Determination of the detective quantum efficiency of a digital x-ray detector: Comparison of three evaluations using a common image data set Ulrich Neitzela) and Susanne Gu¨nther-Kohfahl Philips Medical Systems, Ro¨ntgenstraße 24, D-22335 Hamburg, Germany
Giovanni Borasi Servizio di Fisica Sanitaria, Azienda Ospedaliera Santa Maria Nuova, V. le Risorgimento 80, 42100 Reggio Emilia (RE), Italy
Ehsan Samei Departments of Radiology, Physics, and Biomedical Engineering, Duke University, DUMC 3302, Durham, North Carolina 27710
共Received 17 February 2004; revised 5 May 2004; accepted for publication 7 May 2004; published 14 July 2004兲 The detective quantum efficiency 共DQE兲 of an x-ray digital imaging detector was determined independently by the three participants of this study, using the same data set consisting of edge and flat field images. The aim was to assess the possible variation in DQE originating from established, but slightly different, data processing methods used by different groups. For the case evaluated in this study differences in DQE of up to ⫾15% compared to the mean were found. The differences could be traced back mainly to differences in the modulation transfer function 共MTF兲 and noise power spectrum 共NPS兲 determination. Of special importance is the inclusion of a possible lowfrequency drop in MTF and the proper handling of signal offsets for the determination of the NPS. When accounting for these factors the deviation between the evaluations reduced to approximately ⫾5%. It is expected that the recently published standard on DQE determination will further reduce variations in the data evaluation and thus in the results of DQE measurements. © 2004 American Association of Physicists in Medicine. 关DOI: 10.1118/1.1766421兴 Key words: digital x-ray detector, detective quantum efficiency, modulation transfer function, noise power spectrum, standardization I. INTRODUCTION The detective quantum efficiency 共DQE兲 is considered to be the fundamental performance parameter of digital x-ray detectors.1 It is defined as the squared ratio of the 共spatial frequency dependent兲 signal-to-noise ratio at the output to the signal-to-noise ratio at the input of the detector. The experimental determination of the DQE is usually done by measurements of the modulation transfer function 共MTF兲 and the output noise power spectrum 共NPS兲, the results of which are, after proper normalization, combined to obtain the DQE. In the past few years, DQE evaluations have been reported for a number of digital detector systems by different authors.2– 8 A comparison of the results is sometimes difficult because slightly different assessment methods have been used and it is unclear if observed DQE differences are caused by these experimental variations or are due to real differences of the detectors investigated. Assuming equal detector properties, observed differences in DQE may have their origin in two separate parts of the evaluation process: 共a兲 in the generation of the images used for the determination of the MTF, the NPS, and the characteristic response or 共b兲 in the computational evaluation of the image data. In an effort to investigate the influence of the second part we conducted a study where the same set of digital images was evaluated independently by the three parties involved, each of which was experienced in DQE deter2205
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mination. The methods employed have been used routinely in the past and partly reported in the literature, however, some computational differences between them exist. During the past few years, an effort has been made by the International Electrotechnical Commission 共IEC兲 to standardize the DQE determination for digital x-ray imaging detectors.9 As a result of this activity, the international standard IEC 62220-1 was published in October 2003.10 At the time of the study reported here the standard was not available in its final form. The reported results thus represent the pre-standardization situation. II. MATERIAL AND METHODS A. Image data set
A set of images was generated for the determination of the MTF and the NPS of an indirect-type 共cesium iodide/ amorphous silicon兲 flat-panel detector. An RQA5 x-ray spectrum11 was used (HVL⫽7.1 mm Al, realized with 21 mm Al additional filtration at 74 kVp兲. All images were taken from the same subarea of the full detector area, 5122 pixels in size, with a pixel sampling pitch of 0.143 mm. Image preprocessing comprised offset and gain correction as well as compensation for defective or nonlinear pixels, as applied in normal clinical use of the detector. Pixel scaling was 共nominally兲 linear with respect to exposure 共air kerma兲, with a bit depth of 16 bit.
0094-2405Õ2004Õ31„8…Õ2205Õ7Õ$22.00
© 2004 Am. Assoc. Phys. Med.
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TABLE I. Main features of the three different evaluation methods used in this study. The corresponding parameters as prescribed in the standard IEC 62220-1 are also listed for comparison. See the text for details.
Length of edge profile 共transverse to the edge兲 MTF fitting/smoothing Detrending ROI for NPS Windowing 1-D NPS extraction NPS fitting/smoothing
Method A
Method B
Method C
IEC 62220-1
73.2 mm
14.6 mm
10 mm
100 mm
None 2-D 2nd order polynom 256⫻256 half overlapping None ⫾7 lines excl. axis None
None 2-D 2nd order polynom 128⫻128
None 2-D 2nd order polynom 256⫻256 half overlapping None ⫾7 lines excl. axis None
30 174
30 174
Inverse polynom fit None 256⫻256 half overlapping None ⫾7 lines excl. axis Smoothing with Mathcad™ loess function 29 333
Value for q 关 mm⫺2 • Gy⫺1 兴
Edge images for MTF determination were generated using an edge test device made of 1.5 mm thick copper. Two edge images were acquired, one with the edge in horizontal, the other with the edge in vertical orientation, slightly (⬃2°) tilted with respect to the axes of the image matrix. The edge images were acquired with an exposure of 8.21 Gy. For a determination of the NPS, six independent flat-field images were obtained at each of three exposure levels 共18 images in total兲. The exposure 共air kerma兲 was 0.645, 2.45, and 8.21 Gy, respectively, for the three series. The air kerma values were measured free-in-air in the detector plane with the detector removed. The image data set in general followed the concept put forward in the IEC standard.10 However, as the standard was in a draft stage at the time of our study, there were deviations of our data set to the now published standard; e.g., an edge made of semitransparent copper was used instead of fully absorbing tungsten, and the total number of pixels in the flat-field images was smaller by a factor of ten compared to the requirements in the standard. Although these differences may have an influence on the measured DQE values and especially on their uncertainty, it is assumed that they do not interfere with the purpose of this study, which was to assess the interlaboratory variation of data evaluation. B. DQE determination methods
The image data sets were independently evaluated by the three participants in this study. Each participant used the method usually applied at the respective institution. These methods varied slightly 共cf. Table I兲 and are described in detail in the following sections.
1. Method A For the determination of the presampled MTF, the method given in the IEC standard and described in detail in Ref. 12 was used. Basically, an oversampled edge spread function 共ESF兲 is constructed by interlacing the data of N lines across the edge, where N is the 共integer兲 number of lines leading to a lateral shift of the edge location by one pixel. N is related to the tilt angle ␣ of the edge according to Medical Physics, Vol. 31, No. 8, August 2004
Hamming ⫾5 lines incl. axis None
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N⫽round(1/tan ␣). The sampling distance of the oversampled profile is taken as p/N, where p is the original pixel sampling distance. In this case N was determined to be 29, corresponding to an edge angle of approximately 2°. The total length of the edge profile transverse to the edge was 73.2 mm, corresponding to the full 5122 image size. To reduce the noise in the edge profile, 17 representations of the oversampled ESF were generated using 17 groups of 29 lines each, i.e., a total length of 70.5 mm along the edge; these ESFs were registered to subsampling pitch precision with respect to the edge location and averaged.12 For the determination of the MTF the usual process of derivation of the ESF to obtain the LSF and subsequent fast Fourier transform to obtain the presampled MTF was applied. No resampling, binning, or smoothing was used in this process. The NPS was determined using the six flat-field images for each exposure level. To remove long-range background trends a two-dimensional 2nd order polynomial was fitted to each image and subtracted. The area of each image was divided into half-overlapping regions of interest 共ROIs兲 of 2562 pixels 共9 ROIs for each image, 54 in total兲. The twodimensional NPS was then calculated by applying the fast Fourier transform to each ROI and averaging the resulting spectrum estimates. Neither fixed pattern noise subtraction 共common mode rejection兲 nor windowing was applied prior to the transform.13 One-dimensional cuts through the 2-D NPS were obtained by averaging the central ⫾7 lines 共excluding the axis兲 around the horizontal and vertical axes. The procedure as described follows generally the specifications of the IEC standard, however, in the final version of the standard a larger total number of pixels (16⫻106 ) for the flat-field images is required compared to the 6⫻5122 ⫽1.57 ⫻106 pixels used here. The DQE versus spatial frequency was finally calculated using DQE共 f 兲 ⫽G 2 •
MTF2 共 f 兲 •X , NPS共 f 兲 •q
共1兲
where G is the gain factor 共in digital units per Gy兲, X is the air kerma in Gy and q is the ideal SNR2 of the incident radiation, given by the number of incident x-ray quanta per
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air kerma and mm2 . The gain factor G was determined as the slope of the characteristic curve, relating the mean pixel value to the incident exposure. Using the flat-field images at the three exposure levels the gain factor was determined by linear regression to be G⫽229.2 digital units per Gy. The value for q at radiation quality RQA5 was taken from the IEC standard 62220-1 共draft at that time兲 to be 30174 mm⫺2 Gy⫺1 . Since the spatial frequency sampling steps of MTF( f ) and NPS( f ) are generally not the same, MTF( f ) was linearly interpolated at the frequency sampling points of NPS( f ) and then DQE( f ) was calculated at these points.
2. Method B The presampled modulation transfer function 共MTF兲 of the system in the orthogonal directions was obtained from the edge images using a method described in a previous publication.14 In this method, first the edge image is thresholded and differentiated to create a binary image containing the line of the edge transition. The angle of the edge transition line is determined utilizing a double Hough transformation with 0.01-degree accuracy. The original image data in the region surrounding the edge are then projected along the determined edge angle into data bins of 0.0143 mm to obtain the over-sampled edge spread function 共ESF兲. The ESF is smoothed using a nonparametric fourth order moving polynomial fit. The discrete derivative of the ESF is then computed to form the line spread function 共LSF兲. A Hamming window with a window width of 14.3 mm is applied to the LSF, and the MTF is computed as the normalized Fast Fourier Transform 共FFT兲 of the LSF. The normalized noise power spectrum 共NNPS兲 of the six images from each exposure was determined using previously published methods.15 The central 364⫻364 area of each image was segmented into nine 128⫻128 sequential regions of interest 共ROIs兲. To correct for low-frequency background trends, a two-dimensional surface fit was subtracted from each ROI. The pixel values were then converted to relative exposure by dividing the value by the dc level. To account for intensity variations in the image, each ROI was then scaled by the ratio of its mean to the mean pixel value of the ROI in the top-left-hand corner of the image. A Hamming filter was applied to each ROI, and the NNPS obtained by averaging the absolute magnitude squared of the twodimensional FFTs from each ROI. One-dimensional traces in the horizontal and vertical direction were obtained by averaging together frequency bands including the central axis and ⫾5 frequency lines. The traces were averaged for NNPS obtained from six images of similar exposure. For a first evaluation 共termed B * ), the image data was treated as being linear with exposure with negligible off-set. In a second evaluation 共termed B), the computed NNPS was corrected for a nonzero offset of the image data by applying a multiplicative correction factor equal to
冉
冊
2 PV , PV⫺offset
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共2兲
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where PV is the mean pixel value in the image and offset is the intercept of a linear fit to pixel value versus exposure data, calculated to be 12.73 in this case. Using the measured MTF and NNPS, the DQE was computed using DQE共 f 兲 ⫽
MTF2 共 f 兲 , NNPS共 f 兲 •q•X
共3兲
where MTF( f ) is the measured presampled MTF, q is the signal to noise 共SNR兲 ratio per exposure for an ideal detector, per IEC assumed to be 30174 mm⫺2 Gy⫺1 10 recommendation, and X is the exposure 共air kerma兲 value at the detector plane. As in method A above, MTF( f ) was linearly interpolated at the frequency sampling points of NNPS( f ) in order to calculate DQE( f ) using the above equation.
3. Method C The presampled MTF was calculated considering an evaluation area covering the central part of the image across the edge. The area was 10 mm across the edge and 30 mm in the direction along the edge. This area was subdivided along the edge into five adjacent subregions (10 mm⫻6 mm), in each of which the MTF was evaluated using the same basic procedure as method A. The obtained MTF samples were fitted using an inverse polynomial function and the results of the five evaluations were then averaged. The fitting function used was F共 f 兲⫽
a , 共 1⫹b• f ⫹c• f 6 兲 d 2
共4兲
where four parameters a, b, c, and d were estimated using a nonlinear least-squares method 共Marquardt algorithm16兲. An analytical estimate for the MTF was then obtained according to MTF共 f 兲 ⫽
F共 f 兲 . a
共5兲
For the determination of the NPS the six images for each exposure level were used similar to method A, but no longrange background trends removal was applied. Before NPS calculation, the original images were ‘‘linearized’’ 共i.e., converted into air kerma images兲, by applying to each pixel the inverse of the characteristic curve. This curve was obtained considering a square ROI (70⫻70 pixels) in the center of each image. The resulting average pixel values 共in digital units兲 versus the exposure level 共in Gy兲 were fitted with a linear function y⫽a⫹bx. In the weighted fitting process, the weighting of each digital signal data was taken as inversely proportional to its value 共relative error constant along the function interval兲. The fitted parameters values were a ⫽10.9⫾1.25 digital units and b⫽231.5⫾1.16 digital units per Gy. The regression coefficient (R 2 ) was 0.999814. Before averaging, the NPS samples of each image were smoothed using the ‘‘loess’’ function17 included in the Mathcad™ mathematical package. The smoothing parameter 共span兲 was 0.1.
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FIG. 1. 共a兲 Presampled MTF in horizontal direction as determined from the edge image using the three methods of this study. 共b兲 Magnification of the low spatial frequency part.
The DQE versus spatial frequency was then calculated using DQE共 f 兲 ⫽
MTF2 共 f 兲 , NNPS共 f 兲 •q•X
共6兲
where NNPS( f ) represents the normalized NPS, calculated from the linearized 共air kerma兲 images. The normalized NPS contains the gain factor G, as NNPS共 f 兲 ⫽
NPS共 f 兲 . 共 G•X 兲 2
共7兲
The value for q at radiation quality RQA5 was taken to be 29333 mm⫺2 Gy⫺1 . This value was derived from Table II of Ref. 5, considering the detector as an energy integrating device. III. RESULTS Although the data were evaluated for horizontal and vertical axis directions, only the results for one direction 共horizontal兲 are reported here, as the relative differences between the evaluations according to the three methods were similar for both directions. Figure 1共a兲 illustrates the presampled MTF as determined with the three methods used in this study. Differences are noticeable particularly at low spatial frequencies. This part is magnified in Fig. 1共b兲 where also the individual data points on the three curves are marked. Due to the much longer trace used for the ESF, the point density 共i.e., the spatial frequency Medical Physics, Vol. 31, No. 8, August 2004
FIG. 2. Normalized noise power spectra in horizontal direction as determined from the set of flat-field images. 共a兲 Without offset correction 共method B* ). 共b兲 With offset correction 共method B兲. 共⫹兲 Method A; 共䉭兲 method B/B* ; 共䊐兲 method C.
resolution兲 is the highest for method A, but the MTF curve exhibits also a greater noise level. The higher spatial resolution in the evaluation with method A reveals a MTF low frequency drop of about 7%, which is not seen in any of the other evaluations. Method B uses a five times shorter length of the edge profile resulting in a correspondingly reduced frequency resolution. In method C a function was fitted according to Eq. 共3兲 that was evaluated at spatial frequency steps of 0.1 mm⫺1 , which results in a stronger smoothing of the curve and does not allow to display the initial MTF drop. Figure 2 illustrates the normalized noise power spectrum in the horizontal direction for the three exposure levels as determined using the three methods For the results shown in Fig. 2共a兲, a zero offset of the characteristic curve was assumed for method B* . The results are in reasonably good agreement except for the lowest exposure where method B* results in systematically lower values, especially at low spatial frequencies. When using the offset-corrected NNPS in method B, generally a better agreement with the results of the other methods is found 关Fig. 2共b兲兴; at the lowest exposure and the highest frequencies, however, method B results in a somewhat higher noise power than methods A and C. Figures 3共a兲–3共c兲 show the DQE versus spatial frequency for the three exposure levels as determined using the
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FIG. 4. Detective quantum efficiency in horizontal direction at 0.645 Gy using method B* 共without offset correction兲 instead of B; compare with Fig. 3共a兲.
the standard.10 The results according to method A are generally about 15% lower than the values for method B 共including the offset correction兲 and C. The DQE values obtained with method B* 共without offset correction兲 are approximately 20% higher than those of B at 0.645 Gy 关Fig. 5共a兲兴, but this difference reduces to about 1% at 8.21 Gy 关Fig. 5共c兲兴. The percentage of deviation between the evaluations seem to be rather independent of spatial frequency. IV. DISCUSSION AND CONCLUSIONS
FIG. 3. Detective quantum efficiency in horizontal direction as determined using the three methods for three exposure levels. 共a兲 0.645 Gy, 共b兲 2.45 Gy, 共c兲 8.21 Gy. 共⫹兲 Method A; 共䉭兲 method B; 共䊐兲 method C.
three methods, using offset-corrected data for method B. The straight lines represent linear fits to the individual data sets and serve only as a guide for the eye. Generally, the results according to method A are somewhat lower than those according to methods B and C. When using method B* without offset correction, the DQE values at a low exposure increase 共Fig. 4兲. The differences are illustrated in Fig. 5 which shows the deviations of the individual DQE measurements from the mean at each exposure level. The mean was calculated from the results according to methods A, B, and C. The data points represent binned 共averaged兲 values at spatial frequencies of n•0.5⫾0.07 lp/mm, following the procedure described in Medical Physics, Vol. 31, No. 8, August 2004
The comparison of the DQE results of the three participants in this study, who are all experienced in doing this type of evaluation, demonstrates rather notable differences. Taking into account that the differences originated from the numerical evaluation part only, even larger discrepancies can be expected when the data acquisition part is done individually by each researcher. The comparably low DQE values obtained with method A can be attributed mainly to the lower MTF, due to the low frequency drop 共LFD兲 found with this method. As the MTF enters squared into the DQE formula 关cf. Eq. 共1兲兴 a LFD of about 7% leads to a reduction in DQE by approximately 14%, which is close to the DQE difference found between method A on one side and methods C and B on the other side. Traditionally, the influence of a possible low frequency drop has often been eliminated from the MTF measurement by limiting the length of the tails of the edge or line spread function 共e.g., to 4 mm in Refs. 2 and 5兲 and normalization of the MTF at the corresponding spatial frequency. This approach was mainly based on the limited accuracy of the MTF assessment at low frequencies using the slit method.18 The edge method, however, allows an accurate determination of the MTF even at very low spatial frequencies, including a possible low frequency drop. This is also required in the new IEC standard for correct DQE determination. For the determination of the normalized noise power spectra, the proper consideration of any deviation from a
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FIG. 6. Influence of an offset of the characteristic curve on the determined gain values 共schematically, not to scale兲. The true gain is given by the slope of the characteristic curve. For normalized data, the apparent gain is different for each exposure level 共slope of dashed lines兲.
given in Eq. 共2兲 for method B. Otherwise 共method B* ), an error due to the nonzero offset will occur, which influences the NPS particularly at low exposure, where the offset becomes most prominent relative to the mean pixel value. An uncorrected nonzero offset can be considered as leading to an ‘‘apparent’’ gain value which is given by the mean pixel value divided by the air kerma for each noise image instead of the slope of the characteristic curve 共Fig. 6兲. The relation between the apparent gain G ⫹ and the true gain G can be derived from the equation of the characteristic curve: PV⫽G•X⫹Offset,
共8兲
from which follows that G ⫹⫽
FIG. 5. Deviations of the DQE values from the mean at each exposure level, as determined using the methods of this study. The mean is calculated from the results of methods A, B 共including offset correction兲, and C. 共a兲 0.645 Gy, 共b兲 2.45 Gy, 共c兲 8.21 Gy.
purely linear, zero-offset characteristic curve of the detector is essential. In the case studied here, the mean pixel value versus exposure relation can be fitted with a linear function with very high correlation, but this function exhibits an offset of about 11–15 共depending on evaluation兲 digital units at zero exposure, compared to a mean pixel value of 159 at 0.685 Gy. The calculation of the normalized NPS can be done either by linearization of the pixel data 共including the offset兲 as done in method C or by normalizing the NPS calculated from the direct pixel data with the gain factor G 共being the fitted slope of the characteristic curve兲 multiplied by air kerma X, as done in method A. If the normalized NPS is computed from relative noise images 共flat-field images divided by their mean value兲, a correction must be applied as Medical Physics, Vol. 31, No. 8, August 2004
Offset PV ⫽G⫹ , X X
共9兲
with PV 共mean兲 pixel value at air kerma X. True gain G and apparent gain G ⫹ are equal only if the offset of the characteristic curve is zero. For the three exposure levels used in this study the deviation of G ⫹ from G is 7.4% at 0.645 Gy, 3.5% at 2.45 Gy, and 0.7% at 8.45 Gy. As the DQE depends on the square of G 关cf. Eq. 共1兲兴, the error in DQE will be twice as large when using G ⫹ instead of G, leading to an overestimation of the DQE at low exposure by about 15%. Another, minor difference between the result of method C compared to the results of A and B is due to the different, about 3% larger, value for q 共the ideal SNR2 ) used in method C. Since q appears in the denominator in the equation for the DQE 关cf. Eqs. 共1兲, 共2兲 and 共5兲兴, the DQE determined by method C will be about 3% larger due to this factor even when all other quantities are equal. At the time of this study, the DQE measurement standard was still under development. The methods used and results obtained represent therefore the ‘‘pre-standardization’’ situation. In the meantime the standard IEC 62220-1 has been published.10 The standard fixes most of the experimental and computational boundary conditions, e.g., the linearization procedure, the length of the edge profile to be used for MTF determination, the value of q, the size of the ROI for the NPS calculation, etc. Therefore, it is anticipated that DQE
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the values published in the literature. Compared to earlier investigations, somewhat lower DQE values may result if the investigated detectors exhibit a non-negligible low frequency drop in MTF. a兲
Electronic mail:
[email protected] J. T. Dobbins III, ‘‘Image quality metrics for digital systems,’’ in Handbook of Medical Imaging, Vol. I Physics and Psychophysics, edited by J. Beutel, H. L. Kundel, and R. L. Van Metter 共SPIE, Bellingham, WA, 2000兲. 2 P. R. Granfors and R. Aufrichtig, ‘‘Performance of a 41⫻41-cm2 amorphous silicon flat panel x-ray detector for radiographic imaging applications,’’ Med. Phys. 27, 1324 –1331 共2000兲. 3 E. Samei and M. J. Flynn, ‘‘An experimental comparison of detector performance for computed radiography systems,’’ Med. Phys. 29, 447– 459 共2002兲. 4 E. Samei, ‘‘Image quality in two phosphor-based flat panel digital radiographic detectors,’’ Med. Phys. 30, 1747–1757 共2003兲. 5 E. Samei and M. J. Flynn, ‘‘An experimental comparison of detector performance for direct and indirect digital radiography systems,’’ Med. Phys. 30, 608 – 622 共2003兲. 6 G. Borasi, A. Nitrosi, P. Ferrari, and D. Tassoni, ‘‘On site evaluation of three flat panel detectors for digital radiography,’’ Med. Phys. 30, 1719– 1731 共2003兲. 7 X. Liu and C. C. Shaw, ‘‘a-Si:H/CsI共Tl兲 flat-panel versus computed radiography for chest imaging applications: image quality metrics measurement,’’ Med. Phys. 31, 98 –110 共2004兲. 8 M. Ba˚th, P. Sund, and L. G. Ma˚nsson, ‘‘Evaluation of the imaging properties of two generations of a CCD-based system for digital chest radiography,’’ Med. Phys. 29, 2286 –2297 共2002兲. 9 D. Hoeschen, ‘‘DQE of digital x-ray imaging systems: a challenge for standardization,’’ Proc. SPIE 4320, 280–286 共2001兲. 10 International Electrotechnical Commission, International Standard IEC 62220-1, ‘‘Medical electrical equipment—Characteristics of digital imaging devices—Part 1: Determination of the detective quantum efficiency,’’ Geneva, 2003. 11 International Electrotechnical Commission, International Standard IEC 61267, ‘‘Medical diagnostic X-ray equipment—Radiation conditions for use in the determination of characteristics,’’ Geneva, 1994. 12 E. Buhr, S. Gu¨nther-Kohfahl, and U. Neitzel, ‘‘Accuracy of a simple method for deriving the presampled modulation transfer function of a digital radiographic system from an edge image,’’ Med. Phys. 30, 2323– 2331 共2003兲. 13 A. D. A. Maidment, M. Albert, P. C. Bunch, I. A. Cunningham, J. T. Dobbins, R. Gagne, R. M. Nishikawa, R. Van Metter, and R. F. Wagner, ‘‘Standardization of NPS measurement: Interim report of AAPM TG16,’’ Proc. SPIE 5030, 523–531 共2003兲. 14 E. Samei, M. J. Flynn, and D. A. Reimann, ‘‘A method for measuring the presampled MTF of digital radiographic systems using an edge test device,’’ Med. Phys. 25, 102–113 共1998兲. 15 M. J. Flynn and E. Samei, ‘‘Experimental comparison of noise and resolution for 2k and 4k storage phosphor radiography systems,’’ Med. Phys. 26, 1612–1623 共1999兲. 16 P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences 共McGraw-Hill, New York, 1969兲, pp. 235–242. 17 ‘‘The Mathcad implementation of loess is a variation 共some approximations made for the sake of speed兲 on the algorithm,’’ described in W. S. Cleveland and C. Loader, ‘‘Smoothing by local regression: principles and methods 共with discussion兲,’’ in Statistical Theory and Computational Aspects of Smoothing, edited by W. Hardle and M. G. Schimek 共Physica, Heidelberg, 1996兲, pp. 10– 49, 80–102, 113–120. 18 I. A. Cunningham and B. K. Reid, ‘‘Signal and noise in modulation transfer function determinations using the slit, wire, and edge techniques,’’ Med. Phys. 19, 1037–1044 共1992兲. 1
FIG. 7. Deviations of the DQE values from the mean after compensation for MTF low frequency drop 共methods B and C兲 and difference in q 共method C兲. See Fig. 4; for details see the text. 共䊏兲 0.645 Gy, 共⽧兲 2.45 Gy, 共䉱兲 8.21 Gy.
determinations by different groups following the procedure of the standard will show smaller variation than is the case in this study. However, that needs to be confirmed by further studies. Of the methods used here, method A is closest to the final version of the IEC standard, especially with respect to the MTF determination. Therefore it can be suspected that an evaluation of the data set following the DQE standard would give values comparable to the results of method A. We tentatively corrected the DQE deviations of method B* given in Fig. 5 for low frequency drop in MTF (⫺7%, squared兲 as well as the values of method C for low frequency drop in MTF (⫺7%, squared兲 and difference in ideal SNR2 (⫺3%, linear兲. The result is shown in Fig. 7. Except for the values at a spatial frequency of 3 mm⫺1 , where the DQE has already fallen off to about 0.1, the deviations from the mean are now within a band of approximately ⫾5%, compared to ⫾15% before the correction. In conclusion, we have shown that different, established evaluation routines may lead to differences in the determined DQE of up to 30%, even when the same image data are used. The main reasons for disagreement can be found in the treatment of a possible low frequency drop of the MTF and the handling of signal offsets in nominally linear data. In particular, for methods using normalized noise images an appropriate correction for possible signal offsets is necessary to obtain correct DQE values at low exposure levels. Such offsets may be deliberately introduced during image preprocessing to avoid negative pixel values due to noise. In the case considered here taking into account these factors lead to a reduction of variability by a factor of three. It is expected that the recently published standard on DQE determination will be of help in the process of unifying the applied methods and
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