On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the information capacity of imaging systems in terms of the number of imaging quanta (particles) used in the experiment. These results can be useful in the context of biomedical imaging constrained by the radiation dose delivered to the sample, or in imaging (e.g. astronomical) problems under "low light" conditions

Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images

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, during free-space propagation, of photon shot noise in the object-plane intensity. We show that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the phase shift to the logarithm of intensity in the object plane. 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.Comment: 26 pages, 2 figures, 2 tables, 56 reference

Phase-and-amplitude computer tomography

A tomographic technique is proposed for reconstruction under specified conditions of the three-dimensional distribution of complex refractive index in a sample from a single projection image per view angle, where the images display both absorption contrast and propagation-induced phase contrast. The algorithm achieves high numerical stability as a consequence of the complementary nature of the absorption and phase contrast transfer functions. The method is pertinent to biomedical imaging and nondestructive testing of samples exhibiting weak absorption contrast