Nonuniqueness in diffusion-based optical tomography

A condition on nonuniqueness in optical tomography is stated. The main result applies to steady-state (dc) diffusion-based optical tomography, wherein we demonstrate that simultaneous unique recovery of diffusion and absorption coefficients cannot be achieved. A specific example of two images that give identical dc data is presented. If the refractive index is considered an unknown, then nonuniqueness also occurs in frequency-domain and time-domain optical tomography, if the underlying model of the diffusion approximation is employed.     

Fast analytical approximation for arbitrary geometries in diffuse optical tomography

Diffuse optical tomography is a novel imaging technique that resolves and quantifies the optical properties of objects buried in turbid media. Typically, numerical solutions of the diffusion equation are employed to construct the tomographic problem when media of complex geometries are investigated. Numerical methods offer implementation simplicity but also significant computation burden, especially when large three-dimensional reconstructions are involved. We present an alternative method of performing tomography of diffuse media of arbitrary geometries by means of an analytical approach, the Kirchhoff approximation. We show that the method is extremely efficient in computation times and consider its potential as a real-time three-dimensional imaging tool.     

Finite element approximation of the Fokker-Planck equation for diffuse optical tomography

In diffuse optical tomography, light transport theory is used to describe photon propagation inside turbid medium. A commonly used simplification for the radiative transport equation is the diffusion approximation due to computational feasibility. However, it is known that the diffusion approximation is not valid close to the sources and boundary and in low-scattering regions. Fokker-Planck equation describes light propagation when scattering is forward-peaked. In this article a numerical solution of the Fokker-Planck equation using finite element method is developed. Approach is validated against Monte Carlo simulation and compared with the diffusion approximation. The results show that the Fokker-Planck equation gives equal or better results than the diffusion approximation on the boundary of a homogeneous medium and in turbid medium containing a low-scattering region when scattering is forward-peaked.     

Study of the P1 approximation in an inverse scattering problem

We examine the validity of the P₁ approximation in determining the albedo and asymmetry factor of a scattering medium from the hemispherical transmittance data. For this purpose, an analytical expression of the hemispherical transmittance is derived with the P₁ approximation and then fitted to hemispherical transmittance data of a scattering medium using three methods. These include the asymptotic expansion method, the unconstrained least mean-squares method and the constrained least mean-squares method. We find that estimation of radiative properties with the P₁ approximation is effective only for high albedos. Only the constrained least mean-squares method yields physically resonable values for the radiative properties in all cases.     

Equivalent neutron optical potentials in the separable energy-dependent approximation

The single-term separable energy-dependent approximation for the two-body t-matrix is extended to the case of non-hermitian potentials. The formalism is applied to construct a separable potential for neutron scattering at low energies. Comparison with the exact scattering data gives good agreement.     

Superresolution in diffuse optical tomography

The possibility of applying image reconstruction methods used in optics to improve the resolution of the photon average trajectories method of diffuse optical tomography is demonstrated. The limit resolution determined by Nyquist’s consequence of the Kotel’nikov-Shannon theorem is achieved.     

Nonuniqueness of the factorization scheme in quantum mechanics

We enquire into the consequences of the nonuniqueness of the factorizability of a quantum mechanical Hamiltonian in one dimension. This leads to a hierarchy of potentials, a particular class of which is endowed with the energy spectrum of the harmonic oscillator.     

Polarization-sensitive quantum optical coherence tomography: Experiment

Polarization-sensitive quantum optical coherence tomography (PS-QOCT) makes use of a Type-II twin-photon light source for carrying out optical sectioning with polarization sensitivity. A BBO nonlinear optical crystal pumped by a Ti:sapphire psec-pulsed laser is used to confirm the theoretical underpinnings of this imaging paradigm. PS-QOCT offers even-order dispersion cancellation with simultaneous access to the group-velocity dispersion characteristics of the interstitial medium between the reflecting surfaces of the sample.     

On the accuracy of the WKB approximation in optical dielectric waveguides

Eigenvalues and field distributions for optical waveguides obtained from the WKB approximation have been compared with those found from geometrical optics and from more rigorous weakly-guiding LP mode theories in the cases of the step-index and parabolic-index profiles. In all cases it is found that the zero-order WKB approximation yields very accurate eigenvalues provided care is taken in the choice of phase factors in the eigenvalue equation. Expressions are deduced for the required phase factors for guides of arbitrary index profile in both two- and three-dimensions, and physical interpretations are given in terms of ray optics. The first-order WKB field distributions are found to give good agreement with the mode fields everywhere except in the vicinity of the caustics.     

Bayesian compressive optical imaging within the Rytov approximation

Within the range of validity of the Rytov approximation (RA), an innovative Bayesian compressive sensing (BCS) inverse scattering technique is developed. Potentialities and limitations of the BCS-RA method are validated through numerical experiments and representative results are discussed.     

Bragg optical solitons beyond the coupled mode approximation

Properties of conservative and dissipative Bragg solitons formed in single-mode optical fibers with induced longitudinal modulation of the refractive index are analyzed beyond the standard approximation of coupled modes, or of slowly varying amplitudes. It is shown that, if the initial velocity of a Bragg soliton is smaller than a critical value, the soliton stops in the process of propagation.     

The relevance of optical transducers to the process industries

The first part of the paper deals with the requirements of the process industries for measurement transducers and systems. It classifies the industries and discusses the measurands involved. Reference is made to the desirable characteristics and performances of transducers as discrete units and as system components.The second half of the paper examines these requirements in relation to the potential of optical transducers. It concludes that although these new transducers could have some useful characteristics involving simplicity, safety and freedom from interference, there are many obvious design and development problems and limitations which have to be overcome before optical transducers can replace their electrical counterparts particularly in control systems.     

Application of multimode fiber optical sensor in optical tomography technology

In this paper, an attempt to use a multimode optical fiber sensor in tomography is made. Two types of lens, one sphere and one cylinderical, are designed for two terminals of the fiber. It solves the problem of insufficient power collection of natural light beam using current fiber with polished terminals. A theoretical analysis of the relationships among the sphere lens radius, the cylinderical lens radius, the refractive index of the fiber is carried out. The relationship between the scanning angles and the number of the optical fibers is experimentally investigated in the air medium.     

Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involing effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials—that is, the real and the imaginary folding-model potential—are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions ¹⁶O on nuclei at an energy of E ～ 100 MeV per nucleon.     

Nonuniqueness of the solution of the plane-crack problem

The elastic field around a rectilinear plane crack in a homogeneous field of external forces is considered. It is shown that the well-known Muskhelishvili solution of this problem is nonunique. The potential method is used to find another method which satisfies the same boundary conditions and is linearly independent of the Muskhelishvili solution. It gives a stress concentration around the mouth of the crack, which agrees with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 16–19, April, 1986.     

The imaginary part of the nucleon-nucleus optical potential in semiclassical approximation

We calculate in a novel Thomas-Fermi theory for multiparticle-multihole states the contributions of the correlation and polarization graphs to the imaginary part of the nucleon-nucleus optical potential $\text{W(ω,}\text{R}\text{,}\text{P}\text{)}$ depending on energy, radius and momentum. The present theory generalizes the older Fermi-gas and local-density approximations to this problem in the sense that we can assess precisely the validity of our approach. We show that it yields results which coincide with the average part of a corresponding quantal calculation. We use a gaussian finite-range effective interaction derived from the Gogny force and phenomenological mean-field potentials of the Woods-Saxon or harmonic-oscillator type. With these ingredients and no further adjustable parameters our results for the depth and volume integrals are in good agreement with the average trend of the elastic scattering data. Further, the resulting momentum dependence of W is strong, especially for small P. The influence of the Pauli principle is studied in detail.     

Plasmonic tomography of optical vortices

We present a method for analyzing the wavefront of optical vortices that does not involve interferometry but rather uses surface plasmon polaritons (SPPs). We employ a subwavelength slit in a gold film to cut slices from an optical vortex beam and measure the diffraction of the generated SPPs by scattering them off a second slit. By moving the slits across the vortex beam, we create a tomogram, from which we can determine the vortex charge of the incident beam at a glance. We present results for vortex beams of integer- and half-integer-vortex charge.