Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

wave serves as an input to a hypothetical imaging system, and the amplitude of eachinput sine wave corresponds to 100 units. The amplitude here is a measure of theimage density (e.g., optical density for film, or gray scale units for a digital image)between the peaks and valleys of the sine wave. Each of the input sine waves isblurred by the point spread function of the imaging system, and the resultingblurred response to each sine wave (the output of the imaging system) is shown inFig. 10-18 as dotted lines. Notice that as the spatial frequency increases, the blurringcauses a greater reduction in the output amplitude of the sine wave.The amplitude of the sine wave is really just the contrast between the peaks andvalleys. All six sine waves in Fig. 10-18 have the same input contrast to the hypotheticalimaging system (l00 units), but the output contrast was altered by the blurringinfluence of the point spread function. The output contrast is lower for higherspatial frequencies (i.e., smaller objects), and is identified on Fig. 10-18 by two horizontallinesfor each sine wave. The modulation is essentially the output contrastnormalized by the input contrast. The modulation transfer function (MTF) of animaging system is a plot of the imaging system's modulation versus spatial frequency.In Fig. 10-19, the output modulation for each of the sine waves shown inFig. 10-18 is plotted on the y-axis, and the frequency of the corresponding sinewave is the x-axis value.The MTF of an image system, like that shown in Fig. 10-19, is a very completedescription of the resolution properties of an imaging system. The MTFillustrates the fraction (or percentage) of an object's contrast that is recorded bythe imaging system, as a function of the size (i.e., spatial frequency) of the object.To the reader previously unfamiliar with the concept of the MTF, it is fair to askwhy imaging scientists prefer to use the MTF to discuss the spatial resolution ofan imaging system, over the easier-to-understand spread function description discussedpreviously. A partial answer is seen in Fig. 10-20. Many imaging systemsare really imaging chains, where the image passes through many different intermediatesteps from the input to the output of the system (fluoroscopy systems area good example). To understand the role of each component in the imaging chain,the MTF is measured separately for each component (MTF curves A, B, and Cin Fig. 10-20). The total system MTF at any frequency is the product of all thesubcomponent MTF curves.S 60LLI-:E 40o0.0 1.0 2.0 3.0 4.0Spatial Frequency(cycles/mm)FIGURE 10-19. The output amplitude ofthe sine waves illustrated in Fig. 10-18 isplotted here on the y-axis, and the spatialfrequency is plotted on the x-axis. The modulationtransfer function is a plot thatdemonstrates the resolution capabilities ofan imaging system (signal modulation) as afunction of spatial frequency. Since lowspatial frequencies correspond to largeobjects, and high spatial frequencies correspondto smaller objects, the MTF is just adescription of how an imaging systemresponds depending on the size of the stimulus.