A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

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

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

Since the discovery of X rays, one has benefited from X-ray imaging using its penetrating property. Nowadays, its application expanded into wide variety of fields such as medicine. The contrast obtained with conventional X-ray imaging is generated by the difference in absorption. Because X-ray absorption coefficient is larger for heavier element, strong contrast is obtained when heavy elements are localizing in an object. On the contrary, when an object mainly consisting of light elements such as biological soft tissue is illuminated with X rays, one encounters a problem that sufficient contrast cannot be generated. Although image quality can be improved by increasing X-ray dose, radiation damage is crucial especially in biological imaging. To overcome this problem, contrast media are occasionally used. Recently research activity for using phase contrast is growing remarkably in the field of X-ray imaging. This is because one expects that phase-contrast X-ray imaging would give a breakthrough to this problem from a completely different point of view. As mentioned, formation of conventional X-ray transmission images relies on X-ray absorption, and X-ray wave property has not been used for imaging. As illustrated in Fig. 1, when Xray wave passes an object, its amplitude attenuates by absorption and its phase shifts due to the difference in phase velocity. The advantage of using the X-ray phase shift is that its magnitude is sufficiently large even if absorption is too weak to detect. This feature can be seen by graphing interaction cross sections of X-ray absorption and X-ray phase shift as a function of atomic number. The absorption cross section corresponds to atomic absorption coefficient μ, and the phase-shift cross section can be defined as ) ( 1 f Z r p e + = λ , (1)

http://www.jstage.jst.go.jp/article/analscisp/17icas/0/17icas_0_i527/_pdf

Phase-Contrast X-Ray Imaging Using an X-Ray Interferometer for Biological Imaging

Large-area (25 × 20 mm) phase-contrast X-ray imaging was attained by using a skew-symmetric two-crystal X-ray interferometer. The sub-nrad angular control required to operate the X-ray interferometer was achieved with a sleeve bearing and a feedback-positioning system. As a demonstration, measurements of a phase map of a rat's liver and a phase-contrast tomographic three-dimensional image of a piece of a rabbit's liver were performed at the Photon Factory using 0.07 nm synchrotron radiation X-rays.

Large-area phase-contrast X-ray imaging using a two-crystal X-ray interferometer

A feasibility test of phase tomography using diffraction-enhanced imaging (DEI) was performed with biological tissues consisting of not only soft tissues but also cartilages and bones. Reconstructed three-dimensional images indicated that phase tomography using DEI has an advantage from a biological viewpoint over phase tomography using a crystal X-ray interferometer, which cannot be applied to samples involving marked refractive index changes at boundaries between soft tissues and bones or cartilages.

Ichiro Koyama

Papers

Demonstration of X-Ray Talbot Interferometry

Phase tomography using an x-ray Talbot interferometer

Phase-Contrast X-Ray Imaging Using an X-Ray Interferometer for Biological Imaging

Large-area phase-contrast X-ray imaging using a two-crystal X-ray interferometer

Biological Imaging by X-ray Phase Tomography Using Diffraction-Enhanced Imaging