X-Ray Imaging and Computed Tomography

High Contrast Resolution Phantom

Theo Fuchs

A phantom containing mathematically defined high contrast structures is used to estimate the resolution of a true 3-dimensional CT scanner system depending on the scanner’s geometry and the reconstruction software. One simulated set of rawdata contains hole patterns in z-direction and within the x-y-plane. The high contrast resolution of the simulated scanner system and/or the reconstruction algorithm can be determined qualitatively by eye-checking the detectability of the hole patterns. A quantitative estimation can be achieved by measuring the maximum contrast of the hole patterns as a function of their diameter.

Phantom Description

The hole diameters range from 0.1mm to 1.4mm; the spacing between the centers of the holes is equal to the respective diameter. A large cylinder (Radius R , length l in z-direction) of high contrast material (density = 1) contains the hole patterns (density = 0). By selecting two parameters d and g certain areas of the phantom remain reserved, i.e. free of hole patterns to provide the possibility to include special inserts later (see gray shaded areas in Fig. 1). The reserved area consists of a small cylindrical core (Radius R × d , d <1) at the center of the phantom and a segment in azimuthal direction (angle of segment 2p g , g <1).
The x-y-plane within the cylindrical main cylinder is divided in S segments and T rings. In total the phantom is divided into S × T sectors. The diameter of the holes varies with segment number s. Thereby the holes are divided in two groups:
Within the first group the spatial frequency n ranges between 24Lp/cm and 17Lp/cm with equidistant steps:

with s = 1,...,NLp.

Within the second group the hole diameter increases with Δd=0.1mm.

with s = NLp,...,S.

It should be emphasized that for better optical appearance the holes are arranged so that the hole diameters decrease in counterclockwise direction (cf. Fig. 1 where NLp = 8).

Each segment contains two rows of  holes each: an azimuthal row with each hole having the same distance to the center of the main cylinder and a radial row with all holes aligned along one spoke through the center of the x-y-plane. The holes of the radial and azimuthal row have quasi-infinite length in z-direction, i.e. they are low density cylinders along the whole main cylinder. For each segment the hole pattern of a single sector is repeated T times with increasing distance from the center of the x-y-plane.
A special algorithm calculates iteratively optimal numbers for S and T based on following restrictions:

                                                                                                                          and

with dmax = max{d(s)| s = 1,...,S}.

φ(s) is the angle of segment s, r(t) is the radius of the azimuthal row of ring t, which is the same for all segments and hole diameters. Nh is the number of holes in a row (here: Nh = 5) and Nd is the safety distance between azimuthal, radial respectively the z–row in units of hole diameters (here: Nd = 3).

The segment angle φ(s) is calculated as

and the radius of the azimuthal rows as

In addition to the radial and azimuthal row within each sector a row of spherical holes extends into z–direction (Fig. 3). The rows are positioned symmetrically to the z = 0 plane.
For reasons of comparability we advise to evaluate images of the high contrast resolution phantom as follows: For each row and segment try to find an optimal yet arbitrary window setting. A specific row is defined as resolved if there can be found a window setting where all holes can be distinguished, i.e. recognized as separated low density objects within the high density environment.

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