50th anniversary of the Judd–Ofelt theory: An experimentalist's view of the formalism and its application

The theory on the intensities of 4f-4f transitions introduced by B.R. Judd and G.S. Ofelt in 1962 has become a center piece in rare-earth optical spectroscopy over the past five decades. Many fundamental studies have since explored the physical origins of the Judd–Ofelt theory and have proposed numerous extensions to the original model. A great number of studies have applied the Judd–Ofelt theory to a wide range of rare-earth doped materials, many of them with important applications in solid-state lasers, optical amplifiers, phosphors for displays and solid state lighting, upconversion and quantum-cutting materials, and fluorescent markers. This paper takes the view of the experimentalist who is interested in appreciating the basic concepts, implications, assumptions, and limitations of the Judd–Ofelt theory in order to properly apply it to practical problems. We first present the formalism for calculating the wavefunctions of 4f electronic states in a concise form and then show their application to the calculation and fitting of 4f-4f transition intensities. The potential, limitations and pitfalls of the theory are discussed, and a detailed case study of LaCl3:Er3+ is presented.

A Benzaldehyde Derivative as a Chelating Ligand: Helical Manganese(II) Coordination Polymers Assembling into a Porous Solid

A molecular, porous crystalline material constructed from neutral helical coordination polymers incorporating manganese(II) ions and two types of bridging ligands, namely the deprotonated form of 2-hydroxy-5-methoxy-3-nitrobenzaldehyde (HL) and isobutyrate (iB−), has been obtained and structurally characterized. Structural analysis reveals that within the coordination polymer each benzaldehyde derivative ligates two manganese ions in 6-membered chelating rings, and the isobutyrate ligands cooperatively chelate either two or three manganese ions. The solid state assembly of the resulting polymeric chains of formula [Mn4(L)2(iB)6]n (1), described in the polar space group R3c, is associated with tubular channels occupied by MeCN solvent molecules (1·xMeCN; x ≤ 9). TGA profiles and PXRD measurements demonstrate that the crystallinity of the solid remains intact in its fully desolvated form, and its stability and crystallinity are ensured up to a temperature of 190 °C. Gas adsorption properties of desolvated crystals were probed, but no remarkable sorption capacity of N2 and only a limited one for CO2 could be observed. Magnetic susceptibility data reveal an antiferromagnetic type of coupling between adjacent manganese(II) ions along the helical chains with energy parameters J1 = −5.9(6) cm−1 and J2 = −1.8(9) cm−1.

Observations of the northern seasonal polar cap on Mars II: HiRISE photometric analysis of evolution of northern polar dunes in spring

We present an overview of our analyses of HiRISE observations of spring evolution of selected dune areas of the north polar erg. The north polar erg is covered annually by seasonal volatile ice layer, a mixture of CO2 and H2O with mineral dust contamination. In spring, this layer sublimes creating visually enigmatic phenomena, e.g. dark and bright fan-shaped deposits, dark–bright–dark bandings, dark down-slope streaks, and seasonal polygonal cracks. Similar phenomena in southern polar areas are believed to be related to the specific process of solid-state greenhouse effect. In the north, it is currently unclear if the solid-state greenhouse effect is able to explain all the observed phenomena especially because the increased influence of H2O on the time scales of this process has not yet been quantified. HiRISE observations of our selected locations show that the ground exhibits a temporal behaviour similar to the one observed in the southern polar areas: a brightening phase starting close to the spring equinox with a subsequent darkening towards summer solstice. The resolution of HiRISE enabled us to study dunes and substrate individually and even distinguish between different developments on windward and slip face sides of single dunes. Differences in the seasonal evolution between steep slip faces and flatter substrate and windward sides of dunes have been identified and compared to CRISM data of CO2 and H2O distributions on dunes. We also observe small scale dark blotches that appear in early observations and tend to sustain a low reflectivity throughout the spring. These blotches can be regarded as the analogue of dark fan deposits in southern polar areas, leading us to the conclusion that both martian polar areas follow similar spring evolutions.

Transconvolution and the virtual positron emission tomograph--a new method for cross calibration in quantitative PET∕CT imaging

PURPOSE Positron emission tomography (PET)∕computed tomography (CT) measurements on small lesions are impaired by the partial volume effect, which is intrinsically tied to the point spread function of the actual imaging system, including the reconstruction algorithms. The variability resulting from different point spread functions hinders the assessment of quantitative measurements in clinical routine and especially degrades comparability within multicenter trials. To improve quantitative comparability there is a need for methods to match different PET∕CT systems through elimination of this systemic variability. Consequently, a new method was developed and tested that transforms the image of an object as produced by one tomograph to another image of the same object as it would have been seen by a different tomograph. The proposed new method, termed Transconvolution, compensates for differing imaging properties of different tomographs and particularly aims at quantitative comparability of PET∕CT in the context of multicenter trials. METHODS To solve the problem of image normalization, the theory of Transconvolution was mathematically established together with new methods to handle point spread functions of different PET∕CT systems. Knowing the point spread functions of two different imaging systems allows determining a Transconvolution function to convert one image into the other. This function is calculated by convolving one point spread function with the inverse of the other point spread function which, when adhering to certain boundary conditions such as the use of linear acquisition and image reconstruction methods, is a numerically accessible operation. For reliable measurement of such point spread functions characterizing different PET∕CT systems, a dedicated solid-state phantom incorporating (68)Ge∕(68)Ga filled spheres was developed. To iteratively determine and represent such point spread functions, exponential density functions in combination with a Gaussian distribution were introduced. Furthermore, simulation of a virtual PET system provided a standard imaging system with clearly defined properties to which the real PET systems were to be matched. A Hann window served as the modulation transfer function for the virtual PET. The Hann's apodization properties suppressed high spatial frequencies above a certain critical frequency, thereby fulfilling the above-mentioned boundary conditions. The determined point spread functions were subsequently used by the novel Transconvolution algorithm to match different PET∕CT systems onto the virtual PET system. Finally, the theoretically elaborated Transconvolution method was validated transforming phantom images acquired on two different PET systems to nearly identical data sets, as they would be imaged by the virtual PET system. RESULTS The proposed Transconvolution method matched different PET∕CT-systems for an improved and reproducible determination of a normalized activity concentration. The highest difference in measured activity concentration between the two different PET systems of 18.2% was found in spheres of 2 ml volume. Transconvolution reduced this difference down to 1.6%. In addition to reestablishing comparability the new method with its parameterization of point spread functions allowed a full characterization of imaging properties of the examined tomographs. CONCLUSIONS By matching different tomographs to a virtual standardized imaging system, Transconvolution opens a new comprehensive method for cross calibration in quantitative PET imaging. The use of a virtual PET system restores comparability between data sets from different PET systems by exerting a common, reproducible, and defined partial volume effect.

A detector based on silica fibers for ion beam monitoring in a wide current range

A detector based on doped silica and optical fibers was developed to monitor the profile of particle accelerator beams of intensity ranging from 1 pA to tens of µA. Scintillation light produced in a fiber moving across the beam is measured, giving information on its position, shape and intensity. The detector was tested with a continuous proton beam at the 18 MeV Bern medical cyclotron used for radioisotope production and multi-disciplinary research. For currents from 1 pA to 20 µA, Ce3+ and Sb3+ doped silica fibers were used as sensors. Read out systems based on photodiodes, photomultipliers and solid state photomultipliers were employed. Profiles down to the pA range were measured with this method for the first time. For currents ranging from 1 pA to 3 µA, the integral of the profile was found to be linear with respect to the beam current, which can be measured by this detector with an accuracy of ∼1%. The profile was determined with a spatial resolution of 0.25 mm. For currents ranging from 5 µA to 20 µA, thermal effects affect light yield and transmission, causing distortions of the profile and limitations in monitoring capabilities. For currents higher than ∼1 µA, non doped optical fibers for both producing and transporting scintillation light were also successfully employed.