CT Angular-Longitudinal Diagram and SSPz Geometry Reference

The horizontal axis is the longitudinal distance between a candidate-row center and the target plane, and the vertical axis is the relative tube angle in the model. The left column ignores the transaxial-position-dependent variation in source-to-point distance. The right column applies that variation to candidate-row positions and row widths in an idealized manner. The two conditions coincide at isocenter.

For the right column, the distance ratio to a fixed evaluation point is defined as q(β) = L(β)/R = √{1 + (r/R)² − 2(r/R)cosβ} Here, R is the source-to-isocenter distance, r is the radial distance from isocenter to the evaluation point, β is the relative tube angle with 0° defined when the source lies in the direction of the evaluation point, and L(β) is the source-to-point distance at that angle. The ratio q increases from 0° to 180° and decreases from 180° to 360°. Because the difference from the parallel-beam approximation, q - 1, changes sign within one rotation, the magnitude of the effect first decreases and then increases again. Candidate-row centers are obtained by adding the detector-row position scaled by q(β) to the linear longitudinal table motion. The candidate trajectories in the right column therefore curve gradually and return to the same distance ratio at 360°; they are not straight lines with a constant slope.

Circles identify the nearest acquired candidates on the smaller-z and larger-z sides of the target plane at each angle over 0-360°. Marker size is constant; within each detector-row color, increasing color saturation represents increasing linear interpolation weight. When a candidate coincides with the target plane, that candidate alone receives a weight of 1.

These model SSPz curves include the configured slice thickness T. The horizontal range is determined automatically from only the post-thickness central profiles at or above 10% across all 360 states. Broad low-amplitude tails therefore do not compress the central profiles, allowing direct inspection of full width at half maximum (FWHM) and full width at tenth maximum (FWTM). Each state is normalized by its own maximum, and no additional alignment is performed beyond defining z - z₀=0 at that state's reconstruction plane.

The post-thickness SSPz curves with cone-geometry scaling from 3A are displayed with a logarithmic vertical axis. This separates broad low-amplitude tails, which may persist even when FWHM is nearly constant, from the central profile. Values below 0.1% are not drawn.

Only model SSPz curves after application of the configured slice thickness are summarized using width metrics. The displayed variation compares the potential influence of acquisition geometry relative to that thickness. Intermediate SSPz widths before thickness application are omitted from this primary analysis because they can be mistaken for reconstructed slice thickness. FWHM uses only the two outer 50% crossings and therefore does not retain changes in the tails or centroid.