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

Two-photon excitation provides a means of activating chemical or physical processes with high spatial resolution in three dimensions and has made possible the development of three-dimensional fluorescence imaging, optical data storage, and lithographic microfabrication. These applications take advantage of the fact that the two-photon absorption probability depends quadratically on intensity, so under tight-focusing conditions, the absorption is confined at the focus to a volume of order λ3 (where λ is the laser wavelength). Any subsequent process, such as fluorescence or a photoinduced chemical reaction, is also localized in this small volume. Although three-dimensional data storage and microfabrication have been illustrated using two-photon-initiated polymerization of resins incorporating conventional ultraviolet-absorbing initiators, such photopolymer systems exhibit low photosensitivity as the initiators have small two-photon absorption cross-sections (δ). Consequently, this approach requires high laser power, and its widespread use remains impractical. Here we report on a class of π;-conjugated compounds that exhibit large δ (as high as 1, 250 × 10−50 cm4 s per photon) and enhanced two-photon sensitivity relative to ultraviolet initiators. Two-photon excitable resins based on these new initiators have been developed and used to demonstrate a scheme for three-dimensional data storage which permits fluorescent and refractive read-out, and the fabrication of three-dimensional micro-optical and micromechanical structures, including photonic-bandgap-type structures.

Two-photon polymerization initiators for three-dimensional optical data storage and microfabrication

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

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

Substrate Stiffness Affects the Functional Maturation of Neonatal Rat Ventricular Myocytes

We describe an x-ray differential phase-contrast imaging method based on two-dimensional transmission gratings that are directly resolved by an x-ray camera. X-ray refraction and diffraction in the sample lead to variations of the positions and amplitudes of the grating fringes on the camera. These effects can be quantified through spatial harmonic analysis. The use of 2D gratings allows differential phase contrast in several directions to be obtained from a single image. When compared to previous grating-based interferometry methods, this approach obviates the need for multiple exposures and separate measurements for different directions and thereby accelerates imaging speed.

/pdf/single-shot-x-ray-differential-phase-contrast-and-2jdaee4rfa.pdf

Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings

In grating-based x-ray phase sensitive imaging, dark-field contrast refers to the extinction of the interference fringes due to small-angle scattering. For configurations where the sample is placed before the beamsplitter grating, the dark-field contrast has been quantified with theoretical wave propagation models. Yet when the grating is placed before the sample, the dark-field contrast has only been modeled in the geometric optics regime. Here we attempt to quantify the dark-field effect in the grating-before-sample geometry with first-principle wave calculations and understand the associated particle-size selectivity. We obtain an expression for the dark-field effect in terms of the sample material’s complex refractive index, which can be verified experimentally without fitting parameters. A dark-field computed tomography experiment shows that the particle-size selectivity can be used to differentiate materials of identical x-ray absorption.

/pdf/interpretation-of-dark-field-contrast-and-particle-size-5abcui9qls.pdf

Interpretation of dark-field contrast and particle-size selectivity in grating interferometers.

Purpose: To characterize certain aspects of the microscopic structures of cortical and trabecular bone by using Fourier x-ray scattering imaging. Materials and Methods: Protocols approved by the National Institutes of Health Animal Care and Use Committee were used to examine ex vivo the hind limb of a rat and the toe of a pig. The Fourier x-ray scattering imaging technique involves the use of a grid mask to modulate the cone beam and Fourier spectral filters to isolate the harmonic images. The technique yields attenuation, scattering, and phase-contrast (PC) images from a single exposure. In the rat tibia cortical bone, the scattering signals from two orthogonal grid orientations were compared by using Wilcoxon signed rank tests. In the pig toe, the heterogeneity of scattering and PC signals was compared between trabecular and compact bone regions of uniform attenuation by using F tests. Results: In cortical bone, the scattering signal was significantly higher (P < 10−15) when the grid was parallel to the...

/pdf/fourier-x-ray-scattering-radiography-yields-bone-structural-47ev44gjrp.pdf

Fourier X-ray scattering radiography yields bone structural information.

Coherent X-ray scattering is related to the electron density distribution by a Fourier transform, and therefore a window into the microscopic structures of biological samples. Current techniques of scattering rely on small-angle measurements from highly collimated X-ray beams produced from synchrotron light sources. Imaging of the distribution of scattering provides a new contrast mechanism which is different from absorption radiography, but is a lengthy process of raster or line scans of the beam over the object. Here, we describe an imaging technique in the spatial frequency domain capable of acquiring both the scattering and absorption distributions in a single exposure. We present first results obtained with conventional X-ray equipment. This method interposes a grid between the X-ray source and the imaged object, so that the grid-modulated image contains a primary image and a grid harmonic image. The ratio between the harmonic and primary images is shown to be a pure scattering image. It is the auto-correlation of the electron density distribution at a specific distance. We tested a number of samples at 60-200 nm autocorrelation distance, and found the scattering images to be distinct from the absorption images and reveal new features. This technique is simple to implement, and should help broaden the imaging applications of X-ray scattering.

Spatial Harmonic Imaging of X-ray Scattering—Initial Results

Purpose: The purpose of this study is to develop a single-shot version of the grating-based phase contrastx-ray imaging method and demonstrate its capability ofin vivo animal imaging. Here, the authors describe the principle and experimental results. They show the source of artifacts in the phase contrast signal and optimal designs that minimize them. They also discuss its current limitations and ways to overcome them. Methods: A single lead grid was inserted midway between an x-ray tube and an x-raycamera in the planar radiography setting. The grid acted as a transmission grating and cast periodic dark fringes on the camera. The camera had sufficient spatial resolution to resolve the fringes. Refraction and diffraction in the imaged object manifested as position shifts and amplitude attenuation of the fringes, respectively. In order to quantify these changes precisely without imposing a fixed geometric relationship between the camera pixel array and the fringes, a spatial harmonic method in the Fourier domain was developed. The level of the differential phase (refraction) contrast as a function of hardware specifications and device geometry was derived and used to guide the optimal placement of the grid and object. Bothex vivo and in vivoimages of rodent extremities were collected to demonstrate the capability of the method. The exposure time using a 50 W tube was 28 s. Results: Differential phase contrastimages of glass beads acquired at various grid and object positions confirmed theoretical predictions of how phase contrast and extraneous artifacts vary with the device geometry. In anesthetized rats, a single exposure yielded artifact-free images of absorption, differential phase contrast, and diffraction. Differential phase contrast was strongest at bone-soft tissue interfaces, while diffraction was strongest in bone. Conclusions: The spatial harmonic method allowed us to obtain absorption, differential phase contrast, and diffractionimages, all from a single raw image and is feasible in live animals. Because the sensitivity of the method scales with the density of the gratings, custom microfabricated gratings should be superior to off-the-shelf lead grids.

/pdf/a-grating-based-single-shot-x-ray-phase-contrast-and-46zhmo61xb.pdf

Eric E. Bennett

Papers

Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings

Interpretation of dark-field contrast and particle-size selectivity in grating interferometers.

Fourier X-ray scattering radiography yields bone structural information.

Spatial Harmonic Imaging of X-ray Scattering—Initial Results

A grating-based single-shot x-ray phase contrast and diffraction method for in vivo imaging