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

# Point Spread Function (PSF)

The point spread function (PSF) describes the response of an imaging system to point source. In the case of the Catphan® QA, the point source is either a bead or wire. The image to the left shows 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 how by summing the columns (y-axis) of numbers in the point spread function (PSF) the line spread function (LSF) for the x-axis is obtained.

# Modulation Transfer Function (MTF)

MTF is the most commonly used method of describing spatial resolution capability. The MTF curve is used to graphically represent a system's ability to pass information on to the observer. The MTF curve results from the Fourier Transform of the LSF (described above) data.

A CT system's ability to accurately resolve an object varies according to the size, 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 curve graphs the MTF against the object size measuring a scanner's spatial resolution capabilities. 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 the Catphan® QA 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. 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 wire.

# 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.

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