X-ray microtomography using correlation of near-field speckles for material characterization.

Nondestructive microscale investigation of objects is an invaluable tool in life and materials sciences. Currently, such investigation is mainly performed with X-ray laboratory systems, which are based on absorption-contrast imaging and cannot access the information carried by the phase of the X-ray waves. The phase signal is, nevertheless, of great value in X-ray imaging as it is complementary to the absorption information and in general more sensitive to visualize features with small density differences.

Speckle-based x-ray phase-contrast imaging with a laboratory source and the scanning technique.

The speckle-based scanning method for x-ray phase-contrast imaging is implemented with a liquid-metal-jet source. Using the two-dimensional scanning technique, the phase shift introduced by the object is retrieved in both transverse orientations, and the limitations on spatial resolution inherent to the speckle-tracking technique are avoided. This method opens up possibilities of new high-resolution multimodal applications for lab-based phase-contrast x-ray imaging.

First application of liquid-metal-jet sources for small-animal imaging: high-resolution CT and phase-contrast tumor demarcation.

Purpose: Small-animal studies require images with high spatial resolution and high contrast due to the small scale of the structures. X-ray imaging systems for small animals are often limited by the microfocus source. Here, the authors investigate the applicability of liquid-metal-jet x-ray sources for such high-resolution small-animal imaging, both in tomography based on absorption and in soft-tissue tumor imaging based on in-line phase contrast.

Phase retrieval in X-ray phase-contrast imaging suitable for tomography.

In-line phase-contrast X-ray imaging provides images where both absorption and refraction contribute. For quantitative analysis of these images, the phase needs to be retrieved numerically. There are many phase-retrieval methods available.

Singular-value decomposition of a tomosynthesis system.

Tomosynthesis is an emerging technique with potential to replace mammography, since it gives 3D information at a relatively small increase in dose and cost. We present an analytical singular-value decomposition of a tomosynthesis system, which provides the measurement component of any given object. The method is demonstrated on an example object.

Elementary functions: propagation of partially coherent light.

The theory of propagation of partially coherent light is well known, but performing numerical calculations still presents a difficulty because of the dimensionality of the problem. We propose using a recently introduced method based on the use of elementary functions [Wald et al. Proc.

Systematic design of an anastigmatic lens axicon.

We present an analytical method for systematic optical design of a double-pass axicon that shows almost no astigmatism in oblique illumination compared to a conventional linear axicon. The anastigmatic axicon is a singlet lens with nearly concentric spherical surfaces applied in double pass, making it possible to form a long narrow focal line of uniform width. The front and the back surfaces have reflective coatings in the central and annular zones, respectively, to provide the double pass.

Communication modes in large-aperture approximation.

Simplified versions of the communication modes in the Fresnel domain are derived when the system apertures are large. The approximate modes, which are in the form of spherical waves and sinc functions with a spherical curvature, give physical insight into the communication modes approach and the basic limits of free-space optical communication systems. They also show that Gabor's information theory is readily derived from the communication modes.

Lens axicons in oblique illumination.

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line.

Linearity of the pyramid wavefront sensor.

The pyramid wavefront sensor is very similar to the Fourier knife-edge test, but employs dynamic modulation to quantify the phase derivative. For circular modulation, we compare approximate geometrical optics calculations, more exact diffraction calculations, and experimental results. We show that both the sinusoidal and the approximate linear relationship between wavefront derivative and wavefront sensor response can be derived rigorously from diffraction theory.

Singular-value decomposition for through-focus imaging systems.

Singular-value decomposition (SVD) of a linear imaging system gives information on the null and measurement components of object and image and provides a method for object reconstruction from image data. We apply SVD to through-focus imaging systems that produce several two-dimensional images of a three-dimensional object. Analytical expressions for the singular functions are derived in the geometrical approximation for a telecentric, laterally shift-invariant system linear in intensity.

Simple lens axicon.

We present the design of a cemented doublet-lens axicon made from spherical surfaces only. Compared with diffractive axicons, refractive cone axicons, and earlier lens axicons with aspheric surfaces, this element is inexpensive and easy to manufacture even with large apertures. The lens axicon is based on the deliberate use of the spherical aberration of the surfaces.

Communication modes applied to axicons.

The communication modes, which constitute a convenient method for the propagation and information analysis of optical fields, are formulated in the generalized axicon geometry. The transmitting region is the axicon's annular aperture, and the observation domain is the optical axis containing the focal line segment. We show that in rotational symmetry one may employ the prolate spheroidal wave functions to represent the communication modes.