Introduction
Optical tomography uses light in the visible or near-infrared spectral region to illuminate biological objects and build three-dimensional reconstructions of the interior. Because the energy of optical radiation is much lower than existing high-resolution imaging devices based on X-rays, the penetration of light is much lower, and, more importantly, the effect of scattering is much higher. Based on the mean free path of the photons, the physics of light propagation can be considered on different length scales which in turn gives rise to quite different forward and inverse problems. In this entry, we consider the recent development of methods for modeling and reconstruction in the presence of significant scattering, which is described by either transport or diffuse models. For more details, see [2, 4].
Measurements in Optical Tomography
Absorption of light in biological tissue is caused by chromophores of variable concentration such as hemoglobin in its oxygenated and...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aronson, R.: Boundary conditions for diffusion of light. J. Opt. Soc. Am. A 12, 2532–2539 (1995)
Arridge, S.R.: Optical tomography in medical imaging. Inverse Probl. 15(2), R41–R93 (1999)
Arridge, S.R., Lionheart, W.R.B.: Non-uniqueness in diffusion-based optical tomography. Opt. Lett. 23, 882–884 (1998)
Arridge, S.R., Schotland, J.: Optical tomography: forward and inverse problems. Inverse Probl. 25(12), 123,010 (59pp.) (2009)
Bal, G.: Inverse transport theory and applications. Inverse Probl. 25(5), 053,001 (48pp.) (2009)
Case, M.C., Zweifel, P.F.: Linear Transport Theory. Addison-Wesley, New York (1967)
Corlu, A., Durduran, T., Choe, R., Schweiger, M., Hillman, E., Arridge, S.R., Yodh, A.G.: Uniqueness and wavelength optimization in continuous-wave multispectral diffuse optical tomography. Opt. Lett. 28, 23 (2003)
Corlu, A., Choe, R., Durduran, T., Lee, K., Schweiger, M., Arridge, S.R., Hillman, E.M.C., Yodh, A.G.: Diffuse optical tomography with spectral constraints and wavelength optimisation. Appl. Opt. 44(11), 2082–2093 (2005)
Delpy, D.T., Cope, M., van der Zee, P., Arridge, S.R., Wray, S., Wyatt, J.: Estimation of optical pathlength through tissue from direct time of flight measurement. Phys. Med. Biol. 33, 1433–1442 (1988)
Ishimaru, A.: Wave Propagation and Scattering in Random Media, vol. 1. Academic, New York (1978)
Kaipio, J., Somersalo, E.: Statistical and Computational Inverse Problems. Springer, New York (2005)
Lakowicz, J.R., Berndt, K.: Frequency domain measurement of photon migration in tissues. Chem. Phys. Lett. 166(3), 246–252 (1990)
Markel, V., O’Sullivan, J., Schotland, J.: Inverse problem in optical diffusion tomography. IV. Nonlinear inversion formulas. J. Opt. Soc. Am. A 20, 903–912 (2003)
Ntziachristos, V., Ma, X., Chance, B.: Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography. Rev. Sci. Instrum. 69, 4221–4233 (1998)
Ripoll, J., Nieto-Vesperinas, M.: Index mismatch for diffusive photon density waves both at flat and rough diffuse-diffuse interfaces. J. Opt. Soc. Am. A 16(8), 1947–1957 (1999)
Schmidt, F.E.W., Fry, M.E., Hillman, E.M.C., Hebden, J.C., Delpy, D.T.: A 32-channel time-resolved instrument for medical optical tomography. Rev. Sci. Instrum. 71(1), 256–265 (2000)
Schweiger, M., Arridge, S.R., Nissilä, I.: Gauss-Newton method for image reconstruction in diffuse optical tomography. Phys. Med. Biol. 50, 2365–2386 (2005)
Tarvainen, T., Vauhkonen, M., Arridge, S.R.: Image reconstruction in optical tomography using the finite element solution of the frequency domain radiative transfer equation. J. Quant. Spect. Rad. Trans. 109, 2767–2278 (2008)
Tarvainen, T., Kolehmainen, V., Kaipio, J., Arridge, S.R.: Corrections to linear methods for diffuse optical tomography using approximation error modelling. Biomed. Opt. Exp. 1(1), 209–222 (2010)
Zacharopoulos, A.D., Svenmarker, P., Axelsson, J., Schweiger, M., Arridge, S.R., Andersson-Engels, S.: A matrix-free algorithm for multiple wavelength fluorescence tomography. Opt. Exp. 17, 3042–3051 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Arridge, S.R. (2015). Optical Tomography: Applications. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_43
Download citation
DOI: https://doi.org/10.1007/978-3-540-70529-1_43
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70528-4
Online ISBN: 978-3-540-70529-1
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering