This article covers the following topics:

• Introduction
• MTF Catphan® Modules
• Point Spread Function (PSF)
• Line Spread Function (LSF)
• Modulation Transfer Function (MTF) 
• Nyquist Frequency
• MTF Plot from Wire
• Critical Frequency - Wire
• Line Spread Function (LSF) Plot from Wire
• MTF Plot from Beads
• Critical Frequency - Beads
• Line Spread Function (LSF) Plot from Beads

Introduction

MTF information is given for the following Catphan® models: 500, 503, 504, 600, 700.

MTF Catphan® Modules

Figure 4.1: Diagram of the cross-sectional view of the Catphan® CTP528 High Resolution Module with a 21 line pair per cm gauge and point source. Surrounded by the radial pattern of line pairs, are two 0.28mm diameter tungsten carbide beads that serve as impulse sources for measuring the MTF. These beads can be hard to see in the figure above, but they are found slightly above and below the center of the diagram.

 

The CTP528 High Resolution Module has a diameter of 150mm and is 40mm thick. Its unique design minimizes visual artifacts by reducing the amount of high contrast material. The two 0.28mm diameter spherical tungsten carbide beads are used for MTF measurements. Rather than using a wire, the point source beads enable operators to avoid the tedious and time-consuming step of positioning and aligning the wires with the z-axis. Furthermore, the use of the spherical beads prevents overranging problems (the extension of the scan beyond the planned image boundaries) and streaking artifacts that occur with MTF wires, because the bead densities are volume averaged with the surrounding material. This module is found in Catphan® models 500, 503, 504, and 600.

 

 

Figure 4.2: Diagram of the cross-sectional view of the Catphan® CTP682 Geometry and Sensitometry Module. This module contains three impulse sources for MTF calculations, as seen above: a 0.18mm and 0.28mm diameter tungsten carbide ball, and a 0.05mm tungsten wire.

 

Figure 4.3: Diagram of the cross-sectional view of the Catphan® CTP591 Bead Geometry Module. This module contains three impulse sources for MTF calculations, as seen above: a 0.18mm and 0.28mm diameter tungsten carbide ball, and a 0.05mm tungsten wire.

 

The CTP682 Geometry and Sensitometry Module and CTP591 Bead Geometry Module are 40mm thick, and are found in the Catphan® 700 model and the Catphan® 600, respectively. Both contain three impulse sources to estimate the point source response function used for detailed MTF calculations. They contain two isolated tungsten carbide beads that are 0.28 mm and 0.18 mm in diameter, which are located in the mid-plane of the module. For thin slice high resolution measurements, there is an isolated 0.05 mm diameter tungsten MTF wire that extends through the entire module. While a sphere does produce a different density profile than a cross section of a wire or cylinder, both objects are so small that the actual difference is not usually significant in current CT scanners. The Smári and TotalQA analysis services automatically account for these variables in Point Spread Function (PSF) and MTF calculations.

 

Point Spread Function (PSF)

The point spread function (PSF) describes the response of an imaging system to a point source. In the case of Smári or TotalQA, the point source is either a bead or wire. The image above shows colored pixels representing the pixel values [HU] around the point source, with the highest values at the top of the color scale. The PSF can be thought of as the extended area that represents an unresolved object. The values from the PSF are used to derive the line spread function (LSF).

Line Spread Function (LSF)

The line spread function (LSF) is obtained by averaging the PSF values in the x and y directions. Once the averaged x and y values are symmetrized, the two directions (x and y) are averaged together to derive the LSF.

The above illustrations show the one-dimensional integral of the normalized PSF with respect to y positions. The sum of each column of numbers in the PSF are the y-axis values of the LSF. The LSF obtained plots CT numbers (pixel values) vs the relative x-axis position.

Modulation Transfer Function (MTF) 

MTF is the most commonly used method of describing a system's spatial resolution capability. The MTF curve is used to graphically represent a system's ability to reproduce contrast variations in the object radiographed at a specific spatial frequency. The MTF curve results from the Fourier Transform of the LSF data (described above). It is a useful measure of effective resolution since it accounts for the amount of blur and contrast over a range of spatial frequencies.

A CT system's ability to accurately resolve an object varies according to the size, or the spatial frequency, of the object. As objects become smaller, they are more difficult to accurately resolve on a CT image. The MTF scale is from 0 to 1, with a value of 1 having the object reproduced exactly and a value of 0 having no image reproduced. The MTF measures the reduction of signal amplitude for increasingly higher spatial frequencies and can be represented in a two dimensional graph. Certain factors, including pixel size, field of view (FOV), slice thickness, and kernel, affect spatial resolution. Thin slices and smaller pixel size reduce volume averaging and improve resolution. Some of these factors, obtained from the DICOM header, are reported by Smári or TotalQA to aid in MTF comparisons.

Nyquist Frequency

The Nyquist frequency reported on the MTF curve, represents the point at which the object cannot be accurately resolved. The Nyquist theorem, as applied to CT, tells us that because an object may not lay entirely within a pixel, the object should be two times the pixel size to increase the likelihood of being resolved.  

Information on the Nyquist frequency can be found here.

MTF Plot from Wire

The MTF plot displays the measured points, critical frequencies (50, 10, 5, and 2%), and MTF curve from the line spread function (LSF) data from the wire. Critical frequencies are the spatial frequencies at which the system is only able to produce an image with 50%, 10%, 5%, or 2% of the maximum contrast. The Nyquist frequency, which is the sampling threshold, is also displayed. 

Critical Frequency - Wire

The critical frequency for 50, 10, 5, and 2% of the MTF is displayed for data from the tungsten wire spanning the entire length of the 40mm module. 

Line Spread Function (LSF) Plot from Wire

The line spread function (LSF) is derived by averaging the pixel intensities, the point spread function (PSF) values, surrounding the wire. The x and y-axis PSF values are averaged and symmetrized, and then both directions are averaged to create the LSF plot. 

MTF Plot from Beads

The MTF plot displays the measured points, critical frequencies (50, 10, 5, and 2%), and MTF curve from the line spread function (LSF) data from the bead or beads if both upper and lower beads are found. The Nyquist frequency, which is the sampling threshold, is also displayed. 

Critical Frequency - Beads

The critical frequency for 50, 10, 5, and 2% of the MTF is displayed for data from the found bead(s).

Line Spread Function (LSF) Plot from Beads

The line spread function (LSF) is derived by averaging the pixel intensities, the point spread function (PSF) values, surrounding the bead(s). The x and y-axis PSF values are averaged and symmetrized, and then both directions are averaged to create the LSF plot.