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Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates `unreasonable' effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification of photon shot noise. Here, it is shown that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the real decrement to the imaginary part of the refractive index of the imaged object. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper.

Resolving the electronic structure of single biological molecules in their native state was among the primary motivations behind X-ray free-electron lasers. The ultra-short pulses they produce can outrun the atomic motion induced by radiation damage, but the electronic structure of the sample is still significantly modified from its original state. This paper explores the decoherence of the scattered signal induced by temporal evolution of the electronic structure in the sample molecule. It is shown that the undamaged electron density of a single-molecule sample can often be retrieved using only the two most occupied modes from the coherent mode decomposition of the partially coherent diffraction fluence.

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.

Abstract 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. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.

Abstract The majority of current laboratory based X-ray sources are polychromatic and are not tuneable. This lack of monochromaticity limits the range of applications for these sources and in particular it reduces the elemental specificity of laboratory based X-ray imaging experiments. Here we present a solution to this problem based on the use of Ross filter pairs. Although such Ross filter arrangements have been applied in proof-of-principle spectroscopy experiments, to date there have been no reports of this approach used for full-field X-ray imaging. Here we report on the experimental demonstration of Ross filter pairs being used for quasi-monochromatic, full-field imaging. This arrangement has several important benefits for laboratory based X-ray imaging including, as we demonstrate, elemental contrast enhancement. The method is demonstrated both for two-dimensional radiography and for three-dimensional X-ray tomography.

The Imaging and Medical Beamline (IMBL) is a superconducting multipole wiggler-based beamline at the 3 GeV Australian Synchrotron operated by the Australian Nuclear Science and Technology Organisation (ANSTO). The beamline delivers hard X-rays in the 25–120 keV energy range and offers the potential for a range of biomedical X-ray applications, including radiotherapy and medical imaging experiments. One of the imaging modalities available at IMBL is propagation-based X-ray phase-contrast computed tomography (PCT). PCT produces superior results when imaging low-density materials such as soft tissue (e.g., breast mastectomies) and has the potential to be developed into a valuable medical imaging tool. We anticipate that PCT will be utilized for medical breast imaging in the near future with the advantage that it could provide better contrast than conventional X-ray absorption imaging. The unique properties of synchrotron X-ray sources such as high coherence, energy tunability, and high brightness are particularly well-suited for generating PCT data using very short exposure times on the order of less than 1 min. The coherence of synchrotron radiation allows for phase-contrast imaging with superior sensitivity to small differences in soft-tissue density. Here we also compare the results of PCT using two different detectors, as these unique source characteristics need to be complemented with a highly efficient detector. Moreover, the application of phase retrieval for PCT image reconstruction enables the use of noisier images, potentially significantly reducing the total dose received by patients during acquisition. This work is part of ongoing research into innovative tomographic methods aimed at the introduction of 3D X-ray medical imaging at the IMBL to improve the detection and diagnosis of breast cancer. Major progress in this area at the IMBL includes the characterization of a large number of mastectomy samples, both normal and cancerous, which have been scanned at clinically acceptable radiation dose levels and evaluated by expert radiologists with respect to both image quality and cancer diagnosis.