<title>Simultaneous scattering and absorption images of heterogeneous media using diffusive waves within the Rytov approximation</title>

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ABSTRACT In this work we compare the Born and Rytov approximations for frequency-domain diffusing wave tomography.We confirm that the Rytov approximation gives a more accuate reconstruction of the absorptive properties. Inaddition, the natural separation of amplitude and phase within the Rytov approximation presents the possibility for image reconstruction algorithms which use either the phase shift or the amplitude decay of the diffusive waves. We demonstrate this effect, and apply these algorithms to simultaneously reconstruct the scattering andabsorption properties of heterogeneous turbid media. 1 Introduction Near infrared diffusing light probes offer new possibilties for medical applications such as the non-invasive mea-surement of tissue oxygenation' in homogeneous tissues. Direct imaging of the optical properties of heterogeneoustissue is an important potential improvement to these schemes that has only recently been considered.2'3In this study we employ amplitude modulated (frequency-domain) sources of photons which are injected intoa scattering medium to generate diffuse photon density waves4 (DPDW's). The diffusive waves are composed ofrandomly walking photons, that collectively produce an exponentially damped spherical wave of photon densitypropagating outward from the source with well defined amplitude and phase at each position in the medium. Inour work, measurements of the phase and amplitude of DPDW's are used to derive images of objects embeddedwithin tissue phantoms.The equations used for frequency-domain diffusing-wave tomographic imaging are approximations to the het-erogeneous light diffusion equation. In the Born approximation, the amplitude of the perturbation is assumed tobe small, and in the Rytov approximation, the perturbation is assumed to be slowly varying.5 We have previouslyiresentecl experinnta.l images of absorbing or scattering heterogeneities using the Born approximation.6 In thiswork we demonstrate the relative advantages of working in the Rytov approximation for frequency-domain mea-surements and image reconstruction. We then use the Rytov approximation to create maps of both the absorptionand scattering properties of a turbid sample. Finally, we demonstrate that we are able to use the amplitude and