Do in vivo terahertz imaging systems comply with safety guidelines?

Techniques for the coherent generation and detection of electromagnetic radiation in the far infrared, or terahertz, region of the electromagnetic spectrum have recently developed rapidly and may soon be applied for in vivo medical imaging. Both continuous wave and pulsed imaging systems are under development, with terahertz pulsed imaging being the more common method. Typically a pump and probe technique is used, with picosecond pulses of terahertz radiation generated from femtosecond infrared laser pulses, using an antenna or nonlinear crystal. After interaction with the subject either by transmission or reflection, coherent detection is achieved when the terahertz beam is combined with the probe laser beam. Raster scanning of the subject leads to an image data set comprising a time series representing the pulse at each pixel. A set of parametric images may be calculated, mapping the values of various parameters calculated from the shape of the pulses. A safety analysis has been performed, based on current guidelines for skin exposure to radiation of wavelengths 2.6 µm–20 mm (15 GHz–115 THz), to determine the maximum permissible exposure (MPE) for such a terahertz imaging system. The international guidelines for this range of wavelengths are drawn from two U.S. standards documents. The method for this analysis was taken from the American National Standard for the Safe Use of Lasers (ANSI Z136.1), and to ensure a conservative analysis, parameters were drawn from both this standard and from the IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields (C95.1). The calculated maximum permissible average beam power was 3 mW, indicating that typical terahertz imaging systems are safe according to the current guidelines. Further developments may however result in systems that will exceed the calculated limit. Furthermore, the published MPEs for pulsed exposures are based on measurements at shorter wavelengths and with pulses of longer duration than those used in terahertz pulsed imaging systems, so the results should be treated with caution.

An introduction to medical imaging with coherent terahertz frequency radiation

Methods have recently been developed that make use of electromagnetic radiation at terahertz (THz) frequencies, the region of the spectrum between millimetre wavelengths and the infrared, for imaging purposes. Radiation at these wavelengths is non-ionizing and subject to far less Rayleigh scatter than visible or infrared wavelengths, making it suitable for medical applications. This paper introduces THz pulsed imaging and discusses its potential for in vivo medical applications in comparison with existing modalities.

Preliminary results on the non-thermal effects of 200-350 GHz radiation on the growth rate of S. cerevisiae cells in microcolonies

We report preliminary results from studies of biological effects induced by non-thermal levels of non-ionizing electromagnetic radiation. Exponentially growing Saccharomyces cerevisiae yeast cells grown on dry media were exposed to electromagnetic fields in the 200–350 GHz frequency range at low power density to observe possible non-thermal effects on the microcolony growth. Exposure to the electromagnetic field was conducted over 2.5 h. The data from exposure and control experiments were grouped into either large-, medium- or small-sized microcolonies to assist in the accurate assessment of growth. The three groups showed significant differences in growth between exposed and control microcolonies. A statistically significant enhanced growth rate was observed at 341 GHz. Growth rate was assessed every 30 min via time-lapse photography. Possible interaction mechanisms are discussed, taking into account Frohlich's hypothesis.

Astigmatism in tapered slot antennas

A series of scale model measurements of transverse electromagnetic mode tapered slot antennas are presented. They show that the beam launched by this type of antenna is astigmatic. It is shown how an off-axis spherical mirror can be used to correct this astigmatism to allow efficient coupling to quasi-optical systems. A millimetre wave antenna and mirror combination is described and, with the aid of solid state noise diodes, the coupling of the launched beam to a quasi-optical spectrometer is shown to be in good agreement with that predicted by the scale model measurements.

Virtual reshaping and invisibility in obstacle scattering

We consider reshaping an obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification in particular are studied. Stability estimates are derived for scattering amplitude in terms of the diameter of a small obstacle, which implies that the limiting case for minification corresponds to a perfect cloaking, i.e., the obstacle is invisible to detection.

The role of water vapour in Earth’s energy flows

Water vapour modulates energy flows in Earth's climate system through transfer of latent heat by evaporation and condensation and by modifying the flows of radiative energy both in the longwave and shortwave portions of the electromagnetic spectrum. This article summarizes the role of water vapour in Earth's energy flows with particular emphasis on (1) the powerful thermodynamic constraint of the Clausius Clapeyron equation, (2) dynamical controls on humidity above the boundary layer (or free-troposphere), (3) uncertainty in continuum absorption in the relatively transparent "window" regions of the radiative spectrum and (4) implications for changes in the atmospheric hydrological cycle.

Stability results for the time-harmonic Maxwell equations with impedance boundary conditions

We consider the time-harmonic Maxwell equations with constant coefficients in a bounded, uniformly star-shaped polyhedron. We prove wavenumber-explicit norm bounds for weak solutions. This result is pivotal for convergence proofs in numerical analysis and may be a tool in the analysis of electromagnetic boundary integral operators.

Source splitting via the point source method

We introduce a new algorithm for source identification and field splitting based on the point source method (Potthast 1998 A point-source method for inverse acoustic and electromagnetic obstacle scattering problems IMA J. Appl. Math. 61 119–40, Potthast R 1996 A fast new method to solve inverse scattering problems Inverse Problems 12 731–42). The task is to separate the sound fields uj, j = 1, ..., n of sound sources supported in different bounded domains G1, ..., Gn in from measurements of the field on some microphone array—mathematically speaking from the knowledge of the sum of the fields u = u1 + + un on some open subset Λ of a plane. The main idea of the scheme is to calculate filter functions , to construct uℓ for ℓ = 1, ..., n from u|Λ in the form We will provide the complete mathematical theory for the field splitting via the point source method. In particular, we describe uniqueness, solvability of the problem and convergence and stability of the algorithm. In the second part we describe the practical realization of the splitting for real data measurements carried out at the Institute for Sound and Vibration Research at Southampton, UK. A practical demonstration of the original recording and the splitting results for real data is available online.

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

An iterative contractive framework for probe methods: LASSO

We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far-field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far-field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples.

Interferometric technique for measuring terahertz antenna phase patterns

A quasi-optical interferometric technique capable of measuring antenna phase patterns without the need for a heterodyne receiver is presented. It is particularly suited to the characterization of terahertz antennas feeding power detectors or mixers employing quasi-optical local oscillator injection. Examples of recorded antenna phase patterns at frequencies of 1.4 and 2.5 THz using homodyne detectors are presented. To our knowledge, these are the highest frequency antenna phase patterns ever recovered. Knowledge of both the amplitude and phase patterns in the far field enable a Gauss-Hermite or Gauss-Laguerre beam-mode analysis to be carried out for the antenna, of importance in performance optimization calculations, such as antenna gain and beam efficiency parameters at the design and prototype stage of antenna development. A full description of the beam would also be required if the antenna is to be used to feed a quasi-optical system in the near-field to far-field transition region. This situation could often arise when the device is fitted directly at the back of telescopes in flying observatories. A further benefit of the proposed technique is simplicity for characterizing systems in situ, an advantage of considerable importance as in many situations, the components may not be removable for further characterization once assembled. The proposed methodology is generic and should be useful across the wider sensing community, e.g., in single detector acoustic imaging or in adaptive imaging array applications. Furthermore, it is applicable across other frequencies of the EM spectrum, provided adequate spatial and temporal phase stability of the source can be maintained throughout the measurement process. Phase information retrieval is also of importance to emergent research areas, such as band-gap structure characterization, meta-materials research, electromagnetic cloaking, slow light, super-lens design as well as near-field and virtual imaging applications.

Scattering by infinite one-dimensional rough surfaces

We consider the Dirichlet boundary-value problem for the Helmholtz equation in a non-locally perturbed half-plane. This problem models time-harmonic electromagnetic scattering by a one-dimensional, infinite, rough, perfectly conducting surface; the same problem arises in acoustic scattering by a sound-soft surface. ChandlerWilde & Zhang have suggested a radiation condition for this problem, a generalization of the Rayleigh expansion condition for diffraction gratings, and uniqueness of solution has been established. Recently, an integral equation formulation of the problem has also been proposed and, in the special case when the whole boundary is both Lyapunov and a small perturbation of a flat boundary, the unique solvability of this integral equation has been shown by Chandler-Wilde & Ross by operator perturbation arguments. In this paper we study the general case, with no limit on surface amplitudes or slopes, and show that the same integral equation has exactly one solution in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including the incident plane wave, the Dirichlet boundary-value problem for the scattered field has a unique solution.

A uniqueness result for scattering by infinite rough surfaces

Consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane with an unbounded, piecewise Lyapunov boundary. This problem models time-harmonic electromagnetic scattering in transverse magnetic polarization by one-dimensional rough, perfectly conducting surfaces. A radiation condition is introduced for the problem, which is a generalization of the usual one used in the study of diffraction by gratings when the solution is quasi-periodic, and allows a variety of incident fields including an incident plane wave to be included in the results obtained. We show in this paper that the boundary value problem for the scattered field has at most one solution. For the case when the whole boundary is Lyapunov and is a small perturbation of a flat boundary we also prove existence of solution and show a limiting absorption principle.

Scattering by rough surfaces: the Dirichlet problem for the Helmholtz equation in a non-locally perturbed half-plane

We consider the Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane, this problem arising in electromagnetic scattering by one-dimensional rough, perfectly conducting surfaces. We propose a new boundary integral equation formulation for this problem, utilizing the Green's function for an impedance half-plane in place of the standard fundamental solution. We show, at least for surfaces not differing too much from the flat boundary, that the integral equation is uniquely solvable in the space of bounded and continuous functions, and hence that, for a variety of incident fields including an incident plane wave, the boundary value problem for the scattered field has a unique solution satisfying the limiting absorption principle. Finally, a result of continuous dependence of the solution on the boundary shape is obtained.

Energetic charged particles above thunderclouds

The French government has committed to launch the satellite TARANIS to study transient coupling processes between the Earth’s atmosphere and near-Earth space. The prime objective of TARANIS is to detect energetic charged particles and hard radiation emanating from thunderclouds. The British Nobel prize winner C.T.R. Wilson predicted lightning discharges from the top of thunderclouds into space almost a century ago. However, new experiments have only recently confirmed energetic discharge processes which transfer energy from the top of thunderclouds into the upper atmosphere and near-Earth space; they are now denoted as transient luminous events, terrestrial gamma-ray flashes and relativistic electron beams. This meeting report builds on the current state of scientific knowledge on the physics of plasmas in the laboratory and naturally occurring plasmas in the Earth’s atmosphere to propose areas of future research. The report specifically reflects presentations delivered by the members of a novel Franco-British collaboration during a meeting at the French Embassy in London held in November 2011. The scientific subjects of the report tackle ionization processes leading to electrical discharge processes, observations of transient luminous events, electromagnetic emissions, energetic charged particles and their impact on the Earth’s atmosphere. The importance of future research in this area for science and society, and towards spacecraft protection, is emphasized.