Removing the effects of the “dark matter” in tomography

Remo ing he e ec s o he “da k ma e ”in omog aphy Lionel C. Gon a dQ1 Ins i u o de Ciencia de Ma e iales de Se illa (CSIC), 41092 Se illa, Spain a icle in o A icle his o y: Recei ed 16 Oc obe 2014 Recei ed in e ised o m 10 Ma ch 2015 Accep ed 18 Ma ch 2015 Keywo ds: Tomog aphy Elec on omog aphy Til se ies Image p ocessing abs ac Elec on omog aphy (ET) using di e en imaging modes has been p og essi ely consolida ing i s posi- ion as a key ool in ma e ials science. The fideli y o a omog aphic econs uc ion, o omog am, is a ec ed by se e al expe imen al ac o s. Mos o en, an un ealis ic cloud o in ensi y ha does no co espond o a eal ma e ial phase o he specimen (“da k ma e ”) blu s he omog ams and enhances a e ac s a ising om he missing wedge (MW). He e we show ha by simple p ep ocessing o he backg ound le el o any omog aphic il se ies, i is possible o minimise he nega i e e ec s o ha “da k ma e ”. I e a i e econs uc ion algo i hms con e ge be e , leading o omog ams wi h ewe s eaking a e ac s om he MW, mo e con as , and inc eased accu acy. The conclusions a e alid i - espec i e o he imaging mode used, and he me hodology imp o es he segmen a ion and isualisa ion o omog ams o bo h c ys alline and amo phous ma e ials. We show examples o HAADF STEM and BF TEM omog aphy. &2015 Published by Else ie B.V. 1. In oduc ion Elec on omog aphy (ET) in ma e ials science is a echnique based on he acquisi ion o a se ies o p ojec ed images om a sample by il ing he specimen using a mic oscope goniome e and can be combined wi h spec oscopic da a [1–4]. I p o ides impo an 3D s uc u al and chemical in o ma ion ha makes i possible o co ela e he syn hesis, s uc u e, and unc ionali y o a di e si y o nanos uc u es e en a a omic esolu ion [5–16].ET applica ion ollows a se ies o s eps (Fig. 1a). In ansmission elec on mic oscopy (TEM), usually ‘single-axis il ing’is used, in which he specimen is il ed abou he eucen ic axis o he spe- cimen holde od. A e accu a e alignmen o he omog aphic il se ies, econs uc ion, segmen a ion, and isualisa ion o he 3D olume o omog am a e he s eps necessa y o ex ac quan i a- i e mo phological in o ma ion om he 3D omog ams [17–20]. Fo op imal esul s, he specimen mus be il ed o e a il ha is as close o 790°as possible, bu in p ac ise he maximum il ing ange a ely exceeds 775°. This is he well-known p oblem o he missing wedge (MW) o in o ma ion ha esul s in a dec ease o he spa ial esolu ion and he p esence o a e ac s in he omo- g am [1–4]. Fo ce ain ypes o sample geome ies, he use o double- il ing, ull- o a ion holde s and adap ed p epa a ion me hods can be used o dec easing he MW [21,22]. Impo an p og ess in ET has esul ed om digi al p ocessing o omog aphic il se ies be o e 3D econs uc ion by accu a e in e pola ion o sinog ams, edge de ec ion, con as enhancemen , and accu a e alignmen o il se ies [23–26]. The nex s ep is he econs uc ion o he omog am, ypically using weigh ed back-p ojec ion (WP) o he simul aneous i e a i e econs uc ion echnique (SIRT) [3,24]. None heless, much e o is being pu in o no el e- cons uc ion algo i hms which can no ably imp o e he quali y o omog ams, e en wi h low sampling and limi ed angula ange, using ei he he disc e isa ion o in ensi ies, he calcula ion o si- nusoidal ajec o ies in sinog ams, he inco po a ion o geome ic p io knowledge, o comp essi e sensing [27–31]. Tomog ams ob ained a e he econs uc ion a e 3D da ase s con aining a con inuous ange o in ensi y le els, and he e o e in o de o ex ac use ul in o ma ion, isualisa ion and segmen a ion a e equi ed in combina ion wi h he applica ion o sophis ica ed al- go i hms, such as aniso opic non-linea di usion, o educe noise and enhance local s uc u e wi hou wo sening he esolu ion o s uc u al in o ma ion, adap i e h esholding, o equalisa ion in eal space [32–35]. In he p esen wo k, we ocus on he e ec s o an expe imen al pa ame e : he minimum alue o he in ensi y used o acqui e a omog aphic il se ies. Ou esul s show ha by op imisa ion o he backg ound le el o a omog aphic il se ies i is possible o d ama ically imp o e he quali y o he omog am. 2. Me hods In ou expe imen s we use a comme cial so wa e package o acquisi ion and econs uc ion o omog aphic il se ies called Explo e3D, which is he s anda d o TEMs manu ac u ed by FEI. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Con en s lis s a ailable a ScienceDi ec jou nal homepage: www.else ie .com/loca e/ul amic Ul amic oscopy h p://dx.doi.o g/10.1016/j.ul amic.2015.03.017 0304-3991/&2015 Published by Else ie B.V. E-mail add ess: [email p o ec ed] Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎ The file o ma is a e sion o he o iginal one.m c c ea ed by he Medical Resea ch Council..Wi h his so wa e, he pixel in ensi ies o he il se ies o images a e eco ded as numbe s wi h he o - ma o in ege signed and 16 bi s, meaning ha pixels can ake disc e e alues in he ange be ween 32,678 and þ32,677. In o de o op imise he backg ound o he il se ies, he minimum alue o he ma ix I min is ound and he alues o he ma ix a e downshi ed by an amoun gi en by he di e ence be ween 32,678 and I min . The esul ing ma ix is sa ed back in o he FEI o ma o subsequen omog aphic econs uc ion. I is wo h men ioning he e ha he basis o omog aphy, he Radon ans o m defines a p ojec ion unc ion (an image in TEM) as an in eg al om ze o. Simila ly, in o de o con e ge o a co ec solu ion i e a i e econs uc ion me hods equi e he alues o in ensi ies o be posi i e, i.e., ha he in ensi ies mus be equal o abo e ze o [36]. Because he so wa e o FEI econs uc s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 Fig. 1. Tomog aphic il se ies and minimum in ensi y. (a) Typical Q2 s eps pe o med in elec on omog aphy. A s ep consis ing in he op imisa ion o he backg ound le el o a il se ies is equi ed be o e econs uc ion. (b) Di e ence be ween he bi esolu ion o he de ec o and he ange o in ensi ies used while adjus ing I/C. (c and d) Model o one sphe ical P pa icle suppo ed on a C film su ounded by acuum and he co esponding p ojec ed in ensi y images wi h and wi hou backg ound shi . (e) In ensi y p ofiles measu ed along he a owed lines shown in (c) and (d). In he ideal si ua ion, he acuum le el coincides wi h he absolu e minimum alue o he eco ding sys em (blue cu e wi h squa es). In p ac ise he images o a il se ies a e o en eco ded wi h a di e en minimum ( ed cu e wi h ci cles). The shi is equi alen o he p esence o a laye o ma e ial ha does no exis . (Fo in e p e a ion o he e e ences o colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.) L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎2 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i omog aphic se ies co ec ly we assume he e ha he ange o signed alues used in he FEI so wa e is only o s o age and i- sualisa ion pu poses, and ha he econs uc ion algo i hms mus escale in e nally he in ensi ies so ha hey a e unsigned o e- cons uc ion pu poses. The omog aphic HAADF STEM se ies shown in Fig. 3 was ob- ained using a Tecnai F30 wi h a field-emission gun (FEGTEM) ope a ed a 200 kV. Images in Fig. 4 we e acqui ed using an abe a ion-co ec ed Ti an TEM (FEGTEM) ope a ed a 300 kV and a came a leng h co esponding o inne de ec o semi-angles o E90 m ad o enhance he con as be ween he co es and he shells o he pa icles while minimising di ac ion. Images we e acqui ed using a single- il omog aphy holde model 2020 ( om Fischione Ins umen s). Alignmen and omog aphic econs uc- ion o he il se ies we e pe o med using he SIRT algo i hm wi h 15 i e a ions using Inspec 3D so wa e om FEI. The same so wa e was used o in e he con as o he BF TEM se ies o Fig. 5. Visualisa ion using ol ex and o hoslices, segmen a ion, isosu ace ende ing, and Sobel fil e ing o he 3D da ase s was pe o med using A izo so wa e. The omog aphic BF TEM se ies shown in Figs. 5 and 6was acqui ed using he same Ti an mic o- scope and a CCD came a. Image con as is defined as CI I I I/ max min max min =− + Fo he op imisa ion o he backg ound o he il se ies and algo i hm was implemen ed using Ma lab. An aligned il se ies o images is loaded in o a ma ix. The ma ix con ains he in ensi ies o e e y pixel o he omog aphic se ies. The in ensi ies ha o m an image as measu ed by a de ec o sys em mus be ans o med in o he digi al domain by analogue- o-digi al con e sion so ha pixel in ensi ies ha a e eco ded in an image ake disc e e alues wi hin a ange ha depends on he bi esolu ion o he de ec o sys em. 3. In ensi y o a il se ies and backg ound op imisa ion When an expe imen al omog aphic il se ies o images is acqui ed du ing an expe imen , i is necessa y o fi s adjus he minimum alue and he ange o alues o pixel in ensi ies ac- qui ed by a de ec o by a ying he O se and Gain (O/G) pa a- me e s (which co espond wi h he imaging pa ame e s in ensi y and con as ). No mally, he adjus men o O/G is done by check- ing ha he image is co ec ly eco ded a a fini e numbe o il s (e.g. 0°,730°,770°). Ne e heless, because an use ul il se ies equi es he acquisi ion o many mo e images ( ypically wi h a il s ep o 2°), he O/G adjus men made o some images may no be alid o he whole se ies o images because he e will be hickness changes and a ia ions in di ac ion con as ha canno be con olled a p io i. I he expe imen is pe o med such ha he in ensi y le el is oo low o i he con as ange is oo wide, he pixel in ensi ies o some images can all ou side he dynamic ange o he de ec o , and pa s o he images will become o e sa u a ed o will be unde sa u a ed a se e al il s. The e o e i is a common p ac ise o adjus he O/G le el wi hin a ange o alues ha is na owe han he ull a ailable bi esolu ion o he de ec o (o o he image o ma used o s o ing he images) (see Fig. 1b). The d awback o his s a egy is ha he backg ound le el o e e y image o he expe imen al il se ies will be shi ed by an indefini e cons an owa ds highe alues o in ensi y. This is ce ainly he case o mos specimens when he e is no a ailable a acuum egion o define a ze o e e ence le el o in ensi y. On he o he hand, mos o en when pe o ming ET o a nanos uc u e, we a e no in e es ed in i s su ounding ( he suppo ing film o a con aining ma ix). Hence, we p opose he e o minimise he backg ound le el o in ensi y o he images o a il se ies a he expense o no econs uc ing he space su ounding de nanos- uc u e. Such s ep elimina es he unce ain y o lacking o a e- e ence le el o in ensi y while i imp o es he fideli y o he e- cons uc ion o he nanos uc u e o in e es . Fig. 1c and d shows a simula ed HAADF STEM image ( e- p esen a i e o one image o a omog aphic il se ies) o a model o a high-densi y sphe ical pa icle suspended on a lowe densi y film and su ounded by acuum. In ensi ies can ake alues be- ween 0 (black) and 1 (whi e). In Fig. 1c he minimum in ensi y ( ha o acuum) coincides wi h 0, he minimum alue a ailable wi h a hypo he ical de ec o sys em. In Fig. 1d he minimum in- ensi y ( ha o acuum) is shi ed o a alue 40. Fig. 1e shows he in ensi y p ofiles along he cen e o he images in Fig. 1c and d. The backg ound shi (see dashed o ange line) is equi alen o adding new ma e ial ha is no eal (o ange colou in Fig. 1d) o he model o he specimen. Bu i a il se ies o images such he one in Fig. 1d is used o omog aphic econs uc ion, he o ange laye will show up in he omog am as a eal ma e ial ha will in oduce a e ac s. I is known ha i a ca bon film used as sup- po o omog aphy is hick, hen i can in oduce a e ac s in a econs uc ion such as he op–bo om e ec [37]. Howe e , he p oblem desc ibed in his pape is a wo se si- ua ion because he o ange laye in Fig. 1d is p esen in e e y image o he il se ies, as a hick laye ha is no limi ed in space and i will show up in e e y oxel (3D pixel) o he omog am.Fig. 2a–c com- pa es he omog aphic econs uc ion o an objec model (a “phan om”) shown in Fig. 2a wi h a mo e ealis ic econs uc ion wi h a MW o 40°and using p ojec ions o he “phan om”wi h and wi hou backg ound shi (Fig. 2b and c espec i ely). Fig. 2d shows h ee in ensi y p ofiles along he cen al lines o he “phan oms”. I is clea ha in he case o using a il se ies wi hou a shi o he backg ound le el (blue line, I min E0) he con as o he econs uc ion inc eases, he in ensi ies quan i a i ely ma ch he in ensi y ange o he o iginal “phan om”mo e accu a ely, and he e a e ewe a e ac s ou side he phan om. In summa y, i an inapp op ia e backg ound le el abo e ze o is chosen an a ificial ex a hickness is added o he suppo o he sample in he ex- pe imen al omog aphic il se ies. 4. Expe imen al esul s 4.1. HAADF STEM omog aphy: Imp o ing con as and educing a e ac s Fig. 3a is an expe imen al image acqui ed a 0° ep esen a i e o a HAADF STEM il se ies o a sample o BiPO 4 s a -like pa icles [38]. The il se ies was acqui ed wi h a minimum in ensi y alue o 619. This alue is shi ed by a la ge amoun wi h espec o he absolu e minimum alue allowed by he de ec o sys em, ha is, 32,768 o 16-bi esolu ion. The same il se ies was p ocessed o fline and i s backg ound le el was downshi ed by sub ac ing a cons an alue o þ32,016 om e e y image ( he di e ence be- ween 32,678 and 619). Fig. 3b shows he cen al line p ofiles o in ensi ies measu ed on he images a 0° il o he wo il se ies wi h and wi hou backg ound op imisa ion. Tomog ams we e econs uc ed om bo h il se ies and hei his og ams calcula ed (Fig. 3c). Bo h his og ams display a maximum peak o coun s a low in ensi ies. These peaks co espond wi h oxels (3D pixels) ha su ound he pa icle. The his og am o he o iginal il se ies (wi h an upwa ds backg ound shi a 619) con ains coun s a in ensi ies o he le o he maximum peak. So oxels o acuum a ound he pa icle in a e non-ze o in he omog am and blu he pa icle in Fig. 3d. In con as , in Fig. 3e he con as o he omog am is much highe , and blu ing a ound he pa icle 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎ 3 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 Fig. 2. SIRT econs uc ion and backg ound in ensi y. (a) Model o “phan om” ha would be compu ed in an ideal omog aphic expe imen wi hou MW. The ull in ensi y ange is [0,1]. The backg ound le el is ze o (I min ¼0), and he con as o he omog am is C¼1. (b) Simula ion o a econs uc ed “phan om”wi h a MW o 40°and il s ep o 2°using SIRT wi h 50 i e a ions. I min o he il se ies shi ed o 0.3. The con as o he omog am is now C¼0.63. (c) Recons uc ed “phan om”unde he same condi ions whe eby (c) and he I min o he il se ies a e se exac ly o ze o. The con as o he omog am is 1 and a e ac s ou side he phan om a e minimised. Below he omog ams, he co esponding di ac og ams a e shown. (d) Line p ofiles o he in ensi y o he omog ams (b) and (c) compa ed o he ideal case (a). L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎4 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i disappea s. Mo eo e , s eaking a e ac s cha ac e is ic o he MW ha e almos disappea ed, as shown in he o hoslices in Fig. 3d and e. No e ha he o hoslices we e no manipula ed and hey a e displayed wi h he ull dynamic ange [32,678, 32,677]. 4.2. HAADF STEM omog aphy: imp o emen o segmen a ion Blu ing and a e ac s in omog ams make hei p ocessing o isualisa ion and accu a e segmen a ion di ficul , leading o a e- qui emen o dedica ed human in e en ion ha is subjec i e and ime-consuming [17,19,25,35,39].Fig. 4 shows an example o he imp o emen ha can be ob ained in he p ocess o segmen ing a omog am when he backg ound o he il se ies is op imised. The sample consis o bime allic Au@Ag co e–shell nanopa icles, used as ags in bio ecogni ion, ha we e deposi ed on a hin ca bon suppo o hei in es iga ion using HAADF STEM [40]. When he backg ound is op imised (wi h a alue close o 32,678), he edges and su aces o he pa icles a e much be e defined (see o hoslices in Fig. 4c). Fig. 4d shows he same o hoslices a e applica ion o Sobel fil e ing, which is a common image- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 Fig. 3. Imp o ing con as and educ ion o a e ac s. a HAADF STEM image a 0° il ep esen a i e o a il se ies o images o a BiPO 4 s a -like pa icle acqui ed a 300 keV wi h a ange o il s be ween 70°and þ70°(high il s ep o 1°abo e 60°and 2° il s ep below 60°). (b) The minimum in ensi y le el eco ded was a 619. A e op imising he in ensi ies, i was se o 32,635. (c) His og ams o he econs uc ed omog ams be o e (in ed and ci cles) and a e backg ound op imisa ion (in blue and squa es). The his og am o he unp ocessed se ies has in ensi y alues o he le o he maximum peak (a ea in o ange unde he ed cu e) ha blu he omog am. (d) and (e) show he ol ex isualisa ion and h ee o hogonal cen al sec ions o he omog ams. I he backg ound o he il se ies is shi ed, he omog am will be su ounded by a cloud o in ensi y ha does no co espond o eal ma e ial (“da k ma e ”) (Video S3 suppo ing in o). (Fo in e p e a ion o he e e ences o colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.) L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎ 5 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 Fig. 4. Imp o emen o segmen a ion o omog ams. (a) HAADF STEM image a 0° il ep esen a i e o a il se ies o 39 images o bime allic Au/Ag co e–shell nanopa icles wi h a il ange om 60° o þ70°, a high il s ep o 2°, and a low il s ep o 4°in s eps wi h a il swi ch a 50°. (b) His og ams o he omog ams using he o iginal il se ies ( ed) and he one wi h backg ound op imisa ion (blue). (c) XY o hoslice o he omog am ob ained using he unp ocessed il se ies (le ) o he one wi h backg ound op imisa ion ( igh ). The con as is enhanced and blu ing disappea s. (d) The same as in (c) a e applica ion o a Sobel fil e . (e) Segmen a ion o he omog ams using he anges o in ensi ies in b acke s shown in (a). (Video S2 suppo ing in o). (Fo in e p e a ion o he e e ences o colou in his figu e legend, he eade is e e ed o he web e sion o his a icle.) L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎6 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i p ocessing ope a o used in edge de ec ion algo i hms ha em- phasises ansi ions o in ensi y maps by calcula ing local g a- dien s. I is e iden ha he e is an imp o emen in he quali y o he omog am when he backg ound o he il se ies is op imised (Fig. 4d, igh ). Using su ace ende ing, Fig. 4g and h compa es he di e ences in quali y o he segmen a ion o he omog ams o sepa a ing he Au co es om he Ag shells using he in ensi y anges shown in b acke s in Fig. 4b. In he case o he omog am using a il se ies wi h he op imised backg ound, he e is no gap be ween he wo anges o in ensi ies used o he segmen a ion. Compa ing Fig. 4e wi h he image a 0° il in Fig. 4a, backg ound op imisa ion pe mi s a mo e ai h ul segmen a ion/ isualisa ion in e ms o he sizes and shapes o he Ag pa icles and he Au co es. This is a clea indica ion ha he econs uc ion imp o es, because less blu ing also implies a be e sepa a ion o in ensi y anges co esponding o dis inc ma e ials o phases p esen in he specimen. Supplemen a y ma e ial ela ed o his a icle can be ound online a doi:10.1016/j.ul amic.2015.03.017. 4.3. BF TEM omog aphy: imp o emen o esolu ion. BF TEM is no mally used o ET o amo phous and so ma e ials, which is ypically he case o biological samples [21,41]. Fig. 5a shows a BF TEM image acqui ed a 0° il o a powde o Vulcan XC-72R, a comme cial ca bon black ha find applica ions in he e ogeneous ca alysis and ha lacks long- ange o de [19,20,42]. Fo omog aphic econs uc ion, he in ensi ies o he il se ies we e in e ed (I x,y -I x,y ), as shown in Fig. 5b, because i acili a es u he segmen a ion o he omog am al hough his s ep is no necessa y in gene al. The minimum in ensi y alue o he in e ed se ies is ound o be he alue 5060, which is g ea e han he absolu e minimum o 32,678 o he image o ma used in ou expe imen s. Hence, backg ound op imisa ion o he BF TEM il se ies is a c i ical s ep in o de o econs uc be e omog ams o compensa e o he esul ing o se o he acuum le el. The co ec ion is applied by downshi ing he in- ensi ies by an amoun o 27,618 ha is he di e ence be ween 32,678 and 5060. Fig. 5c shows a model o ca bon black made o a o uous 3D agg ega ion o sphe ical nanoc ys alli es. Fig. 5d and e a e he ol ex isualisa ion o he omog ams wi h and wi hou backg ound op imisa ion o he il se ies. As in he case o HAADF STEM omog aphy. Fig. 5 is he same as Fig. 5d bu wi h he isualisa ion op imised in he ange [1678, 1000] o emo e he e ec o he blu ing. In he case o he ol ex isualisa ion o he omog am ob ained using he op imised il se ies, only was 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 Fig. 5. Backg ound op imisa ion in BF TEM omog aphy. (a) Rep esen a i e image om a omog aphic il se ies o 71 images o a powde o ca bon black deposi ed on an amo phous holey ca bon film and acqui ed in he angula ange be ween 70°and þ70°wi h a s ep o 2°. The in ensi y o he acuum in (a) is no sa u a ed (I accum ¼ 5060osa u a ion alue¼þ32,677). (b) In e ed e sion o (a) o omog aphic econs uc ion. (c) Model o ca bon black as a 3D agg ega ion o hollow sphe es wi h concen ic laye s o ca bon. (d) Th ee-dimensional isualisa ion o he omog am o he sample. ( ) In o de o emo e he cloud o in ensi y in he acuum ha obscu es he sample, i was necessa y o adjus he in ensi y ange o [1678, 1000]. (e) Th ee-dimensional isualisa ion o he omog am o he sample ob ained using he il se ies wi h he backg ound op imised. (Video S3 suppo ing in o). L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎ 7 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i necessa y o se he uppe ange o 0 o display pu poses. Com- pa ing Fig. 5e and i is clea ha when he il se ies is op imised he ca bon film and he ca bon black a e be e sepa a ed and he e is less blu ing in he z-di ec ion. The sphe ical c ys alli es in mos comme cial ca bon blacks ha e an a e age o app oxima ely ou g aphi e concen ic laye s wi h a hollow cen e [42].Fig. 6a and b compa es YZ o hoslices o he omog ams o he ca bon black specimen using he un- p ocessed il se ies wi h he backg ound op imised. In his case, a e ac s a e absen o a g ea ex en , and de ails a e clea ly en- hanced (spa ial esolu ion imp o es). This is mos e iden in Fig. 6e, in which he c ys alli es show a b igh im wi h a da k cen e, as one would expec o he hollow sphe e c ys alli es o his ca bon black. 5. Conclusion In gene al, an absolu e e e ence le el o in ensi ies is no a ailable in ET unless an a ea o he sample in acuum is exposed. I he minimum le el o in ensi y o a il se ies ha co espond wi h a eal phase o he ma e ial is no adjus ed so ha i coincides wi h he absolu e minimum alue o he dynamic ange o he elec on de ec o sys em (o o he image o ma used), he omog am will display ypically in ensi ies in places which should co espond o acuum. These in ensi ies will blu he ull olume and will enhance he a e ac s in oduced by he MW. In such cases, he fideli y o a omog am ob ained using i e a i e e- cons uc ion me hods can be g ea ly imp o ed (wi h mo e con- as , ewe a e ac s, and be e accu acy) easily i he backg ound le el o he il se ies is downshi ed be o e i s econs uc ion. Mo eo e , his s ep acili a es u he segmen a ion and isuali- sa ion o he h ee-dimensional omog am. We belie e ha his ype o p ep ocessing should always be pe o med in o de o ob ain op imal esul s i espec i e o he imaging echnique used. I is also complemen a y wi h he use o o he me hodologies o minimising he MW e ec s. And we en isage ha his simple me hodology can be also an e ec i e way o h esholding an embedding ma e ial o a low-densi y suppo ing hin film ha a e no pa o he sample unde examina ion bu ha a e ypically used o sample p epa a ion o biological samples o as suppo s o nanos uc u es espec i ely. Suppo ing in o ma ion  Th ee ideos S1–S3 showing he isualisa ion o he omo- g ams be o e and a e backg ound p ocessing. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 Fig. 6. Imp o emen o esolu ion in backg ound-op imised BF-TEM omog aphy. (a) ZY o hoslice o he omog am ob ained using he unp ocessed il se ies shown in Fig. 4. (b) The same o hoslice om he omog am calcula ed om he backg ound-op imised il se ies. (c) His og ams o he wo omog ams. (d) and (e) a e de ails o he fideli y o he econs uc ed nanoc ys alli es. When he backg ound is op imised, blu ing la gely disappea s in ZY o hoslices and he hollow cen es o he ca bon sphe es a e clea ly ecognised. ( ) In ensi y p ofiles measu ed along he line p ofiles indica ed in (d) and (e) wi h a owed lines. When he backg ound is op imised, he o hoslices o he omog am co ec ly show he b igh ing s uc u e expec ed om a hollow sphe e. L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎8 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i  A p og amme o so wa e w i en in Ma lab o pe o ming backg ound op imisa ion o .m c files o omog aphic e- cons uc ion using FEI so wa e is a ailable a www.lcgon a d. es. The file called BKG_Op imisa ion_Tomog aphy_LCG_2015.exe is an execu able and he e o e i equi es he p eins alla ion o Ma lab MCR abo e e sion 2012b. Acknowledgemen s The au ho wishes o hank di e en collabo a o s ha p o- ided he samples o suppo , P o . Ra al E Dunin-Bo kowski, D . Ana Bece o, D . Dogan Ozkaya and D . Cuong Cao. The au ho is also g a e ul o P o . Asunción Fe nández as leade o he Eu opean P ojec REGPOT-CTAl-NANOFUNC and o he Eu opean Union Q3 un- de a Con ac o an In eg a ed In as uc u e Ini ia i e 312483- ESTEEM2 o unding. Re e ences [1] R.A. C ow he , D.J. de Rosie , A. Klug., The econs uc ion o a h ee-dimen- sional s uc u e om p ojec ions and i s applica ion o elec on mic oscopy, P oc. R. Soc. Lond. A 319 (1970) 317–340. [2] A.J. Kos e , U. Ziese, A.J. Ve kleij, A.H. Janssen, K.P. de Jong, Th ee-dimensional ansmission elec on mic oscopy: a no el imaging and cha ac e iza ion echnique wi h nanome e scale esolu ion o ma e ials science, J. Phys. Chem. B 104 (2000) 9368–9370. [3] M. Weyland. Two and Th ee-dimensional Nanoscale Analysis: New Techniques and Applica ions (Ph.D. hesis), Uni e si y o Camb idge, 2002. [4] P.A. Midgley, R.E. Dunin-Bo kowski, Elec on omog aphy and holog aphy in ma e ials science, Na . Ma e . 8 (2013) 271–280. [5] P.R. Buseck, R.E. Dunin-Bo kowski, B. De oua d, R.B. F ankel, M.R. McCa ney, P.A. Midgley, M. Pós ai, M. Weyland, Magne i e mo phology and li e on Ma s, P oc. Na l. Acad. Sci. 98 (24) (2001) 13490–13495. [6] M. Weyland, Elec on omog aphy o ca alys s, Top. Ca al. 21 (4) (2002) 175–183. [7] T.J.V. Ya es, The de elopmen o elec on omog aphy o nanoscale ma e ials science applica ions (Ph.D. hesis), Uni e si y o Camb idge, 2005. [8] H. F ied ich, P.E. de Jongh, A.J. Ve kleij, K.P. de Jong, Elec on omog aphy o he e ogeneous ca alys s and ela ed nanos uc u ed ma e ial, Chem. Re . 109 (5) (2009) 1613–1629. [9] G. Möbus, R.C. Doole, B.J. Inkson, Spec oscopic elec on omog aphy, Ul a- mic oscopy 96 (2003) 433–451 (3–4). [10] P. E cius, M. Weyland, D.A. Mulle , L.M. Gignac, Th ee-dimensional imaging o nano oids in coppe in e connec s using incohe en b igh field omog aphy, Appl. Phys. Le . 88 (2006) 243116. [11] A. Yu se e , M. Weyland, D.A. Mulle ., Th ee-dimensional imaging o non- sphe ical silicon nanopa icles embedded in silicon oxide by plasmon omo- g aphy, Appl. Phys. Le . 89 (2006) 151920. [12] M. Weyland, P.A. Midgley, Ex ending ene gy-fil e ed ansmission elec on mic oscopy (EFTEM) in o h ee-dimensions using elec on omog aphy, Mi- c osc. Mic oanal. 9 (2003) 542–555. [13] M.H. Gass, K.K.K. Koziol, A.H. Windle, P.A. Midgley, 4-dimensional spec al- omog aphy o ca bonaceous nano-composi es, Nano Le . 6 (2006) 376–379. [14] L.C. Gon a d, J.R. Jinschek, H. Ou, J. Ve beeck, R.E. Dunin-Bo kowski, Th ee- dimensional ab ica ion and cha ac e isa ion o co e-shell nanocolumns using elec on beam pa e ning o Ge-doped SiO 2 , Appl. Phys. Le . 100 (2012) 263113. [15] M.C. Sco , C.C. Chen, M. Mecklenbu g, C. Zhu, R. Xu, P. E cius, U. Dahmen, B. C. Regan, J. Miao, Elec on omog aphy a 2.4-Å esolu ion, Na u e 483 (2012) 444–448. [16] B. Go is, L. Pola a apu, S. Bals, G. Van Tendeloo, L.M. Liz-Ma za, Moni o ing gal anic eplacemen h ough h ee-dimensional mo phological and chemical mapping, Nano Le . 14 (2014) 3220–3226. [17] N. Volkmann, Chap e wo-me hods o segmen a ion and in e p e a ion o elec on omog aphic econs uc ions, Me hod. Enzymol 483 (2010) 31–46. [18] S. Lozano-Pé ez, P. Rod igo, L.C. Gon a d, Th ee-dimensional cha ac e iza ion o s ess co osion c acks, J. Nucl. Ma e . 408 (2011) 289–295. [19] L.C. Gon a d, R.E. Dunin-Bo kowski, D. Ozkaya, Th ee-dimensional shapes and spa ial dis ibu ions o P and P C ca alys nanopa icles on ca bon black, J Mic osc. 232 (2) (2008) 248–259. [20] L.C. Gon a d, R.E. Dunin-Bo kowski, M.H. Gass, A.L. Bleloch, D. Ozkaya, Th ee- dimensional shapes and s uc u es o lamella - winned cc nanopa icles using ADF STEM, J. Elec on Mic osc. 58 (2009) 167–174. [21] L.C. Gon a d, B.R. Knappe , A.E.H. Whea ley, S.L.-Y. Chang, A. Fe nández, Im- p egna ion o ca bon black o he examina ion o colloids using TEM, Ca bon 76 (2014) 464. [22] J.R. Tong, I. A slan, P.A. Midgley, A no el dual-axis i e a i e algo i hm o elec on omog aphy, J. S uc . Biol. 153 (1) (2006) 55–63. [23] J.J. Fe nández, C.O.S. So zano, R. Ma abini, J.M. Ca azo, Image p ocessing and 3-D econs uc ion in elec on mic oscopy, IEEE Signal P ocess. Mag. 23 (3) (2006) 84–94. [24] J.-J. Fe nández, Compu a ional me hods o ma e ials cha ac e iza ion by elec on omog aphy, Cu . Opin. Solid S a e Ma e . Sci. 17 (2013) 93–105. [25] M. Cao, H.-B. Zhang, Y. Lu, R. Nishi, A. Takaoka, Fo ma ion and educ ion o s eak a e ac s in elec on omog aphy, J. Mic osc. 239 (1) (2010) 66–71. [26] V. O alan, M. He e a, D.G. Mo gan, N.D. B owning, Applica ion o image p ocessing o STEM omog aphy o low-con as ma e ials, Ul amic oscopy 110 (2009) 67–81. [27] T. Roeland s, K.J. Ba enbu g, E. Bie mans, C. Kübel, S. Bals, J. Sijbe s, Accu a e segmen a ion o dense nanopa icles by pa ially disc e e elec on omo- g aphy, Ul amic oscopy 114 (2012) 96–105. [28] A. Lange, A. Kupsch, M.P. Hen schel, I. Manke, N. Ka djilo , T. A l , R. G o hausmann, Recons uc ion o limi ed compu ed omog aphy da a o uel cell componen s using di ec i e a i e econs uc ion o compu ed o- mog aphy ajec o ies, J. Powe Sou ces 196 (2011) 5293–5298. [29] A. Alpe s, R.J. Ga dne , S. König, R.S. Penning on, C.B. Boo h oyd, L. Houben, R. E. Dunin-Bo kowski, K.J. Ba enbu g, Geome ic econs uc ion me hods o elec on omog aphy, Ul amic oscopy 128 (2013) 42–54. [30] B. Go is, W. Van den B oek, K.J. Ba enbu g, H.H. Meze ji, S. Bals, Elec on o- mog aphy based on a o al a ia ion minimiza ion econs uc ion echnique, Ul amic oscopy 113 (2012) 120–130. [31] R. Lea y, Z. Saghi, P.A. Midgley, D.J. Holland, Comp essed sensing elec on omog aphy, Ul amic oscopy 131 (2013) 70–91. [32] A. F angakis, R. Hege l, Noise educ ion in elec on omog aphic econs uc- ions using nonlinea aniso opic di usion, J. S uc . Biol. 135 (2001) 239–250. [33] J.J. Fe nández, S. Li, An imp o ed algo i hm o aniso opic nonlinea di usion o denoising c yo- omog ams, J. S uc . Biol. 144 (2003) 152–161. [34] C.J. Gommes, K. de Jong, J.-P. Pi a d, S. Blache , Assessmen o he 3D locali- za ion o me allic nanopa icles in Pd/SiO 2 cogelled ca alys s by elec on o- mog aphy, Langmui 21 (2005) 12378–12385. [35] R. G o hausmann, G. Zehl, I. Manke, S. Fiech e , P. Bogdano , I. Do band , A. Kupsch, A. Lange, M.P. Hen schel, G. Schumache , J. Banha , Quan i a i e s uc u al assessmen o he e ogeneous ca alys s by elec on omog aphy, J. Am. Chem. Soc. 133 (2011) 18161–18171. [36] G.T. He man, Image Recons uc ion om P ojec ions: Implemen a ion and Applica ions, Topics in Applied Physics, 32, Sp inge -Ve lag, 1979. [37] C. Yang, H. Zhang, J. Li, A. Takaoka, The op-bo om e ec o a il ed hick specimen and i s influence on elec on omog aphy, J. Elec on Mic osc. 54 (4) (2005) 367–371. [38] A.I. Bece o, J. C iado, L.C. Gon a d, S. Ob egón, A. Fe nández, G. Colón, M. Ocaña, Bi unc ional, monodispe se BiPO 4 ‑based nanos a s: pho oca aly ic ac i i y and luminescen applica ions, C ys . G ow h Des. 14 (2014) 3319–3326. [39] A. Ma inez-Sanchez, I. Ga cia, J.J. Fe nandez, A di e en ial s uc u e app oach o memb ane segmen a ion in elec on omog aphy, J. S uc . Biol. 175 (2011) 372–383. [40] C. Cao, L.C. Gon a d, L.L.T. T am, A. Wol , D.D. Bang, Dual enla gemen o gold nanopa icles: om mechanism o scanome ic de ec ion o pa hogenic bac- e ia, Small 7 (12) (2011) 1701–1708. [41] R. G imm, H. Singh, R. Rachel, D. Typke, W. Zillig, W. Baumeis e , Elec on omog aphy o ice-embedded p oka yo ic cells, Biophys. J. 74 (1998) 1031. [42] R.D. Heiden eich, W.M. Hess, L.L.A. Ban, A es objec and c i e ia o high esolu ion elec on mic oscopy, J. Appl. C ys . 1 (1968) 1–19. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 L.C. Gon a d / Ul amic oscopy ∎(∎∎∎∎)∎∎∎–∎∎∎ 9 Please ci e his a icle as: L.C. Gon a d, Remo ing he e ec s o he “da k ma e ”in omog aphy, Ul amic oscopy (2015), h p://dx.doi. o g/10.1016/j.ul amic.2015.03.017i