High Contrast
Resolution PhantomAuthor: Theo Fuchs, IMP Erlangen |

**1. Aims **

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.

**2. 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, lengthlin 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 (RadiusR× 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

Ssegments andTrings. In total the phantom is divided intoS×Tsectors. The diameter of the holes varies with segment numbers. 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

Within the second group the hole diameter increases with D

d=0.1mm.

with

.

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 ).

Each segment contains two rows of holes each: an

azimuthalrow with each hole having the same distance to the center of the main cylinder and aradialrow 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 repeatedTtimes with increasing distance from the center of the x-y-plane.A special algorithm calculates iteratively optimal numbers for

SandTbased on following restrictions:and

with

.

is the angle of segment

s, is the radius of the azimuthal row of ringt, which is the same for all segments and hole diameters. is the number of holes in a row (here: ) and is the safety distance between azimuthal, radial respectively thez–row in units of hole diameters (here: ).The segment angle 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 thez= 0 plane.

**Evaluation**

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.

**Summary**

The described arrangement allows to estimate the high contrast resolution of a CT scanner/reconstruction system enabling

- Clear distinction between the radial and azimuthal direction of a periodic pattern and thereby the resolution.
- Measurement of radial and azimuthal resolution at arbitrary z-Position within main cylinder.
- Estimation in all three directions (radial, azimuthal, z) at the same radius from the x-y-origin within one sector and for different distances from the x-y-origin within each segment.
- Depiction of a large range of detail size (i.e. hole diameter) of periodic structures.
- Minimized influence between each pattern direction by optimally using the allowed areas of the main cylinder and a clear separation between single rows.

**Images**

Fig. 1. Shows the transaxial section at *z* = 0
position. Phantom has been calculated with 3 rings and 22 segments. This was achieved by
choosing g = 0.01 and d = 0.3 (Radius *R* = 100mm). The radii of the azimuthal rows
are found as *r(1)* = 40.50mm, *r(2)* = 63.83mm and *r(3)* = 87.17mm.The
holes are divided in two groups. Within the first group starting at the right in 3
o’clock position the number of linepairs per centimeter (Lp/cm) decreases from 24
Lp/cm to 17 Lp/cm in counterclockwise direction with equidistant steps. Afterwards the
diameter of the holes decreases from 1.4mm down to 0.1mm with 0.1mm steps when proceeding
counterclockwise. The 1.3mm rows in z-direction are depicted in Fig. 3.

Fig. 2: The upper right quadrant of the transversal section. In counterclockwise direction the spatial frequency of the holes decreases from 24Lp/cm to 17Lp/cm in equidistant steps of 1Lp/cm.

Fig. 3. Longitudinal section through 1.3mm holes in z-direction. The main high contrast
cylinder has *R* = 100mm radius and length *l* = 40mm in z–direction.

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