HAL Id: hal-00712699https://hal.archives-ouvertes.fr/hal-00712699

Submitted on 2 Jul 2012

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Outdoor field performances of Insect-based visualmotion sensors

Fabien Expert, Stéphane Viollet, Franck Ruffier

To cite this version:Fabien Expert, Stéphane Viollet, Franck Ruffier. Outdoor field performances of Insect-based visualmotion sensors. Journal of Field Robotics, Wiley, 2011, 28 (4), pp.529-541. 10.1002/rob.20398.hal-00712699

t♦♦r ♣r♦r♠♥s ♦ ♥sts

s ♠♦t♦♥ s♥s♦rs

♥ ①♣rt té♣♥ ❱♦t ♥ r♥ r

♦r♦♦ts ♣rt♠♥t ♥sttt ♦ ♦♠♥t ♥

①rs ❯♥rst②

P ♠♥② rs r♥

④♥①♣rt st♣♥♦t r♥rr⑥♥♠r

strt

♦♥sr tt♥t♦♥ s ♥ ♣ r♥ t st t♦ ♥t♦♥ s②st♠s s ♦♥ t s

♦ s ♦♣t ♦ s ♣t ♦s s♦♠♦t♦r ♦♥tr♦ s②st♠s ♥ ♠♣♠♥t ♦♥

♥ ♥rs♥② r ♥♠r ♦ st t♦♥♦♠♦s r♦♦ts s♥ t♦ tr ♥r s♣ t♥

♦♥t♦♥s ♥② ♦rt♠s s ♦♥ ♦♥♥t♦♥ ♠rs ♦r st♦♠♠ s♥s♦rs r ♥ s

♥♦②s t♦ ♣r♦ss s ♠♦t♦♥ ♥ ts ♣♣r ♦s ♦♥ t rt② ♦ ♦r ♦♣t s♥s♦rs

♥ s t♦ ♠sr t ♦ ♥r s♣ ♦ r♦♦ts ②♥ ♦t♦♦rs ♦r s

s♥ ♥ tr♠s ♦ tr r② r♥ rrs rt ♥ s♥stt② t♦ ♠♥♥ rt♦♥s ❲

s♥ ♦♥strt ♥ rtr③ t♦ ♠♥tr st♦♠♠ s ♠♦t♦♥ s♥s♦rs

t Ps ♦ ♠♦t♦♥ s♥s♦r ♥♦♥ t s ♦ st♦♠♠ ❱ rr② P st♥s

♦r ♣t P①s ♦r ♥sts ♥s♦rs s q♣♣ t rüt②♣ t♦♣t

♣①s ♥ t s s ♦♠♣♦♥♥t ♣rs r♦♠ s ♦ ♠♦t♦♥ s♥s♦r

♥♦♥ t s ♦ ♦ts ♥r② ♠♣ ♣♦t♦s♥s♦rs s q♣♣ t ♥ ♦♥

♣ ♣r♠♣t♦♥ rt ② ♦♠♥♥ ts ♣♦t♦tt♦rs t ♦♦st ♦♣t ss♠②

♥ ♦♥s♣r s ♣r♦ss♥ ♦rt♠ ② t ♠♥tr s♥s♦rs r ♦t♥

♦r ♠sr♥ t s ♥r s♣ ♥ ①♣r♠♥ts ♣rs♥t st② ♦s ♦♥ t

stt rtrsts ♥ t ②♥♠ rs♣♦♥ss ♦ ts ♦ ♠♦t♦♥ s♥s♦rs ♦r r♥ ♦

♠♥♥ s r♥♥ r♦♠ ① t♦ ① ♦t ♥♦♦rs ♥ ♦t♦♦rs t♦ ♦t♦♦rs

①♣r♠♥ts r ♦ rt ♥trst t♦ q♣ r♦r ❱s t s ♠♦t♦♥ s♥s♦rs s♦

♣r♦r♠ ♥♦♦rs ①♣r♠♥ts s ♦♠♣rs♦♥ s s ♠♦t♦♥ s♥s♦r s ♦♥

t♦ ♠♦r rt ♥ ♥rr♦ ♠♥♥ r♥ t Ps s ♠♦t♦♥

s♥s♦r s ♠♦r r♦st t♦ ♠♥♥ ♥s ♥ rr r♥ ♠t♦ ♣rs♥t ♥

ts st② ♣r♦s ♥ ♥♠r tst ♦r t♦r♦② rtr③♥ s ♠♦t♦♥ ♥ ♦♣t ♦

s♥s♦rs s♥ t♦ ♦♣rt ♦t♦♦rs ♥r r♦s t♥ ♦♥t♦♥s ♥ ♥♥♦♥ ♥r♦♥♠♥ts

r tr r♦r ❱s t♦ ♥t s②

♥tr♦t♦♥

r ♦♣t ♦s ♥t♦♥ s②st♠s ♥ ♦♣ r♥ t st ♦r s ♦♥♦r trrstr

♥ r r♦♦ts

♦♠ trrstr r♦♦ts r ♥♦ ♥ q♣♣ t s♠r ♠♥s ♦ tt♥ ♥ ♣r♦ss♥ t ♦♣t ♦ t♦ t♦s

♣r♦♥ ♥sts s s s ♥ s t t t s t② ♥ t♦ ♦♥tr♦ tr ♦♥ trt♦rs r♥s♥

P♦♥ ♥s rrs♦♥ ♦ ♠rt ②s♦♣ ❩♥ ♥t♦s❱t♦r ②st♠s ♦

ts ♥ ♥ ♥ r♥t② s t♦ ♠ ②♥ r♦♦ts t♦ ♦ ♦sts ②r ❩r② ♦r♥♦

r♥ rr♦s r r♥s♥ ❩r② ♦r♥♦ ♦r

rss ss♦tt♦ ♠ ♦♥② ♥♦ ♦♥♠ ♥t♦♥ ♦③♥♦ tr ♠♦♥ trt

♥♦ t r ❱♦t r♥s♥ ❱♦t r♥s♥ ♥ t ♦ ♦♦

trr♥ ♥ ♥ r♥s♥ r rrs r r♥s♥

❲ s ts s ♠♦t♦♥ s♥s♦rs s♥st t♦ ♦♣t ♦ s ♥t♦ t♦ t♦rs s ♦♦s

❼ ♦ ♠♦t♦♥ s♥s♦rs r s ♦♥ ♦♥ ♠♥s♦♥ rt♥ ♥ ♦♠♣t ♥r

s♣

❼ ♣♦t♦s♥s♦r rr②s rs♦ t ♦♣t ♦ t♦r ② ♠sr♥ ts ♦rt♦♦♥ ♦♠♣♦♥♥ts t

s♦ ♦♣t ♦ s♥s♦rs

♥② ♠t♦s ♦ ♠sr♥ t s ♥r s♣ ♥ s ♦r r♦♦t ♣r♣♦ss s s t♦s ♥♦♥ t

♦ ss♥st♥ ♥ rt ♦rrt♦r ss♥st♥ rt s ♠♦♥t ♦♥ trrstr

r♦♦ts rrs♦♥ ♦ ❯ss♦❱rtt t ♥tr♣♦t♦♥ ♠ ♦rt♠ r♥s♥

♦♠♥ t ♠r rr② s s ♦♥♦r ♥ ♥♦♦r ♠r♦②r ❩r② ♦r♥♦

♥ t t♠ ♦ tr s♠ ♥s ♦♠♥ t ♦ts ♣♦t♦♦s s ♠♣♠♥t ♦♥

♦t trrstr r♦♦t r♥s♥ t ♥ sr ttr ②♥ r♦♦ts ttr r♥s♥

r r♥s♥ r ❱♦t ♠ r♥s♥ ❱♦t r♥s♥

♥ t♦♥ s♦♠ ♥♦♦r trrstr r♦♦ts t♥♥♠♠♥s ♥t♦s❱t♦r ♥♥ r♦tt♦ r

♥ q♣♣ t st♥r ♠rs ♦♠♥ t ♥t♦♥ s②st♠s s ♦♥ ♦♣t ♦ ♣r♥♣s

s rr♦♥ t ♠♥ ♦r r ♦ t ♠♥ ♦♣t ♦ t♥qs ts ♦♠♣tr

♠♦s s♥s♦rs ♠sr♥ ♦ ♦♣t ♦ r r♥t② rtr③ ♥ t♦ ♥ ♠♦♥t

♦♥♦r trrstr ♠♥ rs ♦t s♦♥ ♥ rstr♥r ♥ r r♦♦t

♣t♦r♠s ②r t rts ♥rs rts rr ♥ r ♥t♥ ♥r

♦♥st♥t t♥ ♦♥t♦♥s

tr s ♠♦t♦♥ s♥s♦rs ♥ ♦♣ s♥ ♥♦ ♥ t ❱r②r ♥trt♦♥ ❱

t♥♦♦② s rr♦s ② r♥♦rt ♦♠r r♦ rr rt♦♦③③ ♥r

r♣sr r ♦ ❳ ♠rt sr ♥ t s ♦ ♠♦t♦♥ s♥s♦rs ♥s

♠s r♣sr r♠r ♥r ♦ ♥ t s ♦ ♦♣t ♦ s♥s♦rs ♥ s s♦

♦♥ ♦r ♥r r ♦♠ ♦tr ❱ s♥s♦rs s ♦♥ t s ♦ ♦♣t ♦ s ♥

♦♣ ♦r ♦s♦♥ tt♦♥ ♣r♣♦ss s s tt ♥ rr♥③ ❱rs ♥♥ ♦ ♥s♣r

② t ♦st

♦r t♦ ♦r ♥♦ r② r♦♦t sts ♥ ♣s s♦ r ♥ s ♠♦t♦♥ s♥s♦rs

♥ ♠♣♠♥t ♥ tst ♦t♦♦rs r t ♠♥♥ ♥♥♦t s② ♦♥tr♦ s rr♦s ②

♦r ♥r ♠♦t♦♥ s♥s♦rs ♥ s ②r t rrtt rts t

♥♦ ❨ ♦♥♠ ♦r ♦♣t ♦ s♥s♦rs

t♦ s ♠♦t♦♥ s♥s♦rs r ♦ rt ♥trst ♦r r♦♦t ♣♣t♦♥s r② tt♠♣ts ♥ ♠ s♦

r t♦ rtr③ s②st♠s ♦ ts ♥ ♦♠ t♦rs tst tr s ♠♦t♦♥ s♥s♦rs t rt ♦ts

♣rs♥t ♦♥ ♦ sr♥ s♥ ♦ ♠♦t♦♥ s♥s♦r ♦ ♦r ♦♣t ♦ s♥s♦rs í③

♦s s r♥r ♥♦ ❨ ♥ t ♣r♦r♠♥s ♦ s♦♠ ❱ ♠♦t♦♥ s♥s♦rs ♥

sr ♥ t s r♥♦rt t rrs♦♥ ♦ ♦r ♠♦t♦♥ s♥s♦r rtr③

♥♦♦rs ♥ ♥ r♦♥t ♦ ♣♦t♦r♣s ♦ ♥tr s♥s rs♣t② ♥ s t♦r ♦r ♦♣t ♦

s♥s♦r rtr③ ♥♦♦rs

t tr♦r s♠ t♦ ♦rt ♦♣♥ ♠♥s ♦ tst♥ t rt② ♦ t s ♠♦t♦♥ s②st♠s ♦♣

t ♦r ♦rt♦r② ♥ tr♠s ♦ tr rs♦t♦♥ r② s♥stt② ♥ ♥r♥ t♦ ♦♥trst ♥ r ♥r♦♥♠♥ts

♥r r r♥ ♦ ♠♥♥ s ♥ ts st② t s ♣r♦♣♦s t♦ tr♠♥ ♥ ♦♠♣r t ♦t♣t s♥s

♦ t♦ st♦♠♠ ♦♥s♣r ♦ ♠♦t♦♥ s♥s♦rs ❱♦t r ② ♥♦♥ é♣rt r

r♥s♥ s ♦♥ ♣① s②st♠ t r♥t r♦♥t♥s ♥♠②

Ps ♦ ♠♦t♦♥ s♥s♦r ♥♦♥ t s ♦ st♦♠♠ ❱ rr② P st♥s ♦r

♣t P①s ♦r ♥sts ♥s♦rs q♣♣ t rüt②♣ t♦♣t ♣①s rü

♥

s ♦ ♠♦t♦♥ s♥s♦r ♥♦♥ t s ♦ ♦ts ♥r② ♠♣ ♣♦t♦s♥s♦rs t

♦♠♣♦♥♥t s ♣rs r♦♠ s q♣♣ t ♥ ♦♥♣ ♣r♠♣t♦♥ st

r s ♠♦t♦♥ s♠ ♣r♦sss t t♠ ♣s♥ t♥ t tt♦♥ ♦ ♥② ♦♥trst♥ tr ② t♦

♥t ♣♦t♦r♣t♦rs ♥s r♥s♥ t r♥s♥ r rrs ❱♦t

r t ts s♠ s ♦r♥② ♥s♣r ② t ②s ♠♥tr② ♦t♦♥ tt♦r ♥r♦♥s

s s♥ sts ♥ ♥ ♦♣t ♠r♦st♠t♦♥s r ♣♣ sss② t♦ t♦ ♥t

② ♣♦t♦r♣t♦rs s♦ tt t rst ♦♥trst ♥ s t♦ tt t rs♣♦♥s t♦ t s♦♥ ♦♥trst

♥ r♥s♥ st♦r ts rs♣♦♥ss r r♦r tr♦♣②s♦♦② ♥ t ②s

r t♥♥t ♥r♦♥ s ♦ ♠♦t♦♥ ♣r♦ss♥ s②st♠ ♦♥s t♦ t t♦♥♠t♥ t♦r② ♦ s♠s

❯♠♥ ♥ s tr t t♠ ♦ tr s♠ ♥s♦♥ rü ♦ ♥

t ♠s s♠r ♣r♥♣ s s ♥ t♦ s♥ s♠rt ❱ rt t tt ♥ s♠♣

s♥s♦r r♠r r♣sr ♦

rtrsts ♦ t t♦ ♦ ♠♦t♦♥ s♥s♦rs ♥ qst♦♥ r tr♠♥ r ② r♦r♥ tr rs♣♦♥ss

t♦ ♣r② r♦tt♦♥ ♦♣t ♦ ♥rt ② r♦tt♥ t s♥s♦rs ♠♥② ♥♦♦rs ♥ ♦t♦♦rs ♥ t s

♦ stt♦♥r② ♥r♦♥♠♥t t r♦tt♦♥ ♦♣t ♦ ω s ② ♥t♦♥ ♥♣♥♥t ♦ t st♥ r♦♠

t s♥s♦rs t♦ t srr♦♥♥ ♦ts ♦♥r♥ ♥ ♦♦r♥ ♥ rt② ♦♠♣r t♦ t rt ②r♦

♦t♣t s♥ ♥♦t Ωgyro

♥ ts st② s♦ ♥②s t rrs rt ♦ ♦r ♦ ♠♦t♦♥ s♥s♦rs s ts s ② ♣r♠tr ♥ ♦♣t

♦s r♦♦t ♣♣t♦♥s r rrs rt frefresh s ♥ r s t ♥♠r ♦ ♥ s

♠♦t♦♥ ♠sr♠♥ts ♦t♥ ♣r s♦♥ ♥ ♠sr♠♥t ♦rr ♥r ♦♥trst s tt ② t

rst ♣① ♥ t♥ ② t s♦♥ ♣① t t♠ ♦rrs♣♦♥♥ t♦ ♦r ♠sr♠♥t r♥ rrs rt

s ♦♠♣t ♥ ♥②s ♥r r♦s ♠♥♥ ♦♥t♦♥s ♦t ♥♦♦rs ♥ ♦t♦♦rs

sr♣t♦♥ ♦ t t♦ ♦ ♠♦t♦♥ s♥s♦rs tst r s ♥ ♥ st♦♥ t♦♥ s ♥ ♦♥t ♦

t ♣r♦r♠♥s ♦ ts s ♠♦t♦♥ s♥s♦rs r tst ♦t ♥♦♦rs ♥ ♦t♦♦rs ♥ r r♥ ♦

♠♥♥ s ♦r t s ♦ rt② ♦♥st♥t trs♦s ♥ stt♥s r ♣♣ tr♦♦t ts st② t

♣r♦r♠♥s ♦ ♦t s ♠♦t♦♥ s♥s♦rs r ♦♥ t♦ r♠r② stst♦r② ♥ tr♠s ♦ tr r②

rrs rt ♥ r♦st♥ss t♦ ♥s ♥ t s ♥r♦♥♠♥t ♥ t ♠♥♥

s s ♠♦t♦♥ s♥s♦r ♣r♦ t♦ ♦r ♠♦r ♥t② ♥ tr♠s ♦ t rrs rt ♥ t r② ♥

♥rr♦ ②♥♠ r♥ ♦ s rs t Ps s ♠♦t♦♥ s♥s♦r ♠sr t ♥r s♣

rt② ♥ ♠ r r♥ ♦ ♠♥♥ s

r ♥r ♣r♦ss♥ rttr ♦ t Ps ♥ s ♦ ♠♦t♦♥ s♥s♦rs ♥ s♥s♦r t♦t♣t s♥s ♠tt ② t♦ ♥t ♣①s r s♣t② ♥ t♠♣♦r② tr ♥ trs♦ t♦ tr♠♥t ♥r s♣ ω t♠ ♦ tr s♠ ♣r♦s② ♦♣ t r♥s♥s ♦rt♦r② ♥s r♥s♥ t s s t♦ ♠sr t ♦ s ♠♦t♦♥ ♥r s♣ ♠sr ② s♥s♦r ωmeas s t rt♦ t♥ t ♦♥st♥t ♥trr♣t♦r ♥ ∆ϕ ♥ t t♠ ∆t ♣s♥ t♥ t rst♥ s♦♥ trs♦ s♥s ♦r ♣r♦ss♥ ♦ t t♦ ♦ ♠♦t♦♥ s♥s♦rs s rr ♦t ♥ ♣r♦♥ t s♠ ♠r♦♦♥tr♦r sP P t s♠♣♥ rq♥② ♦ ③♥ t s ♦ t s ♠♦t♦♥ s♥s♦r t t♦ ♣♦t♦♦ ♦t♣ts r rst tr ② ♥ ♥♦ ♥♣sstr t t♦ rq♥s [③ ③] ♦r ♥ tr ② t s♦♥ ♦rr ♦♣ss tr t t♦ rq♥② ♦ ③♥ t s ♦ t Ps ♠♦t♦♥ s♥s♦r t t♦ ♣♦t♦♦ ♦t♣ts r tr ② t ♥♣ss trt t♦ rq♥s [③ ③]

sr♣t♦♥ ♦ t ♦ s ♠♦t♦♥ s♥s♦rs

s② ♦ t Ps ♥ s s ♠♦t♦♥ s♥s♦rs ♦♥ssts ♦ ♥s ♣ ♥ r♦♥t ♦ ♣♦t♦

s♥s♦r rr② s ♠♦t♦♥ s♥s♦r ♣r♦sss t ♦t♣t s♥s ♥rt ② ♣♦t♦♦s ♣♦t♦♦s

♦t♣t s♥ s tr♥s♠tt t♦ ♣r♦ss♥ ♥t r t rs♦♥ ♦ t s ♠♦t♦♥ ♦rt♠ sssss

t rt ♥r s♣ ω ♦ ♥② ♦♥trst♥ trs ♥♦♥tr ♥ t ♥r♦♥♠♥t ♦♠♣♦♥♥t ♦

t ♦♣t ♦ ♥ ts st② t♦ ♣① ♠♦t♦♥ s♥s♦rs s ♦♥ t s♠ t♠ ♦ tr ♣r♥♣ t q♣♣

t t♦ r♥t r♦♥t♥s r ♦♠♣r s r

r♦♥t♥ ♦ t Ps ♦ ♠♦t♦♥ s♥s♦r s s ♦♥ ♣t ♣①s ♦r♥② sst ② rü

♦ P ♣t P①s ♦r ♥sts ♥s♦rs rt♥ st♦♠♠ ❱ rt♥

♦♠♣rs♥ ♣①s r s ♦♣ ♥ ♦♦rt♦♥ t t ♥tr ♦r Prt P②ss PP ♥

rss é♣rt é♥♦♥ ♦♥ ♥s♣r r♥s♥ ❱♦t t ♣①

r st♦r tt ♥s ♦t ♦ ♠♦t♦♥ s♥s♦rs t ♦ t ♠♥ s②st♠ ♠♥ r♦tt♦♥ ♥r s♣ Ω s ♠♣♦s ♦♥ t ♦r ②♠♥s ♦ ♠♦t♦r r♦♠ ♥♠♦t♦r rt ♣r♦♣♦rt♦♥♥tr ♦♥tr♦r Ptr ♦ t s♥s♦r ♦r ♥ t t♦ st♦♠♠ s ♠♦t♦♥ s♥s♦rs ♥ ♠♥♥ s♥s♦rs ♦♥ s♥ ♠♥tr② ♣♦t♦♦ ♥ ♦♥ t ♦tr s ♦ t ♦r ♥♦t s r rt ②r♦ ♥♦s ♠sr♥ t rr♥ ♠♥ ♥r s♣ t r♦tt♦♥ s♣ ♦ t ♦r ♥ t ♠r♦♦♥tr♦r sP P q♣♣ t sr t ♥♦ t♦ t ♦♥rtr♥♣ts ♠r♦♦♥tr♦r ♣r♦sss t s s♥s r ② t t♦ s ♠♦t♦♥ s♥s♦rs t s♠♣♥rq♥② ♦ ③ ♠sr s ♠♦t♦♥ ωmeas ♥ t r♦tt♦♥ s♣ Ωgyro r r♦r s②♥r♦♥♦s②♥ s♥t t♦ ♦♠♣tr t♦♦t ♠♦ ♦♥♥t t♦ s♠ ttr② P♦ ♠❱ s rss♥ s t s♥s♦r ♦r r t♦ r♦tt t♦♥♦♠♦s② s ♠♦t♦♥ s♥s♦rs ♠♥tr ♠r ♥s ♣r♥ ♦ ♥t ♠♠ ♥♠r s♦s t rs♣t t♦ t ♦ ♣♥ t♦ rt ss♥ ♥r s♥stt② P s♥s♦r ♦♥ t t ① ♣♦t♦♦ rr② ♥ ♥ t♦♣t rt ♦♥② t♦ ♣①s r ♦♥♥tt♦ t sP ♠r♦♦♥tr♦r

trs ♥ ♥trt ♣♦t♦♦ t s♥st r ♦ 250µm∗250µm ♦♥♥t t♦ ♥ ♣t t♠♦♥t♥♦s

♦rt♠ rt ♥ ②♥♠ r♥ ♦

r♦♥t♥ ♦ t s ♦ ♠♦t♦♥ s♥s♦r s s ♦♥ ♥ ♦ts ♣♦t♦♦ rr② s

♦♠♣♦♥♥t ♣rs r♦♠ s ♦♥sst♥ ♦ r♦s ♦ ♣①s ♦ ♠ t s♥s♦r t♦ st♥s rr

♥♠r ♦ ♦♥trst♥ ♣ttr♥s t ♦ ♠♥♥ s s♠♠ t♦tr t ♣①s ♥ t s♠ ♦♠♥

t♦ ♠♣r♦ t s♥t♦♥♦s rt♦ ② ♥rs♥ t s♥st r t♦ 300µm ∗ 1600µm s t♦ ♦♥t

♣♦t♦s♥s♦rs r ♦♠♥ t ss ①♥ ♣♦t♦rr♥t ♠♣r ♠♣♠♥t s♥ r ♦♥t

♦♠♣♦♥♥ts ♦r♥ ♦ ♠♦t♦♥ tt♦r ♥s r♥s♥ t r

t s♦ t♠ ♦ tr ♦♥sst ♦ ♥ ♥♦ rt ♣r♦♥ ♥ ♦t♣t s♥ tt ♥rs s

t t♠ ∆t t♥ ts t♦ ♥♣ts rs ♦t♣t s♥ tr♦r ♥rs t t ♥r s♣ ω

t ②s ♠♦t♦♥tt♥ ♥r♦♥s r♦♠ t s ♦r♥② ♥s♣r r♥s♥ t ♦r s

♠♦t♦♥ s♥s♦rs ♥ rt t♦ tr rt♦t ♦r tt♦r ♦♥trsts ♦♥s♣r s♥

♣r♦ss♥ ♠t♦ ♠♣♠♥t ♥ ♦ t t♦ ♦ ♠♦t♦♥ s♥s♦rs ♥ ♦♠♣♦s ♥t♦ st♣s ♥s

r♥s♥ t r t s r s ♦♦s

❼ t♣ ♣t s♠♣♥ ♥ ♦♣ss s♣t tr♥ s ② ♦s♥ t ♠♥tr

♠r ♥s t♦ ♦t♥ ss♥ ♥r s♥stt② ♦r ♣①

❼ t♣ ♥♣ss t♠♣♦r tr♥ ♣ss t♠♣♦r tr♥ t♦ r♥tt t s s♥s ♥

♦♣ss t♠♣♦r tr♥ t♦ r t ♥♦s s s t ③ ♥trr♥ ♦r♥t♥ r♦♠ rt

t♥ ts st♣ s ♣rt② ♥♦ ♥ t s ♦ t s s ♠♦t♦♥ s♥s♦r

❼ t♣ ♥ t s♦t ♦ t s♥s t♦ tt ♦t rt♦t ♥ tt♦r ♦♥trst

tr♥st♦♥s

❼ t♣ rs♦♥ t ① s rrss ♦ t ♠♥♥ r♦♥

❼ t♣ sr♥ t t♠ ∆t t♠ ♦ tr ♣s♥ t♥ t trs♦ s♥s

❼ t♣ ♦♠♣t♥ t ♦ ♥r s♣ ② ♣♣②♥

ωmeas =∆ϕ

∆t

♥r s♣ ♠sr s t♥ t♥② t♦♦t ♠♦ r♦♠ r♠♦ ♦♠♣♥②

♥t♦ ♦♠♣tr ♦r ♥②ss

r ss♥ ♥r s♥stts ♦ t ♥ P ♣♦t♦s♥s♦rs t♣ts ♦ t t♦ ♥r② ♠♣ ♣♦t♦s♥s♦rs ♥ t rr② r♥ s♦ r♦tt♦♥ ♦ t s♥s♦r ♣♠ ♥ r♦♥t ♦ ① ♣♦♥t t s♦r ss♥ s♥stt② ♦ t t♦ ♣♦t♦tt♦rs ♣♣r♦①♠t s♥ t♦♦ t ♦s♥ s st♥ ♦rr t♦ ♦t♥ ∆ϕ = ∆ρ s t ♦rrt♦♥ ♦♥t R2

LSC > 0.994 s r② ♥r② q t♦ ts ♦♥r♠stt ♥ ♦t♥ ss♥ s♥stt② ② ♦s♥ t♣ts r♦♠ t t♦ ♣♦t♦s♥s♦rs s ♦t ♦ t ♣①s ♦♥ t P rt♥ ♥ r♦tt ♦r③♦♥t② ♥r♦♥t ♦ rt ♥t ♦♥trst♥ ss♥ s♥stt② ♦ t P ♣♦t♦r♣t♦rs ♦♠♣t r♦♠ t ♣♣r♦①♠t rr♦r ♥t♦♥ erf R2

APIS >0.999

s ♦r ♣r♦ss♥ s rr ♦t ♦♥ sP P ♠r♦♦♥tr♦r ♦r♥ t s♠♣♥ rq♥②

♦ ③ ♥ ♦t♥♣♦♥t rt♠t s♠t♥♦s ♣r♦ss♥ ♦ t t♦ s♥s♦rs Ps ♥ s

♥♥ t sr r♦t ♥tr ♦♣s ♦ t ♣r♦r♠ ♠♠♦r② ♦ t t ♠♠♦r② ♦ t ♠r♦

♦♥tr♦r ♥ ♦♥ts ♦r ♦ t ♣r♦ss♥ t♠ t s♠♣♥ rq♥② ♦ ③ ♦r s♥

♣r♦ss♥ tss ♦ ♥♦t rqr ♣r♦r♠♥ ♥② t♠♦♥s♠♥ tss s s s♦♥ s ♦♦♣ t s

s t♦ tr♥s♦r♠ t ∆t ♥t♦ t s② ♣r ♥r s♣ ωmeas s qt♦♥ ♠ ♦rt♠s

r ♦♣ ♦♥ t t ♠♥ ♦st ♦r sP ♠ rt ♦r sP

♥r s♥stt② ♥t♦♥ ♦ s♥ ② ♣♦t♦r♣t♦r s ss♥ strt♦♥ öt③ rsts

r♦♠ t s♣t ♦♥♦t♦♥ ♦ t ♣♦t♦r♣t♦rs ♠tr t t ♣♦♥t s♣r ♥t♦♥ ♦ t t ♥st

r♥s♥ rs t♥ s s♦♥ ♥ r s♠r ss♥ s♥stt② ♣r♦ t♦

tt ♦ t ② s ♦t♥ r ② ♦s♥ t ♥s ♦ ♠♥tr ♠r ② r♥ t st♥ t♥

t ♥s ♥ t rt♥ ♥ ♦ ♠♦t♦♥ s♥s♦r t t t t ♦ t ss♥ r s

t ♣t♥ ♥ ∆ρ rt② tr♠♥s t t♦ rq♥② ♦ t ♦♣ss s♣t tr♥ ♣r♦ss

st♣ rs t ♥trr♣t♦r ♥ ∆ϕ tr♠♥s t ♥r s♣ ω ♠sr♠♥t r♥ s ♦rs ♥

s♦♠ r♥ ♥sts ♥ ts ♥s r st ♥ ts st② t♦ ♦t♥ t ♦♦♥ ♦♣t ♣r♦♣rt②

∆ϕ = ∆ρ

t s ♦rt ♥♦t♥ tt ts t♦ ♦♣t s♥s♦rs r ♦t ♦♥strt s♥ t s♠ ♦♣t ss♠② ♦r♥t♥

r♦♠ ♦♦st ♠♥tr ♠r ♥s ♣r♥ ♦ ♥t ♠♠ ♥♠r

♥ t s ♦ t s ♣♦t♦r♣t♦rs t ♥r s♥stt② ♥t♦♥ ♦ t ♥s♣♦t♦♦ ss♠② s

ssss ② s♦② r♦tt♥ t ♣♦t♦r♣t♦rs ♣ ♠ ♥ r♦♥t ♦ ① ♣♦♥t t s♦r ♥r

s♥stt② ♠sr tt ss♥ r r ♥ ♥ t t t t ∆ρLSC = 3.8

t ♥trr♣t♦r ♥ ∆ϕLSC = 3.8♥ t ♦rrt♦♥ ♦♥t R2

LSC > 0.994 ♥ t s ♦ t Ps

♣♦t♦r♣t♦rs t ♥r s♥stt② ♥t♦♥ ♦ t ♥s♣♦t♦♦ ss♠② s ssss r♦♠ t ss♥

rr♦r ♥t♦♥ rs ♥ ♦t♥ ② q② r♦tt♥ ♥ t ♦r③♦♥t ♣♥ t s ♠♦t♦♥ s♥s♦r

♣ ♠tr ♥ r♦♥t ♦ rt ♦♥trst♥ r ♦rrt♦♥ ♦♥t t♥ t r

t ♥ t ss♥ rr♦r ♥t♦♥ r s R2

APIS > 0.999 ♥ ts s ♥ ∆ρAPIS = ∆ϕAPIS = 3.3

♠♥ rtrsts ♦ t t♦ s♥s♦rs r s♠♠r③ ♥ t t ♥ ♣r♦s ♦ ♠♦t♦♥ s♥s♦rs Ps

rs♥ ♣♣♦r ♦②r♦♥ ♠ ❱♦t r♥s♥ r t t t♠♣♦r ♥♣ss

tr ♦♥sst ♦ 1st ♦rr ♣ss tr t t♦ rq♥② ♦ ③ ♥ 4th ♦rr ttr♦rt ♦♣ss

tr t t♦ rq♥② ♦ ③ ♦ r t ♣r♦ss♥ r♥ ♦♥ t ♠r♦♦♥tr♦r t ♦rr ♦ t

ttr♦rt tr ♦ ♦t s♥s♦rs s r t♦♦ t♥s t♦ t ♦♥♣ ♣r♠♣t♦♥ ♥t r

♣t♦♥s ♦ t Ps ♥ s s ♠♦t♦♥ s♥s♦rs♦ ♠♦t♦♥ ♥s♦r Ps s

♥trr♣t♦r ♥ ∆ϕ ♣t♥ ♥ ∆ρ P♦t♦♦ s③ µm ① ①

P① ♣t µm ♦ ♥t ♦ t ♥s ♠♠

Fnumber ♦ t ♥s ♥r ♦t② ♥ s ❬ ❪s♦t♦♥ s ❬♥ ① ❪ ❬ ❪ ❬ ❪

♥stt② s st♠t ♠ss t ♦♣ts ♥ st♥♦♥ rs♦♥

t ♥♦s 2nd ♦rr t ♦♣ss tr s tr♦r ♠♣♠♥t ♥ t sP ♠r♦♦♥tr♦r r

♥ t♦♥ s t ♦♥♣ t♦♣t rt r② trs ♥ ♠♥♥♣♥♥t ♣ss tr t

t t♦ rq♥② ♦ t ♣ss tr ♥ t ♣rs♥t Ps s ♠♦t♦♥ s♥s♦r s r t♦ ③

r s♦s t t♦ ♦ ♠♦t♦♥ s♥s♦rs ♠♦♥t ♦♥ ♥ ♥t ♣r♥trt ♦r P ♥ t♦♥

♠♥♥ s♥s♦r ♥ ♣♦t♦♦ P❳ s ♦♥♥t t♦ ♥ ♥♦ ♠♣r rt ♦♣rt♥ ♥ t

♣♦t♦♦t ♠♦ ♥ ♦rr t♦ ♠sr t t ♠♥♥ ♦ t s♥ s♥♥ ② t s ♠♦t♦♥ s♥s♦rs

♣♦t♦rr♥t Iph ♦t♣t ♦ ts ♠♥♥ s♥s♦r s tr♠♥ s ♦♦s

Iph = (eVout/0.125 − 1)Idark

r t r rr♥t Idark s q t♦ 1nA ♥ Vout s t ♠♣rs ♦t♣t ♦t s s♥s♦r

♦r s r♦tt ② ♠♥s ♦ ♠♦t♦r s r ♦♥tr♦ ② ♣r♦♣♦rt♦♥♥tr rt♦r

♥♠r♥ ♦ t s ♠♦t♦♥ s♥s♦rs

t♦ s ♠♦t♦♥ s♥s♦rs r tst ♦t ♥♦♦rs ♥ ♦t♦♦rs s rs ♥ ② ♦♠♣r♥ tr

♦t♣t s♥s t t ♥r s♣ Ωgyro ♠sr ♦♥ rt ②r♦ ♥♦ s ♥

♠sr ♥r s♣s ♥ t 0 t♦ 300/s r♥ ♦r t ♦t♦♦r ♠sr♠♥ts t s♥s♦r ♦r s ♣ ♦♥

t q♣♣ t r s

s s♦♥ ♥ r t s♥s♦r ♦r s ♦♥♥t t♦ ♠♦t♦r t ♠ t ♣♦ss t♦ ♥②

st t ♠♥ ♥r s♣ ♦ t ♦r Ω r♥♥ t♥ 60/s ♥ 300/s ♥ ♦t ♥r♦♥♠♥ts

r Ptr ♦ t ♥♦♦r s♥ r t ♦ ♠♦t♦♥ s♥s♦rs r tst Ptr ♦ t ♦t♦♦r s♥ r t ♦ ♠♦t♦♥ s♥s♦rs r tst st♥s t♦ t srr♦♥♥ ♦ts♥t ② t rr♦ r ♥ ♦ ♣tr Ptr ♦ t s♥s♦r ♦r ♥ t ♠♥ s②st♠ ♣ ♦t♦♦rs

t stt ♥ ②♥♠ rs♣♦♥ss ♦ t s ♠♦t♦♥ s♥s♦rs r ♠sr t sr r♦♥ ♠♥♥

s

❼ ♥♦♦rs ① ① ♦rrs♣♦♥♥ t♦ ♠ rt t ♥ r ♠♦♥t ♦

s♥t r♦♠ t ♥♦s

❼ ♦t♦♦rs ① ① ♦rrs♣♦♥♥ t♦ s ♥ s♥♥② ②

♦ ♠♥♥ s s ♥♦♦rs ♥ ♦t♦♦rs r ♦s♥ t♦ ♦ t s ♦ ♠♦t♦♥ s♥s♦r

t♦ tt ♦♥trsts ♥ t ♠♥♥ s r t ♠①♠♠ ♣♦ss s ♦t♥ t ts ♣r♦ ♦

t ②r ♣r ♥ rss ♥ ①♠tr s ♦r♥t t t s♠ rt♦♥ t♥ t s♥s♦rs

r♦♥ ♠♥♥ s r ♠sr ♥ ① ② t ①♠tr ♦♥ s ♦♥② ♥

st♠t ♦ t ♦r ♥r♦♥♠♥t ♠♥♥ stt rs♣♦♥ss ♦ t s♥s♦rs r ssss ② ♣♣②♥

srs ♦ 30s t♥s♦♥ st♣s t r♦tt♦♥ s♣ Ω r♥♥ r♦♠ 60/s t♦ 300/s ♦ tst t ②♥♠

rtrsts ♦ t s♥s♦rs s♦♥ st♠s s ♣♣ r♥ r② ♦♥ ♣r♦s ♦ ♦♥st♥t②

♥rs♥ ♥ rs♥ ♦t② r♥♥ t♥ 60/s ♥ 300/s r ♠♣♦s

①♣r♠♥t rsts

tt ♥r s♣ rtrsts

r tt ♥♦♦r ♥ ♦t♦♦r rtrsts ♦ t ♥ Ps ♦ ♠♦t♦♥ s♥s♦rs ssss ②♣♣②♥ 30/s st♣s st♥ s♦♥s t♦ t r♦tt♦♥ s♣ r♦♠ 60/s t♦ 300/s r♦♥ ♠♥♥r♥ ♥♦♦rs t♥ ① ♥ ① ♣rt r♦♠ s♦♠ ♣s t ① ♥ ♦t♦♦rs t♥ ① ♥① ♠♥ s ♠♦t♦♥ r♦r t ♥r s♣ Ω s ♣♦tt ♥ ts r t ts st♥r t♦♥ st ♥r ♣♣r♦①♠t♦♥ ♦t♥ ♥ ①♣r♠♥t s ♦♠♣t ♥ t ♣rtr r♦♠ ♥rt②s ♥ s ♣r♥t tt ♥♦♦r ♥ ♦t♦♦r rtrsts ♦ t Ps ♦ ♠♦t♦♥ s♥s♦r tt ♥♦♦r ♥ ♦t♦♦r rtrsts ♦ t s ♦ ♠♦t♦♥ s♥s♦r ❲♥ t ♠♥♥ ♥rs t s♣rs♦♥ ♦ t t r♦r t t Ps s ♠♦t♦♥ s♥s♦r♥rs t♦ sr ♠t♥ rr♦rs ♦rr♥ s ♦ t ♣tt♦♥ ♣r♦ss ♦ t t♦♣t rtt ♦r r♥ t t ♣tr t ♦ ♥r s♣s ♥ ♦ ♠♥♥ s t s ♦ ♠♦t♦♥ s♥s♦r ♥♦t tt ♥② ♦♥trstsr♥ t s♦♥ st♣s s ♦ ♠♦t♦♥ s♥s♦r rs♣♦♥ s s♦♦♥ s t r♦♥ ♠♥♥ s ♥ t r♦tt♦♥ s♣ r ♥♦ ♥ t♦♥ t s ♦ ♠♦t♦♥ s♥s♦r s♦ ♦♦ ♥rt② ♥ tts♣rs♦♥

r rs rts ♦ t ♥ Ps ♦ ♠♦t♦♥ s♥s♦rs ♠sr ♥♦♦rs ♥ ♦t♦♦rs t r♦tt♦♥ s♣ r♥♥ r♦♠ 60/s t♦ 300/s ♥ 30/s st♣s st♥ s rs rt ♦ t Ps ♦ ♠♦t♦♥ s♥s♦r ♥♦♦rs ♥ ♦t♦♦rs t ♥ ♠♥♥ r♦♥r②♥ r♦♠ ① t♦ ① ♦♥♣ t♦♣t rt r♥r t Ps ♦ ♠♦t♦♥ s♥s♦r♥r♥t t♦ t ♠♥♥ ♥ tr♠s ♦ t rrs rt rs rt ♦ t s ♦ ♠♦t♦♥ s♥s♦r ♥♦♦rs ♥ ♦t♦♦rs t ♥ ♠♥♥ r♦♥r♥♥ r♦♠ ① t♦ ① s ♦ ♠♦t♦♥ s♥s♦r s♦ t ♦rr♥ ♦ ♦♥sr rrsrt rt♦♥s t sr ♠♥♥ s s ♦ ♠♦t♦♥ s♥s♦r s ♦♥ t♦ ♠ rrrs rts t ♠♥♥ s t♥ t Ps s s♥s♦r

r s t stt rtrsts ♦ t t♦ s♥s♦rs ♥♦♦rs ♥ ♦t♦♦rs s ssss ② ♣♣②♥ 30/s st♣s

st♥ s♦♥s t♦ t r♦tt♦♥ s♣ r♦♠ 60/s t♦ 300/s r♦♥ ♠♥♥ r♥ ♥♦♦rs

t♥ ① ♥ ① ♣rt r♦♠ s♦♠ ♣s t ① ♥ ♦t♦♦rs t♥ ① ♥ ① ❲t

s ♠♦t♦♥ s♥s♦r ♥ t ♠♥♥ t ♠♥ st♥r t♦♥ ♦ t t s ♦♠♣t s

♦♦s

Std = std(ωmeas)

♦ st♠t t r② ♦ t s♥s♦r t st ♥r ♣♣r♦①♠t♦♥ s t t s♥s♦r ♥

♠♥♥ r♦♥ s ♦♥ t qt♦♥

ωmeas = a× Ω

rrss♦♥ ♦♥t ♦ ts ♥t♦♥ s s t♦ ♦♠♣t t ♥rt② rr♦r ♦r♥ t♦ t qt♦♥

LinearityError(%) = |(a− 1)| × 100

s s♦♥ ♥ r t s ♦ ♠♦t♦♥ s♥s♦r s♦ ♦ ♥r♥ t♦ t ♠♥♥

t ♥rt② ♦ ts stt rtrsts r♠♥ ♥♥ ♣r♦ t ♠♥♥ ♥ t r♦tt♦♥ s♣ r

♠♥t♥ t rt② rss ♦ t ♠♥♥ ♦t s♥s♦rs rs♣♦♥ rt② s s♦♥

② t s♠ ♥rt② rr♦r rt ♥ ♠♦st ss s s♦♥ ♥ r t s ♦ ♠♦t♦♥ s♥s♦r

r♠♥ s♥t t ① ♠♥♥ ♥ t r♦tt♦♥ s♣s ♦ 150/s stt rtrsts ♦

t Ps ♦ ♠♦t♦♥ s♥s♦r s♦ s♦ ♦♦ ♥r♥ t♦ t t♥ ♦♥t♦♥s rs t s♣rs♦♥

♦ t s ♥rs st② t t ♠♥♥ t t ♦st ♥ st s♣s tst rs ♥

s♣rs♦♥ ♦ t t ♦t♥ t t Ps ♦ ♠♦t♦♥ s♥s♦r s ♥♦ ♦t ♠♥② ttrt t♦

t ♣rs♥ t t ♣① ♦ ♥ t♦♣t rt t ♥♦ ♥ts♥ tr t③t♦♥ ♣r♦ss ♠②

tr♦r st♦rt t ♣♦t♦♦ s♥s ts s♥ s ♠♦t♦♥ ♠sr♠♥t rr♦rs rq♥②

rs♣♦♥s ♦ t ♣t rt s♦ r♠t ♥rs ♥ t ♥t t t ♠♥♥ r♥♥ r♦♠

③ t ① t♦ ③ t 105①

rs rt ♥②ss

rrs rts ♦ t t♦ s♥s♦rs ♠sr ♥♦♦rs ♥ ♦t♦♦rs r s♦♥ ♥ r rrs rt

s ♥ s t ♥♠r ♦ ♥ ♠♦t♦♥ ♠sr♠♥ts ♣r s♦♥ ♥ ♠sr♠♥t ♦rs ♥ ♦♥trst

tr♥st♦♥ s tt ② ♦♥ ♣① ♥ t♥ ② t s♦♥ ♣① t t♠ ∆t ♥ ♦r ♠sr♠♥t r♥

♦rrs♣♦♥♥ t♦ ♥ ♥r s♣ ♥ t ❬s s❪ r♥ s qt♦♥ ♦♥trst s tt ♥r

t t♦ ♥t ♣♦t♦♦ ♦t♣ts ① t trs♦ s ♥ t ♣rrr rt♦♥ ♥ t ♦ t

rrs rt ♦ t s s ♠♦t♦♥ s♥s♦r s ♦♥ t♦ ♣♥ ♦♥ t ♠♥♥ ♥ t♦ r② qs♥r②

t t r♦tt♦♥ s♣ Ωgyro

♥♦t ♥ tr♦s ♥♦t tr♦s stt tt ♥ ② r♦tt♥ t ♥ ♥r s♣ ω ♦♥rts

s♣t rq♥② ♥t♦ t♠♣♦r rq♥② s ♥ ② t qt♦♥

fT = ω × fS

r fT s t t♠♣♦r rq♥② ♦ t ♣♦t♦r♣t♦r ♦t♣t s♥ ω s t ♥r s♣ ♦ t s s♥s♦r

t rs♣t t♦ t ♦♥trst♥ ♣ttr♥ ♥ fS s t s♣t rq♥② ss♦t t t ♦♥trst♥ ♣ttr♥

♦r♥ t♦ t ♦ qt♦♥ ♥ ss♠♥ tt t ♦ ♠♦t♦♥ s♥s♦r tt t s♠ ♦♥trsts rrss

♦ t ♥r s♣ t ♥♠r ♦ ♥ ♥r s♣ ♠sr♠♥ts ♣r s♦♥ ♦ ①♣t t♦ ♥rs

♥r② t t r♦tt♦♥ s♣ s t t♠♣♦r rq♥② fT ♥rs ♦r s s♦♥ ② rs ♥

t rrs rt ♦ t s s ♠♦t♦♥ s♥s♦r st♦♣♣ ♥rs♥ t ♥r s♣s ♣t ♦♣ss

tr♥ r ♦♠♥ t t♠♣♦r s♦♥ ♦rr ♦♣ss tr r ♠t t r♥ ♦ t

t♠♣♦r rq♥② fT ♦ ♣♦t♦r♣t♦r ♦t♣t s♥ t♦ rq♥② ♦ ③ ♥ tr♦r ♠t t rrs

rt ♦ t s ♠♦t♦♥ s♥s♦r t♦ ♦ ③ t ♥r s♣s

♦♥trr② t♦ t rrs rts ♦ t s ♠♦t♦♥ s♥s♦r s♦ ♦♥sr rt♦♥s t♥

③ ♥ ③ t 300s s rs ♥ t♦s ♦ t Ps s s♥s♦r r ♦♥ t♦

♥♣♥♥t ♦ t ♠♥♥ ♥ t♦ ♥rs st② t t ♥r s♣ s rs ♥ ♥

♥r♦♥♠♥t ♦♥t♦♥ t ♠♥♥ r♦♥ s♣rs♦♥ s ♦♠♣t r♦♠ t ♠♥♥ s♥s♦r

t r♦r t ♥r s♣ r♥ t stt ①♣r♠♥ts r ♥ s ♦♥ t ♠♥ s

♦t♥ ♥ ①♣r♠♥t t s♣rs♦♥ s ♦♥ t♦ qt ♦ t ♦ ♠♥♥ s ♥ t ① ♥

µ t ① ♥ rtr t ♠♥♥ s ♠ t ① ♥♦♦rs ♥ ♠ t ①

♦t♦♦rs s ♦ ts ♠r rt♦♥s ♥ t r♦♥ ♠♥♥ t rüs ♣①s ♥ t P ♣

r ♦♥st♥t② ♣t♥ t♦ ♥ r♦♥ ♠♥♥ t rt② s♦ t♠ ♦♥st♥t r②♥ t t

♠♥♥ r♦♠ ∼ µs t ① t♦ ∼ ♠s t ① r♦r r♥ t tsts t ♣♦t♦r♣t♦r ♦t♣t

s♥s rq♥t② ① t st♦♥ ♣♦♥t ♦ t ②strss ♥t♦♥ st♣ ♥ r t♦t r♦♣♣♥

st ♥♦ ♦ t st♦ ♣♦♥t ♦r t ♥①t ♦♥trst s ♥♦♥tr ♥r ♥rs ♥ t ♥r

s♣ tr♦r ♥♦t t♦ ♥r ♥rs ♥ t Ps ♠♦t♦♥ s♥s♦rs rrs rt st♦♥ ♥

st♦ ♣♦♥ts ♦ t ②strss trs♦ ♥t♦♥ ♥ t Ps ♠♦t♦♥ s♥s♦r r st s t②

t st tr♦ t♥ ts rrs rt ♥ t ♥r s♣ ♠sr♠♥t r②

②♥♠ s ♠♦t♦♥ rtrsts

②♥♠ ♥♦♦r ♥ ♦t♦♦r rs♣♦♥ss ♦ t t♦ s ♠♦t♦♥ s♥s♦rs r s♦♥ ♥ r r t

♥r s♣ ωLSC ωAPIS ♠sr ♦ts s s♣r♠♣♦s ♦♥ t rr♥ ♥r s♣ Ωgyro r ♥

t ②♥♠ ①♣r♠♥ts t t s♣rs♦♥ s t♥ t♦ t st♥r t♦♥ ♦ t r♥ t♥ t

♥r s♣s ♠sr ② t rt ②r♦ ♥ t ♦ ♠♦t♦♥ s♥s♦r ♦t♣t s♥ ♦r♥ t♦ t ♦♦♥

qt♦♥

Stderror = std(Ωgyro − ωmeas)

s♣t t rt r♥ ♥ t ♠♥♥ r♥ t♥ ① ♥ ① rs ♥

t rs♣♦♥ss ♦ ♦t t P ♥ s s ♠♦t♦♥ s♥s♦rs t② ♦② t tr♥r ♠♣♦s

♦♥ t r♦tt♦♥ s♣ ♦ t ♦r r♥ t ♥♦♦r ①♣r♠♥t t ① s t t ♦♠♥ ♠♥② r♦♠

s♥ ♥♦ s ♥♦♥♥♦r♠② strt str♦♥ rt♦♥s ♥ t ♠♥♥ t♥ ♥ ①

r ♦sr r♥ r♦tt♦♥ s s♦♥ ♥ r

s s♦♥ ♥ rs ♥ t rr♦r ♥ t st♥r t♦♥ ♦ t Ps ♦ ♠♦t♦♥ s♥s♦r ♥rs

st② t t ♠♥♥

t ♦ ♠♥♥ s t r rrs rt ♦ t s ♠♦t♦♥ s♥s♦r s ♦ ③ ♥ s

t ♠♥♥ ♥rs t r rrs rt frefresh ♦ t s ♦ ♠♦t♦♥ s♥s♦r ♥rs t♦t

str♦♥② ♥rs♥ t ♦rrs♣♦♥♥ st♥r t♦♥ rs ♥ s ♠♥t♦♥ ♦ ♥ ♦♥♥t♦♥

t t stt ♠sr♠♥ts t Ps ♠♦t♦♥ s♥s♦rs rrs rt ♥rs st② t t ♠♥♥

rs t rrs rt ♦ t s ♠♦t♦♥ s♥s♦r ♥rs r♦♠ ③ t♦ ③ t♥ ① ♥

①

♦ ♠♦t♦♥ s♥s♦rs t r rrs rts rtr t♥ ③ ♥ st♥r t♦♥s ♦ s ♥ s

t♦ ♦♥sttt r♠r t♦♦s ♦r ♣r♦r♠♥ r♦♦t tss s s ♦st ♦♥ ♦r trr♥ ♦♦♥ t ♥

tr♦r s♥ r♦♠ rs tt t ♥ Ps ♦ ♠♦t♦♥ s♥s♦rs r ♦t ② st

♦r ♣r♦r♠♥ tss ♦ ts ♥ ♥ ♦t♦♦rs t ♠♥♥ s r♥♥ t♥ ① s

♥ ① s rs♣t②

♦♥s♦♥

♦ s ♠♦t♦♥ s♥s♦rs r tst ♥ rtr③ r ♥ ①♣r♠♥ts ♥r r♦s t♥

♦♥t♦♥s ♥♠r tst ♣rs♥t ♦ ♥ s t♦ ② rtr③ r♦s s ♠♦t♦♥ s♥s♦rs

r ②♥♠ ♥♦♦r ♥ ♦t♦♦r rs♣♦♥ss ♦ t t♦ s ♠♦t♦♥ s♥s♦rs ♦ts r ♥ s ♠♦t♦♥ s♥s♦rs ♠♥② r♦tt ♥ tr♥r ♣ttr♥ ♦ ♥r s♣ rt♦♥ r♥♦♥ srs ♦ ♦t② r♠♣s r♥♥ t♥ s ♥ s t r♥t s♦♣s ♥r ♦r r♥tt♥ ♦♥t♦♥s s♣t t str♦♥ ♠♥♥ rt♦♥s ♦t s ♠♦t♦♥ s♥s♦rs ♦♦ t r♦tt♦♥♥r s♣ qt t② ❲t ♦t s♥s♦rs t rr♦r t♥ t ♠sr ♦ ♠♦t♦♥ ωmeas ♥ t♥r ♦t② ♠sr ② t rt ②r♦ Ωgyro s s t♦ ♦♠♣t t st♥r t♦♥ ♦ t rr♦r r rrs rt ♦ t s♥s♦r s ♥ r s t ♥♠r ♦ ♥ ♠sr♠♥ts ♦rr♥ r♥ t ♦①♣r♠♥t ② t rt♦♥ ♦ t ①♣r♠♥t ②♥♠ ♥♦♦r ♥ ♦t♦♦r rs♣♦♥ss ♦ t Ps ♦ ♠♦t♦♥ s♥s♦r s♣t t ♦♥srrt♦♥s ♥ t ♠♥♥ t r rrs rt ♦ t Ps s♥s♦r s ②s ♦ s♠r ♦rr ♦♠♥t t♥s t♦ t t♦♣t rt s s♦♥ ♥ ♥ t st♥r t♦♥ ♦ t rr♦r♥rs t t ♠♥♥ ②♥♠ ♥♦♦r ♥ ♦t♦♦r rs♣♦♥ss ♦ t s ♦ ♠♦t♦♥ s♥s♦r s s t♦ ①♣tr♦♠ t stt rtrsts t r rrs rt ♦ t s s♥s♦r ♥ s♥ ♥ ts rs t♦ ♥rs t t ♠♥♥ ②♥♠ rs♣♦♥s ♦ t ♠♥♥ s♥s♦r ♥ s♣rs♦♥ ♦ t ♣♦t♦♦s ♦t♣t rr♥t rrt♦♥s ♥ t s tt ② t ♠♥♥ s♥s♦r s♦♥ ♥ ♥ ♥rs t s♣rs♦♥ ♦ tPs ♦ ♠♦t♦♥ s♥s♦rs rs♣♦♥s s s♦♥ ♥ ♥

♥♦♦rs ♥ ♦t♦♦rs ♥r sr s ♦ ♠♥♥ ♣r♦r♠♥s ♦ t s ♠♦t♦♥ s♥s♦rs tst

t ts ♠t♦ ♥ s t♦ ♦rrs♣♦♥ r② t♦ t♦s ♦ ♦t♥ t ②♥ r♦♦t s

t s♥s♦rs r tst r ♥ ①♣r♠♥ts ♥r r♦s t♥ ♦♥t♦♥s

s ①♣t ♥ ♦ ts t♦♣t ♣①s t Ps ♦ ♠♦t♦♥ s♥s♦r s ♦♥ st♦♠♠ ❱

rt♥ q♣♣ t ♣t ♣①s t st ♣r♦r♠♥s ♥ tr♠s ♦ ts ♥r♥ t♦ t ♠♥♥

t♦ t s ♦ ♠♦t♦♥ s♥s♦r q♣♣ t ♥r② ♠♣ ♣♦t♦s♥s♦rs t♦ rs♣♦♥ t♦

♦♥trsts ♥♦♥tr t ♦ ♥r s♣s s ♥r ♦ ♠♥♥ ♦♥t♦♥s ① ts ♠

sr♠♥ts r ② rt ♥s t♦ t t♦♣t rt s♥ t♦ tt s ♠♦t♦♥ ♥ sr

s ♦ ♠♥♥ t rtrsts ♦ t Ps ♠♦t♦♥ s♥s♦r r r② ♦♥sst♥t ♥ ts r♥

t♦ s♦♠ ♠♣r♦♠♥ts ♦ ♠ ♥ tr♠s ♦ t r rrs rt ♥ t r② ♥ t ♥ P

♣ t s ♣r♦♣♦s t♦ ♥trt ♥ t tr ♥ t♦♥ rst ♦rr ♦♣ss tr t t ♣① t♦ rs

t s♣rs♦♥ ♦ t Ps ♠♦t♦♥ s♥s♦r

r rrs rt ♦ t s ♠♦t♦♥ s♥s♦rs s ② ♣r♠tr ♥ s ♦♥tr♦ s②st♠s s ♦♥

♠♦t♦♥ s♥s♦rs s st ♥ ♣rtr r t s sts tt t s ♠♦t♦♥ s♥s♦r s r

rrs rts t ♥r s♣s ♥ str♦♥ ♠♥♥ s t♥ t Ps ♠♦t♦♥ s♥s♦r ♦r t

r rrs rt ♦ t ttr s♥s♦r ♥♦ t t♦♣tt ♣①s s st② ♥ t ♦ ♠♥♥

s

s ♠♦t♦♥ s♥s♦r t st rsts ♥ tr♠s ♦ t r② ♥ t r rrs rt ♥ ♥rr♦

♠♥♥ r♥ s rs t Ps ♠♦t♦♥ s♥s♦r tr♥ ♦t t♦ ♣ ♦ ♠sr♥ t

♥r s♣ ♥ r♥ ♦ ♠♥♥ s

♦ s♠♠r③ t s sts r tt ts ♠♥tr s ♠♦t♦♥ s♥s♦rs ♦♥sst♥ ♦ ♦ ♦st ♦♣ts

♥ ss tr♦♥ ♦♠♣♦♥♥ts ♦♠♥ t ♣♣r♦♣rt s s♥ ♣r♦ss♥ ♠t♦s rt ♥

r rsts ♥r ♥tr ♦♥t♦♥s ♥ ♥ ♥ ♦t♦♦r ♥r♦♥♠♥t ss t t♠ ♦ tr s♠ ♦♥

t ① trs♦s ♥ stt♥s ♣r♦ t♦ ♥t ♥ ♥ ♠♥♥ r♥ ♦ sr s ♥ ts st②

♦s ♦♥sst♥t② ♦♥ t s♠ ♣r♠trs ♥ ♦rr t♦ t♦ ♠ ♦♠♣rs♦♥s t t ♣r♦r♠♥s

♦ t s♥s♦rs ♦ ♠♣r♦ ② ②♥♠② st♥ t trs♦s s r st♣ ♣♥♥ ♦♥ t

♠♥♥

st♥♦♥ rs♦♥ ♦ ts s♥s♦rs ♣rt② ss t♥ ♥ t s ♦ s ♥ Ps

♦ ♠♦t♦♥ s♥s♦rs

s s♥s♦rs ♦ s ♥ ♥tr ♥r♦♥♠♥ts ♦♥ r ♦r trrstr r♦♦ts ♦r ♦st ♦♥ t♦

♥ ♥♥ s♣ ♦♥tr♦ ♣r♣♦ss ♣♥♥ ♦♥ t t②♣ ♦ r♦♦t ♦r s rqr t ss♥ ♥r

s♥stt② s t♦ st t♦ t s♣ tt ♥ s♣ r♥ ♥trr♣t♦r ♥ ♣t♥ ♥s

tr♠♥ t ♠♦st st st♥ t ♦ts s♦ tt ♥ ts t ♥r s♣ r♥ tt ♥

♠sr ♦♥ t ss ♦ t ♠♦t♦♥ s♥s♦rs r♥ ♥ ♦r s s♠r s ♠♦t♦♥ s♥s♦r ∆ϕ = ∆ρ = 4

t♦ t♦s tst r s ♥ sss② s ♦♥ t r r♦♦t ❱ r r♥s♥

s t♦ ② t tts ♦ ♣ t♦ ♠ ♥ s♣s ♦ ♣ t♦ ♠s

♣♥♥ ♦♥ t ♦ ♣♣t♦♥ ♦r s ♠♦t♦♥ s♥s♦rs r ♥t♥ rt r s t♦ t♥

♥ ♦♦s♥ ♣♣r♦♣rt tr♦♥ rts t t ♣① t s sts ♥ ts st② tt t♦♣t

♣①s ♦ ♥♦t ②s ② t ♠♦st rt ♠sr♠♥ts ♥ tr♠s ♦ t ♥r s♣ ♥ ♦♥s♦♥ ts st②

r♥s s ♦♥ st♣ rtr t♦rs ♠♣♠♥t♥ t♥② t r♦st s ♠♦t♦♥ s♥s♦rs tt ♦ ♣♣ ♥

♠♥② s s s t♦♠♦t r♦♦t ♥ ♦♥ s♥ ♣♥tr② ♥rs ♥ r②♥ ♠r♦r s

♥ ss t♥ r♠s

♥♦♠♥ts

❲ r ♠♦st rt t♦ ♦②r♦♥ ♦r t tr♦♥ s♥ ❨ ♣r♥ ♥ ♣r ♦r t ♠♥ s♥

♦ ♦r t ♣♥♦r♠ s ♦ t ♥♦♦r ♥ ♦t♦♦r ♥r♦♥♠♥ts ♥♦♥ ♣rt P♦rt

♥ r♥s♥ ♦r tr rt ♦♠♠♥ts ♥ sst♦♥s r♥ ts st② ♥ r ss ♥ ♦r ♦rrt

♥ t ♥s ♠♥sr♣t ❲ r rt t♦ t tr ♥♦♥②♠♦s rrs ♦r tr r♥t sst♦♥s

rt② ♠♣r♦ t ♠♥sr♣t s rsr s s♣♣♦rt ♣rt② ② ♥ ♥♦r♠t♦♥

♥ ♥♥r♥ ♥ ♥ ♥♦♦② ①rs ❯♥rst② t r♥ t♦♥ sr ♥②

❱ ♣r♦t ♥r ♦♥t♥t r♥t ♥♠r ♥ t r♦♣♥ ♦♠♠ss♦♥ t

❯❱ ♣r♦t ♣r♦t ❯❱ ♥♦s t ♥♥ s♣♣♦rt ♦ t tr ♥ ♠r♥

♥♦♦s ♣r♦r♠♠ t♥ t ♥t r♠♦r Pr♦r♠♠ ♦r sr ♦ t r♦♣♥ ♦♠♠ss♦♥

♥r ♣♥ r♥t ♥♠r

r♥s

é♣rt é♥♦♥ ♦♥ ♥s♣r r♥s♥ ♣tr ① ♦♣tq

sé sr ♥ rét♥ ♥téré t ♥ P ♥ ♦♦q ♥trs♣♥r ♥ ♥str♠♥tt♦♥ ♣♣

r♠s

rr♦♥ t ♠♥ Pr♦r♠♥ ♦ ♦♣t ♦ t♥qs ♥tr♥t♦♥ ♦r♥ ♦

♦♠♣tr ❱s♦♥

rr♦s ② ①♠♦ ❱ ♦♣t ♦ s♥s♦rs ♦r ♥t ♦♥tr♦ ♦ r♦ r ❱

♥ P rt t♥♦♦s ♦r t tr ♦ ♦♠♣t♥ ♥ ♦ ❯

♥s♦♥ rü ♥s ♥ r ♥♦r♠t♦♥ Pr♦ss♥ ②st♠s ♣tr rt♦♥ st

s♦♥ rt♥ tt ss ♥ ♥t♦♥ ♣♣ ♦rt③② ♥ t♦ ♦r♥ ♠♥

②r ❩r② ♦r♥♦ ❱s♦♥s ♦♥tr♦ ♦ ♥r♦st t t♦♥♦♠♦s r♦♦ts

♥s ♣♣r s ♠♥tr ♣♦r ♥t♦♥ à ♥ r♦♦t ♠♦ t♦♥♦♠ strs

tss ♥ r♦s♥ ❯♥ ♦ rs r♥

♥s s ♥ r♦♦t ♠♦ t♦♥♦♠ ♥s♣rt♦♥ ♦♦q ♥ Prt P tss

♥sttt t♦♥ P♦②t♥q r♥♦ P r♥♦

r♥♦rt ♦♠r P r♦ rtr③t♦♥ ♦ ♥r♦♠♦r♣ ♠♦t♦♥ tt♦♥ ♣

s ♦♥ ♥st s s②st♠ ♥ t ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♥t♥t ♥s♦rs ♥s♦r t♦rs ♥

♥♦r♠t♦♥ Pr♦ss♥ P ♦r♥ ❱ str

♥ t♦ rtrst♦♥ ♦ ♦♦st ♦♣t ♦ s♥s♦rs ♥ Pr♦♥ ♦ t

strs♥ ♦♥r♥ ♦♥ ♦♦ts ♥ t♦♠t♦♥ rs♥ str

♠♥ rs ♦t ②♥ ♥sts ♥ r♦♦ts ♣tr ♥st ♥s♣r ♦♦♠tr② ②

♦♣t ♦ r♦r t ♦♣t ♠♦s ♣s ♣♣ ♣r♥r r♥ s ♦r♥♦ ♥ ❩r②

♥ r♥s♥ ❱ ♥ ♥t♦♥

rü ♣t ♣♦t♦r♣t♦r t ②♥♠ r♥ ♥ ♥tr♥t♦♥

②♠♣♦s♠ ♦♥ rts ♥ ②st♠s ♦♥♦♥ ❯

í③ ♦s s r♥r ♣r♣♣♥ ♣r♦r♠♥ ♦♣t♦ ♦♠♣tt♦♥ r

ttr ♦♠♣tr ❱s♦♥ ♥ ♠ ❯♥rst♥♥

t♥♥♠♠♥s ♥t♥t r♦♦t s♦♥ s♥s♦rs ♥ ❱ t♦♥♦♠♦s ♦♦ts

r♥s♥ rs ♥ ♦ ♦♣t st② ♦ ♣♦t♦r♣t♦r ♠♥ts ♥ t ♦♠♣♦♥ ② ♦

r♦s♦♣ ♦♦ ②r♥ts

r♥s♥ P♦♥ ♥s r♦♠ ♥st s♦♥ t♦ r♦♦t s♦♥ P♦s♦♣ r♥st♦♥s

♦ t ♦② ♦t② ♦♦ ♥s

r♥s♥ st♦r ts ♦ ❱s♦♥ ♣tr rt♦♥② t ♦t♦♥

tt♦♥ ② ♥st r♦♥s ♣♣ ♣r♥r r♥ s t♥ r

r♥s♥ r rrs ♦♥s♣r ②♥ r♦♦t ss t ♦♥ ♥st ♣♦t♥ ts

rr♥t ♦♦②

r♥s♥ r rrs ❱♦t r s ♣tr ♣t ♦ s s

♥ r♦♠ ②♥ ♥sts t♦ ♠♥tr r s ♣♣ ❱♥♥ ♥ s ♠

rrtt ❱s♦♥s trr♥ ♦♦♥ ♦r ♥ ♥♠♥♥ r♦t♦rrt ♦r♥ ♦

♦♦ts

öt③ ♣t♦♠♦t♦rs ❯♥trs♥ s s♥ s②st♠s ♥r ♥♠t♥t♥ r rt

r♦s♦♣ ♦♦ ②r♥ts

r♥ ❲ P rr♦s ②♥ ♥st ♥s♣r s♦♥ ♦r t♦♥♦♠♦s r r♦♦t ♠♥rs ♥

♥rrt ♥r♦♥♠♥ts ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦♦ts t♦♠t♦♥ r♥s

❯

rts ♥rs rts rr ♥ r ①♠③♥ ♠♥tr r

s ♦♦ts ♥ t♦♠t♦♥ ③♥

rrs♦♥ ♦ r♦st ♥♦ ❱ ♠♦t♦♥ s♥s♦r s ♦♥ t s s②st♠ ♦ t ②

t♦♥♦♠♦s r♦♦ts

ss♥st♥ rt ❲ ②st♠t♦rts ♥②s r ❩t ♥♦♥ ♥

❱♦r③♥srt♥ r ♥s♣r③♣t♦♥ s üssrs ♦r♦♣♥s ❩tsrt ür tr

♦rs♥

rss ss♦tt♦ ♠ ♦♥② ♦r♥ t ♥ rt ♥♥ ♦♥tr♦ ♦ ❱

♥♠♥♥ r s♥ ♦♣t ♦ ♥ Pr♦♥s ♦ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♥t♥t

♦♦ts ♥ ②st♠s r♥

♥s ♠s ♦♦② ♥s♣r ♠♦r ❱ s②st♠ ♦r s ♠sr♠♥t ♦ s♠♦t♦♥

♥s♦rs

♠rt ②s♦♣ ♦♥s♣r s♦♠♦t♦r ♦♥r♥ r♥st♦♥s ♦♥ ♦♦ts

♦rt ♥t♦♥ ♦ ♥ t♦♥♦♠♦s ②♥ r♦♦t s♥ ♦♦② ♥s♣r ♣ s♦♥ ♥

Pr♦♥s ♦ t ♥ ♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ ♦♦ts ♦

s♦♥ ♥ ❲ rstr♥r rt♦♥ ♦r t s ♦ ♦♣t ♠ ♣s ♦r ♦♥♦♠

♥ rt tr♥ Pr♦ ♥tr♥t♦♥ ♦♥r♥ ♦♥ t♦♠t♦♥ ♥ ♥ ♥♥r♥

♦tts ❩ ❯

♥♦ ♦♥♠ ♥t♦♥ ♦③♥♦ ♥ ♣t s♦♥s t♦♣♦t ♦r ♠♥ ②♥

♠♥s ♥ ♥t♦♥ ♥ ♦♥tr♦ t♦♥♦♠♦s r♦♦ts

♥♦ ❨ ❩ ♦♥♠ ♥ ♥ ♥♦♥♥r ♦♥tr♦ s②st♠ ♦r t♦♥♦♠♦s t ♦

♠♥r♦t♦rrt ♥♠♥♥ r s ♦r♥ ♦ ♦♦ts

r ♣trs ♦♣tqs ♠♥♠sts t ré①s ♦♦♠♦trs ♦♠♠étqs ♣♣t♦♥s à r♦♦

tq ér♥♥ P tss ❯♥rst② ♦ ♦♥t♣r r♥

r ❱♦t r♥s♥ tr♥ ② ③♥ ♥ ♥t ♦♠♠t ♦♥tr♦ strt② ♦r

s② ♠r♦ r s r♥st♦♥s ♦♥ ♦♦ts

♦♥r♥ ♥ ♦♦r♥ ts ♦♥ ♦♣t ♦ ♦♦ ②r♥ts

r♠r r♣sr ♦ ♥ ♥♦ ❱ ♦t② s♥s♦r ♥ Pr♦♥s ♦ t

♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ rt ♥ ②st♠s tt ❲ ❯

♥ ❱s t② ♥ ♥sts ♥♥ ♦ ♥t♦♠♦♦②

♥♦t tr♦s ❱s s♥s♦r t rs♦t♦♥ ♥♥♠♥t ② ♠♥ rt♦♥s t♦♥♦♠♦s

♦♦ts

♥ rr♥③ ❱rs ♥♥ ♦ ♦♥s♣r s♦♥ ♣ rttr ♦r

♦s♦♥ tt♦♥ ♥ t♦♠♦t ♣♣t♦♥s ♥ Pr♦♥s ♦ P ♦♥♥r ♥ ♦♥s♣r s②st♠s

s♣♥

❯ss♦❱rtt ② s♦♠♦t♦r rs♣♦♥ss ♦ r♦♦t s♥ ❱ ♠♦t♦♥s♥st ♣s

♦♦ ②r♥ts

♥♦ ❱ ♥ r ②st♠s s♦♥❲s②

♦ ♦t♦♥ tt♦♥ rts ♦r t♠t♦tr ♦rt♠ ♥tr♥t♦♥ ②♠♣♦

s♠ ♦♥ rts ♥ ②st♠s ♦r♥s ❯

♦♥ ❱s♦♥ ♣s r ♠ ♦r

ttr r♥s♥ r♦♦t rrt tt ♦♦s trr♥ s♥ ♥r♦♠♦r♣ ② ♥ Pr♦♥s

♦ ♦♥r♥ ♦♥ ♥t♥t ♦♦ts ♥ ②st♠s s♥♥ t③r♥

♥♦ ❨ ♠① ♥♦t s♦♥ s♥s♦r ♦r tt♥ ♦ts ♣♣r♦♥ ♦♥ ♦s♦♥

♦rs ♦♦ts ♥ t♦♥♦♠♦s ②st♠s

rr rt♦♦③③ ♥r ♣♣②♥ ♥r♦♠♦r♣ s♦♥ s♥s♦rs t♦ ♣♥tr② ♥♥

tss ♥ ♦♠ rts ♥ ②st♠s ♦♥r♥ ♦ ♥ ♥

Ps rs♥ ♣♣♦r ♦②r♦♥ ♠ ❱♦t r♥s♥ ♠♥tr

♦♥s♣r ♦♣t ♦ s♥s♦r s ♦♥ ♦ t♠♣rtr ♦r r♠s t♥♦♦② ♥s♦rs ♥

tt♦r P②s

s ♦ts ♦♥ s♦♥ ♣♦t♦♦ tt♦rs ♥tr♥t♦♥ ♠trPr♦ss♦♥ P♦t♦tr P♦t♦♠

tr② ♦♠♠♥t♦♥s

r r♥s♥ ♣t ♦ rt♦♥ t ② t♦ rrt t♦♠t ♥ ♦♦ts ♥

t♦♥♦♠♦s ②st♠s

r r♥s♥ r r♦♦t ♣♦t ♥ st♣ r ② ♦♣t ♦ s♥s♦rs ♥ ♥tr♥t♦♥

♦♥r♥ ♦♥ ♥t♥t ♦♦ts ♥ ②st♠s r♥

r ❱♦t ♠ r♥s♥ ♦♥s♣r ♦♣t ♦ rts ♦r t s ♥

♦ ♠r♦r s Pr♦♥ ♦ ♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ rts ♥ ②st♠s ♥♦

♥

♥t♦s❱t♦r ♥♥ r♦tt♦ r r♥t str♦ ♥ t♦♥♦♠♦s ♥t♦♥

r♦♠ s t♦ r♦♦ts ♥tr♥t♦♥ ♦r♥ ♦ ♦♠♣tr ❱s♦♥

r♣sr r ❲ ♦ ❱s ♠♦t♦♥ ♦♠♣tt♦♥ ♥ ♥♦ ❱ s♥ ♣ss ♥s

♥ r ♥♦r♠t♦♥ Pr♦ss♥ ②st♠s P ♥r ❯

r♣sr r♠r ♥r ♦ ♥♦ s rttrs ♦r ♠♦t♦♥ ♣r♦ss♥ r♦♠

♥♠♥t ♠ts t♦ s②st♠ ♣♣t♦♥s Pr♦♥s ♦ t

r♥s♥ ♥ ♠♥tr♣♦t♦♥ t♥q ♦r t ♦♠♣tt♦♥ ♦ ♦♣t ♦ ♥ ♦♠♦t♦♥ ♦♦

②r♥ts

t♥ ♥r ♥ s♣tr s♥stt② ♦ ② ♣♦t♦r♣t♦rs ♥trt t ♥s ♥ r

♦♠r ♦♣ts ♦r♥ ♦ ♦♠♣rt P②s♦♦②

t♦r ♥♦ ♥trt ♦♣t ♦ s♥s♦r ♥♦ ♥trt rts ♥ ♥ Pr♦ss♥

❯♠♥ ♥②ss ♦ s ♠♦t♦♥ ② ♦♦ ♥ ♦♠♣tr s②st♠s ♦♠♣tr

❱♦t r♥s♥ ♦♦②♥s♣r s s♥♥♥ s♥s♦r ♦r st③t♦♥ ♥ tr♥

♥ Pr♦♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♥t♥t ♦♦ts ♥ ②st♠ ②♦♥ ♦r

❱♦t r♥s♥ ♣rrt s ♦♥tr♦ ♦ ♥ r ♠♥r♦♦t ♥ t♦♥♦♠♦s ♥r♦♦ts

♦r sr ♥ t♥♠♥t Pr♦r♥ r♠♥②

❱♦t r ② ♥♦♥ é♣rt r r♥s♥ rtrsts

♦ tr ♠♥tr ♦♥s♣r ♦♣t ♦ s♥s♦rs ♥ ♥tr ♥r♦♥♠♥ts ♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥

♥s♦r ♥♦♦s ♥ ♣♣t♦♥s ❱♥ t②

❳ P ♠rt sr P ♥♦ s ♠♣♠♥tt♦♥ ♦ ♥trt♦♥ ♠t♦ ♦r♥

♦ ♥t♥t ♦♦t ②st♠s ♥♥

❩r② ♦r♥♦ ②♥s♣r s str♥ ♦ trt ♥♦♦r rrt r♥st♦♥s

♦♥ ♦♦ts

❩♥ ♥t♦s❱t♦r ♥ ♥st ♥s♣r s s♥s♦r ♦r t t♦♥♦♠♦s ♥t♦♥ ♦ ♠♦

r♦♦t ♥ Pr♦♥ ♦ ♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ ♥t♥t ♦♦t ②st♠s ♦♠r P♦rt