Microgeometry capture and RGB albedo estimation by

photometric stereo without demosaicing

❨♥ é tt P③♥r ♥♥s r♦ ♥ ♥ r♠rs

♥ ❯♥rst② ♥ r♥ r♠♥②

❯♥rsté ♦♦s ❯ ♦♦s r♥

❲ ♣rs♥t ♣♦t♦♠tr str♦s s②st♠ ♦r rtr♥ t ♦ ♥ t ♥s ts ♦ ♥♦♣q sr ♥ ♦rr t♦ ♠t s♣rts t s②st♠ ss ♦♥tr♦ s ♠♥t♦♥ srt s♥ t ♣r♦r ♥ t♦♥ rtr ♥ ❲ ♥♦♥♠♦s ♠s ♦t ♦s ♥♦♥tr♦ ♦♣rt♦♥s ♦♥ t s♥s♦r t ♥ s♠♣s t st♠t♦♥ ♦ t ♦ ♥ ♦♦r ♥♥ ♥ ♦ t ♥♦r♠s ❲ ♥② s♦ ♦♥ r♦r ①♠♣s t ♣♦t♥t ♦ ♣♦t♦♠tr str♦♦r t r♦♥strt♦♥ ♦ r② t♥ strtrs r♦♠ rt② ♦ srs

②♦rs r♦♥strt♦♥ ♣♦t♦♠tr str♦ ♥♦♥♥♦r♠ ♠♥t♦♥ ♠s ②r tr

❯

♠♦♥ t ♥♠r♦s ♦♠♣tr s♦♥ t♥qs ♦r ♥ r♦♥strt♦♥ r♦♠ t ♠rs ♣♦t♦♠tr t♥qs s s s♣r♦♠s♥ ♥ ♣♦t♦♠tr str♦ r ♦t♥ ♦♥sr s rst ♦s♥ t ♦♠s t♦ t r♦r② ♦ t♥ strtrs ♥ t② r t♦ st♠t t sr ♥♦r♠s ♥ ♣① ♥ t trtr ♣① s② rrs t♦ ♥ t r r♥ ♥ ♥♥s ♥tr♣♦t r♦♠ t②r ♠tr① rtr ♦♥sr ♣① s ♥ t ♥♦♥♠♦s ❲ ♠ ♥ ts ♦r ♦s ♦♥srs ♣tr ② ♦♥sst♥ ♦ t ♠r ♥ sr s rr♥ s sr ♥ r

♠r

s♥s

r ♠t r♣rs♥tt♦♥ ♦ t s ♦r r♦♥strt♦♥ ② ♣♦t♦♠tr str♦ ♦♥tr♦s r ♦r♥t t♦rs t s ♦ t ♥ ♦rr t♦ ♠♥t t s♥ ♥ s ♠♥♥r t ♠rs s t♦ ♣tr m = 15 ts ❲ ♠s ♦ t s♥ ♥r r②♥ ♠♥t♦♥ ♦t♥ ② sss② tr♥♥♦♥ t r♥t s ♦ ♠s ♦ ♦ r♦s ♥♥♦t ♦t♥ t ts s ♥t♥♦r s♠s r♦♥strt♦♥ ♥ rs♦t♦♥ 3664× 2748 ♣①s t ♠ r s ♦ s③ 1.6 cm× 1.2 cm tst sr r ♦rrs♣♦♥♥ t♦ ♣① s r♦♥ 5 µm× 5 µm

♦rrs♣♦♥♥❨ é ②♥qt♠ P③♥r ♠tt♣③♥r♥str r♦ r♦rtr r♠rs r♠rst♠

P♦t♦♠tr t♥qs ♥rt ♣♦t♦♠tr ♠♦ sr♥ t ♥trt♦♥s t♥ t ♠♥t♦♥ ♥t sr s ss♠♣t♦♥s ♦ ♣♦t♦♠tr str♦ r tt t t ♦♥sst ♥ m ≥ 3 r② ♠sIi, i ∈ [1,m] ♦t♥ r♦♠ st ♠r t ♥r r②♥ rt♦♥ ♠♥t♦♥ r tt tsr s ♦♣q ♥ tt ts rt♥ s ♠rt♥ ♣rt② s ❯♥r ts ss♠♣t♦♥s ♥♥t♥ s♦♥ ts t r② t ♣① (u, v) ♥ t it ♠ s ♠♦ s

Iiu,v = ρu,vnu,v · si, i ∈ [1,m]

r ρu,v > 0 s t ♦ nu,v s t ♥t ♦tr ♥♦r♠ t♦ t sr t♦r si ♣♦♥ts t♦rs t ts♦r ts ♥t♥st② s ♣r♦♣♦rt♦♥ t♦ t ♠♥♦s ① ♥st② ♥ · s t ♥ sr ♣r♦t

♦ ρu,v ♥ t ♥♦r♠ nu,v ♥ st♠t ♥ ♣① (u, v) ② s♦♥ s②st♠ ♥ t stsqrs s♥s ♥ tr♠s ♦ t t♦r mu,v = ρu,vnu,v ♥ t ♦ s ♦t♥ ② ρu,v = ‖mu,v‖ ♥ t♥♦r♠ ② nu,v = mu,v/‖mu,v‖ ♥t② t ♣t ♠♣ s ♦t♥ ② ♥trt♦♥ ♦ t st♠t ♥♦r♠s

r s♦s t ♦ ♥♦r♠s ♥ ♣t st♠t r♦♠ m = 15 ♠s s s t♦s ♥ r

r r♦♠ st ♦ m ≥ 3 ♠s s s t♦s s♦♥ ♥ r ♦t♥ ♥r r②♥ ♠♥t♦♥ ♣♥ t ♠r st ♦r ♣♦t♦♠tr str♦ ♣♣r♦ s♠t♥♦s② r♦rs ♥ ♦ ♥♦r♠ ♠♣s♦♥ ♠r♦♦♠tr strtrs r r② s ♥ t ♠s ♥ r♦♥strt♦♥ ♦ t sr

s ♣r♦r s t ♠♦st ♦♥sr ♥ t trtr ♦♥ ♣♦t♦♠tr str♦ rs ♦♥ t♦ rstrtss♠♣t♦♥s rst t s ss♠ tt t t ♦♥sst ♥ r② ♠s ❨t ♠♦st ♠♦r♥ t ♠rs♣r♦ ♠s ♥ t♦ ♦♥rt t♦ r② s ♦r t ♥ ♦ ♣♦t♦♠tr str♦ ♥♥ ♦ss ♦ ♥♦r♠t♦♥ ♥ t♦♥ ♠♥t♦♥ t♦r s

i s s♣♣♦s t♦ t s♠ ♥ ♣①s ♥ ♥♦r s t t ♥♥t ♠♥t♦♥ s t② t rst ♦ ♠t♣ rt♦♥s t t srr♦♥♥♥r♦♥♠♥t r ts s r② st ♠♥ ♣r♣♦s ♦ ♦r ♦♥trt♦♥ s t♦ s♦ tt tr② ss♠♣t♦♥ ♥ ♦ r② s♠♣② ② ♦♥sr♥ s ♥♣ts t ❲ ♠s r♦♠ t s♥s♦rt♦t ♠♦s♥ st♦♥ s s♠♣s t st♠t♦♥ ♦ t ♦♦r ♦ ♥ ♦ t ♥♦r♠s ♥♦♠♣rs♦♥ t ♠t♦s ♥ t ♥tr♣♦t ♠s st♦♥ ❨t ♦r ♣♣r♦ rqrs tt ♠♥t♦♥ s rt t rs♣t t♦ ♣① st♦♥

❲

r♦♦♠tr② r♦r② ② ♣♦t♦♠tr str♦ s r② ♥ ② ♣♣②♥ ♠ t♥t sr ♥ t ♠r ♥ ♦rr t♦ ♠rt♥③ t srs ♥ ♦♥trst s ♥♦♥♥trs♠t♦ r②♥ ♦♥② ♦♥ st♥r q♣♠♥t s s s ②t rr♥ ♥ s ② tt t② rt s♠♥t♦♥ ts ♠t♥ s♣rts ♥ t♦♥ ♥ t ♣♣r♥ ♦ sr s ♠♦ ② ♠♣r♦ss ts ♦r♥ ♦ ♥♥♦t st♠t ♥②♠♦r ♦r s t♦ st♠t t

r② ss♠♣t♦♥ s ♥ r① ♥ sr ②s ♥ t trtr ♦♥ ♣♦t♦♠tr str♦ ♥♠♦s ①♠♣ s t rt♠ r♦♥strt♦♥ ♦ ♦r♠ t srs ♦sr ♥r r♥t ♦♦rt s♦rs st♥r ♣♦t♦♠tr str♦ ♣r♦r s s t♦ st♠t t ♥♦r♠s t st♠t ♦s ♥♦t r♥t s♥ t sr s s♣♣♦s t♦ ♥♦r♠② t ♦♥sr♥ t r r♥ ♥ ♥♥ss tr r② ♠s ♠♥ ♥t ♦ ts ♣♣r♦ s tt t ♥ ♣♣ r♦♠ s♥ ♠ ♥ s r② sst ♥ t r② ♦r ② ❲♦♦♠

♥♦tr ♠♣♦rt♥t ♦r s tt ② rs② ♥ Ptr♦ ♦ s ♦r ♠s t♦ st♠t t tr♦ s rt t♦ ♥♥ ♥ t ♥♦r♠s ♦ ts ♣r♣♦s t ♣♦t♦♠tr ♠♦ s rtt♥rt ♦♦r ♥♥ ②t ♦♥sr♥ tt t ♠♥t♦♥ s t

Ii,⋆u,v = ρ⋆u,vnu,v · si, i ∈ [1,m], ⋆ ∈ R,G,B

r t ♦ ρ⋆u,v s ♥♦ rt t♦ t ♦♦r ♥♥ ⋆ ∈ R,G,B st♥r ♣♦t♦♠tr str♦♣r♦r ♦ ♣♣ ♥♣♥♥t② ♥ ♦♦r ♥♥ ♦ ♣r♦ t sr s ♦ t♦ s s tr st♠ts ♦r t ♥♦r♠ ❯♥♦rt♥t② ts ♦ t♦ ♥♦♠♣t st♠ts♦ t ♥♦r♠ rs② ♥ Ptr♦ ♣r♦♣♦s ♣r♥♣ ♦♠♣♦♥♥t ♥②sss ♣r♦r t♦ ♦r♦♠ tsr ② s♠t♥♦s② st♠t♥ t tr s ♦ t ♦ ♥ t ♥♦r♠ t♦r sst♥ tr♥t ♣r♦r ♦♥sst♥ ♥ st♠t♥ t ♦♦r ♦ rst ♥ t♥ t s♣ ② rs♦rt♥ t♦ ♥♦♥♥r P r♠♦r t s s♦ r♥t② s♦♥ tt ♦♥sr♥ rt♦s t♥ ♣rs ♦ ♦♦r s ♥ ts♠ ♥♥ ②s s②st♠ ♦ ♥r Ps ♥ t ♣t ♥ s♦ ♥♣♥♥t② r♦♠ t ♦

rtss ts ♦rs ss♠ tt t tr♣t ♦ s ♦rrs♣♦♥ t♦ t s♠ sr ♣♦♥t❨t ts s ♥♦t ss♠♣t♦♥ t st♥r ♠rs ♥ t ♦♦r trs r s② rr♥♦r♥ t♦ ②r ♣ttr♥ ♦♥ ♦ t s♥s♦r ♥ ♦♥② r ♥♦r♠t♦♥ ♥ ♦♥ s♣ ♦♦r ♥♥♦ ♦t♥ tr♣t ♦ s ♥tr♣♦t♦♥ s rqr s ♥s s s ♥♦r♠ s st♠tr♦♠ ♦♦r s rstr ♥ ♥♦r♥ ♣①s rtr t♥ ♦♥② ♥ t rr♥t ♦♥

s ♦r t rt♦♥ ♠♥t♦♥ ss♠♣t♦♥ t s rq♥t② ♥ qst♦♥ ♥ t ♦♥t①t ♦ ♣♦t♦♠trstr♦ ♦t ♦ ♠♥♦s s♦rs ♥♥ ♣♦♥ts ♥ ①t♥ ♦♥s ♥ ♣♣r♦①♠t ② ♣r♠tr♠♦ s ♦r ♥st♥ ♦r s♦♠ sss♦♥ ♣♦♥ts s♦r ♠♦ s ♦t♥ ♥♦♥tr ♥ r♦r♣♣t♦♥s s s r♣rs♥t ♣ t s♦rs t rtr ts ♠♦ rt♥ t ♣r♠trs♦ s s♦rs ♣♦st♦♥ ♦r♥tt♦♥ ♥ ♥t♥st② s rt② ♥♦♥ ♣r♦♠ s s t♥♠r rs♦t♦♥ ♦ ♣♦t♦♠tr str♦ ♥r s ♥ ♠♥t♦♥ ♠♦

❯♥♦rt♥t② ♣r♠tr ♠♦s r ♥♦t ♣t t♦ ♦r s s strt ♥ r t♦ t trt♦♥s ♥s t ♦ ♠♦ s♥ r♥r♥ t♥qs ♥rt♥ t r♥r♥ qt♦♥ ♦ ♠♣♦ss ♥ ♣rt ♥st ♣rr t♦ rs♦rt t♦ s♠♣ ♣♣r♦①♠t ♠♦ sr♥ t rst♥♠♥♦s ① r♥ t sr rst ♣♦sst② ♦♥ssts ♥ s♠♣♥ t ♥t♥st② ♦ ♠♥t♦♥ ♥ ♣♥ ♦t ♥ t r ♦ ♥trst ♥ t♥ ♥ ♥ ♠ ② ts ♥t♥st② ♠♣s ❨t tst♥q ♥ ♦♥② ♦♠♣♥st ♦r ♥♦♥♥♦r♠ ♠♥t♦♥ ♥t♥sts t ♥♦t ♦r ♥♦♥♥♦r♠ ♠♥t♦♥rt♦♥s ♥♦tr ♣♦sst② ♦ t♦ ♦♠♣♦s t ♠♥t♦♥ rt♦♥ ♦♥ t s♣r r♠♦♥sss ♥ t♦ rt t rst ♦♥ts ♦ ts ♦♠♣♦st♦♥ ♥ t ♦tr ♥ t s t t♦ ♣rtt ♥♠r ♦ r♠♦♥s rqr t♦ ♥sr tt t ♠♦ s rs♦♥② rt ❲ s♦ ♥ st♦♥ ♦ t♦ s♠♣ ♦t t ♠♥t♦♥ ♥t♥sts ♥ rt♦♥s ♥ ♦rr t♦ ♦t♥ ♥ rt r♣rs♥tt♦♥ ♦t ♠♥♦s ① r♥ t sr

P ❲❯

t s ♥♦ ♥tr♦ ♦r ♣♦t♦♠tr str♦ ♠♦ rs ♦♥ ❲ ♥♣ts t♦t ♠♦s♥ s s s ♦♥ ♠♦s♥ ②s ♠ s♠♣r ♣♣r♦ t♦ st♠t t ♦ ♥ t ♥♦r♠s♥ ♦♠♣rs♦♥ t ①st♥ ♦rs sss ♦

♥ ♦rr ♦r ♣♦t♦♠tr ♠♦ t♦ sts ♥ s♥ r♦r ♠s t ♠r rs♣♦♥s s♦ s ♥r s ♣♦ss ♥ ts ♥♦♥tr♦ ♦♣rt♦♥s ♦♥ t ♠s s♦ ♦ s ♠♥stt rr t♦♠t ♦rrt♦♥s s s ①♣♦sr t ♥ ♥ ♠♠ ♦rrt♦♥s s♦ s♦♥rs♦♥ r♦♠ ❲ t t♦ P ♠s s♦ s♦ ♦ s♥ ❲ ♠s s② ttr♣t ♦r ❲ ♠s r ♦ ♦♥ ts ♥ t♦♥ r tt ♠♦s♥ t ❲ t s♦ ♥♦t s♥ ts rsts ♥ ♥t♥ ♠ss♥ t ② ♥tr♣♦t♥ t t ♠sr♠♥ts rstr② t s♥s♦r t♦ ♦rt ♠♦s♥ ♠t♦s ♦ ①st tt t s ♠♦r st t♦ ♦♥srt s r♦♠ t s♥s♦r s t② r t♦t ♥② ♥ ♦ ♠♦t♦♥ ♠t r t rt② ♦ trs♣♦♥s

♥ ♥st ♦ ♦♥sr♥ tt ♥ ♣① (u, v) tr♣t ♦ s s rtr ♦♥srtt s♥ ♠sr♠♥t s ②t ts ♠sr♠♥t s♦ ♥rst♦♦ s rt t♦ ♦♥ s♣♦♦r ♥♥ ♣♥♥ ♦♥ t rr♥♠♥t ♦ t ②r ♠tr① s r ❲ s♦ s♣♣♥♥②t♦ t ♠♥t♦♥ t♦rs s♥ t ♥t♥st② ♦ ♠♥t♦♥ t♦r si s rt t♦ t ♦♦r ♥♥ ♥s♥ ts rt♦♥ rs s t ♠♥t♦♥ s s r s ♥t② s t♦ t ♦♦♥♣♦t♦♠tr ♠♦

Iiu,v = ρu,vnu,v · siu,v, i ∈ [1,m]

♦t tt ♥ ts ♥ ♦♦r P ♠♦ tr s ♥♦ ♥♦♠♣tt② ♥ t st♠t ♥♦r♠s t ♠♥t♦♥t♦r s siu,v r ♥♦♥ s st♦♥ ♥ ♣♣② t st♥r ♣♦t♦♠tr str♦ ♣r♦r t♦ r♦rt ♦ ♥ t ♥♦r♠ ♥ ♣① s ②s ♠ s♠♣r ♣r♦r s ♦♠♣r t ①st♥♦rt♠s rqr ♥♠①♥ ♦♦r ♥ s♣ ♦r rs♦rt♥ t♦ ♠ rt♦s

r P♦t♦♠tr str♦ t♦t ♠♦s♥ ♦s♣ ♦♥ 50 × 50 ♣rt ♦ ♦♥ ♦ ♦r ♥♣t ❲ ♠sr♣rs♥t ♥ ♦r ttr sst♦♥ ❲ sst t♦ s s ♥♦♥♠♦s ♥♣ts s t ♦r st♠t♥ ②r st♠t ♦ t ♦ ♥ rtr ♥tr♣♦t t♦ ♦t♥ ♥ ♦ ♥ ♥ st♠t ♦ t♥♦r♠ ♥ ♣① ② ♦♥ ♠♦s♥ ♦ ♥② ♥♦♥tr♦ tr♥s♦r♠t♦♥ ♦ t t r♦♠ t s♥s♦r♦♥ t r♦r② ♦ ♠r♦♦♠tr② strtrs s st♦♥

♥t② ♥ r♣rs♥tt♦♥ ♦ t ♦ s rqr ♦♥ s♦ ♣♣② ♠♦s♥ ♦rt♠t♦ t ②r st♠t ♦ ρ ♥ r ♠♦st② ♥trst ♥ ts ♦r ♥ r♦r♥ t sr s♣ ♣♣② s♠♣ ♥r ♥tr♣♦t♦♥ ♦r ts ♣r♣♦s ❲ ♠♣s③ tt ♥♦ ♠♦s♥ ♦ t ♥♦r♠ ♠♣ srqr ts rt st♠t♦♥ r♦♠ t ②r ♠tr① r② ♣r♦s ♥s ♠♣ t♦t ♠ss♥ t

s ♥ st ♥ ♦r ♣♣♥ ♣rs♣t ♥trt♦♥ ♦ t ♥♦r♠s ♥t♦ ♣t ♠♣ s ♣r♦r♠ ♦ts ♣r♣♦s ♣♣② t ♠t♦ ♦ ♠♦♥② t t♦ t ♣rs♣t r♥ts st♠t r♦♠ t♥♦r♠ s sr ♥ s ②s ♥ ♣t♦s ♣t ♠♣ ♥ ♥t② t s r♦♠t ♠♥ ♠rt♦sr st♥ s st♠t ♦♠tr② rt♥ t ♠r

P ❯

❲ ♥♦ sr ♣rt ② t♦ s♠♣ t ♠♥t♦♥ rt♦♥s ♥ ♥t♥sts t m t♦rs siu,v

♣♣r♥ ♥ ♥ ♣① (u, v)

♦ ts ♣r♣♦s t ♦ ♥ssr② t♦ ♥rt t ♠♦ ♥ tr♠s ♦ t siu,v t♦r ♥ ♣① (u, v)♥ ♦r ♠♥t♦♥ i s ♥ ♥♣♥♥t② ♦r ♠♥t♦♥ ② s♥ rt♦♥♦t t ♥♦♥ ♦ ρu,v ♥ ♥♦♥ ♥♦r♠s nu,v ❯♥♦rt♥t② s♥ ♦♥② ♦♥ ♥♦r♠ s ♥ ♣① s♦♥ s ♥ ♥r♦♥str♥ ♣r♦♠ ♥sr♥ ♦rrt st♠t♦♥ ♦ ♠♥t♦♥ t♦r siu,v♦ rqr t♦ s srs ♦ ♠rt♥ rt♦♥ ♦ts ♦s s♣ ♥ ♦♦r r ♥♦♥ t♦ ♣tr rt♦♥ ♦t ♥r ♠♥t♦♥ ♥ ♥t② t♦ ♥rt t ♠rt♥ ♠♦ ❨t ts ♣r♦r♦ r② t♠♦♥s♠♥

♥st s♥ s♠♣ rt♦♥ ♠t♦ rqrs s♥ rt♦♥ ♦t ♦♥sst♥ ♥ ♥rr② ♦ ①♦♥ strtrs ♠♥ ♥ s t ♠tr ❲t♦t ♦ss ♦ ♥rt② ss♠ ttts t ♦♦r s ♦ q t♦ rt tr ♦♦r ♥♥s tt s t♦ s② ρu,v ≡ ρ = 1 s ♠♥stt ♥② ♦♦r t♥ st♠t t ts t ♦♦r s rr♥

♥ t r ♥t♦ rt♥r ♣rts Ωj , j ∈ [1, 30] ♥ ♦ ts rt♥r ♣rts ♣t♦ s♥ r♥t ♥♦r♠s t r♦♥t♦♣r ①♦♥ ♣rt ♥ s① s♦♣ s ♦♥ t t ♦rrs♣♦♥♥♦♦r ♠ s r ❲ ss♠ tt t rt♥r ♣rts r s♠ ♥♦ s♦ tt t ♠♥t♦♥♥ ♦② ♦♥sr s rt♦♥ ♥ ♥♦r♠ ♥ ♦♦r ♥♥ ♦r ♥♥ ⋆ ∈ R,G,B ♠♥t♦♥ i ∈ [1,m] ♥ rt♥r ♣rt Ωj ♣♣r♦①♠t t ♠♥t♦♥ s

i,⋆

uj

0,v

j

0

♥ t ♥tr ♣①

(uj0, vj

0) ♦ Ωj ② s♦♥ ♥ t stsqrs s♥s t ♦♦♥ s②st♠ ♦ ♥r qt♦♥s

nu,v · si,⋆

uj

0,v

j

0

= Iiu,v, (u, v) ∈ Ωj,⋆

r Ωj,⋆ s t st ♦ ♣①s ♥ Ωj ♦r ♥ ♥♦r♠t♦♥ ♥ ♥♥ ⋆ s

s s s s♣rs st♠t♦♥ ♦ ♠♥t♦♥ ♥ ♦♦r ♥♥ ♦ ts sttr t srtr ♥tr♣♦t ♥ ①tr♣♦t t♦ t ♦ r ② s♥ r♠♦♥ s♣♥ ♠♦ rst♥ ♥ trC2s♠♦♦t t♦r s ♣r ♠♥t♦♥ s tr s s

i,⋆u,v, (u, v) ∈ Ω r ♥t② ♦♠♥ ♥t♦

s♥ ♦♥ siu,v ② s♥ t s♠ ②r rr♥♠♥t s ♥ t ♠s ② r♣t♥ ts ♣r♦r ♦r

♠♥t♦♥ ♦t♥ t t♦rs siu,v rs ♥ ♠♦ ♥ t r♦♥strt♦♥ ♣r♦r sr♥ st♦♥ ♥ ♣♣

t s ♥♦t ♦r ♦♠♣t♥ss tt s♠r s ♣r♦♣♦s ② ♦♥s♦♥ t ♥ ♦rr t♦ rt s♣r r♠♦♥s ♠♦ ♥ tt ♦r ♣♣r♦ ♥ s ♥ ①t♥s♦♥ ♦ t♥ t♥qs

♠♥ t s♠♣♥ ♥♦t ♦♥② t ♠♥t♦♥ ♥t♥sts t s♦ tr rt♦♥s

P ❱❯

t s ♥♦ s♦ ♦♥ r♦r ①♠♣s tt ♦r s ♣ ♦ r♦r♥ r② t♥ strtrs ♦r rt② ♦ srs

❲ rst s♦ ♥ r t r♦♥strt♦♥ ♦ t r♦s ♥♥♦t ♦ r s ①♣r♠♥ts♦s s t ♣♦t♥t ♦ ♣♦t♦♠tr str♦ ♦r sr ♥s♣t♦♥ ♣♣t♦♥s s ♦r ♥st♥ r②♥ t♣rs♥ ♦ t♥ strtrs s♦ ♣rs♥t ♥ r ♥♥♦ts

♥ s♦ ♥ r t st♠t ♦ ♠♣s ♥ r♦♥strt♦♥s ♦ t♦ ♠t r♦ ♦♥s♦s② ♠t srs ♦ ♥♦t ♦ t ♠rt♥ ss♠♣t♦♥ ♣♦♥ ♦r ♣♣r♦ rs rtss t st♠t ♦ ♠♣s r♠♥ stst♦r② t♦ ♦ s r② ♦rst♠t r♦♥ sr♣strtrs s ♦ str♦♥ ♥trrt♦♥ ts t s ♣t ♠♣s ♥② r s♠ ♠♣ts ♦♥t sr ♦ t ♦♥s ♠② t♦ sr② t♥ t ♥ ♥ t t ♦ t r♥ts ♣♦rtrt♦r ♠② ♣rt ♦ t ♦r♥ ♥r♥ ♦♥ t t ♦ ts rtr

♥t② t♦ q♥ttt② ssss t ♦r r② ♦ t r♦♥strt♦♥ s♦ ♥ r trsts ♦t♥ t ♠♥ sr ♠♦ s ♥ s♥t t♦ t ♠♥ ♥ ♥♦♥ ♥ ♠t ♦r r♦♥strt♦♥ t t ♥ t t s♦t ♦t♦♠s st♥ t♥ ♦tsrs rsts s♦ tt 99% ♦ t st♠t ♣♦♥ts r♦♥strt♦♥ rr♦r ♦ 0.1 mm ♥tt t ♠♥ ♦ t rr♦r s r♦♥ 20 µm ♦sr ♦♦ t t s♣t strt♦♥ ♦ t rr♦rs s♦stt t rr♦rs r ♦③ r♦♥ sr♣ ♦r♥rs ts s ♣r♦② t♦ ♥trrt♦♥ ts ♥ t♦ tt tt s stsqrs ♥trt♦♥ ♦ t ♥♦r♠s t♥s t♦ s♠♦♦t t r♦♥strt♦♥ t♦♥ t ♦tr ♥ t ♠② s♦ t♦ t ♥r② ♦ t ♠♥ ts ♥ ♦r ♦r rr♦r s ♣r♦②♥ ♦r t♥ tt ♠sr

r r♦♥strt♦♥s ♦ t♦ ♠t ♦♥s r♦♠ t t♦ rt ♦♥ ♦ t m = 15 ♥♣t ♠s st♠t ♦♥ r♦♥strt♦♥ rst r♦ t♥ r♦ ♦♥ ♦♥ r♦ ♣♥s ♥ts ♦♥

r ♥ttt t♦♥ ♦ t r♦♥strt♦♥ s♥ ♠♥ sr r r♦♥strt♦♥ s♠t t t ♠♦ ♦s♣ ♦♥ t ♠t s♣s st♦r♠ ♦ t s♦t st♥ t♥♦t srs ♥ mm t ♠♥ s r♦♥ 20 µm ♣t strt♦♥ ♦ t r♦♥strt♦♥ rr♦rs

❯ PP❱

❲ s♦♥ t ♣♦t♥t ♦ ♣♦t♦♠tr str♦ ♦r ♠r♦♦♠tr② ♣tr r②♥ ♦♥② ♦♥ st♥rq♣♠♥t s s t ♠r ♥ s ❯♥ ♣r♦s ♦r ♦ ♥♦t ♥ t♦ rs♦rt t♦ ♥② ♠♣r♦ss ♥ ♦rr t♦ ♥♦r t ♠rt♥ ♦r ♦ t sr s s ♠ ♣♦ss ② ♥♥r ♠♥ts t s♥ t ♦♥tr♦ s t ♥ ② rt② ♠♦♥ t ♣♦t♦♠tr str♦♣r♦♠ r♦♠ t ❲ ♥♦♥♠♦s ♠s s ♥ ♠♦ s♠♣s t st♠t♦♥ ♦ t ♦♥ ♦♠♣rs♦♥ t ♦tr ♦♦r ♣♦t♦♠tr str♦ ♠♦s ♣r♦ tt ♥s st♠t♦♥ ♦ t ♥♥t♠♥♦s ① s ♥ ts s♦ sr rt♦♥ ♣r♦r ♦r s♠♣♥ t ♠♥t♦♥♥t♥sts ♥ rt♦♥s ♦♥ t qst♦♥ ♣♥ ♣r♦s ♠t♦s ♦♥② s♠♣ t ♥t♥sts

rtss ♦r ♠♦ r♠♥s ♦♥② ♦r s♣s t ♠t s♦♣s ♥ t st♣st srs♥trrt♦♥s s♦s ♦r ♣♥♠r ♦r s tr ♦r ♣♥ t♦ ♠♣r♦ t r♦st♥ss ♦ ♦r♠t♦ rt s ts rst strt② ♦ ♦♥sst ♥ ♠♣r♦♥ ♦r s♠♣ rrss♦♥ ♣r♦r s♦♥ stsqrs ② s♥ ♠♦r r♦st st♠t♦rs ♥♦tr ♦♣t♦♥ ♦ t♦ trt② r♥ t ♠♥t♦♥st♠t♦♥ ② tr♥t♥ t t t st♠t♦♥ ♦ t s♣

❲

s rsr s ♥ ② t ♦♦s r♥sr ♦♠♣♥② ♦♦s r♥

❬❪ ♦r♥ P ♣ r♦♠ ♥ t♦ ♦r t♥♥ t ♣ ♦ ♠♦♦t ♣q t r♦♠♥ ❱ P ss ♠r ❯

❬❪ ❲♦♦♠ P♦t♦♠tr ♠t♦ ♦r tr♠♥♥ sr ♦r♥tt♦♥ r♦♠ ♠t♣ ♠s ♣t♥♥r♥

❬❪ ♦r ♥ ❱s ♦srt♦♥ s♣② ♦r r♠t♦♦ ♣♣t♦♥ P Pt♥t ♣♣ P

❬❪ r♦ ♦ ♥ ♦rt ♥trt♥ t ♦r♠ ♦ r ♥ t Prs♥♦ s♦♥t♥ts ♥ ❬♥r② ♥♠③t♦♥ t♦s ♥ ♦♠♣tr ❱s♦♥ ♥ Pttr♥ ♦♥t♦♥ ❱P ❪

❬❪ ♦♥s♦♥ ♦ ♥ s♦♥ r♦♦♠tr② ♣tr s♥ ♥ st♦♠r s♥s♦r r♥st♦♥s ♦♥ r♣s

❬❪ r♥á♥③ ❱♦t③s r♦st♦ t♥r ♥ ♣♦ ♦♥r P♦t♦♠tr tr♦t ♦♦r ts ♥ ❬ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦♠♣tr ❱s♦♥ ❱ ❪

❬❪ rs② ♥ Ptr♦ s♦r ♣♦t♦♠tr str♦ t♥q ♦r tr♠♥s♦♥ srs ♥t ♣rs♥ ♦ ts ♥ s♦s r♥st♦♥s ♦♥ Pttr♥ ♥②ss ♥ ♥ ♥t♥

❬❪ ♥ ♥ ❨ ♦♦r P♦t♦♠tr tr♦ ♦r ♦ ♥ ♣ ♦♥strt♦♥ ♥ ❬❲♦rs♦♣ ♦♥ ♣♣t♦♥s ♦ ♦♠♣tr ❱s♦♥ ❲❱ ❪

❬❪ é ❨ ♥ r♦ ❯♥s ♣♦t♦♠tr str♦ ♦r ♦♦r srs rt♦♥♣♣r♦ ♥ ❬ ♦♥r♥ ♦♥ ♦♠♣tr ❱s♦♥ ♥ Pttr♥ ♦♥t♦♥ ❱P ❪

❬❪ é ❨ ♥ r♦ ♦♠ ♠♥t♦♥ ♦s ♦r ♥str ♣♣t♦♥s ♦ P♦t♦♠tr tr♦♥ ❬t② ♦♥tr♦ ② rt ❱s♦♥ ❱ ❪

❬❪ ❳ ♦♥ ❩ ♦ ♥ ❳ ♥ ♣rt ♠♥s ♦r rt♥ ♥ s♣♦t♦♠tr str♦ s②st♠ ♣ts ♥ srs ♥ ♥♥r♥

❬❪ ♥ ♠t ♠t ♥ r♦♦q ♠♣♥ t ♦r P♦t♦♠tr tr♦ ♥tr♥t♦♥♦r♥ ♦ ♦♠♣tr ♦r② ♥ ♥♥r♥

❬❪ sr ♦s ❲ ♥ ♠♠r P♦t♦♠tr tr♦ t ♥r ❯♥♥♦♥ t♥♥tr♥t♦♥ ♦r♥ ♦ ♦♠♣tr ❱s♦♥

❬❪ ♠♦♥② ♣♣ ♥ ♦ rt ♥②t ♠t♦s ♦r s♦♥ P♦ss♦♥ qt♦♥s ♥♦♠♣tr s♦♥ ♣r♦♠s r♥st♦♥s ♦♥ Pttr♥ ♥②ss ♥ ♥ ♥t♥