An optimal synthetic aperture for circular tomosynthesis.

In circular tomosynthesis obtained from a sufficient number of radiographs with projection directions forming a single cone, object detail at a distance from the plane of interest is blurred according to the zero order Bessel function. The main lobe of this window function defines slice thickness, while its ringing side lobes are undesirable because they permit further outlying structures to "leak" through. Using the orthogonality of Bessel functions, a sampling scheme consisting of multiple, concentric projection cones was designed to synthesize by a finite Fourier-Bessel series a slice window with superior side lobe suppression. The window that concentrates the most "energy" within a finite slice, and can be realized by a limited number of sampling cones, is the zero order circular prolate spheroidal function. Its application to tomosynthesis of 3 mm thick slices with a characteristic detail size of 0.5 mm, concentrated 95% of the total series expansion to only 3 concentric circular scans, yielding a theoretical suppression of the first side lobe of -38 dB, to be compared to -8 dB achieved with the Bessel function. Experimental implementation of this optimal sampling scheme using 3, 8, and 14 projection views, distributed over cones with opening half-anges of 1.92, 4.39, and 6.88 degrees, respectively, resulted in a side-lobe attenuation of at least -20 dB. This attenuation reduced significantly artifacts arising from out-of-plane detail of high spatial frequency (e.g., edges) in tomosynthetic images of clinical interest in dentistry.