Localization of an absorbing inhomogeneity in a scattering medium in a statistical framework

Abstract

An approach for the fast localization and detection of an absorbing inhomogeneity in a tissue-like scattering medium is presented. The probability of detection as a function of the size, location, and absorptive properties of the inhomogeneity is investigated. The detection sensitivity in relation to the source and detector location serves a basis for instrument design. c 2007 Optical Society of America OCIS codes: 170.3010, 290.7050, 100.3010, 100.3190 Optical imaging in scattering media provides important opportunities for clinical imaging and environmental sensing, among others [1]. In the near-infrared wavelength range, soft tissue has both high scatter and low absorption, allowing use of a diffusion equation model for photon transport [2,3], which with exp(jωt) time dependence iswhere φ is the photon flux density, ω is the circular modulation frequency, β is the modulation amplitude, c is the speed of light in the intervening medium between the scatterers, µ a is the absorption coefficient, D is the diffusion coefficient, and a Dirac delta function excitation is assumed. Reconstruction of the unknown optical parameters µ a (r) and D(r) requires inversion of measured data, which is formulated as an optimization problem [1,4]. This is a computationally intensive process, in large part due to the nonlinear relationship between the cost function and the image parameters. Another difficulty is caused by physical limitations of a practical measurement system, which may result in insufficient information for accurate volumetric imaging. These issues motivate interest in simpler, efficient approaches for detecting and localizing a heterogeneity in a scattering medium instead of quantitative three-dimensional reconstruction. Methods have been studied for localizing injected fluorophores. Chen et al. used least squares curve fitting to compare a diffusion equation model for expected fluorescence with measurements based on the perturbation on a cancellation plane, formed by dual-interfering sources [5], to localize a fluorophore in a mouse model [6]. Gannot et al. used the Levenberg-Marquardt method to fit measured data with a forward model based on random-walk theory for three-dimensional 1

Diffuse optical localization of blood vessels and 3D printing for guiding oral surgery

“…The problem then becomes an estimation of the position of an absorption inhomogeneity. Previously, Cao et al [8] described localization of a point absorber, and we extend this treatment to the localization of absorption inhomogeneities with complex geometries. We accomplish this by modeling the absorption inhomogeneity with multiple point absorbers instead of just one.…”

“…In order to form an analytical solution for fast computation [8], we assume that the inhomogeneity has constant Δ μ a and can be represented by L point absorbers at positions r a l such that…”

“…However, this is a computationally intensive process, limiting its application in surgery, where information is often needed in real time. For this reason, fast localization methods are an attractive alternative, where information about the location only is extracted using a small measurement data set [7,8]. Here, we present optical localization as a means for finding the greater palatine artery (GPA) in the roof of the mouth, thereby addressing the need for this information in dental surgery.…”

Imaging Hidden Objects with Spatial Speckle Intensity Correlations over Object Position

“…For example, with a stationary point scatterer of interest in a background of moving scatters, the average intensity transmission can yield the position of the stationary scatterer, and transverse localization information exists in the average of the difference of speckle patterns (with and without the stationary scatterer) [15]. Localization can also be accomplished in a diffusion framework, with weakly interacting scatterers, [16,17]. Control of the coherence in speckle pattern difference images can reveal the presence of hidden inhomogeneities [18].…”

“…We use (17) in (1) to write the normalized intensity correlation in terms of the field correlation as…”