An improved method for flat-field correction of flat panel x-ray detectorAlexander L. C. Kwan, J. Anthony Seibert, and John M. Boone Citation: Medical Physics 33, 391 (2006); doi: 10.1118/1.2163388 View online: http://dx.doi.org/10.1118/1.2163388 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/33/2?ver=pdfcov Published by the American Association of Physicists in Medicine

An improved method for flat-field correction of flat panel x-ray detectorAlexander L. C. Kwan and J. Anthony SeibertDepartment of Radiology, U.C. Davis Medical Center, X-Ray Imaging Laboratory, 4701 X Street,Sacramento, California 95817

John M. Boonea�

Department of Radiology, U.C. Davis Medical Center, X-ray Imaging Laboratory, 4701 X Street,Sacramento, California 95817, and Department of Biomedical Engineering, University of California, Davis,California 95616

�Received 16 December 2004; accepted for publication 8 December 2005; published 24 January 2006�

In this Technical Note, the effects of different flat-field techniques are examined for a cesium iodideflat panel detector, which exhibited a slightly nonlinear exposure response. The results indicate thatthe variable flat-field correction method with the appropriate polynomial fit provides excellentcorrection throughout the entire exposure range. The averaged normalized variation factor, used toassess the nonuniformity of the flat-field correction, decreased from 30.76 for the fixed correctionmethod to 4.13 for the variable flat-field correction method with a fourth-order polynomial fit forthe 60 kVp spectrum, and from 16.42 to 3.97 for the 95 kVp spectrum. © 2006 American Asso-

ciation of Physicists in Medicine. �DOI: 10.1118/1.2163388�

The variation in exposure response of individual detectorelements on a modern pixelated x-ray detector system re-quires that dark-field �offset� and flat-field �gain� correctionsbe made.1,2 The offset correction is used to account for thedark current effects, while the gain correction is used to cor-rect for the nonuniform response of individual pixels and/orgroups of pixels whose output is processed by differentsingle application specific integrated circuits �ASICs�. Theconventional method to correct a raw image �I� is

CE��x,y� = gE

IE�,t2�x,y� − Bt2

�x,y�

GE,t1�x,y� − Bt1

�x,y�, �1�

where C is the corrected image, B is the averaged offsetimage, G is the averaged gain image, and g is the mean �ormedian� pixel value of G. The subscript E denotes the inci-dent exposure, while the subscripts t1 and t2 indicate thetimes at which the image sets are obtained. Last, the primeon the subscript E implies that the raw and gain images maybe acquired at a different exposure level �but at the sametube voltage�.

The typical implementation of Eq. �1� is to acquire thegain images at a constant �fixed� exposure level, and then usethe averaged gain image for all subsequent corrections forthe given tube potential. Images corrected using this proce-dure will be referred to as the “fixed gain” correction methodhere. An alternative way is to acquire the gain image at thesame exposure level as the raw image; thus requiring a num-ber of gain images to be obtained. This method is referred toas the “exact gain” correction method, and will be used asthe gold standard in this study.

In 1998, Seibert et al.3 proposed a different flat-field cor-rection technique for pixelated x-ray detector systems. Thismethod utilizes a number of averaged gain images acquiredat different exposure levels, spanning the dynamic range ofthe detector from very low levels to near saturation. Thepixel values at these exposures were then fitted with a linear

function on a pixel-by-pixel basis, with the individual pixel

391 Med. Phys. 33 „2…, February 2006 0094-2405/2006/33

values �after offset correction� used as the dependent vari-able. This approach will be referred to as the “variable flat-field” �VFF� correction method.

All the correction methods described so far implicitly as-sume a strictly linear characteristic of the detector. Whilemost flat-panel detectors have reasonably linear responsesthroughout the exposure region of interest, slight nonlineari-ties often exist. To address this problem, second- �n=2� andfourth-order �n=4� polynomial fits were examined and com-pared to the linear approaches. The polynomial fit constantsfor each pixel were stored in a multidimensional matrix, withx and y being the detector matrix and the third dimensionbeing the polynomial order �n� plus one. Once this matrixwas calculated, it was used to flat-field the image directly,

CVFF�x,y� = K��j=0

n

Aj�x,y��I�x,y� − B�x,y�� j� , �2�

where CVFF is the corrected image, Aj is the jth power poly-nomial constant, I is the raw image, and B is the averagedoffset image. The values computed inside the large parenthe-ses on the right-hand-side of Eq. �2� were the exposure val-ues, which usually were very small. Therefore, the constantK was used to scale the corrected images to the original14 bit gray scale range to reduce potential roundoff error.

The images for this study were acquired using a dedicatedbreast CT scanner4 designed and fabricated in our institutionusing several “off-the-shelf” components. These included anindustrial tungsten target x-ray tube with 0.4 mm focal spot�Comet AG, Flamatt, Switzerland� and a 14 bit 40�30 cmCsI �cesium iodide� flat panel detector �PaxScan 4030A,Varian Medical Systems, Salt Lake City, UT�. The panelused was a prototype operated in the 2�2 binning mode,with a post-binned matrix size of 1024�768 pixels andpost-binned pixel size of 0.388 mm. The electrical gain ofthe panel was set to unity, with the frame rate fixed to

30 frames per second.

391„2…/391/3/$23.00 © 2006 Am. Assoc. Phys. Med.

392 Kwan, Seibert, and Boone: Flat-field methods for flat panel detectors 392

Images at two different tube voltages �60 and 95 kVp�were acquired at 13 different tube currents �0.5–6.5 mA at0.5 mA steps� for a total of 26 different exposure settings. Inorder to acquire the images at the higher exposures withoutsaturation, 0.3 and 1.7 mm of additional Cu filtration wasadded to the 60 and 95 kVp spectra, with the HVL measuredto be 4.2 and 10.5 mm of aluminum, respectively. An ionchamber �Model 10�5−6� coupled to a dosimeter �Model9010, Radcal Corporation, Monrovia, CA� was placed at theedge of the field and 20 cm in front of the panel to measurethe exposures, with the readings corrected back to the detec-tor plane using the inverse square law. The source-to-detector distance was 78 cm. Table I provides a summary ofthe techniques used in this study.

The gain images were acquired for the same 26 settings�2 kVps and 13 mA levels�. One thousand images were ob-tained at each combination of tube voltage and current. Byvarying the number of images averaged, comparisons be-tween the different flat-field techniques at nearly constanttotal exposure levels could be made. One set of 100 offsetimages was also obtained before each of the gain image se-ries, and was used for all the different flat-field corrections.For these �and subsequent� images, the temporal lag5 has notbeen accounted for. This was because while the images wereacquired in a CT scanner, they were stationary images. Thus,the lag correction should reduce to a constant on a pixel-by-pixel basis, provided that one allowed the lag to reach steadystate.

For the fixed gain correction method, the gain image wasacquired at 3.5 mA, the middle of the dynamic range, corre-sponding to an incident exposure of 48.4 and 25.7 �C/kg at

TABLE I. A summary of the exposures and other experonly the number of images listed at the particular exthe images listed in the VFF column are used for the

60 kVp 95 kVp

Added Cufiltration 0.3 mm 1.7 mm

HVL�mm of Al� 4.2 10.5

Tube current�mA�

Exposure��C/kg�

Exposure��C/kg�

0.5 5.4 2.61.0 12.7 6.41.5 19.8 10.42.0 27.0 14.12.5 34.1 18.03.0 41.3 21.73.5 48.4 25.74.0 55.5 29.44.5 62.6 33.45.0 69.5 37.15.5 77.2 40.76.0 84.0 44.86.5 91.5 48.5

the detector for the 60 and 95 tube voltage, respectively.

Medical Physics, Vol. 33, No. 2, February 2006

These two gain images �G� were computed by averaging 100images. For the exact gain method, the number of imagesused was adjusted such that the total exposure at each settingwas almost equal to the fixed gain image �up to 1000 images,the maximum number of images acquired�. This was neces-sary to demonstrate that improved performance was not dueto simple quantum statistics. A summary of the number ofimages used is also listed in Table I.

For this study, the VFF gain images were acquired at 0.5,1.5, 2.5, 3.5, 4.5, 5.5, and 6.5 mA. To generate the samequantum noise as the fixed gain method, the total exposurefor the 100 images acquired at 3.5 mA was computed using

FIG. 1. A plot of the normalized variation factors for the four differentcorrection methods for the 60 kVp spectrum. The normalized variation fac-tors were equal to one for the exact gain correction method at all exposures,

tal parameters utilized in this study. Notice that whilee setting is used for the exact correction method, all

correction.

60 kVp 95 kVp

Number of images averaged forvarious correction methods

�Exposure is equivalent to 100images for the fixed gain method�

xact VFF Exact VFF

1000 127 1000 142381 0 400 0244 34 247 35179 0 181 0141 20 142 20116 0 118 0100 14 100 14

87 0 87 077 11 76 1069 0 69 062 8 63 957 0 57 052 7 52 7

imenposur

VFF

E

and were not shown to minimize the complexity of the figures.

393 Kwan, Seibert, and Boone: Flat-field methods for flat panel detectors 393

data from Table I. This total exposure was divided by seven�seven data points�, and then by the exposure at the specifictube current to estimate the number of images required. Fi-nally, the number of images was rounded down to the nearestinteger. A summary of the number of images used is alsoincluded in Table I.

To quantify the nonuniformity in the corrected images forthe different methods, eight regions of interest �ROIs� wereselected from the top middle part of each image. Each ofthese ROIs was 50 pixels in width �x direction� by370 pixels in height �y direction�, or seven pixels within eachside of the subsection of the panel controlled by a singleASIC. The mean pixel values of these ROIs were obtainedfrom 13 images, for a total of 104 means. The variationfactor �VF� was calculated as

VF =�C

C, �3�

where �C and C are the standard deviation and the average ofthose mean pixel values, respectively. Ideally, one would ex-pect the VF values to be zero for a uniform image, andincrease as the nonuniformity between the different subsec-tions of the panel increases. However, quantum noise in theimage could affect the VF values slightly, leading to a non-zero value for a uniform image. To account for this, the VFvalues for each correction factor was normalized by the VFvalues of the exact gain corrected image,

VFn,k =VFk

VFExact. �4�

Here the subscript n represents the normalized value whilethe subscript k refers to the different correction methods. TheVFn,k metric was designed to reduce the influence of thequantum noise so that the various flat-field correction meth-ods could be evaluated independently.

The VF results are illustrated in Fig. 1 for the 60 kVpspectrum. From Fig. 1, the fixed gain correction method per-forms best at 48.4 �C/kg. This is because that is the expo-sure where the gain image was acquired for the fixed gaincorrection method. As one moves away from this exposure,the VF values for the fixed gain method increase, droppingonly near the end of the exposure range. For the first- andsecond-order polynomial VFF results, they generally outper-form the fixed gain method in the higher exposure region,but are inferior to the fixed gain method at the middle of theexposure range. For the lower exposure region, the fixed andthe first- and second-order polynomial VFF results areroughly the same. The fourth-order polynomial fit VFF re-sults outperform the fixed gain method across the entire ex-posure range, except at 48.4 �C/kg. The averaged VF values

Medical Physics, Vol. 33, No. 2, February 2006

for the fixed, VFFn=1, VFFn=2, and VFFn=4 correction meth-ods are 30.76, 16.66, 9.49, and 4.13, respectively. These re-sults suggested that the VFFn=4 produces more uniform im-ages over most of the exposure range. Similar results areobserved for the 95 kVp spectrum, with the averaged VFvalues being 16.42, 12.49, 8.33, and 3.97, respectively.

While the VFF correction method is a robust approach toflat field across the exposure differences in a typical x-rayimage, the current method does not take into account theeffect of beam hardening. Another precaution when using theVFF approach is to ensure that the range of calibration im-ages matches the range of exposure in the raw images. Thisis because extrapolation with polynomial functions oftenleads to anomalous results. The order of the fitting polyno-mial should also match the response of the detector whenusing the VFF correction method, as higher-order polynomi-als may lead to inaccuracies within the limits of the cali-brated exposure range. This is illustrated in Fig. 1, where theVF values for the image corrected using the VFFn=4 methodincreases at the lower exposure range.

For clinical applications, the image exposure varies spa-tially due to the attenuation characteristics of the object be-ing imaged �due to subject contrast�. Thus, in any singleimage, the entire range of exposure levels can potentially beutilized. Consequently, the variable flat-field correctionmethod may best accommodate the flat-field conditions ofrealistic imaging. This technique is of particular value forcone-beam CT applications that use a flat-panel detector,since nonuniformities in the projection images often lead toring artifacts in the reconstructed images.

This research was supported by grants from the CaliforniaBreast Cancer Research Program �Grant No. 7EB-0075�, theNational Cancer Institute �Grant No. CA-89260�, and theNational Institute for Biomedical Imaging and Bioengineer-ing �Grant No. EB-002138�.

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2J. P. Moy and B. Bosset, “How does real offset and gain correction affectthe DQE in images from x-ray flat detectors,” Proc. SPIE 3659, 90–97�1999�.

3J. A. Seibert, J. M. Boone, and K. K. Lindfors, “Flat-field correctiontechnique for digital detectors,” Proc. SPIE 3336, 348–354 �1998�.

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