BLENDING OF LOG NORMAL PARTICLE SIZE DISTRIBUTION DATA FROM MULTIPLE IMAGE ANALYSES INTO A SINGLE CONTINUOUS DATA SET
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1 BLENING O LOG NORMAL PARTICLE SIZE ISTRIBUTION ATA ROM MULTIPLE IMAGE ANALYSES INTO A SINGLE CONTINUOUS ATA SET As pbshd JVT, W 211 (Vo17/No1) E Oso ABSTRACT Img ss s o mhod b whh p sz m b msd. I m ss, s osdd h god sdd o p sz msm d s o sd o v h ss o oh hs. Smp p sz dsbos o bod, somms ovg wo o h dds o p dm. I s so ommo o z smps h m-mod (.g., sg smp h m o pm ps d hd ggoms wh ovppg p sz dsbos). Tp ss wh zg hs smps h p sz xms, dpdg o h sm opg pms sd. Ths pp dsbs mhodoog b whh d om mp mg ss h s d opo pms xpod om h sm o sb spdsh. Th d h bdd o s oos p sz dsbo wh opm. INTROUCTION Th m mhods o msg p sz, o o whh s b mg ss. Th poss o p sz msm b mg ss s v w sbshd d pd, s pov b h mb o Io Ogzo o Sddzo (ISO), ASTM, d oh sdds o hs mhodoog. I s o h msm o whh oh p sz mhodoogs ompd d v bd. Img ss s p s o o-sph ps sh s bs d ow-sp o ps sh s ds. Ths s bs wo o h m dg hos s do, ho d M, o ppb o sod sphs. Ths, h h h smp p dvs om sod sph, h g h xpd o msm b s do. Img ss s o govd b h ho o M ho, hs, s o sbj o h sm p shp oss. A smp p sz dsbo shod d b moomod d ow. I, hs s h s. Smp p sz dsbos o bod, somms ovg wo o h dds o p dm. I s so ommo o z smps h m-mod (.g., sg smp h m o pm ps d hd ggoms wh ovppg p sz dsbos). Eh objv o h mg ss ssm hs opm g bsd o s soo. Th soo s dmd b h wvgh o h d gh d h m p o h s. Ths ms h ms, smp p sz dsbo s v bod o m-mod oss bod g, m b ss o o d sg mo h o mgo v. Ths ds o h xs o wo sp d ss, o o vg popo szs, whh hz wo o mo sos o h smp p sz dsbo. I od o mk h wo sos o d s d oos, poss whh h sos m b bdd o ombd s dd. Ths dssso dsbs poss b whh d om mp mg ss xpod om h sm o sb spdsh sh s Moso Ex (1). Ths d h b bdd o oos p sz dsbo h povds mxmm. Img Ass Bss Th ompos o s mg ss ssm v bs op. A mgo ssm p zs ompod gh mosop. Th gh so s mos o dsop gh (gh om bow o
2 smd gh); som ssms, psop gh (gh om bov o d gh) m so b vb. Th do s o h dg m o (hg opd dv) CC. Th ssm ms so hv som p o smp hod sh s mosop sg. I som omd ssms, h s so dspsg ssm o d powds d/o som p o w pb o msg sspdd powds d dsps. Th poss bgs wh h smp ppo. Bo omd ssms, hs w dvopd o dsps d powds o mosop sd o sm smp hod. Mod omd sms z bs o ompssd o dsps ps oo smp hod. Id h dspso sps h oos ggomd m who bkg p. I s so dsb o h dvd ps o b spd d o ohg o ovppg. Sm o d smp dspsd d mdm, oos ggoms shod b spd, b h d o dssovd. Id h smp shod b od o smp hod wh mmm dph o d d mmm p ovp. O h smps pop dspsd, h x sp s o dm h pop mgo v. Ag, h d-os ssod wh hs sp. I oo ow mgo v s hos, sm ps m go obsvd d h shp o h g ps m b skwd s s o h do soo. I oo hgh mgo v s hos, oo w ps m b zd p ISO (2), dg o bsd s. Aso, ss som p o omd poss sh s z-skg s vb, g p d hgh mgo w mos o b o o os, so dg o bsd ss. I h sg s osdd o sd h x- p, h h z-xs wod b ppd o h sg. Z-skg s poss b whh h sg s sd d/o owd mb o sps ov ps dss. o s, h mdd o g p s osdd o h z-xs, z-sk o -1/+1 m b mpod. Ths, o v d o vw, h sg wod mov o h mdd o h p (z = ) s w s som pdd ds bow h mdd (-1) d h sm pdd ds bov h mdd (+1). Ths pdd ds s g sm d o h od o w mos, b s m md b h d podb o h sg moo. Ths ows h sm o p -os mgs o sm ps h m sd os o h mog s s w s g ps whos s m b w mos bov h o h sm ps. A som po, h mosop objv d do ssm ms b bd. Ths s mos o ompshd b obg mg o b sg mom. O h mg s obd, h s o sow s b o h bo o o pxs o gh. I s mpo hs b do wh b sg mom o d h s o vdo. I s so mpv h bo b pomd h s o h ss. Th x sp h poss s o djs h gh s d p hshod. O mod omd ssms, h gh s m b msd d djsd om. Imgs o h dspsd ps pd d dgzd o pxs. Th hshod, pop s, dms h px s whh h p bod o dg s dd. A d o ps s h obsvd d h hshod v s sh h ps o s o xdd, d p mgs h dd o odd. O h dgzd p mgs pd, m sow pkgs om s h bd px mps o dm wd o p msms (.g., gh, wdh,, v dm, sp o,, ogo, ovx, pm, sod,.). EXPERIMENTAL Smp Ppo Th smp sd hs xmp ws pssd hogh 25 µm sv po o ss o mov xos ps o m d o h ps o s. A sm poo o h xmp p smp h pssd hogh h sv ws m spkd o mosop sd d obsvd vos mgos sg Mv
3 Mophoog G3S omd mg ss ssm. Th smp s g ppd o hv v bod p sz dsbo h ws possb m-mod. Th gs ps obsvd ppd o hv dm o bo 2 µm, wh h sms ps obsvd ppd o hv dm 2 µm. Bs o h wo-dd d obsvd m p dms, wo objv mgo vs w hos o h ss, 2.5X d 1X. Th 2.5 objv hs wokg g om bo 4 µm o 1 µm d h 1X objv hs wokg g om bo 1 µm o 13 µm. Ths ombo o objvs hs ovp om bo 4 µm o 13 µm, g o p dms whh h od b obsvd d bdd. Cp, Expo, d Impo P d w od sg sb sdd opg pod o h sm. Th pod zd h smp dspso (SU) o h Mv Mophoog G3S o s h ps w d dspsd wh mm ovp. Th mb o ps zd wh h 2.5X objv ws bo 17,, d h mb o ps zd wh h 1X objv ws bo 41,. Th mb o ps o z s o o h ss od v d h wdh o h dsbo. I ws mpv h s mb o ps b zd. Ths sd h dsbos w w dvopd d psv o h popo. O h p dm d w pd, h w xpod o x dom d sbs o Moso Ex. O o h mos o Moso Ex s h spdsh m o o 65,536 ows. Ths ms h mxmm mb o ps h b mpod h spdsh d om h x dom. I g mb o ps hd b zd d h d sbs xpod o x dom, h wod s b opd spdsh h hs hgh m o ows h Moso Ex sh s JMP 8 (3), d h d opd d psd o mp oms wh Moso Ex spdsh. Bdg h Hsogm O h d mpod o Moso Ex, hsogm b s gd sg h Ass - Hsogm o whh s p o h pogm o. Howv, bo hsogm b gd, s o b szs (.., mmm p dms) ms b sbshd. I g, mos p sz dsbos psd o oghm s. I od o g Gss p sz dsbo o oghm s, h x-xs ms b gom pogsso. I h gom pogsso w s wh g mp, h b szs wod b oo bod d h ssm wod os soo. Howv, h mp w s oo sm, h b szs wod b v ow, mg h mb o ps h b d v dg h sg o os o. I hs xmp, h gom mp ws s o h v h mos pss h v pod b szs o h sm. Th d o h Mv Mophoog G3S ws 1 bs, pod oss h g.1 µm o 2 µm. Th mpo o o h gom pogsso ws
4 Nmb d Vom Wghd Sss I h d o p sz ss, h m ws o xpss m s. Two o h mos ommo h mb m d vom mom m. Mhm, hs d om h hsogm d s oows: [1, ] [4,3] = d 4 = 3 d d [1,] = mb wghd m [4,3] = vom mom m = o ps h b d = p dm o b sz. Th x sp h bdg poss ws o h vs o d, d 3, d d 4. I hs xmp s, h vom-wghd d w mo ppb o h d-s h h mb wghd d. Howv, h ov poss hs b zd wh oh smps o mb-wghd bss s w. RESULTS AN ISCUSSION Smoohg d Ov Po A po o h vom-wghd d w hsogm d ov h g o h bdg go s sd gs 1 d 2, whh ws v jggd d somwh d o p. g 1 shows h w vom-wghd d po ov h g o h ss. Is g 1 s box dg h ppoxm go ov whh h bdg poss os. g 2 shows h w vom-wghd d po, zoomd o h go ov whh h bdg poss os.
5 Appoxm bdg go sd gs 2 o P m (µm) 1X Objv 2.5X Objv g 1. Vom-wghd d p dm - w - g P m (µm) 1X Objv 2.5X Objv g 2. Vom-wghd d p dm - w d bdg go
6 O possb soo h hs b mpmd ws o s smoohg o podzo s. O h mos s vb, h wo h hv b pov h mos s h movg vg d Svzk-Go (4). Pos o h vom-wghd d hsogm d 5-po d 11-po movg vg ov h sm g show gs 3 d 4, spv. Compso o gs 2, 3, d 4 d h s h mb o pos h movg vg ss, h po o h vom-wghd d p dm boms smooh P m (µm) 1X Objv 2.5X Objv g 3. Vom-wghd d p dm - 5-po movg vg bdg go
7 P m (µm) 1X Objv 2.5X Objv g 4. Vom-wghd d p dm - 11-po movg vg bdg go Show h o h pos o h w, 5-po, d 11-po movg vg smoohd d o sv pposs. Howv, os w so ompd o 7-, 9-, 13-, d 17-po s d h ospodg Svzk-Go d d s w. Bdg I hs xmp s, h hgh mgo (sm p) d v sppm h mh mo bod d ompssg ow mgo (g p) d. Ths ws ompshd b bdg o h pwd sop o h sm p o h ow mgo (g p) d. Howv, hs ws o h d so. I g, s bs o bd d oss g wh mm hg sh s wh h s dvv ppohs zo (.., pk h dsbo). Th od d o h ow mgo (g p) d s ws mpd b omzo os. Th omzo os ws dmd b mmzg h sm o h sd ds bw h wo d ss ov h dsgd bdg g. Co, h bdg g ws opmzd b mmzg h sm o h sd ds bw h mxmm hgh mgo (sm p) po d h mmm o h ow mgo (g p) po. Th mxmm d mmm pos w od b kg h s dvv o h spv d ss. Boh sms o sd ds w dmd sg h Sov Too Moso Ex. I hs xmp s, h d bdg g ws 4.4 o 12. µm, whh zd 11 bs. Th ws h g o ovp bw h 2.5X d 1X objvs. Th omzo os ws dmd o b Th po o h omzd d ss s show g 5.
8 P m (µm) 1X Objv 2.5X Objv g 5. Vom-wghd d p dm - 11-po movg vg omzo bdg go Po d C Rss O h bdg go hs b sbshd d h omzo os d, h d d mv pos m b d d h smm sss d. Ths ws bg b bdg h wo omzd d ss. Ths ws ompshd sg h oowg og: I Th x < x bdg go = hgh mgo x = x bdg go = ( hgh mgo + ow mgo ) / 2 x > x bdg go = ow mgo A po o h bdd d o hs xmp s s dmosd g 6. A po o h sm d, ow showg h g s show g 7. A mv % v ws so gd d s show g 8. Vos sss s gv Tb I m b d o h d ov spdsh om.
9 P m (µm) g 6. Vom-wghd d p dm bdg bdg go P m (µm) g 7. Vom-wghd d p dm bdg g
10 1 C m v 8 6 V o m % P m (µm) g 8. Cmv vom % o h bdd smp popo
11 Tb I. Vom d mb wghd sss Pm µm [4,3] [v,.1] 52.9 [v,.5] [v,.9] 22.5 [1,] 11.6 [,.1] 1.1 [,.5] 5.5 [,.9] 24.7 ssso As dmosd gs 5 o 8, ws vd how mh o h smp popo ws hzd b h ow mgo (g p) d, d how v o h vom ws hzd b h hgh mgo (sm p) d. I hs xmp, ss h 1% o h o smp vom ws hzd b h hgh mgo (sm p) d. Ths sm vom m sm sg, b h sg s dpd o how h d o h so bg skd. o s, h s o pmo dg dv, h xss mxmm h dposo o o ps bw 2 d 5 µm (5). I hs xmp s, h s o h bdg go ws 4.4 µm, whh s v h ow m o do o h 2.5X objv. I h so bg skd o hs ss w o p o bovb d dosg o pmo dg, h d pso o h d bow 5 µm wod b, h, ssg h s o h 1X objv d obs bdg pod. Th og obsvd p sz g ws om bo 2 µm o 2 µm, d h msd dsbo hd g om 1 µm o 251 µm, whh ws good gm. Ahogh hs wok osd o g h vomwghd sss d d, h mb-wghd sss d d so show g 9 d Tb I. I ws o s o o 17% o h ps b mb w <4 µm, wh o.1% o h ps b mb w >2 µm. As o wod xp, h mb-wghd d dsbo po ws skwd v hv owds h sm ps s opposd o h vom-wghd d dsbo po, whh ws skwd v hv owds h g ps.
12 P m (µm) g 9. Nmb-wghd d p dm bdg g A o o bo 57, ps w zd. A ogom dsbo o ws o h vom-wghd d d h gom sdd dvo ws ppoxmd o b 1.6. A h 95% od v, hs sggss bo 33, ps w dd o h ss. Ths, s mb o ps w zd. As pvos mod, h mb o hs ov whh h bdg od hs xmp s ws 11. Howv, s mpo o o h hs 11 hs od o 2,327 ps o h o 41, ( 5%) h w zd. As pvos mod, boh h movg vg d Svsk-Go s w vsgd o smoohg h w d. Um, h dso ws md o s h movg vg. Ths dso ws md bsd o wo sos: h movg vg ws s o s, hs po o ss hm o, d h vs, h movg vg ppd o b mo smoohg h d gv h sm mb o smoohg pos. Lkws, g o smoohg pos om 5 o 17 ws vsgd. As show g 3, h 5-po smoohg md mpovm o h po s opposd o h w d (gs 1 d 2), b ws o ogh o dm h opmm bdg g. Appo o h 17-po smoohg sd po h ws xpo smooh. Howv, s h mb o pos h smoohg sd, h [4,3] so sd (s Tb II d g 1) h mb o smoohg pos hd 11, whh po h [4,3] md v os.
13 [4,3] (µm) Nmb o Smoohg Pos (s) g 1. E o h mb o smoohg pos (s) o h [4,3] Tb II. Es o h ppo o smoohg Nmb o Pos (s) Nomzo Cos [4,3](µm) A po o h omzo os vs. h mb o smoohg pos s gv g 11. Wh h d w wh h b poom o s show, h oo o (R 2 ) ws.9963, dg good. Th s dvv o h d g 11 b ogh (R 2 =.84) b pbo wh o po s = 11, wh s s h mb o smoohg pos s show g 12. S hs ws o po, b hogh o s po wh h s mo o hg o h, whh ws mos sb. H, h mb o smoohg pos h ws hos o b 11.
14 N o m z o C o s R 2 = Nmb o Smoohg Pos (s) g 11. Nomzo os s o o h mb o smoohg pos dnom/ds R 2 = Nmb o Smoohg Pos (s) g 12. s dvv o h omzo os s o o h mb o smoohg pos
15 Th og o sd o os h bdd d od po d o os, h gs o whh, wod b xpd h pos o dso. Howv, hs g b mmzd b sg h pop bdg go s hos. CONCLUSIONS Ths pp hs dsbd mhodoog b whh p sz d wh d mgo vs bdd o sg p sz dsbo. Ths mhodoog povds opm dmg h p sz dsbo. Tp p sz pods (.., o-bdd pods) bsd o h sm o g p sz gos o h dsbo. Ths bs od d o sg os jdgm dpdg o h objv o h ss. REERENCES 1. Moso O Ex 23 SP3, P o Moso O Posso Edo 23, Copgh Moso Copoo. 2. ISO :25, P Sz Ass. Img Ass Mhods. S Img Ass Mhods. 3. JMP 8..1, Copgh 29 SAS Is, I. 4. Svzk, A., Go, M., "Smoohg d o o b Smpd Ls Ss Pods," A Chms, 36, 1964, oovh MB, Nwhos MT. Aosos. Go, mhods o dmso, d hp ppos shm. I: Mddo E J, Rd CE, Es E, Adkso N J, Ygg JW, Bss WW, dos, Ag Pps d p. 4. S Los: Mosb Y Book, I.; pp ARTICLE ACRONYM LISTING CC Chg Cops v ISO Io Ogzo o Sddzo SU Smp spso U
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