Optical coherence tomography (OCT) was a technique developed to create a synthetic aperture time-of-flight interferogram. The underlying OCT assumption is that the interogating field is extremely high gain (i.e. a single ray). A high gain beam can be achieved through a low-NA (numerical aperture) interogation system. This system, however, will limit resolution and SNR relative to a converging beam. To achieve high quality image reconstructions with a high-NA interogation system, an accurate description of the beam at all planes of interest must be incorporated into the sensing model. Since the beam exiting the interogating lens can be well-approximated by a Gaussian beam, the beam can be thought of as a band-limited spherical wave. The dispersion relation for the return from a Gaussian beam is q2+β2 = (2k)2. Where q and β are the sampled spatial frequencies of interogated object in the transverse, q, and axial, β, directions. (q = √(u2+v2) the l2 norm of the spatial frequency vector in the transverse direction.) The inverse problem is solved by resampling the measured OCT data in (x,y,k) to (u,v,β) according to the dispersion relationship and deconvolving out the Gaussian bandpass with a Wiener (Gaussian prior) or sparsity inducing (Laplacian) filter. The dispersion relation and a simulation demonstrating the performance benefits of ISAM processing with respect to OCT processing are shown in the figures below.
The left image shows the data color coded in lines of constant β as measured in lines of constant k. The right image shows the data resampled into lines of constant beta.
The left image shows a reconstruction of an array of point scatters by the OCT assumption. The center image shows the out of focus resolution improvement for ISAM. The right image is the interogating beam.
Research in ISAM continues at DISP, and future projects will consist of improvements in reconstruction accuracy, time, and adaptive aquisition strategies. More information about ISAM at THz can be found in M. Heimbeck, D. Marks, D. Brady, and H. Everitt, "Terahertz interferometric synthetic aperture tomography for confocal imaging systems," Opt. Lett. 37, 1316-1318 (2012).