The modulation transfer function (MTF) of an x-raydetector characterizes the spatial frequency responseof an imaging system, from which resolution metricsare commonly derived in radiography and spectro-scopy. In x-ray imaging systems, resolution test pat-terns are routinely used for determining MTF, butthe results can be affected by the penetration of en-ergetic x rays through the test pattern. When deter-mining the MFT using high-resolution test patternswith 10 line pairs per mm or higher, the widths of theopen spaces and bars are often comparable to thethickness of the test pattern and to the x-ray pene-
tration depth, resulting in artificially low contrastand MTF.
In this paper, we discuss techniques for correctingfor the x-ray transmittance of the resolution test pat-tern. Using a laboratory x-ray source with a tungstenanode, spectrally dispersed images of a resolutiontest pattern were recorded by an x-ray spectrometer.The images were recorded on two types of photosti-mulable images plates. After correcting for the trans-mittance of the resolution test pattern, the imageplate MFT was determined and convolved with theslit function of the image plate scanner. The resultingpoint spread functions (PSFs) of the image plate andscanner combinations were in good agreement withthe observed widths and shapes of the W spectrallines and with the PSF determined from the edgespread function across the bars of the resolution testpattern.
The developed techniques can be used to indepen-dently determine the MTF of image plates and scan-ners. This enables the selection of image plate andscanner combinations giving the optimum spatial re-solution for applications such as x-ray spectroscopyand radiography in the >10keV energy range.
2. Resolution Test Pattern
The commercial resolution test pattern consisted ofgroups of four open linear channels machined intoa 50 μm thick Pb plate. The Pb plate was enclosedin a protective plastic case with 2:1mm total thick-ness. For each group of four open channels, the chan-nels were separated by Pb bars that had a widthequal to the channel width. Each open channeland adjacent bar (of equal widths) constituted a linepair, and the number of line pairs per mm (LP=mm)varied from 0:25LP=mm to 10LP=mm. Thus the10LP=mm group consisted of four pairs of channelsand bars, and each channel and bar was 50 μm wide.Shown in Fig. 1 are the calculated transmittances
of the 50 μm thick Pb bars and the 2:1mm plastic(CH) case. Over the 10keV to 50keV energy rangeconsidered here, the Pb bars are opaque at the lowerenergies and become transmissive at the higherenergies. The plastic case has small but significantabsorptance over the entire energy range. Thus cor-rections must be applied to the resolution test datafor all energies in the 10keV to 50keV range.It is possible to thicken a resolution test pattern to
mitigate the transmittance issues. However, then thethickness can become much larger than the openchannel width, and vignetting in the long channelscan occur. An alternative is to record the contrastacross a sharp edge cut into a thick plate, and thistechnique is discussed in Section 4.The line pair test pattern was placed in contact
with an image plate and was illuminated by the x-ray spectrum dispersed by a transmission crystalspectrometer. A schematic of the spectrometer isshown in Fig. 2, and detailed descriptions of this highenergy x-ray spectrometer (HXS) and its spectral re-solving power are given in Refs. [1–3]. This type of
spectrometer was originally developed by Cauchois[4] and was optimized for the characterization ofmedical x-ray sources by Deslattes and coworkers[5–7].
X rays are incident on the convex side of a cylindri-cally bent crystal, are diffracted through a slit, andare recorded by an image plate placed on the Row-land circle. Two spectra are produced on either sideof the spectrometer central axis with energy increas-ing toward the axis. A pinhole on the spectrometeraxis produces an image of the source. Metal filterslocated at the slit provide K absorption edges inthe continuum spectra for in situ calibration of thex-ray energy scale.
With these metal filters removed, the resolutiontest pattern was placed in contact with the imageplate with the open spaces and bars of the test pat-tern oriented in the vertical direction, perpendicularto the spectrometer dispersion direction. Thus thevarious line pairs were illuminated by x rays withdifferent energies.
In general, x-ray energy absorbed in the BaFBrI :Euþ2 image plate phosphor, with typical thickness inthe range 100 μm to 200 μm, forms a latent image(trapped electron–hole pairs) that is stimulated andread out by a scanning laser beamwith focal spot sizein the 50 μm to 100 μm range. The spatial resolutionachieved in the scanned digital image depends on anumber of factors including the phosphor thickness,scattering and spreading in the phosphor and protec-tive layers of the image plate, the laser beam spotsize, the visible light imaging optics, and the scanstep size [8,9]. In this work, the x-ray spectral imageswere recorded on Fuji Superior Resolution (SR) orMaximum Sensitivity (MS) photostimulable phos-phor image plates and were scanned by a LogosDCR810 scanner with 42:3 μm steps. The imageplates were scanned within 10 minutes of x-ray ex-posure to minimize the fading of the latent imagewith time [8].
A portion of the digital image was summed in thevertical (column) direction, perpendicular to the dis-persion direction and along the line pairs, and theresult is a lineout of the spectrum as a function of
Fig. 1. Transmittances of the resolution test pattern’s 50 μmthick Pb bars and the 2:1mm thick plastic (CH) case. Fig. 2. Schematic of the x-ray spectrometer.
the distance from the spectrometer axis. An energyscale was applied based on the energies of the ab-sorption edges of the metal filters, the transition en-ergies of the W spectral lines, and the spectrometergeometry [3].The x-ray spectral image recorded on a Fuji SR im-
age plate without the test pattern is shown in Fig. 3.Identified are the WKα and Lγ spectral lines. Thespectrum is enhanced at energies above the phos-phor’s Ba K absorption edge. The continuum spectraon the left and right sides are practically the same,and the W lines in the left and right spectra differowing to a slight misalignment of the spectrometerwith respect to the source.Shown in Fig. 4 are the left side and the right side
spectra as functions of energy recorded with andwithout the test pattern. The LP=mm groups areidentified. The 0:7LP=mm to 1:22LP=mm region ofthe test pattern was illuminated by 10keV to 50keVx rays on the right side of the spectrometer axis, andthe 2:0LP=mm to 10LP=mm region was illuminatedby the same energy range on the left side. Both imageplates were exposed, with and without the testpattern, under identical x-ray source conditions,spectrometer conditions, and exposure times. Thusthe contrast through the test pattern and the MFTcan be derived from the ratio of the exposures withand without the test pattern.
3. Modulation Transfer Function
As seen in Fig. 4(a), the intensities recorded on theSR image plate and through the open channels ofthe test pattern region with ≤1:2LP=mm are lowerthan the intensities recorded without the test pat-tern, and this results from absorption in the 2:1mmplastic case that covers the open channels. As shownin Fig. 4(b), the relative intensities through the test
pattern decrease with increasing LP=mm, and this isbecause of the decreasing MTF of the image plate for>2:0LP=mm values. It is also apparent in Fig. 4 thatthe intensities through the test pattern bars increasewith energy, and this results from increasing trans-mittance through the 50 μm Pb bars (and the 2:1mmplastic case covering the entire test pattern). Thusthe intensity levels shown in Fig. 4 recorded usingthe test pattern must be corrected at all energiesby the transmittances through the plastic case andthe Pb bars.
Shown in Fig. 5(a) is the ratio of the intensities re-corded on the SR image plate with and without thetest pattern on the right side of the spectrometeraxis. Also shown are the calculated transmittancesof the 2:1mm thick plastic (CH) case and the productof the transmittances of the 2:1mm CH and the50 μm Pb bars. It is seen that the decreasing inten-sity ratio through the open channels with decreasingenergy and the increasing intensity ratio through the
Fig. 3. Spectrum recorded on an SR image plate as a function ofdistance from the spectrometer axis and showing the WKα and Lγspectral lines, the Ba K edge due to absorption in the image plate,and the pinhole image.
Fig. 4. SR image plate spectra recorded on (a) the right side and(b) the left side of the spectrometer axis without (upper curves) andwith (lower curves) the resolution test pattern. The LP=mmgroupsare indicated.
bars with increasing energy can be explained by theCH absorption and by the CH and bar transmittance,respectively.The intensities through the open channels of the
test pattern were corrected by increasing the inten-sities by the absorptance factor in the CH case. Theintensities through the Pb bar regions (which werealso covered by the CH case) were corrected by de-creasing the intensities by the transmittance factorthrough the CH case and Pb bars. The result isshown in Fig. 5(b), where the intensity ratios throughthe channel regions are near 100% and the ratiosthrough the Pb bar regions are in the 5% to 10%range (the image plate and scanner noise level).A similar analysis was performed on the data from
the test pattern region with ≥2:0LP=mm that wasrecorded on the left side of the spectrometer axis.The uncorrected and corrected intensity ratios are
shown in Figs. 6(a) and 6(b), respectively. As seen inFig. 6(b), the corrected intensity ratio for 2:0LP=mmis near 100% through the channels and is 5% to 10%through the bars, consistent with the intensity ratiosfor ≤1:2LP=mm shown in Fig. 5(b). For >2:0LP=mm,the intensity ratios decrease with increasing LP=mmvalues owing to the decreasing MTF of the SR im-age plate.
The contrast levels for channels and bars withinthe same LP=mm group should ideally be equal,while in practice the levels shown in Fig. 6(b) havea small variation. This probably results from thesampling of the contrast by the scanner’s 42:5 μmpix-els. To mitigate this effect, the image plates wererotated with respect to the pixels by typical anglesof 1° to 2°, and the average of the four contrast valueswithin each group was used to derive the MTF.
Fig. 5. (a) Contrast recorded on the SR image plate and throughthe resolution test pattern on the right side of the spectrometeraxis, the transmittance through the 2:1mm thick CH case, andthe product of the transmittances through the 2:1mm CH caseand the 50 μm Pb bars. The LP=mm values are indicated.(b) The contrast after correcting for the transmittances of theCH case and the Pb bars.
Fig. 6. (a) Contrast recorded on the SR image plate and throughthe resolution test pattern on the left side of the spectrometer axis,the transmittance through the 2:1mm thick CH case, and the pro-duct of the transmittances through the 2:1mm CH case and the50 μm Pb bars. (b) The contrast after correcting for the transmit-tances of the CH case and the Pb bars. The LP=mm values are in-dicated.
The MTF is defined as the difference in the inten-sity, which is contrast, through a group of open chan-nels and opaque bars with the same width. Thus theMTF is the difference between the upper contrastvalues in Figs. 5(b) and 6(b), which are the contrastthrough the open channels (after correction for theCH absorptance), and the lower contrast values,which are the contrast through the opaque bars(after correction for the CH and Pb bar transmit-tance). The resulting MTF of the SR image plate isshown in Fig. 7 for ≥2:0LP=mm values; the MTFvalues for <2:0LP=mm are all approximately100%. Each data point of the SR curve in Fig. 7 isthe average value for the four channel/bar pairs ina group with the same LP=mm value, the size ofthe data symbol represents the estimated accuracyof the MTF value, and a smooth curve is drawnthrough the data points.The triangular data points in Fig. 7 are the MTF of
an SR image plate determined using an Fe55 radio-active source with emission primarily at 5:9keV [10].The SR image plate was scanned by a Fuji BAS 2500scanner with 50 μm pixel steps. As seen in Fig. 7, theagreement with the presently determined SRMTF isgood except for large LP=mm values. This disagree-ment at the high-frequency noise level of the MTFmay result from the use of different contrast analysistechniques in the two MTF measurements or possi-bly from the different x-ray energies, 5:9keV inRef. 10 compared to 10keV and higher energies inthe present work.A similar data analysis was performed for MS im-
age plates, and the resulting MTF curve is presentedin Fig. 7. In comparison to the SR image plate, theMS image plate has inferior MTF, although theMS image plate was observed to have higher sensi-tivity in the 10keV to 50keV energy range.
We note that it is possible to rotate the resolutiontest pattern 90° with respect to the spectrometerdispersion direction, making the open channelsand bars parallel with the dispersion direction,and thereby measure the contrast and MTF as a con-tinuous function of energy. However, the commercialtest pattern had insufficient length to cover the10keV to 50keV energy range, and the spectrometercrystal had insufficient height to illuminate numer-ous LP=mm groups when rotated by 90°.
4. Point Spread Function
In general, the MTF derived from the image of a re-solution test pattern is related to the point spreadfunction (PSF), the response of an optical systemto a spatially narrow (impulsive) object. As discussedin Ref. [11], in the spatial frequency domain the Four-ier transform I of the image I is equal to the productof the Fourier transform O of the object O and theoptical transfer function, H : I ¼ H ×O. In general,the optical transfer function is a complex function,the modulus of the optical transfer function is de-fined as the MTF, and the complex part representsthe change in phase produced by the optical system.The MTF therefore represents the decrease in ampli-tude of the modulation produced by the optical sys-tem with increasing spatial frequency. When theoptical system is illuminated by an impulsive object,the inverse Fourier transform of the optical transferfunction is the PSF. In our case, because the imageplate is illuminated by incoherent x rays and pro-duces no change in phase, the object and the opticaltransfer function are real functions, and the PSF isreal and is equal to the inverse Fourier transform ofthe MTF.
The MTF can be exactly determined from the im-age of a resolution test pattern that has a continuoussinusoidal variation in transmittance with spatialfrequency. Then the inverse Fourier transform ofeach spatial frequency is unity, and there is no over-lapping of spatial frequency components when calcu-lating the PSF from the inverse Fourier transform ofthe MTF. In practice, the resolution test pattern isoften composed of groups of transparent open spacesand opaque bars with discrete spatial frequency var-iation. Thus the image’s contrast pattern does notcontain information at all spatial frequencies, the in-formation at each discrete spatial frequency is not apure Fourier frequency component, and small arti-facts can appear in the PSF. In addition, the imageof the resolution test pattern is often recorded byan electronic detector with discrete pixels havingconstant spacing, or the image is recorded on a spa-tially continuous medium and is digitized withevenly spaced pixels. TheMTFand PSF derived fromthe discrete contrast data can have small artifactsresulting from imperfect and overlapping Fouriercomponents. Such aliasing of frequencies can be mi-tigated by designing the bar pattern to optimize thespatial frequency information in the contrast data
Fig. 7. MTFof the SR andMS image plates derived from the spec-tra recorded using the resolution test pattern. The triangular datapoints are the SR MTF from Ref. 10.
and to minimize the overlapping of spatial frequen-cies [12].When an optical system is illuminated by a narrow
linear object, impulsive in the direction perpendicu-lar to the line, the resulting change in contrast acrossthe line is the line spread function (LSF) and is equalto the PSF, assuming that the LSF is isotropic, whichis the case for image plate media. The contribution ofthe image plate scanner is not isotropic since thescan is performed in a square grid of pixels; hencethe pixel resolution along the diagonal, for example,is
p2 times that in the horizontal or vertical direc-
tion. In this work the image plate was aligned onthe scanner platen so that the spectral lines wereperpendicular (within 1° to 2°) to one scan direction,and the scanned image represents the LSF and PSFalong the scan direction.The PSF can also be derived by imaging sharp
edges aligned perpendicular to the scan direction.In this case the contrast variation across the edgeis the edge spread function (ESF), and the derivativeof the ESF is the PSF in the edge-step direction.Wewill determine the PSFof the SR andMS image
plates in three ways: (1) from the MTF derived fromthe resolution test pattern, (2) from the images ofnarrow spectral lines, and (3) from the ESF producedby the Pb bars of the resolution test pattern at lowLP=mm values. The shapes and widths of the PSFcurves determined by these three methods are ingood agreement.In principle, aliasing that results from the resolu-
tion test pattern in the x-ray region could beeliminated by designing the pattern to have a contin-uous and sinusoidal transmittance variation withspatial frequency based on the transmittance ofthe pattern material. However, our results indicatethis is not necessary because the PSF derived fromthe bar pattern agrees with the LSF produced by nar-row spectral lines and with the PSF derived from theESF produced by the bars.Shown in Fig. 8(a) are the two-sided MTF curves of
the SR and MS image plates derived from Fig. 7. Theinverse Fourier transforms of the MTF curves, thePSF curves, are indicated by 1 and 2 in Fig. 8(b).The full widths at half-maximum (FWHM) valuesof the intrinsic SR and MS PSF curves are0:09mm and 0:14mm, respectively.The image plate PSF was compared to the width
and shape of the 11:286keV W Lγ1 spectral line iden-tified in Fig. 3. Since the spectra were recorded byplacing the image plate on the Rowland circle of thespectrometer, the spectral line broadening is domi-nated by the effective resolution of the image platedetector, and the natural line width and other broad-ening mechanisms are negligible [3]. Thus the nar-row spectral line represents an impulsive object,and the line shape is the PSF of the image plate de-tection system consisting of the image plate and thescanner.The data points in Fig. 9 represent the spectral line
shapes derived by scanning across the spectral lines
in the dispersion direction perpendicular to the spec-tral lines, and the FWHM line widths are 0:13mmand 0:19mm when using SR and MS image plates,respectively. The curves in Fig. 9 labeled 1 are theintrinsic image plate PSF curves (derived from theMTF curves) scaled to the same height and back-ground levels as the spectral lines. The spectral linesare significantly wider than the image plate PSFcurves. The larger widths of the spectral lines, com-pared to the PSF derived from the image plate MTF,results from the contribution of the scanner to thespectral line width, which is absent in the intrinsicimage plate MTF.
First consider the case of the spectral line. Whenthe x-ray energy in the narrow spectral line is depos-ited in the image plate phosphor, a latent image isformed that is much narrower than the 42:3 μm scanstep. When scanned, the resulting line width andshape is broadened by the 42:3 μm scan step as wellas by the image plate MTF. Additional scannerbroadening can result from the size of the laser beamused to stimulate the phosphor, scattering of the la-ser light within the phosphor and protective coating,and the visible light imaging optics. These convolvedscanner effects are represented by the scanner PSF.
Fig. 8. (a) Two-sided MTFof the SR andMS image plates. (b) Thepoint spread functions where curve 1 is for the SR image plate, 2 isfor the MR image plate, 3 is the SR image plate PSF convolvedwith the scanner PSF, and 4 is the MS PSF convolved with thescanner PSF.
Thus when recording a narrow spectral line, theeffective resolution of the image plate detection sys-tem (consisting of the image plate and the scanner)results from the convolution of the PSF of the imageplate and the PSF of the scanner.Next consider the procedure for determining the
image plate MTF. The latent image of the resolutiontest pattern is composed of linear regions of high andlow exposure with typical widths >50 μm (for< 10LP=mm), larger than the 42:3 μm scan step.The scan step therefore plays a rather minor rollin broadening the regions of high and low exposure.Moreover, the image plate MTF is determined fromthe differing contrast in these relatively wide expo-sure regions, not from the widths of the exposure re-gions. Thus the image plate MTF determined from
the resolution test pattern is unaffected by the scanprocess if the scan step and the width of the scannerPSF are smaller than the widths of the exposureregions.
The image plate PSF curve determined from theimage plate MTF were convolved with an assumedscanner PSF so that the resulting curve agreed withthe spectral line width. The scanner PSF was as-sumed to be Gaussian, and the inferred FWHMwas found to be 0:10mm. The curves labeled 3 and4 in Fig. 8(b) are the convolutions of the SR andMS image plate PSF (curves 1 and 2) and theGaussian scanner PSF with 0:10mm FWHM. Theseconvolved curves are labeled 2 in Fig. 9 and are ingood agreement with the spectral lines except inthe wings of the spectral lines.
The small discrepancies between the data and thePSF in the spectral line wings result from the gap inMTF data between 1:2LP=mm and 2:0LP=mm,spanning the center axis of the spectrometer wheregood contrast data were not recorded. In Fig. 8(a), theMTF curves have flat tops with artificially sharp cor-ners, and these sharp corners in the low-frequencyparts of the MTF curves result in small oscillationsin the wings of the PSF curves as seen in Fig. 8(b). Inpractice the corners of the image plate MTF curvesare not so sharp, and the small oscillations are notpresent in the PSF.
The data points in Fig. 9, representing the WLγ1spectral lines recorded when using the SR and MSimage plates, were fitted to analytical curves usingthe least squares technique. As shown by the curveslabeled 3 in Fig. 9, it was found that a Gaussian curvewith 0:13mm FWHM and a Lorentzian curve with0:19mm FWHM were good fits to the spectral linesrecorded using the SR and MS image plate detectors,respectively. The discrepancy in the high-energywing of the WLγ1 spectral line recorded by the MSimage plate, as seen in Fig. 9(b), may result fromthe blending of this relatively broad line profile withthe nearby WLγ2;3 spectral line (see Fig. 3).
The different shapes and FWHM values of the SRand MS MTF and PSF curves probably result fromincreased scattering in the thicker phosphor and bin-der in the MS image plate that provides higher x-raysensitivity while reducing spatial resolution. Acomparison of the spectral line intensities in Fig. 9,recorded using the same x-ray source and spectro-meter conditions, indicates that the peak spectralline intensity is approximately 50% higher and thebackground level is twice as high when using anMS image plate compared to using a SR image plate.
The edge spread functions (ESFs) were derivedfrom the change in contrast across an edge of the re-solution test pattern. The edge chosen for analysis isan edge of the middle bar in the 0:85LP=mm groupshown in Fig. 5. This group has a good exposure leveland relatively small corrections for the absorptanceof the CH case and transmittance of the Pb bars, andthe widths of the open channel and Pb bar are0:59mm, large compared to the PSF determined
Fig. 9. (a) Data points are theWLγ1 spectral lines recorded on anSR image plate, curve 1 is the SR image plate PSF, curve 2 is theSR PSF convolved with the scanner PSF, and curve 3 is a Gaussianfitted to the data points with 0:13mm FWHM. (b) The data pointsare the WLγ1 spectral lines recorded on an MS image plate, curve1 is the MS image plate PSF, curve 2 is the MS PSF convolved withthe scanner PSF, and curve 3 is a Lorentzian fitted to the datapoints with 0:19mm FWHM.
from the spectral lines (0:13mm for the SR and0:19mm for MS image plate detectors). The squaredata points in Fig. 10 represent the change in con-trast across the edge of the resolution test pattern,the ESF, and straight lines are drawn between theESF data points. The triangular data points repre-sent the derivative of the ESF, the PSF. Analyticalcurves were fitted to the PSF data points, and itwas found that a Gaussian provided a good fit tothe SR PSF data points and a Lorentzian to theMS PSF data points. The FWHM values of the fittedPSF curves are 0:13mm for the SR and 0:18mm forthe MS image plate detectors, respectively. TheseFWHM values are in good agreement with the corre-sponding PSF FWHM values derived from the spec-tral lines (0:13mm and 0:19mm) and are larger thanthe values (0:09mm and 0:14mm) determined from
the image plate MTF without accounting for thescanner broadening. This is because the PSF curvesderived from the ESF and from the spectral lines in-clude the effect of scanner broadening, while the PSFcurves derived from the image plate MTF do not.Thus the shapes and the FWHM values of the PSFcurves of the SR and MS image plate detectors, con-sisting of the image plate and the scanner, derived bythe three methods give a consistent result: The SRPSF is Gaussian with 0:13mm FWHM, and theMS PSF is Lorentzian with 0:19mm FWHM.
In Ref. [13], the PSF produced by a Fuji BAS 2000scanner and a Fuji image plate was characterized inthe 10keV to 40keV energy range. It was found thatthe FWHM value was 0:142mm at 10keV and de-creased to 0:130mm at 40keV. The FWHM value re-ported in Ref. [14] at 10keV energy, also using a BAS2000 scanner and a Fuji image plate, was 0:126mm.While the types of Fuji image plates used inRefs. [13,14] were not specifically identified, theseFWHM values are comparable to the 0:13mmFWHM determined for the Fuji SR image plate inthe present study.
5. Conclusion
The modulation transfer functions of SR and MS im-age plates were determined using a resolution testpattern with up to 10LP=mmand illuminated by dis-persed x-ray spectra in the 10keV to 50keV energyrange. The corresponding point spread functions hadFWHM values of 0:09mmand 0:14mm, smaller thanthe 0:13mm and 0:19mm widths of spectral lines inthe SR andMS scanned files, respectively. The largerthan expected spectral line widths were attributed toadditional broadening by the scanner, absent in theimage plate MTF and PSF, and the scanner PSF wasinferred to have 0:10mm FWHM. The PSF derivedfrom the ESF, which included scanner broadening,had FWHM values of 0:13mm and 0:18mm, in goodagreement with the PSF widths derived from thenarrow spectral lines. In all three cases, the SRPSF was Gaussian in shape, and the MS PSF wasLorentzian in shape.
The techniques developed for the analysis of thespectral data provide a number of advances over tra-ditional methods of determining the MTF and PSFcurves of image plates and scanners in the hard x-ray region. First, the transmittance of the resolutiontest pattern is accounted for when determining theimage plate MTF. Second, the use of a line-pair reso-lution test pattern enables the determination of theimage plate MTF and PSF irrespective of the PSF ofthe scanner. Finally, the FWHM of the scanner PSFis inferred by comparison with the widths of narrowspectral lines and the edge spread functions, whichinclude the effects of scanner broadening as wellas the PSF of the image plates.
In summary, the PSFof the SR andMS image platedetectors, and the convolution of the image platePSF and the scanner PSF, were determined to beGaussian with 0:13mm FWHM and Lorentzian with
Fig. 10. ESP and PSF curves for the (a) SR and (b) MS imageplates. The square data points represent the change in contrastacross an edge of the resolution test pattern, the ESF, and straightlines are drawn between the data points. The triangular datapoints represent the derivative of the ESF, the PSF. Curves werefitted to the PSF data points and are (a) Gaussian with 0:13mmFWHM and (b) Lorentzian with 0:18mm FWHM.
0:19mm FWHM, respectively. The analysis techni-ques can be applied to other image plate and scannercombinations. This enables the optimization of imageplate and scanner combinations for x-ray spectro-scopy and radiography applications. The accurateknowledge of the image plate detector MTF andPSF also enables the improvement in the spatialresolution of spectroscopy and radiography imagesusing Fourier optics deconvolution techniques [11].For example, in the case that the spectral lines arebroadened by mechanisms other than the imageplate and scanner, such as broadening by the sizeof the x-ray source, those broadenings can be re-vealed by deconvolving the image plate and scannerPSF.
The work at Naval Research Laboratory (NRL)was supported by the Office of Naval Research(ONR). Certain commercial equipment, instruments,or materials are identified in this paper in order tospecify the experimental procedure adequately. Suchidentification is not intended to imply recommenda-tion or endorsement by the US government, nor is itintended to imply that the materials or equipmentidentified are necessarily the best available for thepurpose.
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