Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens–Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s≫1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens–Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

© 2000 Optical Society of America

[Optical Society of America ]

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

Related Journal Articles

• Polarized light propagation through tissue phantoms containing densely packed scatterers (OL)
• Numerical heterodyne holography with two-dimensional photodetector arrays (OL)
• Analysis of optical coherence tomography systems based on the extended Huygens–Fresnel principle (JOSAA)
• Vertex/propagator model for least-scattered photons traversing a turbid medium (JOSAA)
• Multiple scattering in optical coherence tomography. I. Investigation and modeling (JOSAA)

Related Conference Papers

• Blind dispersion compensation for optical coherence tomography
• Dynamic low coherence interferometry as a tool for imaging and quantification of Brownian motion with highly scattering media
• Optical low-coherence tomography using an injection-seeded optical amplifier and a high-speed A-scan rotating plate technique
• Quantitative assessment of flow velocity estimation algorithms for optical Doppler tomography imaging
• Analysis of Multiple Scattering Effects in Optical Doppler Tomography