Nuclear Instruments and Methods in Physics Research A 582 (2007) 621–628

The measurement of the presampled MTF of a high spatialresolution neutron imaging system

Raymond Lei. Cao!, Steven R. Biegalski

Nuclear Engineering Teaching Lab, The University of Texas at Austin, Austin, TX, USA

Received 16 February 2007; received in revised form 1 July 2007; accepted 21 August 2007Available online 31 August 2007

Abstract

A high spatial resolution neutron imaging device was developed at the Mark II TRIGA reactor at The University of Texas at Austin.As the modulation transfer function (MTF) is recognized as a well-established parameter for evaluation of imaging system resolution, thealiasing associated with digital sampling adds complexity to its measurement. Aliasing is especially problematic when using a high spatialresolution micro-channel plate (MCP) neutron detector that has a pixel grid size similar to that of a CCD array. To compensate for thealiasing an angulated edge method was used to evaluate the neutron imaging facility, overcoming aliasing by obtaining an oversamplededge spread function (ESF). Baseline correction was applied to the ESF to remove the noticeable trends and the LSF was multiplied byHann window to obtain a smoothed version of presampled MTF. The computing procedure is confirmed by visual inspection of a testingphantom; in addition, it is confirmed by comparison to the MTF measurement of a scintillation screen with a known MTF curve.r 2007 Elsevier B.V. All rights reserved.

PACS: 29.40.Gx

Keywords: Spatial resolution; Presampled MTF; Edge method; MCP neutron detector; Neutron imaging

1. Introduction

Describing detector resolution with a numeric value suchas the full-width-half-maximum (FWHM) of the LSF isinsufficient for conveying the imaging system signaltransfer ability. As it derives from the linear system theory,the modulation transfer function (MTF) is a betterapproach [1,2]; it is defined as the ratio of outputmodulation to an input sinusoidal modulation with varyingfrequency. After first being applied to medical imagingscience by Rossmann [3] in 1964, the MTF has evolved intoa well-established metric to characterize resolution perfor-mance of X-ray radiography systems [4–6]. It has also beenadopted by the neutron radiography community [7,8] dueto the underlying similar principle. The most commonly

deployed technique to measure MTF is the edge method[9,10], in which an X-ray opaque object with sharp edge isimaged and the edge-spread function (ESF) is obtained byscanning across the edge image. The LSF is the differentia-tion of the ESF and the MTF and is simply calculatedby Fourier transformation. For neutron radiography, amaterial opaque to the transmission of neutrons should beused such as cadmium or gadolinium.The problem associated with digital radiography is that

of the aliasing arising from digital sampling, regardless ofwhat illuminating source is being used. The aliasing mayoccur in both the spatial domain (in the form of a Moirepattern) and the frequency domain (in the form ofspectrum overlapping). Although rare in the spatialdomain, aliasing is often observed in the frequency domainwhen, in the measurement of the MTF, the Nyquistfrequency is not high enough to cover the highest spatialfrequency to be determined. To counter this problem,investigators in X-ray radiography often tilt the edge of theobject by a small angle with respect to the pixel array inorder to obtain the oversampled ESF. This generates a

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!Corresponding author. Nuclear Method Team, Analytical ChemistryDivision, National Institute of Standards and Technology, 100 BureauDrive, Stop 8395, Gaithersburg, MD 20878, USA. Tel.: +1 301 975 8862;fax: +1301 208 9279.

E-mail addresses: rcao@nist.gov, rayfromeast@yahoo.com(R.L. Cao).

presampled MTF that may also be called the non-aliasedMTF [11–13].

This procedure has not been practiced in the field ofneutron radiography. While aliasing does exist in neutronradiography, historically, it has not been significant due tothe fact that the neutron converters generally possess arelatively low-resolution performance in comparison to theimaging camera. For example, in the case of the mostpopular neutron image detector combination, which is thescintillation screen and the CCD camera [14], thecommercial CCD array size is small enough even withlow magnification (i.e. high field-of-view) to ensure arobust number of data samples over the course of theneutron detector’s operation with its relatively low resolu-tion in the range of 100 mm. Thus the shape of the ESF orthe LSF may be faithfully represented via digital sampling(It has to mention that the imaging plate poses higherresolution with readout laser spot as small as 12.5 mm [15],but it is an off-line imaging method and CCD camera is notused as the digital sampling device). We have developed ahigh spatial resolution neutron system by using a micro-channel plate (MCP) neutron detector [16] with instinctresolution of 11.4 mm. In such a case, the CCD camerawould not sample the detector’s pixels array with enoughdata. When working in this range, aliased MTF is prone tooccur. To compensate for aliasing the angulation technique[17] is used to obtain an oversampled ESF. A series ofdigital signal processing techniques are then applied to theissue of the relatively noisy ESF in order to be able tocalculate a smoothed version of presampled MTF.

2. Neutron imaging device

The principle of MCP neuron detector is illustrated byFeller and co-workers [18], as shown in Fig. 1. The incidentneutron would be captured inside the thin glass wall by thenuclear reaction, 10B(n,a)7Li. The heavy reaction products,

a and 7Li, will escape into the adjacent channel and strikeout a large number of secondary electrons. The magnifiedsignals are registered by a phosphor layer with thicknessless than 10 mm on the other side of the detector to producean image. The diameter of the detection area of this tube is2.54 cm. The channel diameter and the pitch between twochannels are 8.7 and 11.4 mm, respectively. This defines thetheoretical maximum spatial resolution that can beachieved by this tube. The MCP thickness is typically0.6mm and is coupled within 100–200 mm of the phosphorscreen. The optimal high voltage applied to this MCP andthe phosphor screen is 1.7 and 4.0 kV, respectively.Two CCD cameras were chosen to be integrated into the

system. One is named ColdBlue from the Perkin-Elmeroptoelectronics and the other is the Astrocam made byCambridge, UK. The specifications of the two cameras arelisted in Table 1. The front illuminated chip used in theColdBlue model offers a high-resolution pixel array with-out sacrificing too much quantum efficiency due to themicro lens technique used in the chip.A schematic drawing and the photos of the imaging

system are shown in Fig. 2. The optical chain includes afront surface mirror and macro lens. A remote controlledstepper motor is also integrated into the system to provideon-line focusing capability. All components are assembledinto an aluminum light-tight box with heavy shielding toprotect the camera as well as to provide dark workingconditions. The box can be covered with a 0.32-cm-thickaluminum-made lip for light tightness, which is removed inthe picture to show the inner structure. As it can be seen,more than a dozen of holes are drilled near CCD for airventilation, while the unwanted light introduced by theseholes are blocked by a snuggly fitted aluminum plate aswell as gamma, neutron shielding material standing in themiddle of the box. All edges that are suspicious of lightleakage are sealed with aluminum tape.

3. Phantom

The edge object used for measuring the MTF for thisneutron radiography system is constructed of 0.22-mm-thick gadolinium foil having a precision-polished edge.To test the system performance visually, a 1-mm-thickcadmium strip is utilized with a sharp polished edge intowhich five holes with diameters of approximately0.6–0.8mm are drilled. The spacing between the holes isminimized to the smallest possible extent, giving a spacingwidth in the range of 60–80 mm.

4. Experiment and visual inspection

The light-tight box is placed on a workbench inside thebeam cave, with the distance to the reactor wall set atapproximately 1.5m, giving an L/D ratio approximatelyequal to 150. Three different combines of neutron detectorsand CCD cameras were tested with working parametersas shown in Table 2. The combinations of MCP with

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Fig. 1. The principle of neutron detection by MCP detector.

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ColdBlue camera gives the best resolution to be character-ized by presampled MTF. The sample–detector distance is8.3mm for this case. A vision comparison of imagingperformance is given by using the MCP with Astrocam andColdBlue CCD. The combines of AST’s screen withColdBlue will be used to validate the calculation procedurefor presampled MTF.

The images of the test object produced by MCP/CCDcombines are shown in Fig. 3. The 80 mm space separatingholes is discernable in the magnified view by using MCPwith Astrocam CCD; the same holes are easily distin-guished by using MCP with ColdBlue CCD suggesting themaximum resolving distance of this imaging device is atabout 30 mm in terms of pixel size.

5. Angulation techniques

Fig. 4 illustrates the angulation method and is similar tothe explanation provided by Kawashita et al. [17]. The edgeobject is tilted to an angle a with respect to the pixel arrayalignment. Thus, N steps moving in the vertical directionare equal to one step moving in the horizontal direction interms of intensity variation. N is calculated as N ! round(1/tan(a)).An oversampled ESF is obtained in the following

manner: starting from row number one, take the first datapoint in this row to produce the first data point in theoversampled ESF, as shown in Fig. 4(c); then take the firstdata point in the second row for the second data of the ESF

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Table 1The specifications of CCD cameras

CCD Format (pixels) Pixels size (mm) Dynamic range (bits) Cooling Quantum efficiency Dark current

Astrocam 512" 512 24" 24 16 LN cooled to #1001 90% for green light o1 e#/pixel/h (#130 1C)ColdBlue 2184(h)" 1472(v) 6.8" 6.8 16 TE air cooled to #301 75% for green light 0.015 e#/pixel/s (#35 1C)

Fig. 2. (a) A schematic drawing of the designed system. (b) Real world photo of the top viewing of light-tight box; some shielding material were removedto show the inside structure. (c) Real world photo of the whole imaging system; the dimension of light-tight box is 88 cm (long)" 31 cm (wide)" 31 cm(high); the position of the MCP detector is about 1.5m to the reactor shielding wall. The light-tight box is covered with a 0.32-cm-thick aluminum-madelip, which was removed to make inner structure visible in this picture.

Table 2Working parameters for different combinations of detector with camera

Neutron detector Scintillation screen (AST’s NDg type) MCP neutron detector

CCD Camera TE cooled CCD (ColdBlue) TE cooled CCD (ColdBlue) LN cooled CCD (Astrocam)Lens Nikon 200mm F/4 macro Nikon 200mm F/4 macro Tamron 90mm F/2.8 plux 2x TCEffective pixel size (mm) 22.4 16.8 72.5Field of view (diameter, cm) 2.54 2.54 2.54Typical exposure time (s) 10min 10–30 s 10–30 s

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Fig. 3. Visual inspection of image of cadmium strip drilled with hole pattern. The top pictures are obtained by Astrocam CCD with MCP, the bottompictures are obtained by ColdBlue CCD with MCP, (a) and (d) are same cadmium strip, (b) and (e) are magnified view of hole region, and (c) and(f) are magnified view of the space, which is approximately 80mm.

Fig. 4. Illustration of sampling an angled edge to achieve an oversampled ESF. (a) An titled edge; (b) five edge profiles; (c) one oversampled ESF.

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and continue sampling accordingly until the fifth row.Then go back to the first row, taking the second data pointfor the sixth data point of the ESF, and repeat the process.In this way, an oversampled ESF may be produced withthe sampling space reduced by a factor of five.

6. The computation of the presampled MTF

The four main steps to compute the presampled MTFare shown in Fig. 5. In the first step, a relatively uniformedge block size of 5mm" 5mm is extracted from the edgeimage and the flat-field image. The median filter is appliedto both images to remove a number of large amplitudenoise impulses, also called white spots, presenting in theimage due to random radiation background. The windowof median filter is 3" 3 pixels and therefore the sharpnessof edge will not be compromised. The edge image is thendivided by the flat-field image to eliminate the inhomoge-neous that might caused by the beam impurity and thedetector non-uniform response. The normalized edge blockis shown in Fig. 6.

The second step is to calculate the angle of the edgeprofile needed for sampling oversampled ESF. The angle ofthe edge is found by applying a Hough transform [19],which requires a binary line image as input. Therefore, theCanny method [20] is used to calculate the binary imagefrom the above normalized edge image. Fig. 7 shows thebinary line image determined by the Canny method andthe Hough spectrum. The x-axis of the peak point in theHough spectrum indicates a 20.721 line angle in thisparticular experimental setup. Therefore, the number of

rows (N) needed to be combined into one oversampled ESFis determined to be equal to three.In the third step, an oversampled ESF is produced by

combining N rows following the method described above.About 40 such obtained oversampled ESFs are thenaveraged together. All of these ESFs are non-overlappingand are kept in the same edge position by lateral shifting ofthe center point, which is determined in the binary lineimage. The final oversampled ESF is shown in Fig. 8.The ESF is differentiated to produce the LSF in the

fourth step. Baseline correction [21] is necessary for theLSF because of noticeable step/trends in the ESF, whichwill introduce a low-frequency drop at the MTF curve if nosuch correction is applied. This second step might becaused by transmitted light reflected back from other endof the mirror. Briefly, the LSF is divided into three partswith the central peak area located in the middle part. A onedimension medial filter with varying window size is appliedto all the three parts. Then a fourth-order polynomial fit isapplied to the smoothed LSF for calculating the baseline,as shown in Fig. 9. The extent of correction is controlled bythe window size of the medial filter.In order to exclude the noise in the data not associated

with the edge transient and at the same time to suppress theside lobes, a modified Hann window [22] is applied toeliminate those noises occurring in the front and the rearpart of the LSF, as shown in Fig. 10.Finally, the presampled MTF is computed by the FFT of

the LSF and its value is normalized to unity at zero spatialfrequency. The frequency axis is also corrected for thesampling scaling error of 1/cos(a) caused by the slantededge. The resulting presampled MTF is shown in Fig. 11 asa smoothed dotted line. The same calculation is alsoapplied to the LSF without applying the Hann window,and the results are shown as the cross-marked curve in thesame figure. It can be seen that the zero setting of the LSFwith the Hann window effectively eliminates the noise notassociated with the edge transition. The smoothed versionof the presampled MTF is therefore obtained withoutcurve fitting of either the ESF or the LSF, which doesrequire some prior knowledge of the imaging system. Thefinal achieved resolution of this device by using ColdBlueCCD with MCP neutron detector at current neutronsource condition is indicated by the obtained presampledMTF, and the spatial frequency at 50%, 10% and 3% ofMTF are at about 6.5, 13 and 16.5 cycles/mm, respectively.

7. Verification

The MTF of the same neutron imaging system withscintillation screen/CCD camera combination is alsomeasured following the above procedures and the resultis shown in Fig. 12(b). Note that Fig. 12(a) is the curveprovided by the manufacturer. Both curves have approxi-mately the same spatial frequency when MTF drops to80%, 50% and 20%, which validates the MTF measure-ment applied in this work.

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Fig. 5. Flow chart to calculate the presampled MTF.

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8. Conclusion and discussion

A procedure is developed using an angulation techniqueto obtain a presampled MTF curve for a high-resolutionneutron imaging system using an MCP neutron detector.Despite the noisy ESF, a smoothed version of MTF isobtained by applying averaging, base-line correctionprocedure and the zero setting of the irrelevant part ofthe LSF with a modified Hann window. As indicated bythe obtained presampled MTF, the spatial frequency at

50%, 10% and 3% of MTF by using ColdBlue CCDwith MCP neutron detector are at about 6.5, 13 and16.5 cycles/mm, respectively. The overall error consistPoison statistics of the incident flux, imprecisely alignedpixels array, uncertainty of determined edge angle andother independent source introduced at the calculationstep. For example, with the 0.021 uncertainty in edge angle,the maximum of difference in the oversampling intervalwould be 0.0053mm, the overall estimated uncertainly ofMTF at 50% is less than 5%.

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Fig. 6. (a) Edge image, (b) flat-field image, and (c) a patch of edge image extracted from the normalized image.

Fig. 7. Binary line image (left) and the Hough spectrum (right). The peak point of Hough spectrum indicates the line parameter; x-axis is the line angle.

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The experimental imaging a cadmium strip suggests amaximum resolving space in terms of pixels size is about30 mm. However, with L/D ratio of 150 the inherit 8.3mmdistance inside MCP along will contribute 55 mm geometricblur, the discrepancy might be interpreted by the estimatedL/D ratio reflecting only large area averaged L/D value,which does not necessarily represents the true beam

divergence effect at small detection area. This suggeststhat the current neutron beam facility needs to beoptimized in order to give higher quality of neutronradiography image. It is interesting to note that aliasing inthe spatial domain might be possible in this MCP/CCDcombination since they both have pixels of a similar size.However, this would bring up issues regarding the blurringcaused by using the phosphor as a readout device locatedat the back of the MCP. The MCP phosphor screenblurring will be useful as an anti-aliasing mechanism, alongwith other degradation factors in the imaging chain.

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Fig. 8. ESF.

Fig. 9. Illustration of LSF after baseline correction: top is the LSF and thesmoothed trend line, the middle is the LSF and baseline fitted by a fourth-order polynomial, and the bottom is the LSF after baseline correction.

Fig. 10. LSF: Hann window and the LSF after applying Hann window.

Fig. 11. MTFs: the dotted line is the MTF after applying the Hannwindow, and the cross-marked curve is the MTF without applying theHann window.

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Acknowledgments

The authors would like to thank Dr. Rodney Padgettand Dr. Craig Mackay for their comments on the spatialresolution and the valuable information from Bruce Fellerat NOVA scientific.

This work is supported by Department of Energy INIEprogram.

References

[1] J.D. Gaskill, Linear System, Fourier Transforms, and Optics, Wiley,New York, 1978.

[2] C.E. Metz, K. Doi, Phys. Med. Biol. 24 (6) (1979) 1079.[3] K. Rossmann, Phys. Med. Biol. 9 (4) (1964) 551.[4] H. Harrison, W.S. Barrett, Radiological Imaging—The Theory

of Imaging Formation, Detection, and Processing, Academic press,New York, 1981.

[5] IEC, IEC 62220-1 2003 Medical Electrical Equipment-Characteristicsof Digital X-ray Imaging Devices—Part 1: Determination of theDetective Quantum Efficiency, Newark, NY, 2003.

[6] T. Dobbins, in: H.L. Kundel, J. Beutel, R.L. Van Metter (Eds.),Handbook of Medical Imaging, Physics and Psychophysics, vol. 1,SPIE Press, Bellingham, 2000, p. 949.

[7] D.S. Hussey, et al., Nucl. Instr. and Meth. A 542 (1–3) (2005) 9.[8] J. Brunner, et al., Nucl. Instr. and Meth. A 542 (1–3) (2005) 123.

[9] I.A. Cunningham, B.K. Reid, Med. Phys. 19 (4) (1992) 1037.[10] S. Ehsan, J.F. Michael, A.R. David, AAPM (1998) 102.[11] H. Fujita, et al., IEEE Trans. Med. Imaging 11 (1) (1992) 34.[12] E. Samei, E. Buhr, P. Granfors, D. Vandenbroucke, X. Wang, Phys.

Med. Biol. 50 (2005) 3613.[13] R. Padgett, C.J. Kotre, Radiat. Prot. Dosimetry 117 (1–3) (2005) 283.[14] S. Koerner, E. Lehmann, P. Vontobel, Nucl. Instr. and Meth. A 454

(1) (2000) 158.[15] Imaging Plate (2007) Cited. Available from: /http://www.duerr.de/

eng/50_3628.aspxS.[16] W.B. Feller, R.G. Downing, P.L. White, Neutron field imaging with

microchannel plates, in: Proceedings of the Hard X-ray Gamma-Rayand Neutron Detector Physics II, SPIE, San Diego, CA, USA,2000.

[17] I. Kawashita, K. Maeda, H. Arimura, K. Morikawa, T. Ishida,Devlopment of an automated method for evaluation of sharpness ofdigital radiographys using edge method, in: Proceedings of theMedical Imaging 2001: Physics of Medical Imaging, SPIE, 2001.

[18] A.S. Tremsin, W.B. Feller, R.G. Downing, Nucl. Instr. and Meth.A 539 (1–2) (2005) 278.

[19] V.F. Leavers, CVGIP: Image Underst. 58 (2) (1993) 250.[20] J. Canny, IEEE Trans. Pattern Anal. Mach. Intell. 8 (1986) 679.[21] B. Williams, A. Crecelius, S. Cornett, R. Caprioli, B. Dawant,

B. Bodenheimer, Baseline correction of MALDI mass spectrometryimaging, in: Proceedings of the ACM 43rd Annual SoutheastConference, Kennesaw, Georgia, 2005.

[22] J.R.S. Saunders, E. Samei, Med. Phys. 33 (2) (2006) 308.

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Fig. 12. Comparison of the factory suggested (a) MTF curve of an AST scintillation screen with (b) the measured MTF curve of screens/CCDcombination in this study.

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