Calculation and analysis of DQE for some image detectors in mammography

Institutionen för medicin och vård

Avdelningen för radiofysik

Hälsouniversitetet

Calculation and analysis of DQE for

some image detectors in mammography

Michael Sandborg

Department of Medicine and Care

Radio Physics

Series: Report / Institutionen för radiologi, Universitetet i Linköping; 86

ISRN: LIU-RAD-R-086

Report 86

March. 1998 ISRN ULI-RAD-R--86--SE

Calculation and analysis of DQE for

some image detectors in mammography

Michael Sandborg

Department of Radiation Physics, IMV Faculty of Health Sciences

Linköping University, Sweden

Full address:

Michael Sandborg, PhD

Department of Radiation Physics Department of Medicine and Care Faculty of Health Sciences

Linköping University SE-581 85 Linköping Sweden phone +46 13 224007 fax +46 13 224749 e-mail michael.sandborg@raf.liu.se http://www.liu.se/hu/imv/radiofysik/

Table of content

Abstract

1. Introduction 2. Theory

2.1. The statistics of photon absorption - the single-event size distribution 2.2. Quantities used to characterise the x-ray absorption of image detectors 3. Method

3.1. Image detectors considered in this study 3.2. Monte Carlo code and sources of data 4. Results

4.1. Comparison with results from the literature 4.2. Aq, IX and DQEq for the detectors

5. Discussion

5.1 Fluorescent screens and screen-film systems 5.2 Semi-conductor and silicon detectors

6. Summary and conclusion Acknowledgements

References

Abstract

The development and clinical testing of digital detector designs for mammography are making rapid progress and there is widespread interest in comparing the performance of these new detectors to that of analogue screen-film mammography systems. In this report, Monte Carlo calculations of the x-ray absorption

characteristics (single-event distribution), the quantum absorption, Aq, and

detective quantum, DQEq, efficiencies are made and compared to results from the

literature. Detectors of CsI and Si of various thicknesses are compared to a state-of-the art analogue, screen-film system (Gd2O2S) in the energy range 1-35 keV. The

results show that 1.5 mm thick Si detectors will have the same DQEq as commonly

used Gd2O2S fluorescent screens and that a CsI phosphor of 80 µm has similar

DQEq as 1.0 mm Si. The total DQE (including added noise and inherent detector

unsharpness) of fluorescent screen-film systems will be significantly reduced from this value due to the light scatter, film noise and the inherent limitations caused by the film characteristic curve. This indicates that also thinner Si detectors (0.3-0.5 mm), which do not suffer from these limitations but from a comparably low Aq may

have a total performance DQE(f) comparable to that of traditional screen-film based, image detectors.

Key words: digital mammography, detective quantum efficiency (DQE), signal-to-noise ratio (SNR), Monte Carlo calculations, silicon detectors.

1. Introduction

Optimisation of image quality in relation to patient risk is an important task in diagnostic radiology, since x-ray examinations is the largest man-made factor contributing to the radiation burden of the population. In mammography screening this is particularly important since a majority of the women are nonsymptomatic of any disease. The lowest limit of patient irradiation possible, while retaining

diagnostic safety is set by the fundamental stochastics of photon interactions in the image detector, i.e., the quantum noise caused by the combined random fluctuations in the number and size of energy-impartation events (Motz and Danos 1978).

The effect of using realistic, partially absorbing detectors on the signal-to-noise ratio (SNR) has been discussed by Dick and Motz (1981), Swank (1973), Chan and Doi (1984) and Sandborg and Alm Carlsson (1992) and expressed in terms of the detective quantum efficiency (DQE). This quantity accounts for the energy

absorption properties and internal screen noise of the detector relative to a totally absorbing one that extracts all information from the incident x-ray beam. Apart from inefficient x-ray absorption and internal screen noise in the detector, other inefficiencies such as unsharpness, non-quantum noise, reduced contrast and limited dynamic range exist. Although very important, these latter sources of inefficiency are beyond the scope of this report and only discussed briefly.

2. Theory

2.1. The statistics of photon absorption - the single-event size distribution

Most image detectors respond with a signal that is proportional to the energy imparted ε to it. The latter is the sum of contributions ε’ from statistically

independent energy impartation events (ICRU 1980). The energy imparted to the detector by an incident photon and its liberated secondary electrons and

characteristic x-rays defines an energy impartation event. This report is confined to the analysis of the absorption and noise caused by the incident x rays (quantum noise) and any effects of the secondary information carriers, such as the light photons or electron-hole pairs, although important, are ignored in the calculation. The variance in the total energy imparted V(ε) to the detector is due to the combined statistical fluctuations in the number (N) and size (ε’) of energy-impartation events. The inverse of the relative variance or the signal-to-noise (SNR) squared, SNR2 _is

given by (Mandel 1959, Dick and Motz 1981, Sandborg and Alm Carlsson 1992)

( )

( )

( )

( ) ( )

( )

( )

( ) ( )

( )

Here V(N) and E(N) are the variance and expectation value, respectively, of the (Poisson distributed) number N of photons incident on the detector; V(ε') is the

variance, E(ε') and E(ε'2_{) the first and second moments of the energy imparted to the}

detector in an energy-impartation event. The first (mean, i=1) and second (mean squared, i=2) moments of the stochastic variable ε' are given by

( )

( )

∫

including ε'=0 (zero energy impartation events) in the integration. The frequency function f(ε') is called the single-event size distribution and describes the frequency of occurrence of energy imparted ε’. Typical detectors are made of high-Z elements to absorb a large fraction of the incident photons. In a high-Z material, the dominating type of interaction is photoelectric absorption. X-ray scatter has a low probability, at least when the photon energy is low. The energy imparted to the detector is thus often either the whole photon energy, ε´=hν or zero, ε´=0. Following a photo-electric absorption in a high-Z element, there is a large probability for escape of the

characteristic x-ray photons generated in the detector and the energy imparted takes the value, ε´=hν - hνK, where hνK is the energy of the characteristic x-ray

photon that escapes the detector volume. The probability of K-photon escape is smaller for low-Z detectors since the fluorescent yield (probability of emitting a K-photon) is low and characteristic photons are likely to be absorbed due to their low energy. To a small extent, intermediate values of ε’ occur when photons are

incoherently scattered before escaping from the detector volume.

2.2. Quantities used to characterise the x-ray absorption of image detectors

Different concepts have been used to describe the absorption properties of image detectors. Chan and Doi (1984) and Swank (1973) calculated the noise equivalent absorption (NEA) defined as the ratio between the squares of the first and second moments of the single-event size distribution, NEA=E2_(ε')/E(ε'2_{). They also derived}

values of the quantum absorption efficiency Aq and the statistical factor I. The

relation between these quantities and the signal-to-noise ratio SNR is given by:

( ) ( )

_{( )}

( )

( )

The quantum absorption efficiency Aq is the fraction of incident photons imparting

energy ε'>0 to the detector. It is less than the fraction of interacting photons, particularly at low photon energies, since singly and/or multiply coherently

scattered photons escaping from the detector contribute like non-interacting photons to zero events (ε'=0). I accounts for the spread in the single event distribution

normalised to event sizes ε'>0. The statistical factor I has two components. The first, IX refers to the fluctuations in energy imparted to the detector and the second, IL to

fluctuations in the emitted light at the film emulsion for a given energy imparted to the screen. With mono-energetic incident photons and a totally absorbing detector,

Aq=IX=1. With a broad energy distribution of the incident photons (x-ray spectrum),

IX <1. However, with a partially absorbing detector, Aq <1 and IX decreases further

due to an additional spread in the sizes of energy impartation events caused by the possibility of partial absorption of the photon energy.

The detective quantum efficiency (DQE) has been defined to express the

degradation in information (SNR) caused by the detector relative to the information in the incident beam (Dainty and Shaw 1974). This concept can be used to compare the internal noise of different detectors and is given by

2 2 2 2 ideal in SNR SNR SNR SNR DQE= = (4)

Here, SNRin is the signal-to-noise ratio in the incident beam. Since an ideal detector

extracts all the information in the beam, SNRin=SNRideal, i.e., DQE=1 for an ideal

detector. As is apparent from equation 3, a totally absorbing, photon counting detector (with both Aq and IX equal to one) yields DQE=1. On the other hand, a

totally absorbing, energy integrating detector will yield DQE<1 in cases with polyenergetic incident photons (broad x-ray spectrum). Thus, the ideal detector disregards the energy information in the beam and simply counts the photons. With this interpretation of the ideal detector, the commonly used definition (Dick and Motz 1981, Swank 1973, Chan and Doi 1984) of DQE is obtained.

I A NEA

DQE_q = = _q⋅ (5)

This is here called the x-ray absorption DQE, DQEq, to emphasise that only the first

stage of image formation is considered. Additional sources of inefficiency are discussed briefly in section 5.

For fluorescent screens there exists an additional source of internal noise due to the emission of secondary light photons. The stochastics of the light emission and of the light transport to the surface of the screen causes a variation in the size of the light pulses at the film even from x-ray absorption events of equal energy imparted ε’. This factor, the statistical factor IL, also goes into equation 5 (I=IX.IL), and is close to

unity (IL=0.95: Rowlands and Taylor 1983) for CsI x-ray image intensifiers but is

generally lower (0.6<IL<0.9: Ginzburg and Dick 1993) for typical screen-film

fluorescent materials such as Gd2O2S. For a Gd2O2S mammography screen, IL is

likely to be closer to the lower end of the span, as these screens often include a light absorbing dye. To some extent IL also depends on the screen thickness. In the

literature, the product I= IX.IL is sometimes called the Swank factor after Swank

3. Method

3.1. Image detectors considered in this study

In this study both fluorescent screens and semiconductor detectors were analysed. Their thicknesses, and atomic compositions are given in table 1.

Table 1. Atomic compositions and thicknesses of the image detectors included in this study.

Material Thickness Thickness

(mg/cm2_{) (µm)} Gd2O2S 31.7 ¤ Gd2O2S 36.5 ¤ CsI 100 222 CsI 67.7 150 CsI 36.1 80 CsI 22.6 50 Si 70 300 Si 117 500 Si 233 1000 Si 350 1500

¤ Unknown due to unknown packing density. Assuming a packing density of 50% gives a total screen thickness slightly less than 100 µm.

3.2. Monte Carlo code and sources of data

The energy imparted to the detector by an x-ray photon and its associated secondary particles is assumed to be confined to the detector element in which the photon interacted. Single-event size distributions f(ε') for photons incident on partially absorbing detectors were derived using analogue photon-transport Monte Carlo simulation (Sandborg and Alm Carlsson 1992). The photons were assumed to impinge perpendicularly to the detector surface and to interact by photoelectric absorption, coherent or incoherent scattering. The probability of emission of K-fluorescence photons (fluorescent yield) subsequent to photoelectric absorption was considered. The generation of L-, M- and higher order of fluorescence photons were neglected due to their low energies.

Values of total interaction cross sections were taken from Berger and Hubbell (1987), atomic form factors from Hubbell and Øverbø (1979) and incoherent

scattering functions from Hubbell et al. (1975). The energies of K-absorption edges were taken from Lederer and Shirley (1978) as were fluorescent yields and relative intensities of K_α and K_β characteristic x-rays. The energies of K_α and K_β photons and the relative probability of a photoelectric absorption taking place with K-shell electrons were taken from Storm and Israel (1970).

All photoelectric absorptions were assumed to occur with the high-Z-element in the detector. For detectors with two high-Z-elements, i.e. CsI, the choice of atom for the

interaction was made considering separately the probabilities of photoelectric

absorption in the two elements. Interactions with the binder material in fluorescent screens were neglected.

4. Results

4.1 Comparison with results from the literature

To check our Monte Carlo code, values of Aq, IX and DQE for mono-energetic

photons were compared to those of Chan and Doi (1984) for a 100 mg/cm2 CsI

detector and with those of Henry et al. (1995) for the other detectors. The results agree within typically 3-4%. Earlier (Sandborg and Alm Carlsson 1992) found good agreement with the results of Chan and Doi (1984) regarding Aq, IX and DQEq using

the same methods as here but for other detector materials and thicknesses.

Table 2. Comparison of calculated quantum absorption efficiencies Aq with results

from the literature.

Photon 0.3 mm Si 31.7 mg/cm2 _{1.5 mm Si 100 mg/cm}2

energy Gd2O2S CsI

hν (keV) # Henry1 _{# Henry}1 _{# Henry}1 _{# Chan}2

10 0.903 0.915 0.998 1.000 0.998 1.000 0.998 0.999 15 0.502 0.510 0.914 0.916 0.970 0.968 0.994 -20 0.256 0.263 0.677 0.695 0.774 0.784 0.923 0.921 25 0.141 0.147 0.459 0.474 0.535 0.552 0.751 -30 0.086 0.089 0.312 0.326 0.365 0.379 0.569 0.567 # This work 1. Henry et al. (1995) 2. Chan and Doi (1984)

4.2. Aq, IX and DQEq for the detectors

In the appendix, values of Aq, IX and DQEq are given for perpendicularly incident

photons and the different detectors. Also included are the first (mean) and second moments (mean squared) of the single-event size distributions including zero-impartation events, E(ε’) and E(ε’2_{), respectively. The ratio between E}2_{(ε’)/ E(ε’}2_{) is}

the DQEq (or NEA). In table 3, a subset of DQEq for the simulated detectors is

Table 3. DQEq for a selection of photon energies and for the simulated image

detectors (full data are given in the Appendix).

hν 0.3 mm0.5 mm1.0 mm1.5 mm 36.5 mg/cm2 _{50 µm 80 µm 150 µm}

(keV) Si Si Si Si Gd2O2S CsI CsI CsI

10 0.903 0.978 0.998 0.998 0.998 0.977 0.996 0.998 15 0.500 0.686 0.901 0.968 0.941 0.720 0.870 0.976 20 0.252 0.384 0.623 0.769 0.727 0.439 0.603 0.825 25 0.136 0.217 0.388 0.524 0.507 0.266 0.394 0.609 30 0.080 0.130 0.246 0.347 0.348 0.171 0.257 0.431 35 0.051 0.084 0.162 0.236 0.243 0.225 0.338 0.541

Aq generally decreases with increasing photon energy but increases strongly at

energies above the K-edge of the high-Z element(s) in the detector due to increased probability for photoelectric absorption. IX is smallest for photon energies just above

the K-edge where escape of K-fluorescent photons broadens the single-event distribution. Just above the K-edge, the K-photon carries away a large fraction of the incident photon’s energy. This fraction decreases as the photon energy increases beyond the K-edge (due to an increased fraction transferred to the photoelectron) and IX increases. Since the K-edge of Si is located at such a low energy (2 keV) and

the fluorescent yield is low for low-Z elements, its influence on the DQEq is

insignificant, contrary to CsI where DQEq is significantly increased at the Iodine

K-edge (33.17 keV) as can be seen in table 3 and figure 2 below. The K-K-edge of

Figure 1. DQEq for four thicknesses of Si as a function of photon energy.

Figure 2. DQEq for three thicknesses of CsI and one Gd2O2S fluorescent screen as

function of photon energy.

Figures 3 and 4 show how DQEq differs between an 80 µm CsI and an 1.0 mm Si

detector and between a 36.5 mg/cm2 _{Gd2O2S screen and an 1.5 mm Si detector,}

respectively. The 1.0 mm Si detector resembles the 80 µm CsI phosphor below 33

0,0 0,2 0,4 0,6 0,8 1,0 1,2 0 5 10 15 20 25 30 35 40

Photon Energy (keV)

DQE

Photon Energy (keV)

DQE

keV at the Iodine K-edge (Figure 3). Figure 4 shows that the 1.5 mm Si detector is similar to the Gd-phosphor screen.

Figure 3. Comparison of DQEq for an 80 µm CsI screen and an 1.0 mm Si detector.

Figure 4. Comparison of DQEq for a 36.5 mg/cm2 Gd2O2S screen and an 1.5 mm Si

detector. 0,0 0,2 0,4 0,6 0,8 1,0 1,2 0 5 10 15 20 25 30 35

Photon Energy (keV)

DQE

Photon Energy (keV)

DQE

q

1,0 mm Si 0,080 mm CsI

5. Discussion

A method to estimate the total detective quantum efficiency DQE as function of both incident photon energy, hν and spatial frequency, f, DQE(hν,f) was proposed by Nishikawa and Yaffe (1990a). It includes four factors, all of which take values between zero and one.

) ( ) ( ) ( ) ( ) , (h f A h I h R f R f DQE ν = _q ν ⋅ ν ⋅ _N ⋅ _C (6)

The first two factors are the ones considered above (due to x-ray absorption) and depend on photon energy. The I-factor is the product of IX and IL. The last two

factors depend primarily on the spatial frequency characteristics of the detector. RN

describes the extent to which the detector is quantum noise limited and RC the

difference in the efficiency of the transfer of the signal and of the noise, respectively through the detector. If RN is close to one, the noise is dominated by quantum noise

and indicates that the system is optimised. The last factor RC is, for each spatial

frequency, given by the ratio

( )

( )

( )

R_C = 2 _Q2 (7)

i.e., the quotient between the detector’s modulation transfer function (MTF) squared and the noise power spectrum (NPS) of the quantum noise (index Q) normalised to one at zero spatial frequency

( )

( )

( )

This method of analysing detector inefficiency or reduction in DQE will be used below and discussed separately for screen-film and digital silicon detectors.

5.1. Fluorescent screens and screen-film systems

The quantum absorption efficiency Aq is the single factor that has the largest effect

on DQEq and is primarily determined by the thickness, density and atomic

composition of the detector, depending strongly on the photon energy. The statistical factor IX also reduces DQEq, particularly, if the photon energy exceeds the K-edge of

a high-Z element in the detector. IX is also reduced by incoherent (Compton)

scatterings in the detector, but this is usually a small effect unless the atomic

number of the detector is low and the photon energy high. The additional statistical factor IL causes a significant reduction in the DQEq for fluorescent screens; the

reduction being approximately 20-30% for Gd2O2S screens and 5% for CsI. The

higher and ‘better’ value of IL for CsI is due to light-guiding channels formed by the

CsI crystals thus reducing the spread of the size of the light bursts from different depth within the phosphor. On the contrary, Gd2O2S screens consist of small

phosphor grains in a binder material which results in a more pronounced lateral diffusion of the light and a depth-dependent light collection efficiency.

For a screen-film system, the film noise (or film granularity) reduces the RN factor

considerably (RN=0.2-0.8: Nishikawa and Yaffe 1990a) at high frequencies since, at

these frequencies, the quantum noise is considerably reduced by the low values of detector MTF. The noise at high frequencies is thus dominated by non-quantum, film granularity. The RN factor also depends on the film optical density since

quantum and film noise depend differently on the optical density.

Typical values of RC range from 0.3-1.0 (Nishikawa and Yaffe 1990b) because the

detector MTF depends on the depth distribution of the x-ray interactions in the screen. X-ray interactions far away from the film cause broader light bursts at the film emulsion than interactions that occur closer to it. These variations in the spatial distribution of the light bursts contribute to reduce RC and DQE. This is

analogous to the reduction in DQE that occurs when the light bursts are of varying size (amplitude), an effect that is characterised by the statistical factor, IL.

One of the weakest point of a screen-film systems is its inability to separate image acquisition and image display; a separation that can be achieved with digital detectors. When a film is used as the optical detector, the shape of the film

characteristic curve reduces the DQE due to the low contrast gain obtained in the toe and shoulder region of the film characteristic curve. This will significantly reduce detection of details located in these regions of the film curve. The film curve is a compromise between high local contrast and large dynamic range. A large dynamic range is useful to simultaneously display a large range of values of energy imparted to the detector, for example to display both the breast skin boundary and the areas within the breast that are dense (glandular) or thick.

5.2. Semi-conductor and silicon detectors

The performance of semiconductor detectors is degraded by additional electronic noise, dark current, and the fill factor of the pixels (Yaffe and Rowlands 1997). The lateral spread of x-rays, electrons liberated in the x-ray interactions (photo- and Compton electrons) and the electron-hole pairs will cause unsharpness and reduce the pre-sample MTF. The pixel size will also affect the overall MTF. Photons incident at oblique angles pass through neighbouring pixels and may cause additional unsharpness (pixel height is between 3-15 times higher than the pixel side, here assumed to 100 µm). Que and Rowlands (1995) have estimated that the two main contributions to the limiting resolution of their amorphous Selenium (a-Se) detector was the range of the photo-electrons and the geometrical effect of oblique incidence of the x rays. In spite of this, the resolution was superior to CsI layers used in x-ray image intensifiers. It has been shown (Henry et al. 1995) that the MTF of a 0.3 mm Si detector with 30 µm pixels was significantly higher at high spatial frequencies than for a state-of-the-art screen-film system.

A fill-factor less than 100% is found when the detector pixel area is utilised for other purposes than x-ray absorption, for example electronics (thin-film transistor

switches). This effect is likely to be an even larger problem when pixel areas are made smaller.

The silicon detector studied by Henry et al. (1995) showed high values of the RN

factor up to high frequencies. Quantum noise dominates the total noise power spectrum over a larger interval of spatial frequencies than for screen-film systems. Also, since the variation in the number of collected charges is lower and their

spatial distribution is less broad than is the case for the corresponding light photons in a screen-film system, the factors IL and RC for a semi-conductor detector are

expected to be close to unity (Henry et al. 1995).

For the a-Se detector mentioned above, Que et al. (1995) concluded that for a 50 µm Se layer and the photon energies used in mammography, the DQE was superior to that of a Gd2O2S based screen-film system. Pedersen et al. (1996) found that DQEq

for a 100 µm thick (53.2 mg/cm2_{) GaAs detector was superior to that of a 150 µm CsI}

fluorescent screen between 17-33 keV. The CsI screen was in turn shown to have superior DQEq compared to the MinR Gd2O2S screen for all photon energies below

35 keV. This is interesting since the atomic numbers of Ga and As are just below that of Se and similar x-ray absorption characteristics can be expected for these materials. The high x-ray absorption in the comparably thin layers of Se and GaAs is partly due to the favourable location of the K-absorption edges for these elements (10.4, 12.7 keV).

6. Summary and conclusion

The photon energy absorption and scatter in flat image detectors have been

calculated using Monte Carlo photon transport simulations in a number of detector materials and thicknesses covering both traditional fluorescent screens and typical detector materials for digital radiography, such as silicon. The DQE at low spatial frequencies, neglecting the influence of the lateral spread of the secondary

information carriers (light, e-hole pairs), has been derived from Monte Carlo calculated first and second moments of the single-event size distributions for perpendicularly incident x rays with energies between 1-35 keV. The results show that a 1.5 mm thick silicon will have the same DQEq as commonly used Gd2O2S

fluorescent screens and that a 80 µm CsI phosphor has similar DQEq as 1.0 mm Si.

The total DQE of fluorescent screen-film systems will be significantly reduced from this value due to the light scatter, film noise and the inherent limitations caused by the film characteristic curve. This indicates that also with thinner silicon detectors (0.3-0.5 mm), which do not suffer from these limitations but from a comparably low quantum absorption efficiency, Aq, a total performance DQE(f) may be achieved

Acknowledgements

This report was initiated and financially supported by IDE AS (Oslo, Norway). The constructive criticism by Professor Gudrun Alm Carlsson is gratefully

acknowledged.

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Appendix. Aq, Ix and x-ray absorption DQEq for the image detectors used in this

study.

Detektor: Si 0,0699 g/cm2 = 0,300 mm Si

hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,00 1,00 1,000 1,000 2 0,985 1,97 3,94 1,000 0,985 3 1,000 2,98 8,91 0,995 0,995 4 1,000 3,98 15,90 0,998 0,998 5 0,999 4,99 24,90 0,999 0,999 6 0,999 5,99 35,90 1,000 0,999 7 0,997 6,98 48,82 1,000 0,997 8 0,987 7,90 63,14 1,000 0,987 9 0,958 8,62 77,52 1,000 0,958 10 0,903 9,03 90,26 1,000 0,903 11 0,828 9,10 100,10 1,000 0,828 12 0,743 8,91 106,88 1,000 0,742 13 0,657 8,53 110,84 0,999 0,656 14 0,575 8,03 112,44 0,998 0,574 15 0,502 7,50 112,52 0,997 0,500 16 0,438 6,98 111,61 0,995 0,436 17 0,381 6,43 109,19 0,994 0,378 18 0,332 5,92 106,53 0,992 0,329 19 0,291 5,47 103,81 0,990 0,288 20 0,256 5,04 100,75 0,986 0,252 21 0,225 4,65 97,45 0,984 0,221 22 0,198 4,27 93,76 0,980 0,194 23 0,176 3,94 90,45 0,975 0,172 24 0,157 3,65 87,38 0,970 0,152 25 0,141 3,38 84,32 0,965 0,136 26 0,126 3,12 80,92 0,958 0,120 27 0,114 2,92 78,55 0,952 0,109 28 0,104 2,73 76,11 0,944 0,098 29 0,094 2,55 73,55 0,936 0,088 30 0,086 2,39 71,15 0,927 0,080 31 0,079 2,22 68,49 0,919 0,072 32 0,073 2,11 66,91 0,909 0,066 33 0,067 1,97 64,48 0,898 0,060 34 0,062 1,86 62,59 0,889 0,055 35 0,058 1,76 60,94 0,878 0,051 Detektor: SI 0,1165 g/cm2 = 0,500 mm Si hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,000 1,000 1,000 1,000 2 0,985 1,970 3,940 1,000 0,985 3 1,000 2,980 8,910 0,995 0,995 4 1,000 3,980 15,900 0,998 0,998 5 0,999 4,990 24,900 0,999 0,999 6 0,999 5,990 35,900 1,000 0,999 7 0,999 6,990 48,890 1,000 0,999 8 0,998 7,980 63,830 1,000 0,998 9 0,994 8,940 80,450 1,000 0,994 10 0,978 9,780 97,800 1,000 0,978 11 0,946 10,400 114,400 1,000 0,946 12 0,895 10,740 128,840 1,000 0,895 13 0,832 10,800 140,350 0,999 0,831 14 0,761 10,630 148,780 0,998 0,759 15 0,688 10,290 154,340 0,997 0,686 16 0,616 9,820 157,100 0,996 0,614 17 0,551 9,320 158,390 0,995 0,548 18 0,490 8,750 157,480 0,994 0,486 19 0,437 8,230 156,260 0,992 0,433 20 0,389 7,680 153,590 0,989 0,384 21 0,346 7,160 150,200 0,986 0,341 22 0,309 6,670 146,510 0,983 0,303 23 0,276 6,210 142,540 0,979 0,270 24 0,248 5,790 138,700 0,974 0,242 25 0,224 5,400 134,790 0,969 0,217 26 0,202 5,030 130,500 0,963 0,194 27 0,183 4,720 126,950 0,957 0,175 28 0,167 4,420 123,170 0,949 0,158 29 0,152 4,140 119,630 0,942 0,144 30 0,139 3,870 115,530 0,932 0,130 31 0,128 3,660 112,780 0,925 0,119 32 0,118 3,450 109,530 0,916 0,108 33 0,109 3,240 106,120 0,906 0,099 34 0,101 3,060 103,210 0,897 0,091 35 0,095 2,900 100,520 0,885 0,084

Detektor: Si 0,233 g/cm2 = 1,000 mm Si

hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,000 1,000 1,000 1,000 2 0,985 1,970 3,940 1,000 0,985 3 1,000 2,980 8,910 0,995 0,995 4 1,000 3,980 15,900 0,998 0,998 5 0,999 4,990 24,900 0,999 0,999 6 0,999 5,990 35,900 1,000 0,999 7 0,999 6,990 48,890 1,000 0,999 8 0,999 7,990 63,860 1,000 0,999 9 0,998 8,980 80,830 1,000 0,998 10 0,998 9,980 99,750 1,000 0,998 11 0,995 10,940 120,370 1,000 0,995 12 0,987 11,840 142,120 1,000 0,987 13 0,971 12,610 163,910 0,999 0,970 14 0,943 13,180 184,430 0,998 0,941 15 0,903 13,510 202,680 0,998 0,901 16 0,854 13,620 217,840 0,997 0,851 17 0,799 13,530 229,930 0,996 0,796 18 0,741 13,280 238,920 0,995 0,738 19 0,683 12,890 244,910 0,994 0,679 20 0,628 12,450 248,970 0,992 0,623 21 0,574 11,930 250,310 0,990 0,568 22 0,524 11,370 249,840 0,987 0,517 23 0,476 10,760 247,190 0,984 0,468 24 0,436 10,240 245,400 0,980 0,427 25 0,397 9,680 241,490 0,976 0,388 26 0,365 9,190 238,550 0,971 0,354 27 0,334 8,680 233,760 0,966 0,322 28 0,306 8,200 228,930 0,959 0,294 29 0,282 7,760 224,190 0,952 0,269 30 0,261 7,350 219,620 0,944 0,246 31 0,241 6,960 214,690 0,936 0,226 32 0,223 6,580 209,390 0,927 0,207 33 0,208 6,260 205,290 0,919 0,191 34 0,192 5,890 198,630 0,908 0,175 35 0,181 5,630 195,220 0,899 0,162 Detektor: Si 0,3495 g/cm2 = 1,5 mm Si hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,000 1,000 1,000 1,000 2 0,985 1,970 3,940 1,000 0,985 3 1,000 2,980 8,910 0,995 0,995 4 1,000 3,980 15,900 0,998 0,998 5 0,999 4,990 24,900 0,999 0,999 6 0,999 5,990 35,900 1,000 0,999 7 0,999 6,990 48,890 1,000 0,999 8 0,999 7,990 63,860 1,000 0,999 9 0,998 8,980 80,830 1,000 0,998 10 0,998 9,980 99,780 1,000 0,998 11 0,998 10,970 120,680 1,000 0,998 12 0,997 11,960 143,470 1,000 0,997 13 0,994 12,910 167,760 0,999 0,993 14 0,985 13,770 192,790 0,999 0,984 15 0,970 14,510 217,620 0,998 0,968 16 0,944 15,060 240,960 0,997 0,942 17 0,910 15,420 262,040 0,997 0,907 18 0,869 15,570 280,210 0,996 0,865 19 0,822 15,530 295,000 0,995 0,818 20 0,774 15,370 307,230 0,993 0,769 21 0,722 15,040 315,570 0,992 0,716 22 0,672 14,620 321,340 0,990 0,665 23 0,624 14,140 325,010 0,987 0,616 24 0,577 13,600 326,020 0,984 0,567 25 0,535 13,080 326,610 0,981 0,524 26 0,494 12,500 324,400 0,976 0,482 27 0,457 11,960 322,120 0,971 0,444 28 0,423 11,410 318,620 0,965 0,409 29 0,392 10,860 313,990 0,958 0,376 30 0,365 10,380 310,150 0,952 0,347 31 0,339 9,870 304,740 0,944 0,320 32 0,316 9,410 299,700 0,936 0,296 33 0,294 8,950 293,500 0,928 0,273 34 0,276 8,550 288,600 0,919 0,253 35 0,259 8,180 284,060 0,910 0,236

Detektor: Cesium Iodine 0,0225 g/cm2 = 0,050 mm CsI hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,000 1,000 1,000 1,000 2 0,999 2,000 4,000 1,000 0,999 3 0,999 3,000 8,990 1,000 0,999 4 0,998 3,990 15,970 1,000 0,998 5 0,999 4,990 24,970 1,000 0,999 6 0,999 5,990 35,970 1,000 0,999 7 0,999 6,990 48,950 1,000 0,999 8 0,998 7,980 63,860 1,000 0,998 9 0,992 8,930 80,340 1,000 0,992 10 0,977 9,770 97,670 1,000 0,977 11 0,947 10,420 114,620 1,000 0,947 12 0,903 10,830 129,980 1,000 0,903 13 0,848 11,020 143,210 1,000 0,847 14 0,783 10,960 153,470 1,000 0,783 15 0,720 10,800 161,950 1,000 0,720 16 0,657 10,510 168,200 1,000 0,657 17 0,598 10,160 172,720 0,999 0,598 18 0,540 9,720 174,880 0,999 0,540 19 0,489 9,290 176,470 0,999 0,489 20 0,439 8,780 175,510 0,999 0,439 21 0,398 8,350 175,420 0,999 0,398 22 0,359 7,890 173,580 0,998 0,359 23 0,325 7,460 171,580 0,998 0,324 24 0,296 7,080 169,890 0,997 0,295 25 0,267 6,650 166,280 0,997 0,266 26 0,244 6,340 164,740 0,997 0,244 27 0,221 5,940 160,220 0,996 0,220 28 0,205 5,710 159,730 0,995 0,204 29 0,186 5,360 155,320 0,994 0,185 30 0,172 5,130 153,730 0,993 0,171 31 0,159 4,890 151,610 0,993 0,158 32 0,145 4,600 147,000 0,991 0,144 33 0,133 4,340 143,220 0,991 0,132 34 0,351 7,130 221,320 0,653 0,229 35 0,333 7,100 224,380 0,675 0,225

Detektor: Cesium Iodine 0,0361 g/cm2 = 0,080 mm CsI hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,000 1,000 1,000 1,000 2 0,999 2,000 4,000 1,000 0,999 3 0,999 3,000 8,990 1,000 0,999 4 0,998 3,990 15,980 1,000 0,998 5 0,999 4,990 24,970 1,000 0,999 6 0,999 5,990 35,970 1,000 0,999 7 0,999 6,990 48,950 1,000 0,999 8 0,999 7,990 63,910 1,000 0,999 9 0,998 8,980 80,860 1,000 0,998 10 0,996 9,960 99,620 1,000 0,996 11 0,989 10,880 119,720 1,000 0,989 12 0,975 11,700 140,350 1,000 0,975 13 0,949 12,340 160,430 1,000 0,949 14 0,915 12,800 179,260 1,000 0,915 15 0,870 13,050 195,810 1,000 0,870 16 0,820 13,110 209,820 1,000 0,820 17 0,766 13,030 221,430 1,000 0,766 18 0,710 12,770 229,930 0,999 0,710 19 0,658 12,490 237,330 0,999 0,657 20 0,604 12,060 241,250 0,999 0,603 21 0,554 11,620 244,020 0,999 0,553 22 0,511 11,230 247,140 0,999 0,511 23 0,467 10,730 246,830 0,998 0,467 24 0,429 10,270 246,350 0,998 0,428 25 0,395 9,860 246,350 0,997 0,394 26 0,362 9,380 243,930 0,997 0,361 27 0,336 9,030 243,780 0,996 0,335 28 0,306 8,520 238,410 0,996 0,304 29 0,280 8,090 234,590 0,996 0,279 30 0,259 7,720 231,460 0,994 0,257 31 0,239 7,370 228,460 0,994 0,238 32 0,222 7,040 225,190 0,992 0,220 33 0,206 6,740 222,270 0,992 0,204 34 0,502 10,920 344,510 0,689 0,346 35 0,476 10,880 350,050 0,711 0,338

Detektor: Cesium Iodine 0,0676 g/cm2 = 0,150 mm CsI hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 1,000 1,000 1,000 1,000 1,000 2 0,999 2,000 4,000 1,000 0,999 3 0,999 3,000 8,990 1,000 0,999 4 0,998 3,990 15,980 1,000 0,998 5 0,999 4,990 24,970 1,000 0,999 6 0,999 5,990 35,970 1,000 0,999 7 0,999 6,990 48,950 1,000 0,999 8 0,999 7,990 63,910 1,000 0,999 9 0,999 8,990 80,890 1,000 0,999 10 0,998 9,980 99,840 1,000 0,998 11 0,998 10,980 120,760 1,000 0,998 12 0,997 11,970 143,620 1,000 0,997 13 0,995 12,930 168,070 1,000 0,995 14 0,988 13,830 193,630 1,000 0,988 15 0,977 14,640 219,670 1,000 0,976 16 0,959 15,330 245,320 1,000 0,958 17 0,933 15,860 269,670 1,000 0,933 18 0,900 16,190 291,410 1,000 0,899 19 0,865 16,430 312,210 1,000 0,865 20 0,826 16,500 330,060 0,999 0,825 21 0,781 16,400 344,320 0,999 0,781 22 0,738 16,230 356,960 0,999 0,738 23 0,693 15,920 366,160 0,999 0,692 24 0,650 15,580 373,820 0,998 0,649 25 0,610 15,220 380,450 0,998 0,609 26 0,570 14,780 384,300 0,998 0,569 27 0,534 14,380 388,170 0,997 0,533 28 0,499 13,930 389,890 0,997 0,498 29 0,463 13,370 387,670 0,996 0,461 30 0,433 12,920 387,540 0,996 0,431 31 0,404 12,450 385,930 0,995 0,402 32 0,378 12,020 384,500 0,994 0,376 33 0,351 11,500 379,350 0,993 0,349 34 0,730 17,850 576,800 0,756 0,552 35 0,703 17,850 588,790 0,770 0,541

Detektor: Gd2O2S 0,0365 g/cm2 MinR2000

hv Aq M1 M2 Ix DQE

(keV) (keV) (keV2₎

1 0,999 1,000 1,000 1,000 0,999 2 1,000 2,000 4,000 1,000 1,000 3 0,999 3,000 8,990 1,000 0,999 4 0,999 3,990 15,980 1,000 0,999 5 0,998 4,990 24,950 1,000 0,998 6 0,997 5,980 35,890 1,000 0,997 7 0,991 6,940 48,560 1,000 0,991 8 0,999 7,990 63,930 1,000 0,999 9 0,999 8,990 80,910 1,000 0,999 10 0,998 9,980 99,850 1,000 0,998 11 0,997 10,970 120,650 1,000 0,997 12 0,993 11,910 142,940 1,000 0,993 13 0,983 12,780 166,100 1,000 0,983 14 0,966 13,520 189,290 1,000 0,966 15 0,941 14,110 211,620 1,000 0,941 16 0,907 14,510 232,140 1,000 0,907 17 0,867 14,740 250,590 1,000 0,867 18 0,823 14,800 266,380 1,000 0,822 19 0,775 14,720 279,640 1,000 0,775 20 0,727 14,540 290,750 0,999 0,727 21 0,680 14,270 299,740 0,999 0,680 22 0,633 13,920 306,280 0,999 0,633 23 0,587 13,490 310,240 0,999 0,587 24 0,547 13,100 314,370 0,999 0,546 25 0,507 12,670 316,590 0,998 0,507 26 0,470 12,200 317,120 0,998 0,469 27 0,437 11,780 318,080 0,998 0,436 28 0,406 11,330 317,040 0,997 0,405 29 0,377 10,890 315,780 0,997 0,376 30 0,350 10,450 313,440 0,996 0,348 31 0,326 10,050 311,520 0,996 0,324 32 0,303 9,640 308,510 0,995 0,302 33 0,282 9,260 305,430 0,995 0,281 34 0,263 8,890 301,960 0,994 0,261 35 0,245 8,510 297,660 0,993 0,243