λ = p/ℏ, suggested that wave optical experiments should be also possible with massive particles (see table 1), and over the last 40 years electron and neutron interferometers have demonstrated many fundamental aspects of quantum mechanics [1].

/pdf/optics-and-interferometry-with-atoms-and-molecules-1vnuwajb51.pdf

Optics and interferometry with atoms and molecules

Phase-contrast x-ray imaging (PCI) is an innovative method that is sensitive to the refraction of the x-rays in matter. PCI is particularly adapted to visualize weakly absorbing details like those often encountered in biology and medicine. In past years, PCI has become one of the most used imaging methods in laboratory and preclinical studies: its unique characteristics allow high contrast 3D visualization of thick and complex samples even at high spatial resolution. Applications have covered a wide range of pathologies and organs, and are more and more often performed in vivo. Several techniques are now available to exploit and visualize the phase-contrast: propagation- and analyzer-based, crystal and grating interferometry and non-interferometric methods like the coded aperture. In this review, covering the last five years, we will give an overview of the main theoretical and experimental developments and of the important steps performed towards the clinical implementation of PCI.

http://iopscience.iop.org/article/10.1088/0031-9155/58/1/R1/pdf

X-ray phase-contrast imaging: from pre-clinical applications towards clinics

This self-contained, comprehensive book describes the fundamental properties of soft x-rays and extreme ultraviolet (EUV) radiation and discusses their applications in a wide variety of fields, including EUV lithography for semiconductor chip manufacture and soft x-ray biomicroscopy. The author begins by presenting the relevant basic principles such as radiation and scattering, wave propagation, diffraction, and coherence. He then goes on to examine a broad range of phenomena and applications. The topics covered include EUV lithography, biomicroscopy, spectromicroscopy, EUV astronomy, synchrotron radiation, and soft x-ray lasers. He also provides a great deal of useful reference material such as electron binding energies, characteristic emission lines and photo-absorption cross-sections. The book will be of great interest to graduate students and researchers in engineering, physics, chemistry, and the life sciences. It will also appeal to practicing engineers involved in semiconductor fabrication and materials science.

X-Rays and Extreme Ultraviolet Radiation: Principles and Applications

First Talbot interferometry in the hard X-ray region was demonstrated using a pair of transmission gratings made by forming gold stripes on glass plates. By aligning the gratings on the optical axis of X-rays with a separation that caused the Talbot effect by the first grating, moire fringes were produced inclining one grating slightly against the other around the optical axis. A phase object placed in front of the first grating was detected by moire-fringe bending. Using the technique of phase-shifting interferometry, the differential phase corresponding to the phase object could also be measured. This result suggests that X-ray Talbot interferometry is a novel and simple method for phase-sensitive X-ray radiography.

https://iopscience.iop.org/article/10.1143/JJAP.42.L866/pdf

Demonstration of X-Ray Talbot Interferometry

X-ray phase tomography with X-ray Talbot interferometry (XTI) is reported. XTI employs two transmission gratings and generates a contrast corresponding to the differential phase shift caused by a sample. Quantitative phase measurement and tomographic image reconstruction with XTI are demonstrated for biological samples. Finally, the possibility of medical applications of XTI is discussed, based on the advantage of XTI that divergent and polychromatic X-rays are available.

Phase tomography using an x-ray Talbot interferometer

An X-ray Talbot interferometer consisting of two capillary plates, which were used as X-ray amplitude gratings, was evaluated for X-ray phase imaging. A theoretical aspect of capillary X-ray Talbot interferometry is presented with a preliminary operation result using synchrotron radiation. A two-dimensional X-ray Talbot effect, or self-imaging effect, which was the basis of Talbot interferometry, was observed with the capillary plate, and moire images formed by the X-ray Talbot interferometer exhibited contrasts corresponding to the differential phase shift caused by phase objects placed in front of the interferometer. Finally, the possibility of quantitative phase measurement with a fringe scanning technique is discussed.

X-ray Talbot Interferometry with Capillary Plates

X‐ray Talbot Interferometry (XTI) is demonstrated as a novel and simple X‐ray phase‐sensitive imaging method. Differential phase contrast is generated with XTI and quantitative determination of the differential phase is attained in combination with a phase‐shifting technique, further enabling phase tomography. Because XTI does not use crystals but transmission gratings, divergent X‐rays with a broad energy band are available. This is an advantage for medical applications especially using a compact X‐ray source.

X‐Ray Talbot Interferometry for Medical Phase Imaging

Phase‐contrast X‐ray imaging, including phase tomography, was performed at the medium‐length beamline BL20XU of SPring‐8, where undulator X rays were available at 245 m from the source point. A crystal X‐ray interferometer and an X‐ray Talbot interferometer with transmission gratings were used to perform different kinds of phase‐contrast imaging. The crystal X‐ray interferometer was devised in that a crystal lamella for beam recombination was thinned down to 40 μm to achieve high‐resolution imaging. A quick fringe‐scanning mechanism was also constructed enabling the phase measurement with a few second and therefore phase tomography with several minutes. The X‐ray Talbot interferometer was studied as a novel and simple method that generated a contrast corresponding to differential phase. Phase tomography was also attained with the X‐ray Talbot interferometer.

Shinya Kawamoto

Papers

Demonstration of X-Ray Talbot Interferometry

Phase tomography using an x-ray Talbot interferometer

X-ray Talbot Interferometry with Capillary Plates

X‐Ray Talbot Interferometry for Medical Phase Imaging

Development of Apparatus for Phase Imaging Using X-Ray Interferometers at BL20XU of SPring-8