Three-dimensional contrast-transfer-function approach in phase-contrast tomography.

A new method is developed for 3D reconstruction of multimaterial objects using propagation-based x-ray phase-contrast tomography (PB-CT) with phase retrieval via contrast-transfer-function (CTF) formalism. The approach differs from conventional PB-CT algorithms, which apply phase retrieval to individual 2D projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D.

Effect of x-ray energy on the radiological image quality in propagation-based phase-contrast computed tomography of the breast.

Breast cancer is the most common cancer in women in developing and developed countries and is responsible for 15% of women's cancer deaths worldwide. Conventional absorption-based breast imaging techniques lack sufficient contrast for comprehensive diagnosis. Propagation-based phase-contrast computed tomography (PB-CT) is a developing technique that exploits a more contrast-sensitive property of x-rays: x-ray refraction.

Noise-resolution uncertainty principle in classical and quantum systems.

We show that the width of an arbitrary function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is then demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields.

Comparison of propagation-based CT using synchrotron radiation and conventional cone-beam CT for breast imaging.

Objectives: To evaluate and compare the image quality of propagation-based phase-contrast computed tomography (PB-CT) using synchrotron radiation and conventional cone-beam breast computed tomography (CBBCT) based on various radiological image quality criteria.

Methods: Eight excised breast tissue samples of various sizes and containing different lesion types were scanned using PB-CT at a synchrotron facility and using CBBCT at a university-affiliated breast imaging centre. PB-CT scans were performed at two different mean glandular dose (MGD) levels: standard (5.

Fast three-dimensional phase retrieval in propagation-based X-ray tomography.

The following article describes a method for 3D reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogeneous form of the transport of intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localized region of the CT-reconstructed volume. This work demonstrates, via numerical simulations, the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it with both conventional absorption tomography and 2D TIE-Hom phase retrieval applied to projection images.

Signal-to-noise, spatial resolution and information capacity of coherent diffraction imaging.

It is shown that the average signal-to-noise ratio (SNR) in the three-dimensional electron-density distribution of a sample reconstructed by coherent diffractive imaging cannot exceed twice the square root of the ratio of the mean total number of scattered photons detected during the scan and the number of spatially resolved voxels in the reconstructed volume. This result leads to an upper bound on Shannon's information capacity of this imaging method by specifying the maximum number of distinguishable density distributions within the reconstructed volume when the radiation dose delivered to the sample and the spatial resolution are both fixed. If the spatially averaged SNR in the reconstructed electron density is fixed instead, the radiation dose is shown to be proportional to the third or fourth power of the spatial resolution, depending on the sampling of the three-dimensional diffraction space and the scattering power of the sample.

Advantages of breast cancer visualization and characterization using synchrotron radiation phase-contrast tomography.

The aim of this study was to highlight the advantages that propagation-based phase-contrast computed tomography (PB-CT) with synchrotron radiation can provide in breast cancer diagnostics. For the first time, a fresh and intact mastectomy sample from a 60 year old patient was scanned on the IMBL beamline at the Australian Synchrotron in PB-CT mode and reconstructed. The clinical picture was described and characterized by an experienced breast radiologist, who underlined the advantages of providing diagnosis on a PB-CT volume rather than conventional two-dimensional modalities.

Toward Improving Breast Cancer Imaging: Radiological Assessment of Propagation-Based Phase-Contrast CT Technology.

Rationale And Objectives: This study employs clinical/radiological evaluation in establishing the optimum imaging conditions for breast cancer imaging using the X-ray propagation-based phase-contrast tomography.

Materials And Methods: Two series of experiments were conducted and in total 161 synchrotron-based computed tomography (CT) reconstructions of one breast mastectomy specimen were produced at different imaging conditions. Imaging factors include sample-to-detector distance, X-ray energy, CT reconstruction method, phase retrieval algorithm applied to the CT projection images and maximum intensity projection.

High-Resolution X-Ray Phase-Contrast 3-D Imaging of Breast Tissue Specimens as a Possible Adjunct to Histopathology.

Histopathological analysis is the current gold standard in breast cancer diagnosis and management, however, as imaging technology improves, the amount of potential diagnostic information that may be demonstrable radiologically should also increase. We aimed to evaluate the potential clinical usefulness of 3-D phase-contrast micro-computed tomography (micro-CT) imaging at high spatial resolutions as an adjunct to conventional histological microscopy. Ten breast tissue specimens, 2 mm in diameter, were scanned at the SYRMEP beamline of the Elettra Synchrotron using the propagation-based phase-contrast micro-tomography method.

On the "unreasonable" effectiveness of transport of intensity imaging and optical deconvolution.

The effectiveness of reconstructive imaging using the homogeneous transport of intensity equation may be regarded as "unreasonable," because it has been shown to significantly increase signal-to-noise ratio while preserving spatial resolution, compared to equivalent conventional absorption-based imaging techniques at the same photon fluence. We reconcile this surprising behavior by analyzing the propagation of noise in typical in-line holography experiments. This analysis indicates that novel imaging techniques may be designed that produce high signal-to-noise images at low radiation doses without sacrificing spatial resolution.

On the van Cittert-Zernike theorem for intensity correlations and its applications.

A reciprocal relationship between the autocovariance of the light intensity in the source plane and in the far-field detector plane is presented in a form analogous to the classical van Cittert-Zernike theorem, but involving intensity correlation functions. A "classical" version of the reciprocity relationship is considered first, based on the assumption of circular Gaussian statistics of the complex amplitudes in the source plane. The result is consistent with the theory of Hanbury Brown-Twiss interferometry, but it is shown to be also applicable to estimation of the source size or the spatial resolution of the detector from the noise power spectrum of flat-field images.

On noise-resolution uncertainty in quantum field theory.

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck's constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode.

Spatial resolution, signal-to-noise and information capacity of linear imaging systems.

A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the constraints of this model, the square of the signal-to-noise ratio is always proportional to the "volume" of the spatial resolution unit. In the case of Poisson statistics, the ratio of these two quantities divided by the incident density of the imaging particles (e.

Partially coherent contrast-transfer-function approximation.

The contrast-transfer-function (CTF) approximation, widely used in various phase-contrast imaging techniques, is revisited. CTF validity conditions are extended to a wide class of strongly absorbing and refracting objects, as well as to nonuniform partially coherent incident illumination. Partially coherent free-space propagators, describing amplitude and phase in-line contrast, are introduced and their properties are investigated.

A feasibility study of X-ray phase-contrast mammographic tomography at the Imaging and Medical beamline of the Australian Synchrotron.

Results are presented of a recent experiment at the Imaging and Medical beamline of the Australian Synchrotron intended to contribute to the implementation of low-dose high-sensitivity three-dimensional mammographic phase-contrast imaging, initially at synchrotrons and subsequently in hospitals and medical imaging clinics. The effect of such imaging parameters as X-ray energy, source size, detector resolution, sample-to-detector distance, scanning and data processing strategies in the case of propagation-based phase-contrast computed tomography (CT) have been tested, quantified, evaluated and optimized using a plastic phantom simulating relevant breast-tissue characteristics. Analysis of the data collected using a Hamamatsu CMOS Flat Panel Sensor, with a pixel size of 100 µm, revealed the presence of propagation-based phase contrast and demonstrated significant improvement of the quality of phase-contrast CT imaging compared with conventional (absorption-based) CT, at medically acceptable radiation doses.

Young's double-slit experiment: noise-resolution duality.

Statistical aspects of Young's double-slit diffraction experiment are analysed quantitatively. It is shown that the signal-to-noise ratio and the spatial resolution in the detected diffraction pattern satisfy a duality relationship which implies that both of them cannot be improved simultaneously beyond a certain limit if the total number of particles forming the image is fixed. As a consequence of this duality, it is possible to estimate the minimal number of particles that have to be detected in order for two slits separated by a given distance to be resolved with a confidence level corresponding to a pre-defined signal-to-noise ratio, e.

Duality between noise and spatial resolution in linear systems.

It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging.

Quantitative evaluation of in-line x-ray phase contrast for a class of edge objects.

In order to quantify the effect of phase contrast on X-ray image formation, the theory of statistical decision making has been applied to a binary classification task between two signals known exactly, namely, a phase-contrast image (that combines both the absorption and phase contrast) and the corresponding hypothetical pure absorption image that would be obtained under the same imaging conditions but without diffraction/refraction effects. The signal-to-noise ratio (SNR) for two widely used observers, including the ideal observer (also known as the prewhitening matched filter) and a non-ideal observer (the non-prewhitening matched filter) has been estimated in the case of in-line phase-contrast imaging, thus providing a figure-of-merit for the optimisation of the imaging conditions. A broad class of edge objects has been investigated and simple analytical expressions for the corresponding SNRs have been obtained and discussed.

Analysis and interpretation of the first monochromatic X-ray tomography data collected at the Australian Synchrotron Imaging and Medical beamline.

The first monochromatic X-ray tomography experiments conducted at the Imaging and Medical beamline of the Australian Synchrotron are reported. The sample was a phantom comprising nylon line, Al wire and finer Cu wire twisted together. Data sets were collected at four different X-ray energies.

Some simple rules for contrast, signal-to-noise and resolution in in-line x-ray phase-contrast imaging.

Simple analytical expressions are derived for the spatial resolution, contrast and signal-to-noise in X-ray projection images of a generic phase edge. The obtained expressions take into account the maximum phase shift generated by the sample and the sharpness of the edge, as well as such parameters of the imaging set-up as the wavelength spectrum and the size of the incoherent source, the source-to-object and object-to-detector distances and the detector resolution. Different asymptotic behavior of the expressions in the cases of large and small Fresnel numbers is demonstrated.

Soft tissue small avascular tumor imaging with x-ray phase-contrast micro-CT in-line holography.

To assess the feasibility of small soft tissue avascular tumor micro-CT imaging with x-ray phase-contrast in-line holography, we have studied micro-CT imaging with in-line geometry of small spheroidal avascular tumor models with quiescent cell core (< 250 mum) and various distributions of the proliferating cell density (PCD) forming the outer shell. We have simulated imaging with an ultrafast laser-based x-ray source with a Mo target. We observe phase-contrast enhancement of the tumor boundaries in the reconstructed transaxial images, resulting in improved detection of small soft tissue tumors, providing that the PCD density gradient is sufficiently large.

Development of ultrafast laser-based x-ray in-vivo phase-contrast micro-CT beamline for biomedical applications at Advanced Laser Light Source (ALLS).

We are developing and exploring the imaging performance of, an in vivo, in-line holography, x-ray phase-contrast, micro-CT system with an ultrafast laser-based x-ray (ULX) source. By testing and refining our system, and by performing computer simulations, we plan to improve system performance in terms of contrast resolution and multi-energy imaging to a level beyond what can be obtained using a conventional microfocal x-ray tube. Initial CT projection sets at single energy (Mo K(alpha) and K(beta) lines) were acquired in the Fresnel regime and reconstructed for phantoms and a euthanized mouse.

Computed tomography with linear shift-invariant optical systems.

Optical systems capable of three-dimensional transmission imaging are considered; these systems employ a conventional tomographic setup with an added linear shift-invariant optical system between the sample and the detector. A theoretical analysis is presented of image formation and sample reconstruction in such systems, examples of which include diffraction tomography and phase-contrast tomography with the use of analyzer crystals. An example is introduced in which the image is obtained by scanning the beam along the line orthogonal to the optic axis and to the axis of rotation with a one-dimensional slit or grating parallel to the rotation axis.