to develop a compact system for basic experiments , we chose a sealed x - ray tube with a molybdenum target ( oxford instruments inc . , ca ) .
the voltage we could apply ranged from 10 to 50 kvp ( voltage - peak ) , and the maximum current was 1 ma .
we clearly observed strong characteristic radiations of 17.479 kev and 19.608 kev , which corresponded to the k and k , respectively , of molybdenum .
the bremsstrahlung broadband spectrum was also generated by bombarding of the target material with electrons .
the x - rays generated from the target were reflected on the inner wall of each capillary and they passed through the parabolic polycapillary optics . as the shape of the each capillary was a parabola , the x - rays radiated from a focus of the parabola passed through each capillary and they were parallel to the optical axis . in other words , the polycapillary optics transferred the divergent x - rays to a parallel beam along the optical axis .
the outer diameter and length of the parabolic polycapillary optics were 10 mm and 133 mm , respectively .
for mo k radiation , the critical angle of each capillary was 1.7 mrad and the reflectivity of a single reflection on the capillary was greater than 0.8 .
the incidence x - rays with the critical angle were reflected approximately 17 times on the inside wall of each capillary , and in this case , the reflectivity was approximately 0.02 .
however , when the incidence x - rays with less than the critical angle were included , the final transmission efficiency of the generated x - rays could be as high as 0.3 .
taking into consideration the transmission efficiency , the applied tube voltage was 40 kvp which was higher than the applied tube voltage for conventional mammography . in this study ,
the operating condition of the x - ray tube for imaging test objects was fixed at a tube voltage of 40 kvp and a current of 0.5 ma , and the exposure time to let the image develop was three seconds .
the parabolic polycapillary cut the high energy of more than 20 kev by its x - ray reflection properties , but the low energy x - ray of less than 20 kev was passed by the parabolic polycapillary .
thus , a tube voltage more than 40 kvp could be applied and the number of photons generated on the x - ray tube could be increased . in a tube voltage of 40 kvp with a current of 0.5 ma ,
the number of photons generated by the molybdenum target x - ray tube in front of the polycapillary optics was ~ 610 photons / sec .
it meant that the number of photons on the detector was enough to make a digital image . in our experiment ,
, nj ) with a 24 m  24 m pixel size was used for imaging .
the nyquist frequency of the captured image using the ccd detector was 21 lp / mm for which the spatial resolution was limited by the pixel size of the ccd detector . in order to obtain a higher spatial resolution of 21 lp / mm in our system configuration
, the pixel size of the ccd detector would have to be less than 24 m  24 m . the ccd chip was cooled down to 223 k to reduce the dark noise of the ccd detector .
figure 1 shows the experimental setup used to evaluate the performance of the small - field digital mammography .
parallel x - ray beams by the parabolic polycapillary optics entered a filter and then passed through a test sample .
all images used in these experiments were corrected by post - image processing , and the contrast ( imax - imin ) / imin , was calculated by maximum and minimum pixel values .
the objects on an image are distinguished by their contrast difference and achievable spatial resolution of the system .
the mtf of an imaging system shows a performance of the spatial resolution connected with the contrast ( 12 ) .
we directly examined the mtf to verify the spatial resolution of the small - field digital mammographic imaging system by taking images of the line - pairs instead of indirectly obtaining the images from an edge spread function .
the exposure time was three seconds when we took the linear pattern images of a phantom of a gold - line .
x - ray exposure gives rise to energy accumulation in an object , and the energy can destroy biological tissue and its chemical state .
when x - ray photons n with a wavelength  are irradiated on the area d of a sample , then the dose of the specimen with the thickness  and density  can be written as : which is the radiation dose for a single x - ray wavelength or energy of hc/ , and where  is the linear absorption coefficient of the sample .
all the x - rays that arrive on the sample contribute to the radiation dose of the sample .
therefore , the radiation dose d for a general x - ray tube source can be expressed as : we measured the radiation exposure to enter the test sample using an ionization chamber ( fluke corp .
, oh ) with an exposure time of three seconds and measured the spectrum of incident x - rays to the test sample together .
the absolute number of x - ray photons with energy hc/ was known by the radiation exposure and the x - ray spectrum , and the radiation dose of the test sample was obtained from equations   and   and the material information of the test sample .
this method is similar to the dose measurement in which x - ray tube voltage and half - value layer ( or equivalent other parameters ) should be known .
we obtained an image more than 10 mm in diameter by scanning a test standard phantom of breast and combining each scanned image .
breast tissue which was fixed by paraffin and proven on biopsy to be a ductal carcinoma in situ was imaged with the small - field digital mammographic imaging system .
a conventional projection - type digital mammography of the breast tissue sample was taken to compare with the findings of the small - field digital mammographic imaging system .
the breast tissue study was carried out in accordance with the regulations of the institutional review board of university .
there were various choices of filters for our mammographic imaging system , e.g. , molybdenum ( mo ) and rhodium ( rh ) .
the spatial resolution of 12 lp / mm for the molybdenum and rhodium filters with a 25 m thickness was achieved at a mtf of 10% as shown in figure 2 .
the spatial resolution of 12 lp / mm corresponded to 41.7 m in spatial resolution . from the standpoint of the ccd detector ,
this spatial resolution was matched to almost two pixels . when we used molybdenum filters with 25 m and 50 m thickness , the mtf values for each filter were n't very different .
however , the contrasts for the molybdenum filter with a 25 m and 50 m thick was 1.7 and 1.5 , respectively . the contrast was measured with a step - like acrylic object . in the case of a 25-m molybdenum filter , the contrast for was 12% higher than that for a 50-m molybdenum filter .
the image contrast was proportional to the square of the photon number detected on the ccd camera .
thus , the thick filter led to a lower contrast . when a 100-m - thick molybdenum filter was used in the mammographic imaging system ,
the contrast rapidly decreased to 0.48 and the spatial resolution was 11 lp / mm .
figure 4 shows the radiation dose using rhodium filters of 25-m thickness for an acrylic phantom with a 44 mm thickness ( mammographic accreditation phantom , cirs , va ) , equivalent to a 42 mm compressed breast with 50% glandular tissue and 50% adipose tissue , as a function of the tube current and fixed voltage for molybdenum .
the radiation dose , as a function of the voltage at a fixed current , increased quadratically .
the radiation dose shown in the table 1 is when the parabolic polycapillary optics was not combined with the x - ray tube in our system configuration .
when no parabolic polycapillary optics was used , the system became a conventional projection - type digital mammography .
the radiation dose of the system without the parabolic polycapillary optics was three times higher than with the parabolic polycapillary optics .
the field that was exposed to the radiation dose for the small - field digital mammographic imaging system was 3% of the field for the projection - type system .
the small - field digital mammographic imaging system compared to the projection - type digital mammography had advantages in terms of the radiation dose , dose field and absorbed x - ray energy as shown in table 1 .
radiation dose was calculated from the measured x - ray energy absorbed and the measured dose field which led to mass information . in the mammography system without the parabolic polycapillary optics ,
the field illuminated x - ray could be controlled by lead block or collimator . in this case , the radiation field could be small . however , the radiation dose was still three times higher because the radiation dose was not proportional to the field size but to the accumulated x - ray energy and mass of the object . in our small - field mammographic imaging system ,
the radiation doses for the molybdenum and the rhodium filters were 0.18 mgy and 0.13 mgy , respectively .
theoretical estimation of the radiation dose ( 13 , 14 ) for the phantom was 0.32 mgy at a radiation exposure of 0.15 r , a half - value layer of 0.41 , and a tube voltage of 35 kvp for a mo / rh tube - filter combination .
the value of 0.32 mgy was very close to the 0.38 mgy in table 1 .
in addition , the american college of radiology advocates that the maximum value of the mean glandular dose must not exceed 3 mgy ( 15 ) .
we compared spectra for x - ray beams passing through parabolic polycapillary optics combined with the x - ray tube and direct x - ray beam as shown in figure 5a .
the high energy x - rays larger than 20 kev were almost removed by propagating the parabolic polycapillary optics although low energy x - rays were also reduced simultaneously .
the cut - off of the high energy could also be verified by the calculation of the x - ray reflectivity on the inner surface of the parabolic polycapillary optics ( 16 ) .
figure 5b shows the x - ray reflectivity as a function of x - ray energy at the fixed incidence angle of 1.7 mrad .
after two reflections , the high energy x - rays of more than 20 kev were almost removed . the x - ray generated from the x - ray tube
could be reflected up to 17 times on the inner surface of the parabolic polycapillary optics .
low energy x - rays have a larger critical angle than that of high energy x - rays , but the reflectivity of the low energy x - rays decrease at a larger incidence angle than its critical angle .
thus , the intensity of low energy x - rays passing through the parabolic polycapillary optics with various incident angles was also reduced as shown in figure 5a .
additionally , the molybdenum and rhodium filters remarkably reduced the low energy of the x - ray beam which passed through the parabolic polycapillary optics removing the high energy larger than 20 kev of the generated x - rays because the critical angles for the high energy x - rays were smaller than that for molybdenum radiation . because of the parabolic polycapillary optics and the filter , the radiation doses were remarkably reduced , and the fact that the rhodium filter allowed a lower radiation dose could be verified by measuring the energy spectra shown in figure 6 . within the overall energy region ,
the number of photons for the rhodium filter was lower than that for the molybdenum filter .
we were able to obtain an enlarged image more than 10 mm in diameter by scanning a test object and combining each scanned image .
each scanned image was overlapped by approximately 30% of the field in order to guarantee that no scan field was missed on the test sample .
x - ray exposure to make an image was three seconds and the object was moved for next imaging during one second .
figure 7a presents the scanned and recombined phantom image of 0.32-mm - al2o3 specks which simulate the microcalcifications of breast cancer .
the 44-mm - thick acrylic phantom contained fibers , specks and masses that were composed of various materials .
figure 7b shows an image of the same specks taken on projection - type digital mammography .
the system produced a magnified image of 1.07 x , and the spatial resolution of the system was 11 lp / mm which was tested by a line - pair phantom .
the spatial resolution was limited by the spot size of 100 m rather than the pixel size of the detector because of the cone beam . comparing both sets of images in figure 7a ,
b , the ratio of background noise , which was defined as small - field mammographic imaging system / projection - type digital mammography , was 0.8 .
it meant that the image contrast of the small - field mammographic imaging system might be 1.2 times higher than that of the projection - type , digital mammography .
figure 8a clearly shows microcalcifications within breast tissue which was fixed by paraffin and proven by biopsy to be ductal carcinoma in situ .
a small figure located on the left upper position in figure 8b shows a full image of the breast tissue sample taken with a projection - type digital mammography , and the outer black circle in figure 8b was the same field taken with the small - field scanning mammographic imaging system .
calcifications located within two small circles in figure 8a were clearly observed . in figure 8b , it was difficult to distinguish calcifications located at the same positions because of lower image contrast .
however , the same objects in figure 8b seemed to one unseparated object . because of the high spatial resolution of 12 lp / mm for the small - field mammographic imaging system , two microcalcifications could be distinguished
. however , the projection - type digital mammography could not distinguish two objects because of the separation distance was at the resolution limit of 11 lp / mm .
there were various choices of filters for our mammographic imaging system , e.g. , molybdenum ( mo ) and rhodium ( rh ) .
the spatial resolution of 12 lp / mm for the molybdenum and rhodium filters with a 25 m thickness was achieved at a mtf of 10% as shown in figure 2 .
the spatial resolution of 12 lp / mm corresponded to 41.7 m in spatial resolution . from the standpoint of the ccd detector ,
this spatial resolution was matched to almost two pixels . when we used molybdenum filters with 25 m and 50 m thickness , the mtf values for each filter were n't very different .
however , the contrasts for the molybdenum filter with a 25 m and 50 m thick was 1.7 and 1.5 , respectively . the contrast was measured with a step - like acrylic object . in the case of a 25-m molybdenum filter , the contrast for was 12% higher than that for a 50-m molybdenum filter .
the image contrast was proportional to the square of the photon number detected on the ccd camera .
thus , the thick filter led to a lower contrast . when a 100-m - thick molybdenum filter was used in the mammographic imaging system ,
the contrast rapidly decreased to 0.48 and the spatial resolution was 11 lp / mm .
figure 4 shows the radiation dose using rhodium filters of 25-m thickness for an acrylic phantom with a 44 mm thickness ( mammographic accreditation phantom , cirs , va ) , equivalent to a 42 mm compressed breast with 50% glandular tissue and 50% adipose tissue , as a function of the tube current and fixed voltage for molybdenum .
the radiation dose , as a function of the voltage at a fixed current , increased quadratically .
the radiation dose shown in the table 1 is when the parabolic polycapillary optics was not combined with the x - ray tube in our system configuration .
when no parabolic polycapillary optics was used , the system became a conventional projection - type digital mammography .
the radiation dose of the system without the parabolic polycapillary optics was three times higher than with the parabolic polycapillary optics .
the field that was exposed to the radiation dose for the small - field digital mammographic imaging system was 3% of the field for the projection - type system .
the small - field digital mammographic imaging system compared to the projection - type digital mammography had advantages in terms of the radiation dose , dose field and absorbed x - ray energy as shown in table 1 .
radiation dose was calculated from the measured x - ray energy absorbed and the measured dose field which led to mass information . in the mammography system without the parabolic polycapillary optics ,
the field illuminated x - ray could be controlled by lead block or collimator . in this case , the radiation field could be small . however , the radiation dose was still three times higher because the radiation dose was not proportional to the field size but to the accumulated x - ray energy and mass of the object . in our small - field mammographic imaging system , the radiation doses for the molybdenum and
theoretical estimation of the radiation dose ( 13 , 14 ) for the phantom was 0.32 mgy at a radiation exposure of 0.15 r , a half - value layer of 0.41 , and a tube voltage of 35 kvp for a mo / rh tube - filter combination .
the value of 0.32 mgy was very close to the 0.38 mgy in table 1 .
in addition , the american college of radiology advocates that the maximum value of the mean glandular dose must not exceed 3 mgy ( 15 ) .
we compared spectra for x - ray beams passing through parabolic polycapillary optics combined with the x - ray tube and direct x - ray beam as shown in figure 5a .
the high energy x - rays larger than 20 kev were almost removed by propagating the parabolic polycapillary optics although low energy x - rays were also reduced simultaneously .
the cut - off of the high energy could also be verified by the calculation of the x - ray reflectivity on the inner surface of the parabolic polycapillary optics ( 16 ) .
figure 5b shows the x - ray reflectivity as a function of x - ray energy at the fixed incidence angle of 1.7 mrad .
after two reflections , the high energy x - rays of more than 20 kev were almost removed . the x - ray generated from the x - ray tube
could be reflected up to 17 times on the inner surface of the parabolic polycapillary optics .
low energy x - rays have a larger critical angle than that of high energy x - rays , but the reflectivity of the low energy x - rays decrease at a larger incidence angle than its critical angle .
thus , the intensity of low energy x - rays passing through the parabolic polycapillary optics with various incident angles was also reduced as shown in figure 5a .
additionally , the molybdenum and rhodium filters remarkably reduced the low energy of the x - ray beam which passed through the parabolic polycapillary optics removing the high energy larger than 20 kev of the generated x - rays because the critical angles for the high energy x - rays were smaller than that for molybdenum radiation . because of the parabolic polycapillary optics and the filter , the radiation doses were remarkably reduced , and the fact that the rhodium filter allowed a lower radiation dose could be verified by measuring the energy spectra shown in figure 6 . within the overall energy region ,
the number of photons for the rhodium filter was lower than that for the molybdenum filter .
we were able to obtain an enlarged image more than 10 mm in diameter by scanning a test object and combining each scanned image .
each scanned image was overlapped by approximately 30% of the field in order to guarantee that no scan field was missed on the test sample .
x - ray exposure to make an image was three seconds and the object was moved for next imaging during one second .
figure 7a presents the scanned and recombined phantom image of 0.32-mm - al2o3 specks which simulate the microcalcifications of breast cancer .
the 44-mm - thick acrylic phantom contained fibers , specks and masses that were composed of various materials .
figure 7b shows an image of the same specks taken on projection - type digital mammography .
the system produced a magnified image of 1.07 x , and the spatial resolution of the system was 11 lp / mm which was tested by a line - pair phantom .
the spatial resolution was limited by the spot size of 100 m rather than the pixel size of the detector because of the cone beam .
comparing both sets of images in figure 7a , b , the ratio of background noise , which was defined as small - field mammographic imaging system / projection - type digital mammography , was 0.8 .
it meant that the image contrast of the small - field mammographic imaging system might be 1.2 times higher than that of the projection - type , digital mammography .
figure 8a clearly shows microcalcifications within breast tissue which was fixed by paraffin and proven by biopsy to be ductal carcinoma in situ .
a small figure located on the left upper position in figure 8b shows a full image of the breast tissue sample taken with a projection - type digital mammography , and the outer black circle in figure 8b was the same field taken with the small - field scanning mammographic imaging system .
calcifications located within two small circles in figure 8a were clearly observed . in figure 8b , it was difficult to distinguish calcifications located at the same positions because of lower image contrast .
because of the high spatial resolution of 12 lp / mm for the small - field mammographic imaging system , two microcalcifications could be distinguished
. however , the projection - type digital mammography could not distinguish two objects because of the separation distance was at the resolution limit of 11 lp / mm .
previous studies ( 7 - 9 ) have demonstrated the potential for x - ray capillary optics , non - parabolic polycapillary optics , aligned between the object and computed radiography phosphor imaging plate , to be incorporated into digital mammographic image .
consequently , the post - object capillary optics had the potential to increase image contrast by eliminating scattered x - rays . a scanning process is also required to obtain an image because the size of the capillary optics is small . in the system configuration
, the capillary optics played a role as a small ' grid ' , and there was no improvement on the spatial resolution which was approximately 5 lp / mm because the divergent x - ray source of 100 m spot size illuminated the object and the pixel size of detector was large .
in addition , the system configuration could not avoid a high radiation dose because of long exposure time , i.e. , six seconds per one scanned image during scanning . in the scanning process , the capillary optics and the detector were combined with each other and moved together .
we modified the system configuration to improve the spatial resolution and to reduce radiation dose instead of sacrificing the contrast slightly ( fig .
the spot size of the x - ray tube used in this system was not an important factor in effecting the spatial resolution due to the use of a parallel beam .
for the parallel beam , there was no image blurring by finite spot size of the x - ray tube , and the pixel size of the detector was a critical factor to determine the spatial resolution .
the illumination area of the parallel beam was small because the diameter of the parabolic polycapillary optics was small .
however , there was enough space to increase the field of view by scanning the object .
when the x - ray tube of 100-m - spot size without the parabolic polycapillary optics and the same ccd detector are used to make a projection - type x - ray image , we may obtain a similar spatial resolution of 12 lp / mm at a magnification of 1.48 . in the imaging system
using the divergent x - ray beam , the edge gradient blurring for the spot size and the magnification may correspond with the two pixels of the ccd detector which is almost equal to the spatial resolution .
if the magnification is larger than 1.48 , the spatial resolution will be worse , and if the magnification is smaller than 1.48 , the spatial resolution will not improve because one line - pair needs two pixels to separate the pattern at least . in this sense , only similar spatial resolution of 12 lp / mm will be available at a magnification of less than 1.48 for the divergent x - ray beam .
in addition , a high radiation dose compared to the low radiation from small - field digital mammographic imaging system can not be avoided for the divergent beam . in general
, a thick filter considerably reduces low - energy x - rays including also characteristic radiations and requires a longer exposure time to obtain the same number of photons on the ccd detector compared to a thin filter . with using a thick filter ,
the detector noise could be increased and the image quality might be reduced if the x - ray source was not strong enough .
spatial resolutions of 12 lp / mm for molybdenum and rhodium filters with a 25-m thickness were obtained using the small - field digital mammographic imaging system .
the resolution in the digital mammographic imaging system strongly depended on the pixel size of the detector .
the resolution should be improved in future with advances in the manufacturing technology for ccd or cmos detectors thereby creating a smaller pixel size .
the small - field digital mammographic imaging system was able to diminish the radiation dose compared to that of the conventional projection - type mammography , for which an entire object receives the radiation dose .
in addition , the parabolic polycapillary optics itself plays a role of a low - pass filter to eliminate x - rays which have higher energy than molybdenum radiation . image blur and radiation dose by x - ray beams of high energy which are not removed by conventional molybdenum and rhodium filters
the x - ray beams of high energy larger than 20 kev removed contributes to improve image quality and to reduce the radiation dose . in other applications ,
e.g. , conventional radiography , high energy x - ray , for instance , 75 kev , is required . to propagate the high energy x - ray
, each diameter of glass capillary in the polycapillary optics should be very small , i.e. , sub - micrometer size , because the critical angle for the high energy x - ray is extremely small . in current manufacturing technology
thus , general x - ray imaging using parallel beam through the parabolic polycapillary optics can be restricted .
therefore , to obtain a parallel beam of high photon flux , the x - ray tube should have a high capacity . in conclusion , due to its high spatial resolution and low radiation dose , a small - field digital mammographic imaging system has the potential to be used for examining local volumes of breast tissue . a relatively large field image
this system can be a useful diagnostic tool for examining a small field of breast cancer with a low radiation dose to the patient after conducting conventional mammography studies . to improve the small - field digital mammographic imaging system using parabolic polycapillary optics , large
 objectiveto evaluate the efficacy for spatial resolution and radiation dose of a small - field digital mammographic imaging system using parabolic polycapillary optics.materials and methodswe developed a small - field digital mammographic imaging system composed of a ccd ( charge coupled device ) detector and an x - ray source coupled with parabolic polycapillary optics . the spatial resolution and radiation dose according to various filters were evaluated for a small - field digital mammographic imaging system . 
 the images of a test standard phantom and breast cancer tissue sample were obtained.resultsthe small - field digital mammographic imaging system had spatial resolutions of 12 lp / mm with molybdenum and rhodium filters with a 25-m thickness . with a thicker molybdenum filter ( 100 m thick ) , the system had a higher spatial resolution of 11 lp / mm and contrast of 0.48 . 
 the radiation dose for a rhodium filter with a 25-m thickness was 0.13 mgy within a 10-mm - diameter local field . 
 a larger field image greater than 10 mm in diameter could be obtained by scanning an object . on the small - field mammographic imaging system , microcalcifications of breast cancer tissue 
 were clearly observed.conclusiona small - field digital mammographic imaging system with parabolic polycapillary optics may be a useful diagnostic tool for providing high - resolution imaging with a low radiation dose for examination of local volumes of breast tissue . 