Photon hitting density

Abstract

Optical and near-IR spectroscopy and imaging of highly scattering tissues require information about the distribution of photon-migration paths. We introduce the concept of the photon hitting density, which describes the expected local time spent by photons traveling between a source and a detector. For systems in which photon transport is diffusive we show that the hitting density can be calculated in terms of diffusion Green's functions. We report calculations of the hitting density in model systems.

Linear reconstruction of absorption perturbations in coherent ultrasound-modulated optical tomography

“…In the context of DOT, Arridge generalized such sensitivity functions in the framework of photon-measurement density functions. 22,24 This work followed earlier derivations of the measurement sensitivity to perturbations in absorption by Schotland et al, 25 who termed this the photon hitting density, and others. [26][27][28] We now explore the correlation measurement density functions (CMDFs) which arise in correlation-based UOT.…”

Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy

“…This is the basis of image reconstruction algorithms in which an image of Dl a (i.e., the vector x) can be obtained from a set of measurements (i.e., the vector y) through inversion of the matrix A (i.e., the effective pathlengths L i,j ). While several advanced imaging algorithms have been developed-including analytic diffraction tomography approaches (Cheng and Boas, 1998;Li et al, 1997;Matson and Liu, 1999;Schotland, 1997), perturbation approaches (Arridge and Schweiger, 1995;Barbour et al, 1995;O'Leary et al, 1995;Schotland et al, 1993;Yao et al, 1997), the Taylor series expansion approach (Jiang et al, 1996;Paulsen and Jiang, 1995), gradient-based iterative techniques (Arridge and Schweiger, 1998), elliptic systems method (ESM) (Gryazin et al, 1999;Klibanov et al, 1997), and Bayesian conditioning (Barnett et al, 2003;Eppstein et al, 1999) -the most widely used methods for diffuse optical functional brain imaging incorporate a semiinfinite forward model (Kienle and Patterson, 1997a;Patterson et al, 1989) and either backprojection (Colak et al, 1997;Franceschini et al, 2000;Maki et al, 1995, Walker et al, 1997 or perturbation approaches (Arridge, 1999).…”

Three-dimensional diffuse optical mammography with ultrasound localization in a human subject

“…[40][41][42][43][44][45][46][47][48] We have chosen to follow a Green's function ͑or adjoint͒ method. [15][16][17][18]27,28 The inverse problem, therefore, is formulated in the following way:…”

“…A variety of methods have been developed for DOT. These include fits to analytic solutions, [1][2][3] backprojection methods, [4][5][6][7] diffraction tomography in k-space, [8][9][10][11][12][13][14] perturbation approaches, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] elliptic systems method ͑ESM͒, [31][32][33] and a direct method. 34 All of these approaches have various advantages and disadvantages.…”