Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

.g tides:eis.Ec(~ co~o o 2 4 6 8 10 12 14 16 1820 22 24Time (hours)OD O~ 1D 1~ 2D 2~ 3DFrequency (mHertz)BFIGURE 10-31. A: The height (1 dm = 10 cm) ofthe ocean against a glass wall is monitoredfor a 24-hour period. Large sinusoidal fluctuations corresponding to tidalchanges are seen, and overlaid on the tidal background are large amplitude infrequentfluctuations (wave sets) and smaller amplitude more frequent ones (waves). B: Fourieranalysis of the trace in A reveals the frequency of the various surf components.of tides is seen, as are spikes representing the occasional big sets of waves rolling in,and the ordinary ocean waves represent the short-duration fluctuations on this plot.Figure IO-3IB illustrates the results when the Fourier transform is computed onthese data. In this plot, the different frequencies of the various wave and tidal phenomenacan be seen. The tides are very low frequency but are high in amplitude(tidal variations are usually larger than wave height). The tides experience about twocomplete cycles per 24-hour period, corresponding to a frequency of I cycle/I2hours = 2.3 X 10- 5 hertz (very close to zero on this plot). The wave sets show up inthe general vicinity of 0.0002 to 0.0005 hertz, corresponding to a periodicity ofaround 50 minutes. The waves occur much more often, corresponding to theirhigher frequency.Noise on an image often has frequency components to it as well, and a frequencyanalysis similar to the ocean wave example is performed. Just like the Fourier transformof how the imaging system passes "signal" (i.e., the LSF) leads to the calculationof the MTF, the Fourier transform of how an imaging system passes noise leads1000 1009050080N300E 70oS 200Q; 60:= 100050Q.Q)40III 50'0 30z 302020101000 1 2 3 4 5 0 1 2 3 4 5A Frequency (cycles/mm) Frequency (cycles/mm) BFIGURE 10-32. A: A noise power spectrum. B: A plot of the detective quantum efficiency(DOE).