Time-resolved diffusion tomographic 2D and 3D imaging in highly scattering turbid media

A method of forming a map of a highly scattering turbid medium, the highly scattering turbid medium being a biological tissue, said method comprising the steps of:

• (a) illuminating the highly scattering turbid medium with a first pulse of light along a first axis of incidence, whereby the light emergent from the highly scattering turbid medium due to said first pulse of light consists of a ballistic component, a snake component and a diffusive component;
• (b) determining, at a plurality of times, the intensity of said diffusive component of the first pulse of light emergent from the highly scattering turbid medium at a plurality of locations;
• (c) illuminating the highly scattering turbid medium with a second pulse of light along a second axis of incidence, said second axis of incidence intersecting with said first axis of incidence, whereby the light emergent from the highly scattering turbid medium due to said second pulse of light consists of a ballistic component, a snake component and a diffusive component;
• (d) determining, at a plurality of times, the intensity of said diffusive component of the second pulse of light emergent from the highly scattering turbid medium at a plurality of locations;
• and
• (e) using the intensity determinations from steps (b) and (d) to generate a map of the highly scattering turbid medium, said using step comprising using a mathematical inversion algorithm to generate said map, said mathematical algorithm being ##EQU9## wherein W is a matrix relating output at source and detector positions r.sub.s and r.sub.d, respectively, at time t to position r, .LAMBDA. is a regulation matrix, chosen for convenience to be diagonal but selected in a way related to the ratio of the noise, <nn>
• to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine:
• .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =<nn>/<.DELTA.Xj.DELTA.Xj>
• Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absorption information.

A method of forming a map of a highly scattering turbid medium, the highly scattering turbid medium being a biological tissue, said method comprising the steps of:

• (a) illuminating the highly scattering turbid medium with a first pulse of light along a first axis of incidence, whereby the light emergent from the highly scattering turbid medium due to said first pulse of light consists of a ballistic component, a snake component and a diffusive component;
• (b) determining, at a plurality of times, the intensity of said diffusive component of the first pulse of light emergent from the highly scattering turbid medium at a plurality of locations:
• (c) illuminating the highly scattering turbid medium with a second pulse of light along a second axis of incidence, said second axis of incidence intersecting with said first axis of incidence, whereby the light emergent from the highly scattering turbid medium due to said second pulse of light consists of a ballistic component, a snake component and a diffusive component;
• (d) determining, at a plurality of times, the intensity of said diffusive component of the second pulse of light emergent from the highly scattering turbid medium at a plurality of locations;
• and
• (e) using the intensity determinations from steps (b) and (d) to generate a map of the highly scattering turbid medium, said using step comprising using a mathematical inversion algorithm to generate said map, said mathematical inversion algorithm combining a two-dimensional matrix inversion with a one-dimensional Fourier transform inversion.