Affine diffractive beam dividers.

Diffractive optical elements that divide an input beam into a set of replicas are used in many optical applications ranging from image processing to communications. Their design requires time-consuming optimization processes, which, for a given number of generated beams, are to be separately treated for one-dimensional and two-dimensional cases because the corresponding optimal efficiencies may be different. After generalizing their Fourier treatment, we prove that, once a particular divider has been designed, its transmission function can be used to generate numberless other dividers through affine transforms that preserve the efficiency of the original element without requiring any further optimization.

Tracking flowpaths in a complex karst system through tracer test and hydrogeochemical monitoring: Implications for groundwater protection (Gran Sasso, Italy).

Groundwater in karst aquifers is frequently tapped for drinking purposes, due to frequent huge volumes of resources. Unfortunately, vulnerability of these aquifers can be high, due to possible fast transfer of recharge water on springs by the karst network. On Gran Sasso Mountain regional aquifer, several springs are subjected to drinking withdrawal and an updated evaluation of their potential is now a fundamental issue to be considered, facing climate change effects, which reflect on variation of discharge regimen and values. To distinguish between different contribution of spring recharge, a tracer test has been carried out on the Vitella d'Oro spring, fed both by the regional aquifer and by a local system exposed to karst features developed in the Rigopiano Conglomerates formation. Thanks to hydrogeological, hydrogeochemical and isotopic data, a conceptual model of spring recharge has been proposed and subsequently validated by the tracer test results. All information confirms the superimposition on the regional base flow, by a relevant contribution of the karst network, influencing the spring discharge in recharge periods. In detail, a fast flow component is responsible for discharge peaks and frequently of turbidity events, having a mean velocity ranging from 30 to 70 m/h in the aquifer. Besides of this fast flow, an additional aliquot of the recharge is due to the same local aquifer, but slower flow clearly identifiable by hydrochemistry and isotopic data. Thanks to these findings, a renewed management of the spring has been suggested, considering the different degrees of aquifer vulnerability (turbidity occurrence) directly related to the discharge regimen.

The role of mesotherapy in the management of spinal pain. A randomized controlled study.

Background: Mesotherapy is a technique through which active ingredients are administered into the thickness of the skin in order to increase the local analgesic effect. Methods: 141 patients with spinal pain not responding to systemic therapy with NSAIDs were randomized to receive one or more intra-cutaneous drugs on a weekly basis. Results: All patients achieved a pain reduction of at least 50% compared to baseline, and all tolerated the therapy without having to resort to systemic drug dose increases. Conclusions: The data from our study show that the active ingredients infiltrated into the skin induce a mesodermal modulation between the infiltrated liquid and the cutaneous nervous and cellular structures from which the typical drug-saving effect of mesotherapy arises. Although further studies are needed to establish how to integrate mesotherapy in various clinical settings, it appears to be a useful technique available to the practicing physician. This research is also useful in guiding future clinical research.

Three-dimensional polarization of fields radiated by partially coherent electromagnetic cylindrical sources.

Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outward are introduced. Their 3 × 3 cross-spectral density matrix is given through expansions of the field components in terms of basis functions related to the Hankel functions. The spectral density and the three-dimensional degree of polarization of such sources and the fields they radiate are examined. Several examples are presented and discussed. Among them, a class of cylindrical sources whose coherent vector modes coincide with the above basis functions is defined and studied.

Partially coherent spherical sources with spherical harmonic modes.

A class of partially coherent spherical sources is introduced whose cross-spectral density across the surface has a modal expansion made up of spherical harmonics. For such sources, the solution of the propagation problem in all the outer spaces can be written through a series of the propagated modes, which maintains the spherical harmonic structure. The main features of this class of cross-spectral densities are derived illustrating their coherence properties with examples. Attention is paid to the properties of radial coherence. In particular, it is clearly shown that sources with perfect radial coherence exist with angular coherence that is only partial.

Cylindrical partially coherent scalar sources.

Partially coherent scalar sources with cylindrical symmetry radiating outwards are introduced. Homogeneous cross-spectral densities are shown to possess angularly modulated Hankel modes, whose amplitudes are subject to a filtering process during propagation. Simple criteria for treating such sources are given. For the case of an incoherent cylinder, the number of effective modes is found and spatial coherence is shown to appear in the radiated light. The radial coherence of the radiated field is then examined. Non-homogeneous cylindrical sources are also introduced.

On-axis polarization of beams radiated by electromagnetic circularly coherent sources.

On-axis spectral density and degree of polarization of beams radiated by electromagnetic (EM) sources with circular correlations are shown to be finely controlled by changing the source parameters. We reveal, in particular, that in this beam class, unlike for all previously known stationary beams, it is possible to control independently the dynamics of the on-axis spectral density and the degree of polarization. This was enabled by the obtained analytical expression for the on-axis polarization matrix, derived for general EM sources with circular coherence and Gaussian spectral density across the source plane. A simple experimental scheme for generating a broad class of EM circularly coherent sources is devised involving only a line source, a lens, and a transparency, possibly anisotropic.

Tailoring on-axis spectral density with circularly coherent light beams.

The on-axis cross-spectral density (CSD) of a beam radiated by a stationary source with a circular coherence state and a Gaussian spectral density is obtained in the closed form. It is revealed that the on-axis CSD is expressed via the Laplace transform of the source's degree of coherence or the Hilbert transform of the corresponding pseudo-mode weighting function. Such relations enable efficient tailoring of the on-axis spectral density, as we show with a slew of numerical examples.

On z-coherence in self-focusing.

Both the intensity distribution and the degree of coherence between pairs of points along the propagation axis (z-coherence) are derived in closed form for a phenomenon of self-focusing produced by circularly coherent light. The first confirms results previously obtained numerically, while the second exhibits new complex features. The physical interpretation is obtained by a suitable pseudo-modal expansion that suggests an analogy with a simple two-mode structure.

On z-coherence of beams radiated by Schell-model sources with Gaussian profile.

The degree of coherence and the intensity distribution on the axis of the beam radiated by a planar partially coherent source of the Schell-model type are investigated. We present an expression for the on-axis cross-spectral density which is valid for a very general Schell-model source, with the only constraint that the intensity distribution across the source is Gaussian. Furthermore, we show that such an expression takes very simple analytical forms for several commonly used degrees of coherence of the source.

Intradermal therapy (mesotherapy): the lower the better.

BACKGROUND: Intradermal therapy (mesotherapy) is a technique used to inject drugs into the surface layer of the skin. The intradermal micro deposit allows to modulate the kinetics of drugs, slowing down its absorption and prolonging the local mechanism of action. This technique is applied in the treatment of some forms of localized pain when a systemic drug-saving effect is useful, when it is necessary to synergize with other pharmacological or non-pharmacological thera-pies, when other therapies have failed or cannot be used. AIM: The purpose of our study was to evaluate the effect of a mixture with respect to its lower concentration. We also wanted to evaluate the number of sessions needed to reach the therapeutic goal (50% reduction in pain from baseline) in patients with acute or chronic neck pain. METHOD: We analyzed retrospectively data from 62 patients with cervicobrachial pain treated with intradermal drugs. Group A received a mixture of drugs; group B received half the dose of drugs. RESULTS: Patients who received a lower concentration of drugs achieved similar results to those who received a higher dose. The therapeutic goal was achieved on average with 3.5 + 1.7 sessions on a weekly basis (min 1; max 9). Subjects in group A required 4+1.7 treatments (min 1; max 9), while subjects in group B required 3+1.5 treatments (min 1; max 7). CONCLUSIONS: Our study confirms that even a lower dose of drugs can induce a clinically useful result. This study confirms that the useful effect of mesotherapy is only partly due to the pharmacological action. Further randomized prospective studies are needed to standardize the technique in the various pain syndromes, but it is recommended to follow the guidelines of the Italian Society of Mesotherapy to ensure patients receive appropriate treatment.

Evidence based recommendations on mesotherapy: an update from the Italian society of Mesotherapy.

INTRODUCTION: Mesotherapy, also known as local intradermal therapy, widely used all over the world, is a technique used to inject substances into the surface layer of the skin. There are no international guidelines for the correct use of this technique and in many countries, it is still applied empirically without valid patient consent. The Italian society of mesotherapy has planned a study to assess the rationale and clinical applications based on current evidence. METHODS: An independent steering committee, based on the available scientific literature, has formulated a series of clinical questions. 21 experts responded by writing an evidence-based document. From this document 30 statements were obtained which were presented to 114 experts using the Delphi method. RESULTS: 28 statements reached a broad agreement on definition, technique, pharmacological rationale, indications and some crucial ethical aspect. CONCLUSIONS: Although further studies are needed to establish the clinical role of this technique in each field of application, our statements recommend the correct application according to the needs of the individual patient in full respect of ethics.

Evidence of Air Trapping During Ex Vivo Lung Perfusion: A Swine Experimental Lung Imaging and Mechanics Study.

Ex vivo lung perfusion (EVLP) allows the ventilation and perfusion of lungs to evaluate their viability for transplantation. The aim of this study is to compare the mechanical, morphologic and functional properties of lungs during EVLP with values obtained in vivo to guide a safe mechanical ventilation strategy. Lungs from 5 healthy pigs were studied in vivo and during 4 hours of EVLP. Lung compliance, airway resistance, gas exchange, and hemodynamic parameters were collected at positive end-expiratory pressure (PEEP) of 5 cm H2O. Computed tomography was performed at PEEP 0, PEEP 5, and total lung capacity (TLC). Lung pressure-volume (PV) curves were performed from PEEP 0 to TLC. Lung compliance decreased during EVLP (53 ± 5 mL/cm H2O vs 29 ± 7 mL/cm H2O, P < .05), and the PV curve showed a lower inflection point. Gas content (528 ± 118 mL vs 892 ± 402 mL at PEEP 0) and airway resistance (25 ± 5 vs 44 ± 9 cmH2O/L∗s-1, P < .05) were higher during EVLP. Alveolar dead space (5% ± 2% vs 17% ± 6%, P < .05) and intrapulmonary shunt (9% ± 2% vs 28% ± 13%, P < .05) increased ex vivo compared to in vivo, while the partial pressure of oxygen to inspired oxygen fraction ratio (PO2/FiO2) did not differ (468 ± 52 mm Hg vs 536 ± 14 mm Hg). In conclusion, during EVLP lungs show signs of air trapping and bronchoconstriction, resulting in low compliance and increased alveolar dead space. Intrapulmonary shunt is high despite oxygenation levels acceptable for transplantation.

Efficacy of tapentadol prolonged release for pre- and post-operative low back pain: a prospective observational study.

OBJECTIVE: Low back pain (LBP) is a highly prevalent chronic pain condition with a neuropathic component of pain that limits the benefits of classical opioids. Tapentadol is an innovative drug for the treatment of chronic severe pain, with a dual mechanism of action combining µ-opioid receptors agonism and noradrenaline re-uptake inhibition (NRI). Its efficacy is equal to that of strong opioids, with a better tolerability profile and a consequently lower risk of treatment discontinuation. The aim of this study was to evaluate the analgesic efficacy and tolerability of tapentadol prolonged release (PR) vs. other analgesics in patients with moderate-to-severe neuropathic low back pain, before and after back surgery. PATIENTS AND METHODS: The primary endpoints of the study were the rate of response to treatment, measured as ≥30% reduction in pain intensity on the Numeric Rating Scale (NRS), and tapentadol PR efficacy for pain relief. The secondary endpoints were the improvements of the neuropathic component of pain and of sleep quality. RESULTS: A total of 40 patients were enrolled in the study, receiving either tapentadol PR (n=21, 52.5%) or other analgesics (n=19, 47.5%), both before and after surgery. The rate of response to treatment was statistically in favor of tapentadol PR (p<0.01). The reduction in pain intensity was statistically significant in the group treated with tapentadol PR, both before and after surgery (p<0.01), with a complete resolution of pain 90 days after surgery. The quality of sleep after surgery improved more in patients treated with tapentadol PR than in the comparator group (p<0.01), with 100% of the patients reporting a "good" sleep quality 2 months after surgery. CONCLUSIONS: Tapentadol PR was well tolerated by all patients, and its efficacy for pain relief was also confirmed in our small group of "real-life" patients with chronic, severe low back pain. Overall, the tolerability of this treatment may help to improve patients' quality of life, which is frequently compromised because of pain and its related comorbidities.

Higher-order twisted/astigmatic Gaussian Schell-model cross-spectral densities and their separability features.

Adding a twist phase term to the cross-spectral density (CSD) function of a partially coherent source can be done if and only if the resulting function remains nonnegative definite. Constraints on the twist term that guarantee the validity of the resulting CSD have been derived only for Twisted Gaussian Schell-model (TGSM) sources. Here, an infinite family of higher-order TGSM sources is introduced, whose CSDs are expressed as products of the CSD of a standard TGSM source times Hermite polynomials of arbitrary orders and suitable arguments. All the members present the same twist term and for all of them the twist-coherence constraint keeps obeying the form valid for a standard TGSM source. They can be used as building blocks for constructing an endless number of valid twisted CSDs, with an assigned value of the twist parameter and intensity and/or coherence features that can be very different from those of a standard TGSM source. Through partial transposition, higher-order TGSM CSDs are converted into higher-order Astigmatic Gaussian Schell-model (AGSM) CSDs. The problem of the separability of higher-order TGSM and AGSM CSDs is addressed, and conditions ensuring their separability are derived.

Maximizing Young fringe visibility with a universal SU2 polarization gadget.

When a Young interferometer is fed by a general electromagnetic field, the fringe visibility may change upon insertion of an anisotropic optical element over one of the interferometer pinholes. The maximum visibility that the fringes may exhibit in this way is theoretically known, but no direct experimental check seems to be available. Here we discuss the scheme of an experimental test. In particular, maximum fringe visibility is obtained with a three-component universal SU2 polarization gadget for arbitrary coherence features of the illuminating field. Confirming results obtained with a suitable experimental setup are presented.

Partially coherent sources with radial coherence.

Partially coherent sources with radial coherence are proposed. They present a circularly symmetric intensity profile and a degree of coherence whose absolute value only depends on the angular difference between the two considered points. In particular, the source is completely coherent at pairs of points belonging to the same radius. The modal structure of such sources is determined in the general case, and conditions are derived under which the field propagated in paraxial approximation remains radially coherent at any transverse plane. In such cases, the angular dependence of the correlation function is preserved upon propagation, although the intensity profile generally changes. An example of this kind of source has been experimentally synthesized by means of a simple setup, and its coherence characteristics have been tested by means of a Young interferometer.

Devising genuine twisted cross-spectral densities.

Sticking a twist to a partially coherent source cannot be done at will, since the result can violate the definiteness property of the corresponding cross-spectral density. As a matter of fact, the study of twisted sources has been mainly concentrated on the original case proposed by Simon and Mukunda [J. Opt. Soc. Am. A10, 95 (1993)JOAOD60740-323210.1364/JOSAA.10.000095] of circularly symmetric Gaussian Schell-model sources. Here, we discuss a modeling procedure that can be used to generate numberless genuine twisted sources without symmetry constraints. As geometrically simple examples, two cases of non-Gaussian twisted sources endowed with circular or rectangular symmetry are explicitly worked out.

Synthesis of circularly coherent sources.

An experiment is presented in which a partially coherent source endowed with circular coherence is generated. The source is synthesized through a time averaging procedure, so that the mutual intensity is used as the basic correlation function. The correlation between points at different radial distances from the source center is tested by means of a Young interferometer. To confirm the perfect coherence among points along a circle concentric with the source center, the Young mask is replaced by an array of equally spaced pinholes arranged along a circle. The observed pattern is identical to that produced by the same mask, illuminated by perfectly coherent light.

Partially coherent sources with circular coherence.

A new class of partially coherent light sources is introduced. At the source plane, they exhibit perfect coherence along any annulus that is concentric to the source center. Between two points at different distances from the center, coherence can be partial or even vanishing. Such sources can be synthesized by using a generalized form of van Cittert-Zernike theorem where axial sources are used. Beams radiated by this type of source are analyzed at the source plane and upon free propagation for some simple cases.