MTF and DQE enhancement using an apodized-aperture x-ray detector design

Transcription

1 MTF nd DQE enhncement sing n podized-pertre -ry detector design Tomi F. Nno, ) Terenz Escrtin, nd Elin Ismilov Robrts Reserch Institte nd Deprtment of Medicl Biophysics, Western University, London, Ontrio, Cnd N6A 5B7 Krim S. Krim Deprtment of Compter Engineering, University of Wterloo, Wterloo, Ontrio, Cnd Jn Lindstr om Krolinsk University Hospitl, Soln, Sweden Ho Kyng Kim School of Mechnicl Engineering, Psn Ntionl University, Bsn, Kore In A. Cnninghm Robrts Reserch Institte nd Deprtment of Medicl Biophysics, Western University, London, Ontrio, Cnd N6A 5B7 (Received 28 October 26; revised 6 My 27; ccepted for pbliction 8 Jne 27; pblished 2 Agst 27) Prpose: Acqisition of high-qlity -ry imges sing low ptient eposres reqires detectors with high detective qntm efficiency (DQE). We describe novel podized-pertre piel (AAP) design tht increses high-freqency modltion trnsfer fnction (MTF) nd DQE vles. The AAP design mkes seprtion of physicl sensor elements from imge piels by sing very smll sensor elements (e.g.,..25 mm) to synthesize desired lrger imge piels (e.g.,..2 mm). Methods: A cscded systems model of signl nd noise propgtion is developed to describe the benefits of the AAP pproch in terms of the MTF, Wiener noise power spectrm (NPS), nd DQE. The theoreticl model ws vlidted eperimentlly sing CMOS/CsI detector with.5 mm sensor elements to synthesize.2 mm imge piels nd clinicl Se detector with.7 mm sensor elements to synthesize.28 mm piels. A Monte Crlo stdy nd -ry imges of str-pttern nd rt leg re sed to vislly compre AAP imges. Reslts: When sed with high-resoltion converter lyer nd sensor elements one qrter the size of imge piels, the MTF is incresed by 53% nd the DQE by fctor of 2.39 t the imge smpling ct-off freqency. Both simlted nd demonstrtion imges show improved detectbility of high-freqency content nd removl of lising rtifcts. Evidence of Gibbs ringing is sometimes seen ner high-contrst edges. Conclsions: It is shown tht the AAP pproch preserves the MTF of the smll sensor elements nd ttentes freqencies bove the imge smpling ct-off freqency. This hs the doble benefit of improving the MTF while redcing both signl nd noise lising, reslting in n increse of the DQE t high sptil freqencies. For optiml implementtion, the converter lyer mst hve very high sptil resoltion nd the detector mst hve low redot noise. 27 Americn Assocition of Physicists in Medicine [ Key words: podized pertre piel (AAP), cscded-systems nlysis (CSA), detective qntm efficiency (DQE), digitl rdiogrphy, -ry detectors. INTRODUCTION The need to prodce high-qlity medicl imges while minimizing risks ssocited with rdition eposre,2 is key motivtor for the development of new -ry detector technologies. Two criticl detector-performnce metrics re the modltion trnsfer fnction (MTF) nd detective qntm efficiency (DQE), epressed s fnction of sptil freqency. The MTF describes sptil resoltion nd the ppernce of high-contrst nd high signl-tonoise rtio (SNR) strctres. The DQE describes imge SNR for given nmber of -ry qnt incident on the detector with n idel photon-conting detector hving nity DQE. 3 5 Not ll systems re ble to prodce eqivlent imge qlity nd SNR for given eposre, de to differences in DQE. 6 For emple, DQE cn be redced by: () rebsorption nd escpe of chrcteristic nd sctter photons from photoelectric nd Compton interctions; (b) indeqte nmber of secondry qnt collected (opticl photons in phosphor or chrges in photocondctor); (c) sctter of secondry qnt (opticl sctter or chrge migrtion); (d) noise lising; nd (e) electronic red-ot noise. 7 2 When red-ot noise is sfficiently smll, noise lising is the primry cse of DQE degrdtion in -Se detectors t high sptil freqencies. 8,3,4 Severl investigtors hve stdied methods of redcing signl nd noise lising. For emple, lising rtifcts cn be minimized by preferentilly sppressing freqencies 4525 Med. Phys. 44 (9), September /27/44(9)/4525/ 27 Americn Assocition of Physicists in Medicine 4525

2 4526 Nno et l.: MTF nd DQE of the AAP -ry detector 4526 where lising my be epected. The effective presmpling filter described by Ji et l. 5 is liner filter tht sppresses both signl nd noise, reslting in redced lising rtifcts bt no improvement in the DQE. Rowlnds described method of chrge shring between elements in sensor rry to redce lising. 6,7 This pproch redced the MTF slightly, bt incresed the DQE t freqencies where noise is redced more thn the sqred MTF. We describe method of sppressing both signl nd noise lising while improving the MTF nd DQE t high freqencies. 8,9 The method reqires detector consisting of n rry of sensor elements tht re smller thn the desired imge piel size. This provides n over-smpled imge signl tht is sed to synthesize imge piels while mimizing the MTF nd sppressing lising. The gol ws to develop n pproch of improving the DQE by tking dvntge of new technologies (e.g., CMOS) tht cn be sed to mnfctre sensor elements so smll they my hve no clinicl importnce s imge piels directly, or reslt in imge files too lrge for modern PACS nd disply systems. The reslt is detector with n podized pertre piel (AAP) design in which piels hve weighted nd overlpping pertre response rther thn conventionl nonoverlpping piel pertres. The converter lyer mst lso be very high resoltion, sch s morphos selenim deposited on CMOS sensor rry In this rticle, we present theoreticl description of the AAP design nd describe improvements in detector performnce in terms of the MTF nd DQE. Reslts re vlidted with simple Monte Crlo simltion nd eperimentl proof-of-concept stdies. 2. THEORY The SNR performnce of the AAP design is described sing cscded systems nlysis (CSA) tht qntifies signl nd noise properties of qntm-bsed imging systems sing liner-systems pproch. 5,2,4 It describes propgtion of imge signl nd noise in the sptil freqency domin throgh cscde of simple physicl processes. Inpt to the CSA model is rndom point process 23 describing sptil distribtion of -ry qnt ~q o ðþ incident on the detector s illstrted in Fig., consisting of the sperposition of Dirc d-fnction for ech incident -ry photon. The overhed tilde ( ~ ) is sed to indicte rndom vrible (RV) or fnction, nd overhed br ( ) indictes n epecttion vle. We se one-dimensionl illstrtions for simplicity bt reslts re esily generlized to two-dimensionl spce. The model otpt is ~ d y ðþ, seqence of niformly spced d-fnctions scled by ssocited discrete nmericl vles representing imge piel dt where the sperscript is sed to indicte smpled fnction. Cscded models of both simple conventionl detector nd n AAP detector re compred in Fig. 2. For ech, the three colmns represent: () imge signl in the sptil domin; (b) imge signl in the sptil freqency domin (mgnitde only); nd (c) Wiener noise power spectrm. The FIG.. Inpt to the cscded model is ~q o ðþ, rndom point process consisting of d-fnctions representing -ry qnt incident on the detector. The otpt is ~d y ðþ, niformly spced seqence of d-fnctions scled by ssocited discrete imge piel vles. [Color figre cn be viewed t wileyonlinelibrry.com] letter q is sed to indicte rndom point process describing sptil distribtion of qnt (d fnctions), d detector nmericl vle, nd n n dditive detector redot noise term. In the freqency domin, dshed lines indicte lised terms, wheres solid lines indicte fndmentl components (in the 2nd colmn) nd sm of hrmonics (in the 3rd colmn). The inpt to step is ~q o ðþ representing -ry qnt incident on the detector: 24 ~q o ðþ ¼ X~ N o n¼ dð e n Þ; () where e n is vector RV describing the coordinte of the nth of ~N o photons. In prctice, ~ n is not niformly distribted to reflect nonniform -ry trnsmission throgh the ptient, bt for Forier metrics of noise we mst ssme wide-sense sttionry noise processes, reqiring tht ~ n be niformly distribted over n infinite detector tht we represent s hving width L in the limit L? nd N o ¼ q o L. The Forier trnsform (FT) of ~q o ðþ is ~Q o ðþ, the sperposition of the FT of mny shifted d-fnctions. Appliction of the Forier shift theorem gives: ~Q o ðþ ¼F f~q o ðþg ¼ X~ N o e i2p~ n (2) n¼ nd j~q o ðþj ¼ ~N o which is independent of freqency. The Wiener NPS of Poisson rndom distribtion, 25 ~q o ðþ, is therefore W qo ðþ ¼q o. It is ssmed tht ll incident -ry qnt interct (nity qntm efficiency) in n idel converter lyer sch tht ech sensor element is n idel energyintegrting sensor. Medicl Physics, 44 (9), September 27

3 4527 Nno et l.: MTF nd DQE of the AAP -ry detector 4527 Conventionl Detector AAP Detector SPATIAL DOMAIN FREQUENCY DOMAIN (Mgnitde) WIENER NPS SPATIAL DOMAIN FREQUENCY DOMAIN (Mgnitde) WIENER NPS q o () Qo () W o () = q o q o () Qo () W o () = q o ) kπ( ) k sinc () kπ( ) ( ) k 2 2 sinc 2 () sinc k 2 2 sinc 2 ( ) ) = d () = D () =W = d () = D () () =W() 2) i δ( i) j δ( j ) i δ( ) j δ( j ) j δ( j ) 2 2 2) j δ( j ) = d () = D () W () =k 2 q o = d () = D () W () =k 2 q o 3) +ñ () +Ñ () + σ2 +ñ () +Ñ () + σ 2 3) = d ñ() = D ñ () W ñ () =k 2 q o + σ 2 3.) f() F() F() 2 = d f () = D f () W f () =Wñ () F() 2 3.2) i δ( i) j δ( j ) 2 j δ( j ) = d C() = D C () W C () =k 2 q o + σ2 = d A() = D A () W A () FIG. 2. Grphicl illstrtion of the CSA model compring signl nd noise trnsfer throgh conventionl (left) nd AAP (right) detectors. The three colmns illstrte sptil domin signl, Forier domin signl (mgnitde only plotted), nd Wiener NPS. The inpt t the top consists of rndom sptil distribtion of -ry qnt intercting in ech detector. The detector otpt t the bottom consists of seqence of d-fnctions scled by discrete piel vles representing the finl digitl imge. Dshed lines indicte lised contribtions. [Color figre cn be viewed t wileyonlinelibrry.com] Medicl Physics, 44 (9), September 27

4 4528 Nno et l.: MTF nd DQE of the AAP -ry detector A. Conventionl detector As illstrted in step () of Fig. 2, the nmber of photons intercting in the ith element of width of conventionl detector, scled by constnt k representing detector gin, is given by: ~d ;i ¼ ~d ðþ ¼i ¼ k~q o ðþ Y (3) ¼i where * represents convoltion opertion nd ~d ðþ is the detector presmpling signl describing the sensor signl tht wold be obtined for n element centered t. The FT of ~d ðþ is given by: F ~d ðþ ¼ ~D ðþ ¼k~Q o ðþsincðþ (4) where sinc() sin (p)/p nd the Wiener NPS by W ðþ ¼k 2 2 q o sinc 2 ðþ: (5) The process of evlting ~d ðþ to obtin the set of discrete signl vles from ll elements is illstrted in step (2): ~d y ðþ ¼ ~d ðþ X i¼ dð iþ ¼ X i¼ ~d ;i dð iþ; (6) reslting in series of d-fnctions scled by vles ~d ;i where the d-fnctions give positionl significnce to the discrete vles. The FT of ~d y ðþ is given by ~D yðþ ¼k ~Q o ðþsincðþ þ X k ~Q o j (7) sincð jþ: j¼ The Wiener NPS is determined by noting tht ~d y ðþ is wide-sense cyclosttionry rndom process s the men nd tocovrince re sttionry with shifts of i. 9,26 Ths, while signl lising is described s convoltion of ~D ðþ with P j dð j Þ, noise lising is described s convoltion of W d ðþ with Pj dð j 2 Þ, giving: W yðþ ¼ 2 W ðþþ X 2 W j (8) j¼ " # ¼ k 2 q o sinc 2 ðþþ X sinc 2 ð jþ (9) ¼ k 2 q o : () The lst reslt comes from the property tht n infinite seqence of sinc 2 ð) fnctions, shifted by integer mltiples of, sm to nity. 3 Detector electronic dditive redot noise is represented s the ddition of ~n y ðþ, seqence of d-fnctions scled by discrete zero-men Gssin RV ~n ;i hving vrince r 2 : ~n y X ðþ ¼ ~n ;i dð iþ: () i¼ With dditive noise, the conventionl detector signl is shown t step (3): j¼ ~d y C ðþ ¼~ d y ðþþ~ny ðþ (2) hving NPS given by W C yðþ ¼k 2 q o þ r2 : (3) It is convenient to epress the NPS s normlized NPS, W ðnþ C y ðþ W C yðþq o =h~d y C ðþi2, giving: W ðnþ r2 ðþ ¼ þ C y k 2 ; (4) q o where the verge of scled d-fnctions with spcing is h~d y ðþi ¼ d. This form is helpfl for nderstnding performnce chrcteristics s n idel detector in this model hs W ðnþ ðþ ¼. C y The presmpling MTF is determined s the rtio of the otpt to inpt men signl in the sptil freqency domin, normlized to nity t = : jd MTF C ðþ ¼ ðþj D ðþ ¼ jsincðþj (5) nd DQE by DQE C ðþ ¼ MTF2 C ðþ W ðnþ ðþ ¼ sinc 2 ðþ : (6) þ r2 C y k 2 q o 2.B. AAP detector The AAP detector is represented s n rry of sensor elements of size e, where e is smller thn. With this difference, the cscded model of the AAP detector in Fig. 2 is similr to tht of the conventionl detector p to nd inclding step (3). The synthesis of imge piel vles from sensor dt is epressed s discrete convoltion nd resmpling opertion, corresponding to convoltion integrl in step (3.) giving ~d f ðþ ¼~d y ~n ðþfðþ where f() is the kernel of the presmpling AAP filter, followed by evltion of the reslt t niform spcings in step (3.2). Similr to ~d ðþ, ~d ðþ nd ~ d f ðþ re presmpling fnctions tht re not physiclly ccessible. The otpt from the AAP detector is therefore given by ½mm Š: h ~d y A ðþ ¼ ~d y ~n i ðþfðþ X dð iþ (7) i¼ nd ~D A yðþ ¼ D ~ ~n yðþfðþ þ X ~D ~n y j F j (8) j¼ where F() is the FT of f() nd the NPS of ~d f ðþ is given by [mm]: W f ðþ ¼ k 2 q o þ r2 jfðþj 2 : (9) Medicl Physics, 44 (9), September 27

5 4529 Nno et l.: MTF nd DQE of the AAP -ry detector 4529 The NPS of the AAP detector is ½mm Š: W A yðþ ¼ 2 W f ðþþ X 2 W f j j¼ ¼ 2 k 2 q o þ ( r2 jfðþj 2 þ X F j ) 2 (2) nd the corresponding normlized NPS [nitless]: D E 2 W ðnþ ðþ ¼W A y A yðþq o = ~d y A ðþ ( ¼ þ r2 jfðþj 2 k 2 q o F 2 ðþ þ X F j 2 ) F 2 ðþ (2) where F() is the zero-freqency vle of F() nd F()6¼. The MTF of the AAP detector is therefore given by: jd MTF A ðþ ¼ ðþfðþj D ðþfðþ ¼ jfðþj j FðÞ sincðþ j: (22) The DQE is more sbtle de to the combined effects of noise lising from smpling t spcings of both nd e: DQE A ðþ ¼ MTF2 A ðþ W ðnþ ðþ A y jfðþsincðþj 2 ¼ h in þ r2 k 2 q o jfðþj 2 þ P j¼ F j o 2 j¼ j¼ jsincðþj 2 ¼ h i P þ r2 j¼ k 2 q o þ F : j ð j Þj 2 jfðþj 2 (23) Inspection of Eq. (23) sggests tht good choice for F() is low-pss filter tht blocks ll freqencies bove the smpling ct-off freqency c ¼ :5=. This ensres imge content t freqencies bove ¼ c (in smples with spcings e) is not lised below the imge smpling ct-off freqency c, nd the DQE simplifies to: DQE A ðþ ¼ sinc2 ðþ : (24) þ r2 k 2 q o 2.C. MTF nd DQE improvement The presmpling MTF, normlized NPS, nd DQE crves predicted by the CSA model for conventionl (binned) nd AAP detectors (idel converter-lyer with nity qntm efficiency, rectnglr low-pss AAP filter, e =.5 mm nd =.2 mm) hving the sme piel size re compred in Fig. 3. The conventionl presmpling MTF follows the sinc () shpe given by Eq. (5) while the AAP presmpling MTF follows sinc(e) p to the ct-off freqency c ¼ :5= nd sppresses freqencies bove c s described by Eq. MTF Normlized NPS DQE Conv AAP Sptil Freqency (cycles/mm) Sptil Freqency (cycles/mm) Sptil Freqency (cycles/mm) FIG. 3. Theoreticl MTF, normlized NPS, nd DQE, compring n AAP detector with conventionl detector hving the sme piel size, ssming negligible red-ot noise nd idel -ry converter lyer with nity qntm efficiency nd no sptil blr. The normlized NPS of conventionl nd AAP detectors overlp. (22). Ths, while the AAP method reslts in n MTF increse by the fctor sinc(e)/sinc(), giving 53% increse t the ct-off freqency (regrdless of converterlyer blr), it lso removes lising from the imge if present. Comprison of W C yðþ nd W A yðþ t step (3) shows the AAP pproch redces noise lising by sppressing Medicl Physics, 44 (9), September 27

6 453 Nno et l.: MTF nd DQE of the AAP -ry detector 453 freqencies.5/ < <.5/e. As illstrted in Fig. 3, the NPS is independent of freqency for both conventionl nd AAP detectors when sed with n idel (no blr) -ry converter lyer. Eqtions (23) nd (24) show the DQE is independent of AAP filter F() shpe s long s it describes low-pss filter with ct-off freqency c ¼ :5= nd redot noise is negligible. Under these conditions, the DQE-improvement fctor is sinc 2 ðþ=sinc 2 ðþ, eql to 2.39 increse t the imge smpling ct-off freqency. Also, comprison of Eqs. (6) nd (24) shows the AAP pproch will generlly be less tolernt of redot noise, reqiring r 2 ¼ r2 for the sme effect on the DQE, de to the smller sensor size. In two-dimensions, the red-ot noise reqirement scles with the sqre of the element-to-piel size rtio, r 2 ¼ 2r 2. Achieving lower redot noise my not be trivil. Redcing sensor re my decrese the reqired storge cpcitnce in ech element, which my redce noise, bt the corresponding redced signl size nd incresed nmber of sensors on ech dtline will plce greter demnds on the electronics. These my be difficlt to chieve with some technologies. 2.D. Simlted sinsoidl ptterns The visl impct of the epected MTF nd DQE improvements is illstrted with simple simltion compring conventionl with AAP imges. An oversmpled imge (representing microelements with e =.5 mm) ws creted to synthesize both conventionl (4 9 4 binned, =.2 mm) nd AAP ( =.2 mm) imges ssming no red-ot noise. The AAP pproch ws implemented in the freqency domin sing low-pss filter with nity height p to the smpling ct-off freqency c ¼ :5=. Other AAP imges (open field, edge, str-pttern, nd rt leg) were synthesized similrly differing only in piel size. Ech imge hs 5 two-dimensionl sinsoidl ptterns in three rows of differing contrst nd five colmns of differing sptil freqency (.,.5, 2., 2.4, nd 3. cycles/mm) chosen to be below, jst below, nd bove the smpling ct-off freqency of 2.5 cycles/mm. Ptterns in the rows from top to bottom hve mplitdes of 6,, nd 4 piel vles. Gssin noise (stndrd devition of ) ws dded to ech piel in the oversmpled imge to simlte qntm-noise. 3. MATERIALS AND METHODS 3.A. Eperimentl str-pttern nd biologicl imges Proof-of-concept imges for the AAP design were obtined sing str-pttern (Tielng,.5 mm Pb thickness, 45 mm dimeter, with 2 ngled brs) nd clinicl mmmogrphy system (Hologic Inc.) hving Se converter lyer nd.7 mm sensor elements. Both conventionl (494 binning) nd AAP imges were synthesized to crete imges with =.28 mm. With similr Hologic detector, n imge of rt leg perfsed with lnthnide-bsed vsclr contrst gent ws cqired in ccordnce with the protocol (#25 8) pproved by The University of Western Ontrio Concil on Animl Cre. The rw imge ws log-trnsformed nd gry-scle inverted. Conventionl nd AAP imges were synthesized s described bove. While this reslts in reltively low-resoltion (.28 mm piel) imges, they re sed to eperimentlly demonstrte the reltive MTF improvement with the AAP pproch. 3.B. Eperimentl MTF nd DQE Eperimentl vlidtion of the AAP theory ws performed sing both lb-bsed nd clinicl imging systems. The lb system consisted of CMOS-bsed pnel hving.5 mm sensor elements (Xmr, Ryence Co. Ltd., Seol, Kore) with.5-mm CsI converter lyer. Conventionl imges were generted with 494 binning (.2 mm piels) nd AAP imges were synthesized s described in Section 2.D. The MTF nd DQE were determined sing both conventionl nd AAP imges with detector eposre of 4 lgy ir KERMA nd IEC RQA-5 spectrm (7 kv, 2. mm dded Al, 6.4 mas, 7. mm Al HVL, 5 cm sorce-imge distnce) sing DQE-testing instrment (DQEPro, DQE Instrments Inc., London, Cnd) following IEC gidelines. 27 Additive red-ot noise ws verified to be negligible reltive to -ry qntm noise. The sme MTF nd DQE comprison ws mde sing Hologic detector with Se converter lyer. Imges hving.28 mm piels were synthesized for both AAP nd binning methods s described bove. The MTF nd DQE were mesred sing 9 lgy ir KERMA with n IEC W/Rh spectrm (28 kv, 2 mm dded Al, 24 mas,.75 mmal HVL, 65 cm sorce-imge distnce, no grid). 4. RESULTS 4.A. Simlted sinsoidl ptterns The simlted imges in Fig. 4 compre the visl ppernce of conventionl (binned, pper) nd AAP (lower) methods. The first observtion is tht noise in both imges is indistingishble. This is epected s they ech hve flt NPS nd imges re shown with the sme disply windows. The conventionl imge shows decresing contrst with incresing freqency in the first for colmns s epected, nd the fifth colmn shows pttern tht hs been lised to lower freqency. In comprison, the AAP imge shows very little loss of contrst with freqency in the first for colmns, consistent with the epected fltter MTF, nd the fifth-colmn pttern hs been removed completely s it contins only freqencies bove the smpling ct-off freqency c. This observtion gives confidence in the bility of the AAP method to sppress both signl nd noise freqencies bove c. Medicl Physics, 44 (9), September 27

7 453 Nno et l.: MTF nd DQE of the AAP -ry detector B. Eperimentl str-pttern nd biologicl imges Str-pttern imges in Fig. 5 show obvios difference between the conventionl (left) nd AAP (right) imges. The conventionl imge contins the distinct Moire pttern rtifct de to interference effects from ndersmpled signls (lising) reslting in misrepresenttion of the str-pttern with contrst reversl ner the imge smpling ct-off freqency (ner the circle). The AAP imge shows improved contrst, prticlrly t high freqencies, nd removl of lising rtifcts. The AAP imge of the biologicl specimen in Fig. 6 shows shrper bone edges (white rrow) nd finer vscltre detil (white circle) thn the conventionl imge. This is de to improved high-freqency response with the AAP pproch. The AAP imge preserves high-freqency content p to the ct-off freqency while the conventionl imge ppers blrred. Also, the AAP imge hs no visible ringing. Both conventionl nd AAP imges were sinc interpolted (49 oversmpling) to ensre ll three imges hve the sme nmber of piels in the pbliction to llow for direct comprison. FIG. 4. Simlted sinsoidl pttern imges with freqencies.,.5, , nd 3. cycles/mm illstrting the visl difference in conventionl (pper) nd AAP (lower) imges (e =.5 mm, =.2 mm, c ¼ 2:5 cycles/ mm). Noise hs similr ppernce in conventionl nd AAP imges. The conventionl imge shows decresing contrst with incresing freqency s epected in the first for colmns nd lised pttern in the fifth (which is bove the smpling ct-off freqency). The AAP imge shows less chnge in contrst with incresing freqency in the first for colmns nd no (lised) pttern in the fifth. Imges re sinc interpolted (49 oversmpling) for disply prposes nd best viewed on high-resoltion disply. 4.C. Eperimentl MTF nd DQE 4.C.. CMOS/CSI detector The eperimentl presmpling MTF, normlized NPS, nd DQE crves obtined with the CMOS/CsI detector re shown in Fig. 7, compring conventionl (binned) nd AAP methods. This detector hs etremely low redot noise. The mesred normlized redot NPS for both conventionl nd AAP methods ws pproimtely.3 over ll freqencies which is considered negligible compred to the totl NPS s shown. Opticl sctter in the CsI converter lyer redces FIG. 5. Conventionl (left) nd AAP (right) imges of str-pttern cqired with clinicl mmmogrphy Se detector. The imge piel size is 49 the detector element size nd the imge smpling ct-off freqency is.8 cycles/mm (circle otline). In the conventionl imge, there re lising rtifcts (Moiré pttern) t high freqencies ner the center of the pttern. The AAP imge shows sppression of the Moiré pttern nd incresed contrst of the br ptterns t higher freqencies. Medicl Physics, 44 (9), September 27

8 4532 Nno et l.: MTF nd DQE of the AAP -ry detector 4532 FIG. 6. Comprison of conventionl nd AAP imges of contrsted rt leg. The originl imge (left) ws cqired with Se detector nd sed to synthesize conventionl (middle) nd AAP (right) imges. The AAP imge hs shrper bone edges (white rrow), finer detil of vscltre (white circle), nd more ccrtely shows originl imge fetres. sptil resoltion nd hence the mesred MTF decreses with freqency more qickly thn the theoreticl model of Eq. (5) which does not inclde converter. The AAP MTF shows modest improvement only, still consistent with the epected 53% increse, nd the low-pss chrcteristic of the AAP method s freqencies bove c ¼ :5= re sppressed. The CsI converter lso sppresses high-freqency noise, nd hence there is less noise lising thn predicted by the theoreticl model. As conseqence, while the DQE is still improved by fctor of two (from.2 to.4) ner the ct-off freqency, it is less thn wht is predicted by Eq. (24). 4.C.2. Se detector Reslts obtined with the Se detector re closer to the theoreticl prediction s the Se converter lyer reslts in very little loss of sptil resoltion. 28 Figre 8 shows mesred presmpling MTF, normlized NPS, nd DQE crves compring conventionl (binned) nd AAP methods sing the Se detector. The conventionl MTF is similr to the theoreticl crve of Eq. (5) nd the AAP MTF is closer to Eq. (22) inclding the low-pss ct-off freqency of c ¼ :5= :8 cycles/mm. Redot noise is negligible compred to the totl imge noise s shown nd the NPS is reltively flt for both conventionl nd AAP imges. The DQE ner c is pproimtely dobled from.3 to.6, reslting in DQE tht is less dependent of freqency p to the smpling ctoff freqency. The AAP response in the sptil domin is shown in the edge-response fnction (ERF), nd its derivtive the linespred fnction (LSF), in Fig. 9 for both conventionl nd AAP pproches. The AAP crves, prticlrly the LSF, show Gibbs ringing de to or se of rectnglr filter with shrp trnction in the freqency domin. 5. DISCUSSION The pproch described in this work is the first description of how high-freqency DQE vles cn be incresed by redcing spectrl lising withot simply sppressing content t freqencies where lising my occr. Spectrl lising cn be the primry cse of DQE degrdtion t high freqencies for Se-bsed detectors nd for CsI-bsed detectors t -ry energies below the K-edge energies of Cs nd I ( 33 kev). The AAP method improves both the MTF nd DQE, bt my be less effective when other fctors sch s dditive detector noise, secondry qntm sinks 7, or sctter rebsorption re the min cse of SNR degrdtion. Sptil-resoltion limittions of the converter mteril eplins the nderwhelming improvement in DQE of the CMOS/CsI detector shown here, nd illstrtes the need for very high-resoltion converter mterils to mke this sccessfl. For emple, Se/CMOS combintion my be ner optiml Also, the shrp low-pss filter sed in this demonstrtion reslts in slight Gibbs ringing rond edges, s shown in the edge-response fnction nd the str-pttern imge. This cn likely be redced with less-brpt filter ctoff, bt mybe t the epense of redced benefit on the MTF nd DQE. Filters with shrp-ctoff in the freqency domin reslt in detector implse response tht is not locl, sch s off-center oscilltions in the sptil domin s shown in the AAP line-spred fnction. This cold potentilly reslt in visible ringing rtifcts ner shrp-edges, bt it preserves imge contrst nd improves visibility of fetres in noise-limited low-contrst regions. Conventionl nd AAP pproches wold hve the sme DQE if lising did not occr, bt imges from conventionl high-resoltion converter lyer detectors slly hve noise Medicl Physics, 44 (9), September 27

9 4533 Nno et l.: MTF nd DQE of the AAP -ry detector Conv AAP.8 Conv AAP.6.6 MTF MTF Sptil Freqency (cycles/mm) Sptil Freqency (cycles/mm) Conv Red-ot NPS AAP Red-ot NPS.5 Conv Red-ot NPS AAP Red-ot NPS Normlized NPS.5 Normlized NPS Sptil Freqency (cycles/mm) Sptil Freqency (cycles/mm).8.8 DQE.6.4 DQE Sptil Freqency (cycles/mm) FIG. 7. Presmpling MTF, normlized NPS, nd DQE crves obtined with the CMOS/CsI detector compring conventionl (binned) nd AAP pproches. While these reslts demonstrte n increse in high sptil freqency DQE, the improvement is not s gret s predicted by the CSA model de to resoltion limittions of the CsI. lising. Removing noise lising improves high-freqency DQE nd provides greter visibility of high-freqency fetres present in noise-limited low-contrst regions s shown in Fig. 4. For imges tht re not noise-limited, modest contrst improvement is epected from MTF improvement t high-freqencies with the AAP pproch s observed in Sptil Freqency (cycles/mm) FIG. 8. Mesred presmpling MTF, normlized NPS, nd DQE crves from n Se detector in which.28 mm () piels re synthesized from.7 mm () sensors, compring conventionl (binned) piels of the sme size with the AAP pproch. Fig. 6. This proof-of-concept eperiment demonstrtes shrper edges nd finer detil in AAP imges, even thogh the imge is contrst-limited so we only epect 5% improvement t high freqencies. Greter improvement in visibility of high-freqency content in noise-limited regions is epected. Medicl Physics, 44 (9), September 27

10 4534 Nno et l.: MTF nd DQE of the AAP -ry detector 4534 Conv AAP Conv AAP ERF.4 LSF (mm) (mm) FIG. 9. Edge-response fnction (ERF) nd line-spred fnction (LSF) mesred with Se detector compring conventionl nd AAP designs. The AAP profiles show the Gibbs ringing phenomenon de to shrp trnction of freqencies. Oscilltions in both AAP profiles hve zero-crossings with ectly one piel spcing prt (.28 mm). We view the AAP pproch s hving role to ply on detectors hving sbstntil compttionl bility nd where sensor elements cn be mnfctred smller thn wht might be of prcticl vle for clinicl imging. For emple, the high-freqencies vilble with fll-size detectors hving.25 mm sensors (2 cycles/mm) my hve no direct clinicl vle, nd the reslting file sizes ( TByte) my be too lrge for prcticl disply, trnsmission, nd storge t present. The AAP method my provide n rchitectrl pproch in which imge piels re seprted from physicl sensor elements. On CMOS nd other new detector designs with very smll sensors this my be wy to improve the DQE t freqencies of prcticl importnce. The synthesis of lrger piel vles cold tke plce in rel time, directly on the detector, eliminting the need for very high dt-trnsfer bndwidths in the redot systems. As illstrted here, the AAP pproch my be sefl for CMOS/CsI systems, bt wold likely hve greter impct on CMOS/Se or relted technologies hving very high resoltion converter lyers tht re crrently nder development. 2,22 Development of -ry sensors with microelement sizes for clinicl se reqires converter lyer tht chieves desirble qntm detective efficiency withot redcing sptil resoltion. The low noise performnce of CMOS sensor rrys might best stisfy the red-ot noise reqirement for AAP implementtion de to redced signl strength in ech sensor nd the need for mltiple redots per imge piel. 6. CONCLUSION A method is described in which high-freqency MTF nd DQE performnce of -ry detectors cn be improved throgh the se of detectors with physicl sensor elements tht re smller thn the desired imge piels. It is shown theoreticlly tht the method works by preserving the sperior pertre MTF of the smller physicl sensor elements nd redcing noise lising by implementing low-pss filter tht elimintes freqencies bove the imge smpling ct-off freqency c ¼ :5= where is the imge piel size. This hs the dditionl benefit of removing signl lising from the imge. The reslt is potentil 53% increse in the MTF nd more thn dobling of the DQE t the smpling ct-off freqency when sed with high-resoltion converter lyer. ACKNOWLEDGMENTS The thors re grtefl to Michel McDonld for ssistnce with the eperimentl work nd to the Cndin Instittes of Helth Reserch for finncil spport (Operting Grnt MOP 33596). We re grtefl to Jstin Tse nd Dr. Dvid Holdsworth for providing s with rt leg specimen, nd Gord Mwdsley for helping s cqire imges. Spported by the Brest Cncer Society of Cnd, Tomi F. Nno. CONFLICTS OF INTEREST The thors hve no conflicts of interest to report. ) Athor to whom correspondence shold be ddressed. Electronic mil: tnno@wo.c. REFERENCES. Hll EJ, Brenner DJ. Cncer risks from dignostic rdiology. Br J Rdiol. 28;8: Medicl Physics, 44 (9), September 27

11 4535 Nno et l.: MTF nd DQE of the AAP -ry detector Berrington de Gonzlez A, Drby S. Risk of cncer from dignostic - rys: estimtes for the UK nd 4 other contries. Lncet. 24;363: Shw R. The eqivlent qntm efficiency of the photogrphic process. J Photogr Sc. 963;: ICRU Report 54. Medicl Imging The Assessment of Imge Qlity, ICRU 54, Interntionl Commission of Rdition Units nd Mesrements. Bethesd, MD: ICRU; Cnninghm IA, Shw R. Signl-to-noise optimiztion of medicl imging systems. J Opt Soc Am A. 999;6: Chirelli AM, Edwrds SA, Prmmel MV, et l. Digitl compred with screen-film mmmogrphy: performnce mesres in concrrent cohorts within n orgnized brest screening progrm. Rdiology. 23;268: Cnninghm IA, Westmore MS, Fenster A. A sptil-freqency dependent qntm cconting digrm nd detective qntm efficiency model of signl nd noise propgtion in cscded imging systems. Med Phys. 994;2: Cnninghm IA. Degrdtion of the detective qntm efficiency de to non-nity detector fill fctor. Proc SPIE. My 997;332: Cnninghm I. Hndbook of Medicl Imging, Volme. Physics nd Psychophysics, Chpter 2. Bellinghm, WA: SPIE Press; 22.. Hjdok G, Yo J, Bttist JJ, Cnninghm IA. Signl nd noise trnsfer properties of photoelectric interctions in dignostic -ry imging detectors. Med Phys. 26;33: Hjdok G, Bttist JJ, Cnninghm IA. Fndmentl -ry interction limits in dignostic imging detectors: freqency-dependent Swnk noise. Med Phys. 28;35: Yn S, Tngy J, Kim HK, Cnninghm IA. Cscded-systems nlyses nd the detective qntm efficiency of single-z -ry detectors inclding photoelectric, coherent nd incoherent interctions. Med Phys. 23;4: Zho WZ, Rowlnds JA. Digitl rdiology sing ctive mtri redot of morphos selenim: theoreticl nlysis of detective qntm efficiency. Med Phys. 997;24: Cnninghm IA, Yo J, Sbotic V. Cscded Models nd the DQE of flt-pnel imgers: noise lising, secondry qntm noise nd rebsorption. Proc SPIE. 22;4682: Ji WG, Zho W, Rowlnds JA. Digitl -ry imging sing morphos selenim: redction of lising. Med Phys. 998;25: Rowlnds JA, Ji WG, Zho W, Lee DL. Directconversion flt pnel - ry imging: redction of noise by presmpling filtrtion. Proc SPIE. 2;3977: Zho W, Ji WG, Debrie A, Rowlnds JA. Imging performnce of morphos selenim bsed flt-pnel detectors for digitl mmmogrphy: chrcteriztion of smll re prototye detector. Med Phys. 23;3: Ismilov E, Krim K, Cnninghm IA. Apodized-pertre piel design to increse highfreqency DQE nd redce noise lising detectors in - ry. Proc SPIE. 25;942:942D- 942D-. 9. Nno T, Escrtin T, Krim K, Cnninghm IA. A novel -ry detector design with higher DQE nd redce lising: theoreticl nlysis of - ry rebsorption in detector converter mteril. Proc SPIE. 26;9783: Abbszdeh S, Allec N, Krim KS. Improving morphos selenim photo-detector performnce sing n orgnic semicondctor. Key Eng Mter. 23;543: Fng Y, Bdl A, Bdno A, Krim KS. Sptil resoltion chrcteristics of -Se imging detectors sing sptiotemporl Monte Crlo methods with detiled trnsport of rys, electrons nd electron-hole pirs nder pplied bis. Proc SPIE. 23;8668:86683R Scott CC, Abbszdeh S, Ghnbrzdeh S, et l. Amorphos selenim direct detection CMOS digitl -ry imger with 25 micron piel pitch. Proc SPIE. 24;933:933G. 23. Snyder DL, Miller MI. Rndom Point Processes in Time nd Spce. New York: Springer-Verlg; Brrett HH, Swindell W. Rdiologicl Imging: The Theory of Imge Formtion, Detection, Processing. Cmbridge, MA: Acdemic Press; Brrett HH, Myers KJ. Fondtions of Imge Science. New Jersey: JohnWiley & Sons, Inc.; 24; Chpter, pg Ppolis A. Systems nd Trnsforms with Appliction in Optics. New York, NY: McGrw-Hill Book Compny; Regltory Report by Interntionl Electrotechnicl Commission. Medicl electricl eqipment chrcteristics of digitl ry imging devimging Prt -: Determintion of the detective qntm efficiency Detectors sed in rdiogrphic imging, Medicl Electricl Eqipment IEC , Interntionl Electrotechnicl Commission; Hjdok G, Bttist JJ, Cnninghm IA. Fndmentl -ry interction limits in dignostic imging detectors: sptil resoltion. Med Phys. 28;35: Medicl Physics, 44 (9), September 27