One-dimensional inverse scattering problem for optical coherence tomography

Optical coherence tomography is a non-invasive imaging technique based on the use of light sources exhibiting a low degree of coherence. Low-coherence interferometric microscopes have been successful in producing internal images of thin pieces of biological tissue; typically samples of the order of 1 mm in depth have been imaged, with a resolution of the order of 10 mu m in some portions of the sample. In this paper we deal with the imaging problem of determining the internal structure of a multi-layered sample from backscattered laser light and low-coherence interferometry. In detail, we formulate and solve an inverse problem which, using the interference fringes that result as the back scattering of low-coherence light is made to interfere with a reference beam, produces maps detailing the values of the refractive index within the imaged sample. Unlike previous approaches to the OCT imaging problem, the method we introduce does not require processing at data collection time, and it produces quantitatively accurate values of the refractive indexes within the sample from back-scattering interference fringes only.