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Practical expressions describing detectivequantum efficiency in flat-panel detectorsTo cite this article H K Kim 2011 JINST 6 C11020

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2011 JINST 6 C11020

PUBLISHED BY IOP PUBLISHING FOR SISSA

RECEIVED September 6 2011ACCEPTED November 9 2011

PUBLISHED November 24 2011

13th INTERNATIONAL WORKSHOP ON RADIATION IMAGING DETECTORS3ndash7 JULY 2011ETH ZURICH SWITZERLAND

Practical expressions describing detective quantumefficiency in flat-panel detectors

HK Kim

School of Mechanical Engineering Pusan National UniversityJangjeon-dong Geumjeong-gu Busan 609-735 Republic of Korea

E-mail hokyungpusanackr

ABSTRACT In radiology image quality excellence is a balance between system performance andpatient dose hence x-ray systems must be designed to ensure the maximum image quality is ob-tained for the lowest consistent dose The concept of detective quantum efficiency (DQE) is widelyused to quantify understand measure and predict the performance of x-ray detectors and imagingsystems Cascaded linear-systems theory can be used to estimate DQE based on the system designparameters and this theoretical DQE can be utilized for determining the impact of various phys-ical processes such as secondary quantum sinks noise aliasing reabsorption noise and othersHowever the prediction of DQE usually requires tremendous efforts to determine each parameterconsisting of the cascaded linear-systems model In this paper practical DQE formalisms assessingboth the photoconductor- and scintillator-based flat-panel detectors under quantum-noise-limitedoperation are described The developed formalisms are experimentally validated and discussed fortheir limits The formalisms described in this paper would be helpful for the rapid prediction of theDQE performances of developing systems as well as the optimal design of systems

KEYWORDS Detector modelling and simulations I (interaction of radiation with matter interac-tion of photons with matter interaction of hadrons with matter etc) X-ray detectors Detectordesign and c onstruction technologies and materials

ccopy 2011 IOP Publishing Ltd and SISSA doi1010881748-0221611C11020

2011 JINST 6 C11020

Contents

1 Introduction 1

2 Background and theory 2

3 Model validation 3

4 Results and discussion 3

5 Conclusion 5

1 Introduction

In diagnostic radiology excellence in image quality is a balance between system performance andpatient radiation dose hence x-ray systems must be designed to ensure the maximum image qualityis obtained for the patient dose as low as possible [1] The concept of detective quantum efficiency(DQE) is universially used to quantify understand measure and predict the performance of x-raydetectors and imaging systems [2] Both the empirical and theoretical estimation of the DQE arebased on linear-systems theory and Fourier concepts [3] As such the DQE analysis assumes alinear and shift-invariant system and wide-sense stationary random noise processes A practicalexpression for use when measuring the DQE is given by [1 3]

DQE(k) =qG2 MTF2(k)

NPS(k)=

MTF2(k)

q[NPS(k)

d

2] (11)

where k is the Fourier conjugate of the two-dimensional (2D) spatial variable and G = d

q is thesystem large-area gain factor This equation shows that the DQE of any detector can be determinedif the system modulation-transfer function (MTF) and the image noise-power spectrum (NPS) withthe associated mean image pixel value d and the incident number of quanta per unit area q canbe determined It is noted that while the NPS in the DQE calculation includes the effect of noisealiasing the MTF should not because the siganl aliasing is non-linear process

The theoretical DQE based on the cascaded linear-systems theory is powerful because it canbe used to determine all quantities related to system design parameters such as secondary quantumsinks noise aliasing reabsorption noise and others [1 3] In this paper simple practical DQE for-malisms assessing photoconductor- and scintillator-based flat-panel detectors are described undertypical operation conditions such as quantum-limited operation The developed formalisms arevalidated by comparing with the measured DQE values and discussed for their limits

ndash 1 ndash

2011 JINST 6 C11020

Figure 1 Cascaded model used to describe signal and noise propagation in a flat-panel detector Theoverhead tilde designates a random variable The symbol ldquosrdquo is the quantum scatter operator

2 Background and theory

Signal and noise propagation in a flat-panel detector can be understood using a simple serial cas-cade of simple elemental transfer relationships as illustrated in figure 1 consisting of the followingsteps [4] 1) absorption of x-ray quanta in the x-ray converter (eg photoconductor or scintillator)with a probability α equal to the quantum efficiency 2) random relocation of the interaction loca-tions described as a scatter operation with the probability density function pr(r) in the image planeor T1(k) in the Fourier domain to determine where x-ray energy is deposited 3) production of sec-ondary quanta (eg charge carriers or optical quanta) with an average gain of β secondary quantaper x-ray interaction 4) random relocation of secondary quanta (due to charge-carrier diffusionor optical scattering) as described as T2(k) in the Fourier domain 5) random escape of secondaryquanta from the x-ray converter 6) random collection of secondary quanta (eg charge carriersby the pixel electrode or conversion of optical quanta into charge carriers in the photodiode) withprobability η 7) realization of a measurable signal by aperture integration of secondary quanta andscaling to detector units 8) spatial sampling represented by multiplying the presampled detectorsignal with a train of delta functions to determine discrete detector-element values and 9) addi-tion of detector readout noise caused by peripheral addressingsignal-processing circuitries duringsignal readout The average image signal and NPS for the model can be determined by cascadingexpressions of signal and noise propagation through each process [3] Assuming square pixel ge-ometry with width p and active aperture width a the theoretical DQE in this paper consistent withothers [5 6] is given by

DQE(k) =qa4g2T 2

1 (k)T 22 (k)sinc2(πak)

qa4gγ

+qa4ginfin

sumj=0

gm

(β

I minus1)

T 22 (kplusmn j

p)sinc2[πa(kplusmn j

p)]

+ p2σ2read

(21)

where m = αβ g = αβκη and γ = a2

p2 Although more detailed models have recently beenintroduced for an improved assessment of the NPS [7]ndash[9] eq (21) is reasonable for the DQEestimation of conventional flat-panel detectors

Equation (21) is impractical for repeated estimations of the DQE for new technological devel-opments and detector designs because of expensive 2D NPS computations which are required evenfor the one-dimensional (1D) analysis of a 2D detector Since both the signal blur and noise corre-lation occur over 2D space the 1D DQE is obtained by evaluating eq (21) along the appropriateaxis for example DQE(u) = DQE(uv)|v=0 = DQE(u0) where u and v are Fourier variables inCartesian coordinates

ndash 2 ndash

2011 JINST 6 C11020

In a direct-conversion flat-panel detector based on photoconductor we may neglect the signalspreading due to negligible charge diffusion [10] and then we have

DQEdirect(k)asymp DQEconv(0)γT 21 (k)sinc2(πak)

1+ DQEconv(0)m

(mg minus1

)+ DQEconv(0)σ2

readqa2g2

(22)

where DQEconv(0) is the large-area DQE of the x-ray converter and is given by the quantum ef-ficiency times the Swank factor (= αI) When the detector is operated in quantum-noise-limited

exposure region ie σread lt agradic

q

DQEconv(0) eq (22) can be reduced to

DQEdirect(k)asymp DQEconv(0)γT 21 (k)sinc2(πak)

[1minus

DQEconv(0)σ2read

qa2g2

] (23)

Similarly with an assumption that optical scattering is most dominant in signal spreadingprocesses in an indirect-conversion flat-panel detector based on scintillator eq (21) can be simpli-fied to

DQEindirect(k)asymp DQEconv(0)

1+DQEconv(0)(

1γg2T 2

2 (k) minus1m

)+ DQEconv(0)σ2

readγqa2g2T 2

2 (k)

(24)

For σread lt agT2(k)radic

γq

DQEconv(0) eq (24) is reduced to

DQEindirect(k)asymp DQEconv(0)minus DQE2conv(0)

γg2T 22 (k)

[1minus

σ2read

qa2

] (25)

3 Model validation

The developed DQE formalisms were validated by comparisons with the measured DQEs from twodifferent-type flat-panel detectors amorphous selenium (a-Se) based detector with a pixel pitch of139 microm and cesium iodide (CsI) based detector with a pixel pitch of 143 microm The thicknessesof both converters are the same as 500 microm Two detectors are respectively denoted by D1 andD2 hereinafter The DQE analyses were compliant with IEC 62220-1 (IEC Geneva Switzerland2004) using a 70 kV RQA-5 spectrum Detailed measurement procedures can be found in ref [11]

The physical parameters involved in the cascaded models were estimated based on the ab-sorbed energy distributions and the optical pulse-height distributions obtained from the MonteCarlo simulations We employed two Monte Carlo codes MCNPX (Version 250 ORNL USA)and DETECT2000 (Laval University Quebec Canada) for x-ray and optical quanta transports re-spectively Extraction methods of physical parameters from the Monte Carlo simulation results arebased on ref [12] and the extracted values are summarized in table 1

4 Results and discussion

Figure 2 summarizes comparisons of the measured and theoretical image quality for two detectorsFor the direct-conversion D1 detector the measured MTF is slightly less than the aperture transferfunction which can be described by the sine cardinal function sinc(πau) This observation may im-ply that the quantum-relocation processes due to primary andor secondary quanta slightly degrade

ndash 3 ndash

2011 JINST 6 C11020

Table 1 Numerical values used in the theoretical DQE calculations for a-Se (D1) and CsI (D2) basedflat-panel detectors

Parameter Description ValueD1 (direct) D2 (indirect)

a Pixel aperture [mm] pradic

γ

p Pixel pitch [mm] 0139 0143γ Fill factor 079 068q0 Incident photon fluence [mmminus2mRminus1] 26times105

α Average quantum absorption efficiency 053 081I Swank factor 096 076

T1 MTF due to primary quanta scattering 1β Secondary quantum gain per interacting quanta 1070 2600T2 MTF due to secondary quanta scattering 1 Measuredκ Average coupling efficiency 1 032η Average collection efficiency 1 065T3 MTF due to aperture integration |sinc(πau)sinc(πav)|

σread Additive readout electronic noise [eminus] 3000 4600

Figure 2 Comparisons between empirical and theoretical MTF NPS and DQE for a-Se (D1) and CsI (D2)based flat-panel detectors NNPS designates the normalized NPS [see the bracketed term in the denominatorof eq (11)]

the total system transfer function The agreement between empirical and approximate theoreticalNPSs is excellent Theoretical white-spectral characteristic due to noise aliasing [5] is well provedby the measured NPS Although there are some discrepancies at the spatial frequencies greater thanabout 1 mmminus1 the approximate DQE model reasonably describes the measured data

For indirect-conversion D2 detector there is a large discrepancy between the aperture transferfunction and the measured MTF and which is mainly due to the secondary quanta scattering withinthe CsI layer The agreement between the calculated and measured NPSs is excellent Approximate

ndash 4 ndash

2011 JINST 6 C11020

Figure 3 Calculated DQEs for hypothetical 1D direct and indirect-conversion detectors with respect tovarious additive electronic noise levels uN denotes the Nyquist frequency

DQE formalism underestimates the measured DQE values for the spatial frequency greater than15 mmminus1

Figure 3 shows the DQE simulation results with respect to various additive electronic noiselevels The simulation assumes 1D line detector configurations for simplicity in the calculationsAll the simulations were performed for exposure of 1 mR at the detector entrance surface The MTFof the hypothetical indirect-conversion 1D detector is based on the Gaussian point-spread functionwith the standard deviation σ = p Other simulation parameters were taken from table 1 As shownin figure 3 where the spatial frequency u was normalized by the Nyquist frequency uN the elec-tronic readout noise affects the approximate DQE model for direct-conversion detectors over theentire spatial frequency band while the approximate DQE model for indirect-conversion detector isrelatively insensitive to the additive noise at lower frequencies For the direct-conversion detectorit is expected that the approximate DQE model [eq (23)] well follows the complete DQE model[eq (21)] when the detector is operated in quantum-noise-limited region or σread = 0 eminus Equa-tion (23) well describes eq (21) up to the electronic noise level of 104 eminus in this simulation Forσread gt 104 eminus however eq (23) gradually underestimates eq (21) as σread further increases Forthe indirect-conversion detector the approximate DQE model [eq (25)] underestimates eq (21)in the high frequency band even for σread = 0 eminus This frequency band widens as σread increases

In the quantum-noise-limited operation the DQE(0) of indirect-conversion detectors can besimply determined by the DQE(0) of scintillator or αI while that of direct-conversion detectorsis determined by the DQE(0) of photoconductor scaled by the pixel fill factor γ To preserve thephotoconductor DQE(0) performance in direct-conversion detectors therefore it is required thatthe pixel should be designed to have a fill factor as high as possible Electrical design in which allfield lines terminate on the pixel electrode is essential

5 Conclusion

Practical DQE formalisms have been described in this paper and it has been demonstrated that thedeveloped DQE formalisms reasonably agree to the measured DQE values for the conventional

ndash 5 ndash

2011 JINST 6 C11020

flat-panel detectors Especially the approximate DQE model of direct-conversion detectors welldescribes the complete DQE model when the detectors are operated in the quantum-noise-limitedregion On the contrary the approximate DQE model of indirect-conversion detectors describesthe complete DQE model up tosim75 of the Nyquist-frequency limit at the quantum-noise-limitedoperation The approximate DQE formalisms would be very useful for the rapid evalution of themeasured DQE and the extraction of detector performance parameters such as quantum absorptionefficiency Swank noise factor and secondary quantum gain

Acknowledgments

This research was supported by Basic Science Research Program through the National ResearchFoundation of Korea (NRF) funded by the Ministry of Education Science and Technology (2011-0009769)

References

[1] HK Kim et al On the development of digital radiography A review Int J Precis Eng Manuf 9(2008) 86

[2] CE Metz et al Toward consensus on quantitative assessment of medical imaging systems MedPhys 22 (1995) 1057

[3] IA Cunningham Applied Linear-Systems Theory in Handbook of Medical Imaging J Beutel HLKundel and RL Van Metter eds SPIE Press Bellingham USA 2000 vol 1 pp 79ndash159

[4] S Yun et al Finding the best photoconductor for digital mammography detectors Nucl InstrumMeth A 652 (2011) 829

[5] W Zhao and JA Rowlands Digital radiology using active matrix readout of amorphous seleniumTheoretical analysis of detective quantum efficiency Med Phys 24 (1997) 1819

[6] JH Siewerdsen et al Signal noise power spectrum and detective quantum efficiency ofindirect-detection flat-panel imagers for diagnostic radiology Med Phys 25 (1998) 614

[7] J Yao and IA Cunningham Parallel cascades New ways to describe noise transfer in medicalimaging systems Med Phys 28 (2001) 2020

[8] HK Kim Generalized cascaded model to assess noise transfer in scintillator-based x-ray imagingdetectors Appl Phys Lett 89 (2006) 233504

[9] R Akbarpour et al Signal and noise transfer in spatiotemporal quantum-based imaging systems JOpt Soc Am A 24 (2007) B151

[10] W Que and JA Rowlands X-ray imaging using amorphous selenium Inherent spatial resolutionMed Phys 22 (1995) 365

[11] MK Cho et al Measurements of x-ray imaging performance of granular phosphors withdirect-coupled CMOS sensors IEEE Trans Nucl Sci 55 (2008) 1338

[12] S Yun et al Signal and noise characteristics induced by unattenuated x rays from a scintillator inindirect-conversion CMOS photodiode array detectors IEEE Trans Nucl Sci 56 (2009) 1121

ndash 6 ndash

2011 JINST 6 C11020

Figure 1 Cascaded model used to describe signal and noise propagation in a flat-panel detector Theoverhead tilde designates a random variable The symbol ldquosrdquo is the quantum scatter operator

2 Background and theory

Signal and noise propagation in a flat-panel detector can be understood using a simple serial cas-cade of simple elemental transfer relationships as illustrated in figure 1 consisting of the followingsteps [4] 1) absorption of x-ray quanta in the x-ray converter (eg photoconductor or scintillator)with a probability α equal to the quantum efficiency 2) random relocation of the interaction loca-tions described as a scatter operation with the probability density function pr(r) in the image planeor T1(k) in the Fourier domain to determine where x-ray energy is deposited 3) production of sec-ondary quanta (eg charge carriers or optical quanta) with an average gain of β secondary quantaper x-ray interaction 4) random relocation of secondary quanta (due to charge-carrier diffusionor optical scattering) as described as T2(k) in the Fourier domain 5) random escape of secondaryquanta from the x-ray converter 6) random collection of secondary quanta (eg charge carriersby the pixel electrode or conversion of optical quanta into charge carriers in the photodiode) withprobability η 7) realization of a measurable signal by aperture integration of secondary quanta andscaling to detector units 8) spatial sampling represented by multiplying the presampled detectorsignal with a train of delta functions to determine discrete detector-element values and 9) addi-tion of detector readout noise caused by peripheral addressingsignal-processing circuitries duringsignal readout The average image signal and NPS for the model can be determined by cascadingexpressions of signal and noise propagation through each process [3] Assuming square pixel ge-ometry with width p and active aperture width a the theoretical DQE in this paper consistent withothers [5 6] is given by

DQE(k) =qa4g2T 2

1 (k)T 22 (k)sinc2(πak)

qa4gγ

+qa4ginfin

sumj=0

gm

(β

I minus1)

T 22 (kplusmn j

p)sinc2[πa(kplusmn j

p)]

+ p2σ2read

(21)

where m = αβ g = αβκη and γ = a2

p2 Although more detailed models have recently beenintroduced for an improved assessment of the NPS [7]ndash[9] eq (21) is reasonable for the DQEestimation of conventional flat-panel detectors

Equation (21) is impractical for repeated estimations of the DQE for new technological devel-opments and detector designs because of expensive 2D NPS computations which are required evenfor the one-dimensional (1D) analysis of a 2D detector Since both the signal blur and noise corre-lation occur over 2D space the 1D DQE is obtained by evaluating eq (21) along the appropriateaxis for example DQE(u) = DQE(uv)|v=0 = DQE(u0) where u and v are Fourier variables inCartesian coordinates

ndash 2 ndash

2011 JINST 6 C11020

In a direct-conversion flat-panel detector based on photoconductor we may neglect the signalspreading due to negligible charge diffusion [10] and then we have

DQEdirect(k)asymp DQEconv(0)γT 21 (k)sinc2(πak)

1+ DQEconv(0)m

(mg minus1

)+ DQEconv(0)σ2

readqa2g2

(22)

where DQEconv(0) is the large-area DQE of the x-ray converter and is given by the quantum ef-ficiency times the Swank factor (= αI) When the detector is operated in quantum-noise-limited

exposure region ie σread lt agradic

q

DQEconv(0) eq (22) can be reduced to

DQEdirect(k)asymp DQEconv(0)γT 21 (k)sinc2(πak)

[1minus

DQEconv(0)σ2read

qa2g2

] (23)

Similarly with an assumption that optical scattering is most dominant in signal spreadingprocesses in an indirect-conversion flat-panel detector based on scintillator eq (21) can be simpli-fied to

DQEindirect(k)asymp DQEconv(0)

1+DQEconv(0)(

1γg2T 2

2 (k) minus1m

)+ DQEconv(0)σ2

readγqa2g2T 2

2 (k)

(24)

For σread lt agT2(k)radic

γq

DQEconv(0) eq (24) is reduced to

DQEindirect(k)asymp DQEconv(0)minus DQE2conv(0)

γg2T 22 (k)

[1minus

σ2read

qa2

] (25)

3 Model validation

The developed DQE formalisms were validated by comparisons with the measured DQEs from twodifferent-type flat-panel detectors amorphous selenium (a-Se) based detector with a pixel pitch of139 microm and cesium iodide (CsI) based detector with a pixel pitch of 143 microm The thicknessesof both converters are the same as 500 microm Two detectors are respectively denoted by D1 andD2 hereinafter The DQE analyses were compliant with IEC 62220-1 (IEC Geneva Switzerland2004) using a 70 kV RQA-5 spectrum Detailed measurement procedures can be found in ref [11]

The physical parameters involved in the cascaded models were estimated based on the ab-sorbed energy distributions and the optical pulse-height distributions obtained from the MonteCarlo simulations We employed two Monte Carlo codes MCNPX (Version 250 ORNL USA)and DETECT2000 (Laval University Quebec Canada) for x-ray and optical quanta transports re-spectively Extraction methods of physical parameters from the Monte Carlo simulation results arebased on ref [12] and the extracted values are summarized in table 1

4 Results and discussion

Figure 2 summarizes comparisons of the measured and theoretical image quality for two detectorsFor the direct-conversion D1 detector the measured MTF is slightly less than the aperture transferfunction which can be described by the sine cardinal function sinc(πau) This observation may im-ply that the quantum-relocation processes due to primary andor secondary quanta slightly degrade

ndash 3 ndash

2011 JINST 6 C11020

Table 1 Numerical values used in the theoretical DQE calculations for a-Se (D1) and CsI (D2) basedflat-panel detectors

Parameter Description ValueD1 (direct) D2 (indirect)

a Pixel aperture [mm] pradic

γ

p Pixel pitch [mm] 0139 0143γ Fill factor 079 068q0 Incident photon fluence [mmminus2mRminus1] 26times105

α Average quantum absorption efficiency 053 081I Swank factor 096 076

T1 MTF due to primary quanta scattering 1β Secondary quantum gain per interacting quanta 1070 2600T2 MTF due to secondary quanta scattering 1 Measuredκ Average coupling efficiency 1 032η Average collection efficiency 1 065T3 MTF due to aperture integration |sinc(πau)sinc(πav)|

σread Additive readout electronic noise [eminus] 3000 4600

Figure 2 Comparisons between empirical and theoretical MTF NPS and DQE for a-Se (D1) and CsI (D2)based flat-panel detectors NNPS designates the normalized NPS [see the bracketed term in the denominatorof eq (11)]

the total system transfer function The agreement between empirical and approximate theoreticalNPSs is excellent Theoretical white-spectral characteristic due to noise aliasing [5] is well provedby the measured NPS Although there are some discrepancies at the spatial frequencies greater thanabout 1 mmminus1 the approximate DQE model reasonably describes the measured data

For indirect-conversion D2 detector there is a large discrepancy between the aperture transferfunction and the measured MTF and which is mainly due to the secondary quanta scattering withinthe CsI layer The agreement between the calculated and measured NPSs is excellent Approximate

ndash 4 ndash

2011 JINST 6 C11020

Figure 3 Calculated DQEs for hypothetical 1D direct and indirect-conversion detectors with respect tovarious additive electronic noise levels uN denotes the Nyquist frequency

DQE formalism underestimates the measured DQE values for the spatial frequency greater than15 mmminus1

Figure 3 shows the DQE simulation results with respect to various additive electronic noiselevels The simulation assumes 1D line detector configurations for simplicity in the calculationsAll the simulations were performed for exposure of 1 mR at the detector entrance surface The MTFof the hypothetical indirect-conversion 1D detector is based on the Gaussian point-spread functionwith the standard deviation σ = p Other simulation parameters were taken from table 1 As shownin figure 3 where the spatial frequency u was normalized by the Nyquist frequency uN the elec-tronic readout noise affects the approximate DQE model for direct-conversion detectors over theentire spatial frequency band while the approximate DQE model for indirect-conversion detector isrelatively insensitive to the additive noise at lower frequencies For the direct-conversion detectorit is expected that the approximate DQE model [eq (23)] well follows the complete DQE model[eq (21)] when the detector is operated in quantum-noise-limited region or σread = 0 eminus Equa-tion (23) well describes eq (21) up to the electronic noise level of 104 eminus in this simulation Forσread gt 104 eminus however eq (23) gradually underestimates eq (21) as σread further increases Forthe indirect-conversion detector the approximate DQE model [eq (25)] underestimates eq (21)in the high frequency band even for σread = 0 eminus This frequency band widens as σread increases

In the quantum-noise-limited operation the DQE(0) of indirect-conversion detectors can besimply determined by the DQE(0) of scintillator or αI while that of direct-conversion detectorsis determined by the DQE(0) of photoconductor scaled by the pixel fill factor γ To preserve thephotoconductor DQE(0) performance in direct-conversion detectors therefore it is required thatthe pixel should be designed to have a fill factor as high as possible Electrical design in which allfield lines terminate on the pixel electrode is essential

5 Conclusion

Practical DQE formalisms have been described in this paper and it has been demonstrated that thedeveloped DQE formalisms reasonably agree to the measured DQE values for the conventional

ndash 5 ndash

2011 JINST 6 C11020

flat-panel detectors Especially the approximate DQE model of direct-conversion detectors welldescribes the complete DQE model when the detectors are operated in the quantum-noise-limitedregion On the contrary the approximate DQE model of indirect-conversion detectors describesthe complete DQE model up tosim75 of the Nyquist-frequency limit at the quantum-noise-limitedoperation The approximate DQE formalisms would be very useful for the rapid evalution of themeasured DQE and the extraction of detector performance parameters such as quantum absorptionefficiency Swank noise factor and secondary quantum gain

Acknowledgments

This research was supported by Basic Science Research Program through the National ResearchFoundation of Korea (NRF) funded by the Ministry of Education Science and Technology (2011-0009769)

References

[1] HK Kim et al On the development of digital radiography A review Int J Precis Eng Manuf 9(2008) 86

[2] CE Metz et al Toward consensus on quantitative assessment of medical imaging systems MedPhys 22 (1995) 1057

[3] IA Cunningham Applied Linear-Systems Theory in Handbook of Medical Imaging J Beutel HLKundel and RL Van Metter eds SPIE Press Bellingham USA 2000 vol 1 pp 79ndash159

[4] S Yun et al Finding the best photoconductor for digital mammography detectors Nucl InstrumMeth A 652 (2011) 829

[5] W Zhao and JA Rowlands Digital radiology using active matrix readout of amorphous seleniumTheoretical analysis of detective quantum efficiency Med Phys 24 (1997) 1819

[6] JH Siewerdsen et al Signal noise power spectrum and detective quantum efficiency ofindirect-detection flat-panel imagers for diagnostic radiology Med Phys 25 (1998) 614

[7] J Yao and IA Cunningham Parallel cascades New ways to describe noise transfer in medicalimaging systems Med Phys 28 (2001) 2020

[8] HK Kim Generalized cascaded model to assess noise transfer in scintillator-based x-ray imagingdetectors Appl Phys Lett 89 (2006) 233504

[9] R Akbarpour et al Signal and noise transfer in spatiotemporal quantum-based imaging systems JOpt Soc Am A 24 (2007) B151

[10] W Que and JA Rowlands X-ray imaging using amorphous selenium Inherent spatial resolutionMed Phys 22 (1995) 365

[11] MK Cho et al Measurements of x-ray imaging performance of granular phosphors withdirect-coupled CMOS sensors IEEE Trans Nucl Sci 55 (2008) 1338

[12] S Yun et al Signal and noise characteristics induced by unattenuated x rays from a scintillator inindirect-conversion CMOS photodiode array detectors IEEE Trans Nucl Sci 56 (2009) 1121

ndash 6 ndash

2011 JINST 6 C11020

In a direct-conversion flat-panel detector based on photoconductor we may neglect the signalspreading due to negligible charge diffusion [10] and then we have

DQEdirect(k)asymp DQEconv(0)γT 21 (k)sinc2(πak)

1+ DQEconv(0)m

(mg minus1

)+ DQEconv(0)σ2

readqa2g2

(22)

where DQEconv(0) is the large-area DQE of the x-ray converter and is given by the quantum ef-ficiency times the Swank factor (= αI) When the detector is operated in quantum-noise-limited

exposure region ie σread lt agradic

q

DQEconv(0) eq (22) can be reduced to

DQEdirect(k)asymp DQEconv(0)γT 21 (k)sinc2(πak)

[1minus

DQEconv(0)σ2read

qa2g2

] (23)

Similarly with an assumption that optical scattering is most dominant in signal spreadingprocesses in an indirect-conversion flat-panel detector based on scintillator eq (21) can be simpli-fied to

DQEindirect(k)asymp DQEconv(0)

1+DQEconv(0)(

1γg2T 2

2 (k) minus1m

)+ DQEconv(0)σ2

readγqa2g2T 2

2 (k)

(24)

For σread lt agT2(k)radic

γq

DQEconv(0) eq (24) is reduced to

DQEindirect(k)asymp DQEconv(0)minus DQE2conv(0)

γg2T 22 (k)

[1minus

σ2read

qa2

] (25)

3 Model validation

The developed DQE formalisms were validated by comparisons with the measured DQEs from twodifferent-type flat-panel detectors amorphous selenium (a-Se) based detector with a pixel pitch of139 microm and cesium iodide (CsI) based detector with a pixel pitch of 143 microm The thicknessesof both converters are the same as 500 microm Two detectors are respectively denoted by D1 andD2 hereinafter The DQE analyses were compliant with IEC 62220-1 (IEC Geneva Switzerland2004) using a 70 kV RQA-5 spectrum Detailed measurement procedures can be found in ref [11]

The physical parameters involved in the cascaded models were estimated based on the ab-sorbed energy distributions and the optical pulse-height distributions obtained from the MonteCarlo simulations We employed two Monte Carlo codes MCNPX (Version 250 ORNL USA)and DETECT2000 (Laval University Quebec Canada) for x-ray and optical quanta transports re-spectively Extraction methods of physical parameters from the Monte Carlo simulation results arebased on ref [12] and the extracted values are summarized in table 1

4 Results and discussion

Figure 2 summarizes comparisons of the measured and theoretical image quality for two detectorsFor the direct-conversion D1 detector the measured MTF is slightly less than the aperture transferfunction which can be described by the sine cardinal function sinc(πau) This observation may im-ply that the quantum-relocation processes due to primary andor secondary quanta slightly degrade

ndash 3 ndash

2011 JINST 6 C11020

Table 1 Numerical values used in the theoretical DQE calculations for a-Se (D1) and CsI (D2) basedflat-panel detectors

Parameter Description ValueD1 (direct) D2 (indirect)

a Pixel aperture [mm] pradic

γ

p Pixel pitch [mm] 0139 0143γ Fill factor 079 068q0 Incident photon fluence [mmminus2mRminus1] 26times105

α Average quantum absorption efficiency 053 081I Swank factor 096 076

T1 MTF due to primary quanta scattering 1β Secondary quantum gain per interacting quanta 1070 2600T2 MTF due to secondary quanta scattering 1 Measuredκ Average coupling efficiency 1 032η Average collection efficiency 1 065T3 MTF due to aperture integration |sinc(πau)sinc(πav)|

σread Additive readout electronic noise [eminus] 3000 4600

Figure 2 Comparisons between empirical and theoretical MTF NPS and DQE for a-Se (D1) and CsI (D2)based flat-panel detectors NNPS designates the normalized NPS [see the bracketed term in the denominatorof eq (11)]

the total system transfer function The agreement between empirical and approximate theoreticalNPSs is excellent Theoretical white-spectral characteristic due to noise aliasing [5] is well provedby the measured NPS Although there are some discrepancies at the spatial frequencies greater thanabout 1 mmminus1 the approximate DQE model reasonably describes the measured data

For indirect-conversion D2 detector there is a large discrepancy between the aperture transferfunction and the measured MTF and which is mainly due to the secondary quanta scattering withinthe CsI layer The agreement between the calculated and measured NPSs is excellent Approximate

ndash 4 ndash

2011 JINST 6 C11020

Figure 3 Calculated DQEs for hypothetical 1D direct and indirect-conversion detectors with respect tovarious additive electronic noise levels uN denotes the Nyquist frequency

DQE formalism underestimates the measured DQE values for the spatial frequency greater than15 mmminus1

Figure 3 shows the DQE simulation results with respect to various additive electronic noiselevels The simulation assumes 1D line detector configurations for simplicity in the calculationsAll the simulations were performed for exposure of 1 mR at the detector entrance surface The MTFof the hypothetical indirect-conversion 1D detector is based on the Gaussian point-spread functionwith the standard deviation σ = p Other simulation parameters were taken from table 1 As shownin figure 3 where the spatial frequency u was normalized by the Nyquist frequency uN the elec-tronic readout noise affects the approximate DQE model for direct-conversion detectors over theentire spatial frequency band while the approximate DQE model for indirect-conversion detector isrelatively insensitive to the additive noise at lower frequencies For the direct-conversion detectorit is expected that the approximate DQE model [eq (23)] well follows the complete DQE model[eq (21)] when the detector is operated in quantum-noise-limited region or σread = 0 eminus Equa-tion (23) well describes eq (21) up to the electronic noise level of 104 eminus in this simulation Forσread gt 104 eminus however eq (23) gradually underestimates eq (21) as σread further increases Forthe indirect-conversion detector the approximate DQE model [eq (25)] underestimates eq (21)in the high frequency band even for σread = 0 eminus This frequency band widens as σread increases

In the quantum-noise-limited operation the DQE(0) of indirect-conversion detectors can besimply determined by the DQE(0) of scintillator or αI while that of direct-conversion detectorsis determined by the DQE(0) of photoconductor scaled by the pixel fill factor γ To preserve thephotoconductor DQE(0) performance in direct-conversion detectors therefore it is required thatthe pixel should be designed to have a fill factor as high as possible Electrical design in which allfield lines terminate on the pixel electrode is essential

5 Conclusion

Practical DQE formalisms have been described in this paper and it has been demonstrated that thedeveloped DQE formalisms reasonably agree to the measured DQE values for the conventional

ndash 5 ndash

2011 JINST 6 C11020

flat-panel detectors Especially the approximate DQE model of direct-conversion detectors welldescribes the complete DQE model when the detectors are operated in the quantum-noise-limitedregion On the contrary the approximate DQE model of indirect-conversion detectors describesthe complete DQE model up tosim75 of the Nyquist-frequency limit at the quantum-noise-limitedoperation The approximate DQE formalisms would be very useful for the rapid evalution of themeasured DQE and the extraction of detector performance parameters such as quantum absorptionefficiency Swank noise factor and secondary quantum gain

Acknowledgments

This research was supported by Basic Science Research Program through the National ResearchFoundation of Korea (NRF) funded by the Ministry of Education Science and Technology (2011-0009769)

References

[1] HK Kim et al On the development of digital radiography A review Int J Precis Eng Manuf 9(2008) 86

[2] CE Metz et al Toward consensus on quantitative assessment of medical imaging systems MedPhys 22 (1995) 1057

[3] IA Cunningham Applied Linear-Systems Theory in Handbook of Medical Imaging J Beutel HLKundel and RL Van Metter eds SPIE Press Bellingham USA 2000 vol 1 pp 79ndash159

[4] S Yun et al Finding the best photoconductor for digital mammography detectors Nucl InstrumMeth A 652 (2011) 829

[5] W Zhao and JA Rowlands Digital radiology using active matrix readout of amorphous seleniumTheoretical analysis of detective quantum efficiency Med Phys 24 (1997) 1819

[6] JH Siewerdsen et al Signal noise power spectrum and detective quantum efficiency ofindirect-detection flat-panel imagers for diagnostic radiology Med Phys 25 (1998) 614

[7] J Yao and IA Cunningham Parallel cascades New ways to describe noise transfer in medicalimaging systems Med Phys 28 (2001) 2020

[8] HK Kim Generalized cascaded model to assess noise transfer in scintillator-based x-ray imagingdetectors Appl Phys Lett 89 (2006) 233504

[9] R Akbarpour et al Signal and noise transfer in spatiotemporal quantum-based imaging systems JOpt Soc Am A 24 (2007) B151

[10] W Que and JA Rowlands X-ray imaging using amorphous selenium Inherent spatial resolutionMed Phys 22 (1995) 365

[11] MK Cho et al Measurements of x-ray imaging performance of granular phosphors withdirect-coupled CMOS sensors IEEE Trans Nucl Sci 55 (2008) 1338

[12] S Yun et al Signal and noise characteristics induced by unattenuated x rays from a scintillator inindirect-conversion CMOS photodiode array detectors IEEE Trans Nucl Sci 56 (2009) 1121

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2011 JINST 6 C11020

Table 1 Numerical values used in the theoretical DQE calculations for a-Se (D1) and CsI (D2) basedflat-panel detectors

Parameter Description ValueD1 (direct) D2 (indirect)

a Pixel aperture [mm] pradic

γ

p Pixel pitch [mm] 0139 0143γ Fill factor 079 068q0 Incident photon fluence [mmminus2mRminus1] 26times105

α Average quantum absorption efficiency 053 081I Swank factor 096 076

T1 MTF due to primary quanta scattering 1β Secondary quantum gain per interacting quanta 1070 2600T2 MTF due to secondary quanta scattering 1 Measuredκ Average coupling efficiency 1 032η Average collection efficiency 1 065T3 MTF due to aperture integration |sinc(πau)sinc(πav)|

σread Additive readout electronic noise [eminus] 3000 4600

Figure 2 Comparisons between empirical and theoretical MTF NPS and DQE for a-Se (D1) and CsI (D2)based flat-panel detectors NNPS designates the normalized NPS [see the bracketed term in the denominatorof eq (11)]

the total system transfer function The agreement between empirical and approximate theoreticalNPSs is excellent Theoretical white-spectral characteristic due to noise aliasing [5] is well provedby the measured NPS Although there are some discrepancies at the spatial frequencies greater thanabout 1 mmminus1 the approximate DQE model reasonably describes the measured data

For indirect-conversion D2 detector there is a large discrepancy between the aperture transferfunction and the measured MTF and which is mainly due to the secondary quanta scattering withinthe CsI layer The agreement between the calculated and measured NPSs is excellent Approximate

ndash 4 ndash

2011 JINST 6 C11020

Figure 3 Calculated DQEs for hypothetical 1D direct and indirect-conversion detectors with respect tovarious additive electronic noise levels uN denotes the Nyquist frequency

DQE formalism underestimates the measured DQE values for the spatial frequency greater than15 mmminus1

Figure 3 shows the DQE simulation results with respect to various additive electronic noiselevels The simulation assumes 1D line detector configurations for simplicity in the calculationsAll the simulations were performed for exposure of 1 mR at the detector entrance surface The MTFof the hypothetical indirect-conversion 1D detector is based on the Gaussian point-spread functionwith the standard deviation σ = p Other simulation parameters were taken from table 1 As shownin figure 3 where the spatial frequency u was normalized by the Nyquist frequency uN the elec-tronic readout noise affects the approximate DQE model for direct-conversion detectors over theentire spatial frequency band while the approximate DQE model for indirect-conversion detector isrelatively insensitive to the additive noise at lower frequencies For the direct-conversion detectorit is expected that the approximate DQE model [eq (23)] well follows the complete DQE model[eq (21)] when the detector is operated in quantum-noise-limited region or σread = 0 eminus Equa-tion (23) well describes eq (21) up to the electronic noise level of 104 eminus in this simulation Forσread gt 104 eminus however eq (23) gradually underestimates eq (21) as σread further increases Forthe indirect-conversion detector the approximate DQE model [eq (25)] underestimates eq (21)in the high frequency band even for σread = 0 eminus This frequency band widens as σread increases

In the quantum-noise-limited operation the DQE(0) of indirect-conversion detectors can besimply determined by the DQE(0) of scintillator or αI while that of direct-conversion detectorsis determined by the DQE(0) of photoconductor scaled by the pixel fill factor γ To preserve thephotoconductor DQE(0) performance in direct-conversion detectors therefore it is required thatthe pixel should be designed to have a fill factor as high as possible Electrical design in which allfield lines terminate on the pixel electrode is essential

5 Conclusion

Practical DQE formalisms have been described in this paper and it has been demonstrated that thedeveloped DQE formalisms reasonably agree to the measured DQE values for the conventional

ndash 5 ndash

2011 JINST 6 C11020

flat-panel detectors Especially the approximate DQE model of direct-conversion detectors welldescribes the complete DQE model when the detectors are operated in the quantum-noise-limitedregion On the contrary the approximate DQE model of indirect-conversion detectors describesthe complete DQE model up tosim75 of the Nyquist-frequency limit at the quantum-noise-limitedoperation The approximate DQE formalisms would be very useful for the rapid evalution of themeasured DQE and the extraction of detector performance parameters such as quantum absorptionefficiency Swank noise factor and secondary quantum gain

Acknowledgments

This research was supported by Basic Science Research Program through the National ResearchFoundation of Korea (NRF) funded by the Ministry of Education Science and Technology (2011-0009769)

References

[1] HK Kim et al On the development of digital radiography A review Int J Precis Eng Manuf 9(2008) 86

[2] CE Metz et al Toward consensus on quantitative assessment of medical imaging systems MedPhys 22 (1995) 1057

[3] IA Cunningham Applied Linear-Systems Theory in Handbook of Medical Imaging J Beutel HLKundel and RL Van Metter eds SPIE Press Bellingham USA 2000 vol 1 pp 79ndash159

[4] S Yun et al Finding the best photoconductor for digital mammography detectors Nucl InstrumMeth A 652 (2011) 829

[5] W Zhao and JA Rowlands Digital radiology using active matrix readout of amorphous seleniumTheoretical analysis of detective quantum efficiency Med Phys 24 (1997) 1819

[6] JH Siewerdsen et al Signal noise power spectrum and detective quantum efficiency ofindirect-detection flat-panel imagers for diagnostic radiology Med Phys 25 (1998) 614

[7] J Yao and IA Cunningham Parallel cascades New ways to describe noise transfer in medicalimaging systems Med Phys 28 (2001) 2020

[8] HK Kim Generalized cascaded model to assess noise transfer in scintillator-based x-ray imagingdetectors Appl Phys Lett 89 (2006) 233504

[9] R Akbarpour et al Signal and noise transfer in spatiotemporal quantum-based imaging systems JOpt Soc Am A 24 (2007) B151

[10] W Que and JA Rowlands X-ray imaging using amorphous selenium Inherent spatial resolutionMed Phys 22 (1995) 365

[11] MK Cho et al Measurements of x-ray imaging performance of granular phosphors withdirect-coupled CMOS sensors IEEE Trans Nucl Sci 55 (2008) 1338

[12] S Yun et al Signal and noise characteristics induced by unattenuated x rays from a scintillator inindirect-conversion CMOS photodiode array detectors IEEE Trans Nucl Sci 56 (2009) 1121

ndash 6 ndash

2011 JINST 6 C11020

Figure 3 Calculated DQEs for hypothetical 1D direct and indirect-conversion detectors with respect tovarious additive electronic noise levels uN denotes the Nyquist frequency

DQE formalism underestimates the measured DQE values for the spatial frequency greater than15 mmminus1

Figure 3 shows the DQE simulation results with respect to various additive electronic noiselevels The simulation assumes 1D line detector configurations for simplicity in the calculationsAll the simulations were performed for exposure of 1 mR at the detector entrance surface The MTFof the hypothetical indirect-conversion 1D detector is based on the Gaussian point-spread functionwith the standard deviation σ = p Other simulation parameters were taken from table 1 As shownin figure 3 where the spatial frequency u was normalized by the Nyquist frequency uN the elec-tronic readout noise affects the approximate DQE model for direct-conversion detectors over theentire spatial frequency band while the approximate DQE model for indirect-conversion detector isrelatively insensitive to the additive noise at lower frequencies For the direct-conversion detectorit is expected that the approximate DQE model [eq (23)] well follows the complete DQE model[eq (21)] when the detector is operated in quantum-noise-limited region or σread = 0 eminus Equa-tion (23) well describes eq (21) up to the electronic noise level of 104 eminus in this simulation Forσread gt 104 eminus however eq (23) gradually underestimates eq (21) as σread further increases Forthe indirect-conversion detector the approximate DQE model [eq (25)] underestimates eq (21)in the high frequency band even for σread = 0 eminus This frequency band widens as σread increases

In the quantum-noise-limited operation the DQE(0) of indirect-conversion detectors can besimply determined by the DQE(0) of scintillator or αI while that of direct-conversion detectorsis determined by the DQE(0) of photoconductor scaled by the pixel fill factor γ To preserve thephotoconductor DQE(0) performance in direct-conversion detectors therefore it is required thatthe pixel should be designed to have a fill factor as high as possible Electrical design in which allfield lines terminate on the pixel electrode is essential

5 Conclusion

Practical DQE formalisms have been described in this paper and it has been demonstrated that thedeveloped DQE formalisms reasonably agree to the measured DQE values for the conventional

ndash 5 ndash

2011 JINST 6 C11020

flat-panel detectors Especially the approximate DQE model of direct-conversion detectors welldescribes the complete DQE model when the detectors are operated in the quantum-noise-limitedregion On the contrary the approximate DQE model of indirect-conversion detectors describesthe complete DQE model up tosim75 of the Nyquist-frequency limit at the quantum-noise-limitedoperation The approximate DQE formalisms would be very useful for the rapid evalution of themeasured DQE and the extraction of detector performance parameters such as quantum absorptionefficiency Swank noise factor and secondary quantum gain

Acknowledgments

This research was supported by Basic Science Research Program through the National ResearchFoundation of Korea (NRF) funded by the Ministry of Education Science and Technology (2011-0009769)

References

[1] HK Kim et al On the development of digital radiography A review Int J Precis Eng Manuf 9(2008) 86

[2] CE Metz et al Toward consensus on quantitative assessment of medical imaging systems MedPhys 22 (1995) 1057

[3] IA Cunningham Applied Linear-Systems Theory in Handbook of Medical Imaging J Beutel HLKundel and RL Van Metter eds SPIE Press Bellingham USA 2000 vol 1 pp 79ndash159

[4] S Yun et al Finding the best photoconductor for digital mammography detectors Nucl InstrumMeth A 652 (2011) 829

[5] W Zhao and JA Rowlands Digital radiology using active matrix readout of amorphous seleniumTheoretical analysis of detective quantum efficiency Med Phys 24 (1997) 1819

[6] JH Siewerdsen et al Signal noise power spectrum and detective quantum efficiency ofindirect-detection flat-panel imagers for diagnostic radiology Med Phys 25 (1998) 614

[7] J Yao and IA Cunningham Parallel cascades New ways to describe noise transfer in medicalimaging systems Med Phys 28 (2001) 2020

[8] HK Kim Generalized cascaded model to assess noise transfer in scintillator-based x-ray imagingdetectors Appl Phys Lett 89 (2006) 233504

[9] R Akbarpour et al Signal and noise transfer in spatiotemporal quantum-based imaging systems JOpt Soc Am A 24 (2007) B151

[10] W Que and JA Rowlands X-ray imaging using amorphous selenium Inherent spatial resolutionMed Phys 22 (1995) 365

[11] MK Cho et al Measurements of x-ray imaging performance of granular phosphors withdirect-coupled CMOS sensors IEEE Trans Nucl Sci 55 (2008) 1338

[12] S Yun et al Signal and noise characteristics induced by unattenuated x rays from a scintillator inindirect-conversion CMOS photodiode array detectors IEEE Trans Nucl Sci 56 (2009) 1121

ndash 6 ndash

2011 JINST 6 C11020

flat-panel detectors Especially the approximate DQE model of direct-conversion detectors welldescribes the complete DQE model when the detectors are operated in the quantum-noise-limitedregion On the contrary the approximate DQE model of indirect-conversion detectors describesthe complete DQE model up tosim75 of the Nyquist-frequency limit at the quantum-noise-limitedoperation The approximate DQE formalisms would be very useful for the rapid evalution of themeasured DQE and the extraction of detector performance parameters such as quantum absorptionefficiency Swank noise factor and secondary quantum gain

Acknowledgments

This research was supported by Basic Science Research Program through the National ResearchFoundation of Korea (NRF) funded by the Ministry of Education Science and Technology (2011-0009769)

References

[1] HK Kim et al On the development of digital radiography A review Int J Precis Eng Manuf 9(2008) 86

[2] CE Metz et al Toward consensus on quantitative assessment of medical imaging systems MedPhys 22 (1995) 1057

[3] IA Cunningham Applied Linear-Systems Theory in Handbook of Medical Imaging J Beutel HLKundel and RL Van Metter eds SPIE Press Bellingham USA 2000 vol 1 pp 79ndash159

[4] S Yun et al Finding the best photoconductor for digital mammography detectors Nucl InstrumMeth A 652 (2011) 829

[5] W Zhao and JA Rowlands Digital radiology using active matrix readout of amorphous seleniumTheoretical analysis of detective quantum efficiency Med Phys 24 (1997) 1819

[6] JH Siewerdsen et al Signal noise power spectrum and detective quantum efficiency ofindirect-detection flat-panel imagers for diagnostic radiology Med Phys 25 (1998) 614

[7] J Yao and IA Cunningham Parallel cascades New ways to describe noise transfer in medicalimaging systems Med Phys 28 (2001) 2020

[8] HK Kim Generalized cascaded model to assess noise transfer in scintillator-based x-ray imagingdetectors Appl Phys Lett 89 (2006) 233504

[9] R Akbarpour et al Signal and noise transfer in spatiotemporal quantum-based imaging systems JOpt Soc Am A 24 (2007) B151

[10] W Que and JA Rowlands X-ray imaging using amorphous selenium Inherent spatial resolutionMed Phys 22 (1995) 365

[11] MK Cho et al Measurements of x-ray imaging performance of granular phosphors withdirect-coupled CMOS sensors IEEE Trans Nucl Sci 55 (2008) 1338

[12] S Yun et al Signal and noise characteristics induced by unattenuated x rays from a scintillator inindirect-conversion CMOS photodiode array detectors IEEE Trans Nucl Sci 56 (2009) 1121

ndash 6 ndash