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2.4.1 DQE operating definition. This definition can be extended to take into account the spatial modulation of the input signals if we consider the spatial frequency dependence. From this point of view, the DQE is the transfer coefficient, for each spatial frequency, of the signal to noise ratio through the system. It can be compared to the MTF, which describes the modulation transfer. In order to obtain an efficient operating definition of the DQE, it is necessary to rely on the linearity property of the system under investigation (see Section 2.1). Let us define the input two dimensional signal � Ü� Ý (in this case a dose distribution) and the output of the system � Ü� Ý (which is the dose distribution map obtained applying the inverse sensitometric curve to the image data). The corresponding input and output fluctuations are ¡� Ü� Ý and ¡� Ü� Ý and their respective power spectra Ï ¡� Ù� Ú and Ï ¡� Ù� Ú . The power spectrum of an ideal system, which does not generate an intrinsic noise, is related to the input power spectrum through the MTF: Ï ¡� Ù� Ú �ÅÌ� Ù� Ú ¡ Ï ¡� Ù� Ú (2.43) The DQE definition based on the average signals: ¬ ¬ ¬ �É� � ��ÇÍÌ ℄ ��ÁÆ℄ ¬ ��Ò �ÓÙØ can be extended so to obtain: �É� Ù� Ú � ÅÌ� Ù� Ú Ï ¡� Ù� Ú Ï ¡� Ù� Ú (2.44) (2.45) where the generic average signal has been replaced by a monochromatic wave, with spatial frequencies Ù� Ú . The input output relation is ruled by the ÅÌ� Ù� Ú coefficient, while the variance is given by the Ù� Ú component of the corresponding power spectra. The whole analysis is consistent since, if we introduce a signal of amplitude � Ù� Ú ,we obtain once more that the DQE is the transfer function of the signal to noise ratio: ËÆÊ ÓÙØ � ËÆÊ �Ò � ÅÌ� Ù� Ú � Ù� Ú Ï ¡� Ù� Ú � Ù� Ú Ï ¡� Ù� Ú �É� Ù� Ú � ËÆÊ ÓÙØ ËÆÊ �Ò � ÅÌ� Ù� Ú Ï ¡� Ù� Ú Ï ¡� Ù� Ú 29 (2.46) (2.47) (2.48)
The experimental data will be analyzed following Eq. 2.45 , as described in Chapter 4. 2.5 NEQ The quantities described in the previous section lead to the definition of the Noise Equivalent Quanta, frequently used to evaluate the performances of imaging systems. Since an ideal detector has the same SNR in the output as in the input, the quantity �ÁÆ ℄ in Eq. 2.41 represents the flux that makes the variance of the output equal to the one of the real system in an ideal detector. The ideal system in fact works with a bigger flux in input, and consequently with a better input signal. It can be also written: �ÁÆ ℄�� Ò (2.49) with �ÁÆ ℄ � �ÁÆ℄ due to the second, adimensional factor smaller than one appearing in Eq. 2.41. The quantity �ÁÆ ℄ is thus the signal that makes the ideal system equivalent to the real system from a noise point of view, and it is the so-called Noise Equivalent Quanta NEQ. From Eq. 2.42 it is straightforward to derive the relation between NEQ and DQE: �É� � Æ�É �ÁÆ℄ (2.50) The physical meaning of the NEQ can be also described from a slightly different point of view. The detector is exposed to a flux �ÁÆ℄ and a ËÆÊÓÙØ is obtained. If the detector were ideal, the same ËÆÊÓÙØ would be obtained with a flux given by NEQ (� �ÁÆ℄); the ratio of the two flux gives an operating definition of the detector efficiency. 30
Page 1 and 2: UNIVERSITÀ DEGLI STUDI DI FIRENZE
Page 3 and 4: 3.6 Histogram analysis and IP sensi
Page 5 and 6: made, allowing the diffusion of the
Page 7 and 8: Figure 1.1: Block diagram of the im
Page 9 and 10: function and to replace the very ge
Page 11 and 12: energy of the proper wavelength by
Page 13 and 14: Figure 1.4: Energy levels of the PS
Page 15 and 16: Figure 1.5: Single-side reading met
Page 17 and 18: digital levels. The system under in
Page 19 and 20: ¯ multiplying � Ü� Ý by a co
Page 21 and 22: frequency properties of our system.
Page 23 and 24: on the gain £ and on the function
Page 25 and 26: (a) (b) (c) -u N MTF pre MTF pre -u
Page 27 and 28: (a) (b) (c) -u N -u N -u N MTF p re
Page 29 and 30: -2u N Re { OTF } dig u1 u2 u3 uN 2u
Page 31: for every exposition. The output va
Page 35 and 36: Console Value Measured Value (kVp)
Page 37 and 38: mAs Dose (�Gy) mAs Dose (�Gy) 2
Page 39 and 40: Al thickness Dose (mm) (�Gy) 0.0
Page 41 and 42: (a) (b) Figure 3.4: X-ray spectrum
Page 43 and 44: Figure 3.6: The graphical workstati
Page 45 and 46: theless a set of cassettes has been
Page 47 and 48: ing plate is very wide, a variable
Page 49 and 50: Chapter 4 Measurement of the physic
Page 51 and 52: Figure 4.1: Section along the short
Page 53 and 54: Figure 4.4: Pixel Value plotted as
Page 55 and 56: was filtered by a 30 mm block of PM
Page 57 and 58: 17 13 9 5 1 18 14 10 6 2 19 15 11 7
Page 59 and 60: y the pixel size (� �m) and the
Page 61 and 62: Figure 4.13: Comparison between MTF
Page 63 and 64: 4.3 EMTF The phase dependence of Å
Page 65 and 66: Figure 4.18: Differences between EM
Page 67 and 68: Figure 4.20: 2 dimensional NPS The
Page 69 and 70: The Noise Equivalent Quanta was com
Page 71 and 72: Figure 4.26: NEQ scan vs NEQ subsca
Page 73 and 74: Figure 4.29: DQEsubscan. In Fig. 4.
Page 75 and 76: Conclusions The work performed in t
Page 77 and 78: Bibliography [1] M.J. Yaffe and J.A
Page 79 and 80: [21] “Characteristics of digital

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