We study the performance of a previously proposed perturbation theory for the diffusion equation in frequency and time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography. We have derived approximate formulas for calculating higher order self- and mixed path length moments, up to the fourth order, which can be used in general diffusive media regardless of geometry and initial distribution of the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is used to extend the validity of the theory to a wider range of absorption contrasts between defects and background. By using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries for the cases of single and multiple absorbing defects having sizes of interest (d=4–10 mm, where d is the diameter of the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximants and Monte Carlo simulations) was within 10% for absorption contrasts Δμa≤0.2 mm−1 for alternating current data, and usually to within 1° for Δμa≤0.1 mm−1 for phase data. In time domain, the average discrepancy in the temporal range of interest (a few nanoseconds) was 2%–3% for Δμa≤0.06 mm−1. The proposed method is an effective fast forward problem solver: all the time-domain results presented in this work were obtained with a computational time of less than about 15 s with a Pentium IV 1.66 GHz personal computer.

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results / A. Sassaroli; F. Martelli; S. Fantini. - In: JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION. - ISSN 1084-7529. - ELETTRONICO. - 27(2010), pp. 1723-1742. [10.1364/JOSAA.27.001723]

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results

MARTELLI, FABRIZIO
Membro del Collaboration Group
;
2010

Abstract

We study the performance of a previously proposed perturbation theory for the diffusion equation in frequency and time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography. We have derived approximate formulas for calculating higher order self- and mixed path length moments, up to the fourth order, which can be used in general diffusive media regardless of geometry and initial distribution of the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is used to extend the validity of the theory to a wider range of absorption contrasts between defects and background. By using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries for the cases of single and multiple absorbing defects having sizes of interest (d=4–10 mm, where d is the diameter of the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximants and Monte Carlo simulations) was within 10% for absorption contrasts Δμa≤0.2 mm−1 for alternating current data, and usually to within 1° for Δμa≤0.1 mm−1 for phase data. In time domain, the average discrepancy in the temporal range of interest (a few nanoseconds) was 2%–3% for Δμa≤0.06 mm−1. The proposed method is an effective fast forward problem solver: all the time-domain results presented in this work were obtained with a computational time of less than about 15 s with a Pentium IV 1.66 GHz personal computer.
27
1723
1742
Goal 3: Good health and well-being
A. Sassaroli; F. Martelli; S. Fantini
File in questo prodotto:
File Dimensione Formato  
JOSA_perturbation_Moments_time_domain_2010.pdf

Accesso chiuso

Descrizione: Articolo principale
Tipologia: Pdf editoriale (Version of record)
Licenza: DRM non definito
Dimensione 2.38 MB
Formato Adobe PDF
2.38 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2158/627658
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 15
social impact