A Comparison between the Face of the Veil of Manoppello and the Face of the Shroud of Turin

Recently we have studied the unusual optical properties of the Veil of Manoppello, a canvas representing the face of Jesus Christ, and restored digitally the face, by eliminating the distortions of the anatomic details due the yielding of the very fine structure of the fabric. The aim of the present paper is to compare the restored face of the Veil with that visible on the Turin Shroud. In particular, the paper focuses on assessing whether the two images can be superimposed, i.e., whether they are different images of the same face. Indeed, some scholars have suggested that the Veil of Manoppello and the Turin Shroud show different images of the same face. We demonstrate that the face of the Turin Shroud, after a logarithmic transformation of the intensity and the correction of the background noise, shows cheeks’ profiles, not visible before the digital processing, which overlap very well with those of the restored face of the Veil of Manoppello. These correlations between the two images of the face of Jesus raise the question of their historical relationship

Diffraction theory applied to X-ray imaging with clessidra prism array lenses.

Clessidra (hourglass) lenses, i.e. two large prisms each composed of smaller identical prisms or prism-like objects, can focus X-rays. As these lenses have a periodic structure perpendicular to the incident radiation, they will diffract the beam like a diffraction grating. Refraction in the prisms is responsible for blazing, i.e. for the concentration of the diffracted intensity into only a few diffraction peaks. It is found that the diffraction of coherent radiation in clessidra lenses needs to be treated in the Fresnel, or near-field, regime. Here, diffraction theory is applied appropriately to the clessidra structure in order to show that blazing in a perfect structure with partly curved prisms can indeed concentrate the diffracted intensity into only one peak. When the lens is entirely composed of identical perfect prisms, small secondary peaks are found. Nevertheless, the loss in intensity in the central peak will not lead to any significant widening of this peak. Clessidras with perfect prisms illuminated by full coherent X-ray radiation can then provide spatial resolutions, which are consistent with the increased aperture, and which are far below the height of the single small prisms

Assembled Nanostructured Architectures Studied By Grazing Incidence X-Ray Scattering

In this chapter, we will focus on a specific X‐ray-based technique among those employed in surface science and which is especially suitable for the study of self‐assembled nanocrystals: Grazing Incidence Small Angle X‐ray Scattering (GISAXS). We will first introduce the main field of investigation considered herein, with basic notions of X‐ray scattering from surfaces, and then address basic concepts about GISAXS. Finally, we will describe a few relevant examples of studies, of nanostructured architectures, through ex situ and in situ experiments of grazing incidence X‐ray scattering. This manuscript is focused on the former, showing that they can be performed by using laboratory instruments. In situ investigations still need synchrotron radiation sources in most cases; therefore, only a few examples selected from the literature are reported here, for the sake of completeness. The experiments described are mainly performed in the small angle range, providing information on the size and shape of nanocrystals, together with their spatial arrangement. Both 2D and 3D architectures are considered. In particular, GISAXS measurements of 2D superlattices of nano‐octapods, performed both at a third generation synchrotron beamline and with a table‐top set‐up, are compared; the employed table‐top set‐up is described in a dedicated paragraph. Further examples of grazing incidence studies as performed by the authors with a table‐top set‐up are reported: a GISAXS study of 3D iron oxide nanocrystal superlattices, showing the importance of modelling in order to obtain structural information from data; a combined small/wide angle scattering (GISAXS/GIWAXS) study of 3D PbS nanocrystal superlattices; and a GIWAXS study of P3HT nanofibres, showing how the ordering at the molecular and atomic length scales can be obtained by exploring different angular ranges in the same grazing incidence geometry. Finally, selected examples of in situ GISAXS studies, performed with synchrotron radiation sources, are described

Three-dimensional coherent diffractive imaging on non-periodic specimens at the ESRF beamline ID10.

The progress of tomographic coherent diffractive imaging with hard X-rays at the ID10 beamline of the European Synchrotron Radiation Facility is presented. The performance of the instrument is demonstrated by imaging a cluster of Fe2P magnetic nanorods at 59 nm 3D resolution by phasing a diffraction volume measured at 8 keV photon energy. The result obtained shows progress in three-dimensional imaging of non-crystalline samples in air with hard X-rays

Analysis of tapered front-coupling X-ray waveguides.

The coupling and propagation of electromagnetic waves through planar X-ray waveguides (WG) with vacuum gap and Si claddings are analyzed in detail, starting from the source and ending at the detector. The general case of linearly tapered WGs (i.e. with the entrance aperture different from the exit one) is considered. Different kinds of sources, i.e. synchrotron radiation and laboratory desk-top sources, have been considered, with the former providing a fully coherent incoming beam and the latter partially coherent beams. It is demonstrated that useful information about the parameters of the WG can be derived, comparing experimental results with computer simulation based on analytical solutions of the Helmholtz equation which take into account the amplitude and phase matching between the standing waves created in front of the WG, and the resonance modes propagating into the WG

Determination of the Projected Atomic Potential by Deconvolution of the Auto-Correlation Function of TEM Electron Nano-Diffraction Patterns

We present a novel method to determine the projected atomic potential of a specimen directly from transmission electron microscopy coherent electron nano-diffraction patterns, overcoming common limitations encountered so far due to the dynamical nature of electron-matter interaction. The projected potential is obtained by deconvolution of the inverse Fourier transform of experimental diffraction patterns rescaled in intensity by using theoretical values of the kinematical atomic scattering factors. This novelty enables the compensation of dynamical effects typical of transmission electron microscopy (TEM) experiments on standard specimens with thicknesses up to a few tens of nm. The projected atomic potentials so obtained are averaged on sample regions illuminated by nano-sized electron probes and are in good quantitative agreement with theoretical expectations. Contrary to lens-based microscopy, here the spatial resolution in the retrieved projected atomic potential profiles is related to the finer lattice spacing measured in the electron diffraction pattern. The method has been successfully applied to experimental nano-diffraction data of crystalline centrosymmetric and non-centrosymmetric specimens achieving a resolution of 65 pm

The Number of Elementary Fermions and the Electromagnetic Coupling

Electric charges and masses of elementary fermions of the Standard Model and fundamental physical constants (speed of light in vacuum, Planck constant, gravitational constant, vacuum permittivity, electron charge) are related through a simple equation. This new relation links 10 of the free parameters of the Standard Model—the masses of the three charged leptons and six quarks, and the electromagnetic coupling—in a compact formula, leaving strong constraints for allowing further elementary charged fermions beyond the Standard Model’s physics. The formula is not derived by theoretical calculations, but it is based on the empirically measured values of the electric charges and proper masses of the known elementary fermions

A Mathematical Analysis of Maria Valtorta’s Mystical Writings

We have studied the very large amount of literary works written by the Italian mystic Maria Valtorta to assess similarities and differences in her writings, because she claims that most of them are due to mystical visions. We have used mathematical and statistical tools developed for specifically studying deep linguistic aspects of texts. The general trend indicates that the literary works explicitly attributable to Maria Valtorta differ significantly from her other literary works, which she claims are attributable to the alleged characters Jesus and Mary. Mathematically, they seem to have been written by different authors. The comparison with the Italian literature is very striking. A single author, namely Maria Valtorta, seems to be able to write texts so diverse as to cover the entire mathematical range (suitably defined) of the Italian literature spanning seven centuries

A Deep-Language Mathematical Analysis of Gospels, Acts and Revelation

The paper aims at casting some light on the interrelations among the Gospels, Acts and Revelation. We do not consider words ranking and their frequency of occurrence, as largely done in the literature, but we analyze, statistically, some mathematical aspects of the texts, which the authors were not conscious of. We use mathematical methods developed for specifically studying deep-language parameters of literary texts, such as the number of words per sentence, the number of characters per word, the number of words per interpunctions, the number of interpunctions per sentence, all very likely peculiar to the writer’s style, after having recalled the punctuation in classical languages. First, we consider the full texts of the canonical Gospels, Acts and Revelation, then the partial texts attributable to the Triple Tradition (Matthew, Mark and Luke), to the Double Tradition (Matthew and Luke), Own Tradition (Matthew and Luke) and Q source. The mathematical/statistical tool used confirms and reinforces some general results concerning the Gospels, Acts, Revelation and Q source, but also evidences some interesting differences concerning the number of words per sentence and words per interpunctions, likely casting some light on the capacity of the short-term memory of the readers/listeners of these texts. All these New Testament writings fit very well in the larger Greek literature of the time. The existence of a proto gospel seems more probable than other possible hypotheses

Literary fiction or ancient astronomical and meteorological observations in the work of maria valtorta?

In The Gospel as revealed to me, Maria Valtorta reports a lot of information on the Holy Land at the time of Jesus: historical, archaeological, astronomical, geographical, meteorological. She states she has written what seen “in vision”. By a detailed astronomical analysis of explicit and implicit calendar information reported while she narrates detailed episodes concerning the three years of Jesus’ public life—possible because of many references to lunar phases, constellations, planets visible in the night sky in her writings—it is ascertained that every event described implies a precise date—day, month, year—without being explicitly reported by her. For example, Jesus’ crucifixion should have occurred on Friday April 23 of the year 34, a date proposed by Isaac Newton. She has also recorded the occurrence of rain so that the number of rainy days reported can be compared to the current meteorological data, supposing random observations and no important changes in rainfall daily frequency in the last 2000 years, the latter issue discussed in the paper. Unexpectedly, both the annual and monthly averages of rainy days deduced from the data available from the Israel Meteorological Service and similar averages deduced from her writings agree very well