Inverse Transport Theory and Optical Tomography
Interferometric synthetic aperture microscopy
P Scott Carney
University of Illinios
Methods of computed imaging have historically provided new levels of insight and utility when coupled with established instrumentation. Examples include the growth of X-ray projections into modern computed tomography (CT), nuclear magnetic resonance spectroscopy into magnetic resonance imaging (MRI), and radar ranging into synthetic aperture radar imaging (SAR). Optical coherence tomography (OCT) has provided an alternative to physical sectioning and histology that allows for imaging of living samples and even in vivo examination of cell structure and dynamics. Applications range from monitoring the development of engineered tissues to the diagnosis of malignancies. The sectional imaging of OCT is achieved by direct visualization of raw data obtained in focused optical range finding. As a result, there is, in the OCT community, a widely held belief that there exists a trade-off between transverse resolution and the thickness of the volume that may be imaged with a fixed focal plane. The extreme manifestation of this effect may be seen in optical coherence microscopy (OCM) where a single plane is imaged using a highly focused beam to achieve micron scale resolution, but no sectioning is possible because of the defocus away from this plane.
In this talk I will show that solution of the inverse scattering problem leads to algorithms that provide a spatially invariant point-spread function for the system with resolution everywhere equal to the best resolution in the raw data (in the focal plane). Thus the supposed trade-off between resolution and depth of imaging is eliminated. The resultant reconstructions show a marked qualitative improvement in all regions and moreover are quantitatively meaninful. This new modality is formally related to SAR and we refer to it as interferometric synthetic aperture microscopy (ISAM). I will present the theoretical analysis, numerical simulations and experimental results for samples including a tadpole, a human tumor, and a titanium dioxide particle suspension.