high resolution x - ray computed tomography ( xct ) has gained considerably in importance and acceptance for the examination and 3d - characterization of materials and industrial specimens in recent years [ 110 ] .
xct systems with cone beam geometry with a -focus or a nano - focus x - ray tube in combination with a high speed and high resolution flat panel matrix detector are widely used in materials science [ 15 ] . using cone beam xct ,
a specimen is placed on a rotary stage between the x - ray source and the detector .
the specimen is rotated step by step , taking a projection image at each angular position .
a computer cluster reconstructs the projections to a volume dataset using , for example , the filtered back projection algorithm . at each position of the resulting dataset
a grey - value is calculated in the scanned sample volume , which corresponds to the effective x - ray attenuation coefficient (x , y , z ) .
the major problems of cone beam xct with a polychromatic source are the limited transparency of the sample , the restricted geometrical accuracy and resolution and measurement artefacts .
artefacts are structures resulting from the reconstruction algorithm of the dataset , which do not correspond to a real sample feature and which lead to problems with contrast , noise as well as measurement interpretation and dimensional accuracy .
these problems are more pronounced for polychromatic cone beam xct as compared with xct with a monochromatic source .
continuous improvements in x - ray tubes and xct devices have led to cone beam ct systems which can now achieve resolutions down to 1  m ( -xct ) and even below ( sub-xct ) .
synchrotron radiation offers significant advantages by its adjustability , partial coherence and nearly parallel beam of high brilliance .
these advantages cause fewer artefacts , improved contrast and resolution , as well as faster recording for synchrotron tomography ( sxct ) .
sxct has been known since mid-1980  s and resolutions available now are below 1  m , e.g. at esrf / id19 , allowing in - situ experiments due to the short measuring period
. spatial resolution of about 180  nm has recently been achieved for relatively large metallic samples on esrf / id22 by using magnifying kb - mirrors .
in addition , sxct produces also phase contrast due to the high lateral coherence of the beam , so that even interfaces between phases with very low absorption contrast can be displayed . phase contrast for cone beam sub-xct was also reported but to a much lower extent .
the specifications of typical xct systems ( x - ray source and voxel sizes ) are compared in table 1 .
there have been several investigations of cone beam xct and sxct applied to various materials [ 7,1113 ] .
xct and sxct for the 3d - characterization of inhomogeneities in steel are presented in , but no quantitative comparison was carried out .
the possible applications of sub-xct are described in , but no comparison with sxct is presented .
a quantitative comparison was carried out in , but the resolutions ( voxel sizes ) used are in the range of several micron ( 210  m ) and thus not in the sub-m - xct region . in   cone beam xct and sxct are compared quantitatively but no sub-xct cone beam xct measurements were performed . in summary , there are no systematic investigations on metallic samples with up - to - date spatial resolutions down to 1  m ( voxel sizes below 1  m ) published .
this paper deals with the application of high resolution cone beam xct in comparison with synchrotron xct applied to fe- and al - based samples containing several phases .
the xct - data are analysed with respect to measurement artefacts , detection of details , sharpness , contrast and signal - to - noise ratio .
one steel and two al alloys were investigated ; all the samples included various inhomogenities such as inclusions , pores or metallic phases with a higher or lower density than the matrix resulting in distinguishable features in the corresponding ct - data - sets .
a summary of these samples together with the inhomogeneities present can be found in table 2 .
regions of the samples were investigated by metallographic analysis and scanning electron microscopy to identify the different inhomogeneities and phases investigated .
the elemental analysis was carried out by energy dispersive x - ray analysis ( edx ) .
the -focus xct - measurements were performed with two -focus cone beam xct - devices , namely a v|tome|x s constructed by ge sensing & inspection technologies phoenix|x - ray equipped with a 240  kv--focus tube and a 10241024 pixel a - si flat panel detector by perkin elmer and a rayscan 250e xct - device constructed by rayscan inc .
the rayscan 250e system is equipped with a 225  kev--focus tube by viscom and a 10241024 a - si at panel matrix - detector by perkin elmer .
the target for both devices is made of tungsten and the minimum size of the x - ray focal spot for both sources is about 5  m .
the minimum voxel sizes for both systems are around 3  m , the actual value used was 3.5  m for all measurements .
the tube energies used for scanning were between 90 and 160  kv , the current between 25 and 70  a and the number of projections 10001480 .
the sub-m - ct x - ray tomograms were scanned using a nanotom 180nf ct device developed and manufactured by ge sensing & inspection technologies phoenix|x - ray with a 180  kev high power nanofocus tube and a 23002300 pixel hamamatsu detector .
targets made of tungsten and molybdenum was used at a voltage of 5060  kv and a current between 325 and 400  a .
the voxel size used was between 0.4 and 0.6  m , and the number of projections 15001700 .
these parameters required measurement periods between 120 and 240  min . the x - ray tube of the nanotom is equipped with an external liquid cooling system to ensure stable measurement conditions and to minimize the thermal influences during the long - time scans .
european synchrotron radiation facility in grenoble   provided monochromatic x - rays with 29  kv in parallel beam geometry .
the sxct projections were recorded by a 2d - ccd camera with 20482048 pixels and an effective pixel size of 0.3  m . for reconstruction
the samples were measured in phase contrast mode using a distance sample - to - detector of 39  mm .
table 3 gives an overview of the most important measurement parameters for xct , sub-xct and sxct measurements .
two xct and sub-xct measurements were performed with the steel sample ( scan a and scan b ) .
the cone beam xct - data were reconstructed by means of a filtered back projection feldkamp - algorithm .
for some of the cone beam xct - data a beam hardening correction was performed .
the sxct data were reconstructed by using a filtered back projection algorithm for parallel beam geometry .
the reconstructed xct - data were visualised and processed with the software vgstudio max 2.0 by volume graphics gmbh .
various parameters were evaluated for interpreting and classifying the xct - data - sets quantitatively : sharpness , contrast , signal - to - noise ratio and a feature of the grey - value histogram ( the width of the material peak ) . in order to evaluate the sharpness of the ct - data ,
the grey - values for air and material were transformed to values between 0 and 65,535 in all ct - measurements .
line profiles were deviated and the mean value of the rising and falling exterior edges of the metallic samples was considered as a parameter for the sharpness .
the -xct , sub-xct and sxct - data were evaluated in the same way and the values determined were compared relatively to each other .
line profiles were taken to quantify the contrast of the different measurements in the first step , and contrast - values were determined at certain inhomogeneities based on the following formula:(1)contrast = greyvaluematerialgreyvalueinhomogenitygreyvaluematerial by a polynomial interpolation of parts of the line profiles it was possible to determine grey - values of the material ( = grey - valuematerial ) and grey values of the inhomogeneities ( = greyvalueinhomogenity ) .
the same inhomogeneities were evaluated for all three kinds of xct - measurements . the standard deviation (  ) for the material grey - values was set as the denominator for the signal - to - noise ratio ( snr ) .
snr was calculated by the following formula:(2)snr=|greyvaluematerialgreyvalueinhomogenity| the data were evaluated in the following way to compare the grey - value histograms of the xct , sub-xct and the sxct - measurements . the fwhm - values ( full widths at half maximum ) were calculated for the material - peak in relation to the grey - value difference of the material- and the air - peak .
these evaluations could only be done for the xct - results of the steel sample , where the absorption contrast dominates the measurements . for the al - samples this comparison was not possible , since phase contrast dominates the sxct - data .
in the following the ct - results , ct cross - sectional images of slices of the steel sample measured by xct , sub-xct and sxct are presented in fig . 1 :
target metallography and edx revealed non - metallic inclusions in the ct - images shown in fig .
the ct - data for xct are rather diffuse due to the much larger x - ray emission spot and voxel size compared with the much sharper images obtained by sub-xct and sxct .
beam hardening artefacts are visible for xct and sub-xct , whereas the sxct - data show no beam hardening manifested with more or less homogeneous grey values for steel .
ring artefacts are most pronounced for the sxct - data , whereas the cone beam xct results show almost no ring artefacts .
2 shows ct - cross - sectional images of a different region of the steel sample ( scan b ) measured with a different -xct - device as compared with scan a ( see table 3 ) . in this case a beam hardening correction of the ct - data was performed so that the grey values within the material are constant similar to the sxct - data . in fig .
xct gives a rather diffuse picture with a much lower resolution of details , but a rather low noise , whereas sub-xct gives much sharper data with more details , but the dataset has a higher noise level . in fig .
the spatial and contrast resolutions are so good , that four different grey value contrasts appear .
these contrasts can be classified as pores , low - density inclusion , steel and high - density inclusion . in both cone
beam xct - methods investigated it is not possible to distinguish between pores and inclusions .
these results show the much better contrast resolution of sxct as compared with cone beam xct . in fig .
4 xct - results for an alsi12ni1 sample are shown , where different metallic phases are visible .
ni- and fe - aluminides appear as high - absorbing inhomogeneities within the al matrix due to the high density and atomic number of ni . in the xct - dataset areas with aluminides
can be identified but an accurate segmentation and quantification is not possible as a result of blurred edges .
the sub-xct and the synchrotron - xct measurements show the high - absorbing aluminides in much more detail .
the xct - data for all three measurement methods show no beam - hardening and no ring artefacts .
the data for sxct show not only an absorption contrast but also a phase contrast .
set , where the detectable features , pores , fe - aluminides and mg2si , are shown with a higher magnification .
the results for the alsi12ni1 sample show once again , that xct gives rather diffuse pictures with a much lower resolution of detail but a rather low noise , whereas sub-xct and sxct give much sharper data with more details and a better contrast .
also sxct shows a phase contrast for the alsi12ni1-dataset which results in a more pronounced representation of the interfaces and edges .
in addition , the sxct - data present less noise compared with those of sub-xct .
different features of the ct - data were analysed qualitatively and quantitatively in order to compare the cone beam xct and synchrotron xct .
measurement artefacts and detection of details are now discussed from the point of view of quality .
beam - hardening artefacts can not appear in the sxct - data due to the monochromatic nature of the source used . to a certain extent ,
beam - hardening artefacts are present in the cone beam xct - data of steel , but these artefacts can be corrected so that the grey - values for steel are as constant as in the synchrontron xct - data . both cone beam xct and synchrotron xct - data show ring artefacts ,
but they do not appear very prominently . only in the sxct - data of the steel sample
ring artefacts are well known and caused by faults of the detector pixels . in the detection of details -xct shows worst performance .
-xct can distinguish between air and steel as well as between steel and inclusions but it is not possible to differentiate between pores and inclusions . for the al - sample -xct can tell apart between air , al - matrix and the higher absorbing ni - and fe - aluminides .
it is possible to identify four different phases using sxct ( air pores , low density inclusion , steel matrix and high density inclusion ) in the steel sample . for the almg5si7 sample , sub-xct and synchrotron - ct datasets
reveal four different phases : air pores , mg2si , almg - matrix and fe - phases .
the spatial resolution of sub-xct and sxct seems to be very similar , but the rather high noise which is always present in the sub-xct data and the better contrast in the s - xct - data achieved by phase contrast leads to higher quality images for s - xct .
the following properties were evaluated quantitatively : sharpness , contrast , signal - to - noise ratio and full width at half maximum of the material peak in the grey value histogram .
the results are shown in the next figures for the three investigated materials using the various xct - methods .
7 . due to the phase contrast within sxct - data of the al - samples the sharpness values between cone beam xct and sxct can be compared qualitatively but not quantitatively .
it is clear that the phase contrast gives steeper edges and therefore high sharpness values .
the sharpness - data for steel - fe and for the cone beam xct results can be compared also quantitatively . as expected from the results shown in figs .
15 , the sharpness increases from xct to sub-xct and to sxct for all samples .
this behaviour is more pronounced for the results of the al - based samples due to the strong phase contrast within the sxct - data .
8 , where the relative contrast for the different xct - datasets is depicted . for steel and the alsi12ni1 ,
the best contrast is given by sxct , whereas for the almg5si7 samples the best contrast is obtained by sub-xct .
this is caused by the amount of phase contrast in the sxct - data for the almg5si7-sample .
the signal- to - noise ratio ( snr ) for the different measurements is shown in fig .
for -xct the measurement time was around 120  min , for sub-xct around 180  min and for sxct 15  min .
the highest snr - values are for the -xct and for the sxct measurement , depending on the material and on the measurement parameters .
a comparison of the snr for a definite measurement time reveals the best results for sxct . in all three cases ,
the snr is lowest for sub-xct since in this case the intensity of the x - ray source is lowest .
a further common method for the evaluation of ct - data is an analysis of the grey - value histogram : for this evaluation the features of the air and material peaks are analysed .
only an evaluation of the histogram of steel was meaningful due to the strong phase contrast obtained for the al - alloys .
the results are shown in table 4 . here , where the full widths at half maximum of the material peaks relative to the distance between the air peak and the material peak for the dataset of fig .
the material peak for the sub-m - ct data set is broadened due to higher noise and due to beam hardening effects .
the investigations presented here show , that cone beam xct at high resolution can give comparable results to synchrotron - xct .
sharpness and contrast resolution for cone beam xct can be almost as good as for sxct - systems .
the biggest problem with sub-xct devices is the rather low intensity of the nano - focus tubes which results in high noise and low snr - values .
however , sub-xct offers many other advantages , especially reduced measurement costs , a usually higher scanning volume , better accessibility and user - friendliness .
three x - ray computed tomography methods , namely cone beam xct - systems with a -focus and a sub-m ( nano - focus ) x - ray source as well as synchrotron computed tomography , were compared . a steel sample and two al - samples ( alsi12ni1 , almg5si7 ) containing different inhomogeneities and material phases
ct data features like beam - hardening , detection of details , sharpness , contrast , signal - to - noise ratio and the grey value histogram were evaluated and compared .
the results arebeam - hardening artefacts were present in cone beam xct - data of the steel sample , but can be corrected fairly easily.sxct and sub-xct give data with the highest detection of details , sharpness and have the best spatial and contrast resolution . in several cases sxct and
sub-xct gave very similar results.xct is always inferior with regard to detection of details , sharpness , spatial and contrast resolution.sub-xct suffers from a rather bad signal - to - noise ratio due the limited power of x - ray tubes with focal spots below 1  m .
beam - hardening artefacts were present in cone beam xct - data of the steel sample , but can be corrected fairly easily .
sxct and sub-xct give data with the highest detection of details , sharpness and have the best spatial and contrast resolution .
xct is always inferior with regard to detection of details , sharpness , spatial and contrast resolution .
sub-xct suffers from a rather bad signal - to - noise ratio due the limited power of x - ray tubes with focal spots below 1  m .
all in all , sxct gives the best results , but the quality of sub-xct - data comes quite close in certain cases .
this means that high resolution cone beam xct is a very useful and attractive method for materials science and industrial research , since the costs are much lower and both accessibility and user - friendliness are much better than for sxct .
 x - ray computed tomography ( xct ) has become a very important method for non - destructive 3d - characterization and evaluation of materials . due to measurement speed and quality , xct systems with cone beam geometry and 
 matrix detectors have gained general acceptance . 
 continuous improvements in the quality and performance of x - ray tubes and xct devices have led to cone beam ct systems that can now achieve spatial resolutions down to 1  m and even below . however , the polychromatic nature of the source , limited photon flux and cone beam artefacts mean that there are limits to the quality of the ct - data achievable ; these limits are particularly pronounced with materials of higher density like metals . 
 synchrotron radiation offers significant advantages by its monochromatic and parallel beam of high brilliance . 
 these advantages usually cause fewer artefacts , improved contrast and resolution.tomography data of a steel sample and of two multi - phase al - samples ( alsi12ni1 , almg5si7 ) are recorded by advanced cone beam xct - systems with a -focus ( xct ) and a sub-m ( nano - focus , sub-xct ) x - ray source with voxel dimensions between 0.4 and 3.5  m and are compared with synchrotron computed tomography ( sxct ) with 0.3  m / voxel . 
 ct data features like beam hardening and ring artefacts , detection of details , sharpness , contrast , signal - to - noise ratio and the grey value histogram are systematically compared . in all cases 
 xct displayed the lowest performance . 
 sub-xct gives excellent results in the detection of details , spatial and contrast resolution , which are comparable to synchrotron - xct recordings . 
 the signal - to - noise ratio is usually significantly lower for sub-xct compared with the two other methods . with regard to measurement costs 
  for industrial users  , scanning volume , accessibility and user - friendliness sub-xct has significant advantages in comparison to synchrotron - xct . 
Introduction
Experimental
Results
Discussion
Conclusions