By Benjamin Graham, Jason Zweig, Warren E. Buffett

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10) (11) Equation (8) is a quadratic ﬁeld gradient whose coeﬃcient is varied in the zdirection. The center position of the quadratic ﬁeld can be moved to an arbitrary position (x ), as shown in Eq. (6), by simultaneous application of the scanning ﬁeld written as Eq. (9). Equation (10) is a ﬁeld gradient in the z-direction under the presence of a ﬁeld oﬀset of b0y , and Eq. (11) is a ﬁeld gradient in the y-direction whose coeﬃcient increments by α in the z-direction. The ﬁeld gradient of Eq. (9) can be rewritten as Gy y + Gyz yz, thus Eq.

Simply ignoring the cone angle and analyzing the longitudinal sampling engendered by helical scans is not sound since the eﬀect of the cone angle on aliasing is signiﬁcant even for four-slice scanners, as discussed above. One potential approach to characterizing sampling in conebeam CT is to make use of Fourier crosstalk analysis,77 –79 a generalized, object-independent form of aliasing analysis in which one quantiﬁes the transmission of Fourier components through an imaging system as well as the ability to distinguish diﬀerent Fourier components from the measured data.

25 (1998) 550–560. 26. S. Schaller, T. Flohr, K. Klingenbeck, J. Krause, T. Fuchs and W. Kalender, Spiral interpolation algorithms for multi-slice spiral CT part I: Theory, IEEE Trans. Med. Imag. 19 (2000) 822–834. 27. P. J. La Rivi`ere and X. Pan, Interlaced interpolation weighting functions for multislice helical CT, Optical Engineering 42 (2003) 3461–3470. 28. P. E. Danielsson, P. Edholm and M. Seger, Towards exact 3D-reconstruction for helical cone-beam scanning of long objects. A new detector arrangement and a new completeness condition, in Proceedings of the 1997 International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine (D.