Acoustic scattering mediated single detector optoacoustic tomography

A c ou st i c s catter i ng m edi ate d s i ng l e d ete c tor opto ac o ust i c to m og rap hy X. L UÍ S D E Á N - B EN , 1 , 2 ,3 ,* A L I Ö Z B E K , 1, 2, 3 H E R N Á N L Ó P EZ - S C H I E R 4 , A N D D A N I E L R A Z A N S K Y 1, 2 , 3 ,* 1 Faculty of Medicine an d Inst itute of Pha rm acology an d Tox icology, Uni vers ity of Zuric h, Switzerland 2 Institut e for Biome dical Engineeri ng an d De partment of Informat ion Tec hnology and E lec trical Engineer ing, ETH Zur ich, Swit zer land 3 Institut e of Biological and Me dical Imagi ng ( IBMI) , Tec hnical Universit y of Munich and He lm holtz Center M unic h, Germa ny 4 Researc h Unit Sensory Biology and O rgano genesis , Helmholt z Center Munich, Neuherbe rg, Germ any *Corres pond ing aut hor: xl.dea nben@p harm a.uzh .ch Abst ract Op toa c ou s tic im ag e for m a t ion i s c on ve n ti onal ly base d up on ul tras o und time - of -f l igh t r ea dings fr om mult iple de tec tion pos iti ons . Her ein , w e ex ploi t a cous tic sca tter ing to ph ys ical ly enc ode the pos iti on of opti ca l abs or bers in the ac qu i re d s ig nals , t hus re duce th e amo un t of da ta re quire d to re cons tr uc t an ima ge fro m a sin gle wa ve for m. Th is con cept i s exp er imen tally tes ted by i ncl ud in g a r an dom dis trib utio n of sca tter ers be twee n the sa mpl e an d an ul tras ou nd de tec tor arra y. Ul tra sou nd tra nsm iss ion thr ou gh a r and omiz e d s ca tt er i n g me diu m was cal ibra ted by ras ter s can nin g a li ght-a b s or bi n g mi cr opar ti cle acr os s a Car tes ian gri d. I ma ge rec ons tr uc tion fr om a s in gle time-r esol ve d s ig nal was the n ena ble d wi th a re gula rize d m odel- bas e d it era tiv e alg o r ith m re ly in g o n th e c ali b ra ti on s ign als. T he s igna l co mpre ss ion e ff ic ien cy is fac ili ta ted by t he r ela tiv el y sh or t a cq uis iti on time wind ow nee ded to c a pture th e en tire sca ttere d wave fiel d. The de mons tra ted f eas ib ili ty to for m a n ima ge us ing a s ingl e r ec o r de d op toac ous tic wav efor m pa ves a way to the de vel opme nt o f fas ter an d aff o r dabl e op toa cous tic ima ging s yste ms. O p to a c o u s t i c ( O A, p h o t o ac o u s ti c ) i m a gi n g h a s en a b l e d b r ea k in g t h r o u g h t h e l ig h t d i ff u s io n b a rr i er to m a p o p t i ca l c o n t r a s t ( ab s o r p t io n ) w i th h i g h r es ol u t i o n d e ep i n t o l i v in g o rg a n is m s [ 1 -3 ] . T h i s i s a c h i e v e d b y c a p i t al iz i n g o n t h e l o w s c at t e r in g o f u l t r as o u n d , as co m p ar e d to t h a t o f l i gh t , i n s o f t b io l o g ic a l t is s u e s . A m y r ia d o f O A s y s t e ms b a s ed o n s i n g l e d et e ct o r s c an n in g a s w e l l a s s i m ul ta n e o us ac q u is i t io n o f t o mo g r ap h i c in f o rm a t i o n u s i n g ar r a y d e t e c t o r s h a v e be e n s u g g es te d [ 4 ] . I n al l c as es , i m ag e f o r m at i o n is b a s ed o n t h e as s u mp t i o n t h a t u l t r as o u n d w a v e s u n d er g o n o d is t o r ti o n a n d p r o p a g at e w i th c o n s t an t v e l o c i ty a c ro s s t h e s am p l e an d c o u pl i n g me d i u m (t y p ic a l l y w at e r) . I n t er n a l r ef l e c t i o n s an d ac o us t i c s c at t er i n g ma y s e v e r el y d e t e r io ra t e t h e q u a l i ty o f t he r e n d e r ed i m ag e s , t h u s g e n e r al l y h av e t o b e av o i d e d [ 5 , 6 ]. A c o n s e q u en c e o f a co u s t ic r ef l e c t i o n s a n d s c a tt e r i n g i s t he a p p e a ra n c e o f l a te r e s p o n s es i n t he c o l l e c t e d t i m e- r es o l v e d s ig n a l s , l e a d i n g to ar c -t y p e a r t e fa c ts a n d o v er a l l d i s to rt i o n i n O A im a g e s [ 7 ] . S u c h l at e r es po n s e s ma y n e v e rt h e l e s s c o n t a in u s ef u l i n fo r m a ti o n . F o r e x am p l e, ac o u s ti c r ef l e c to rs h a v e be e n in c l u d e d in O A t o mo g r ap h i c i ma g in g s y s t e m s t o m ax i m i z e t h e ef f e ct i v e a n g u l ar co v e r a ge a n d a v o i d so - ca l l e d l im i te d - v i e w e f fe c ts [ 8 ,9 ] . T h e l at e p a rt s o f O A s i g n a l s c o rr e s p o n d in g t o r ef l e c te d w a v es c an i n f ac t b e c o ns id e r e d a s a d d i t io n a l s i g n al s c o l l e c t e d f ro m mi r r o r ed l o ca t io n s , t h us e f f ec t iv el y d o u b l in g th e a mo un t o f i n f o r ma t io n c o n t a in e d i n ea c h s i gn a l a cq u i s i ti o n . I n t h is w ay , ad d i t i o n al i n f o r ma t io n a s s o c ia t ed t o a co us t i c r ef l e c t i o n s ca n ef f e ct i v el y b e u s ed t o r e d u c e t he n u m be r o f s ig n a l s r eq u i r ed f o r i m ag e f o r ma t i o n. I d ea l l y , a s i n g l e r ec o r d e d w a v ef o r m w o u l d e n c o d e t h e l o c at i o n o f mu l t i pl e a b s o r b e r s, p r o v id e d th a t a s u ff i ci e n t n u m be r o f r ef l e ct e d w a v e s i s a c q u ir e d . I n th i s w o rk , w e s u g ge s t an al t e rn a t iv e a p p r o a ch t o e n c o d e t h e l o c a ti o n o f l i gh t - a bs o r b i n g s t ru c t u r es in O A s ig n a ls b as e d o n mu l t ip l e s c at t e r in g o f u l t r as ou n d w av es . F o r t h i s , r a n d o ml y d i s t r i bu t e d a co u s t i c s c at t e r er s i n f ro n t o f a t ra n s du c er a r r ay r es u l t i n a un i q ue c o mp l e x p r o p a g at i o n p at h fo r t h e ul t r a s o u n d w av e s ge n e r at e d a t ea c h s o u r ce l o c a ti o n w it h i n t h e e f fe c ti v e f i e l d o f v i ew . As a re s u l t, d i s t in c t o p t o a c o us t i c w av e fo r m s a re g en e r a te d b y ab s o r b er s l o c at e d a t d i f fe r e n t p o s it i o ns . T h e n u mb e r o f s ig n a ls r eq u i r ed f o r r e co n s t r u c ti n g a n O A im a g e c a n t h e n b e s ig n i fi c an t l y re d u ce d w it h o u t c o n s i d e r ab l y e x te n d in g t h e a c q u is it i o n t im e w i n d ow . A l a y - o u t o f t h e e x p e r im e n t al s y s te m us ed t o t es t t h e s u g g e s t e d c o n c ep t is d ep i c t ed i n F i g. 1 a . A f u ll -r i n g (3 6 0 ° ) ar r ay o f cy l i n d r ic a l l y - f o c u s e d t r a n s d u c er s w a s e m p l o y ed . T he OA s i gn al s w er e g e n e ra t ed b y d i r ec t l y i l l u mi n a t in g t h e r e gi o n o f i n t er e s t ( RO I ) b y a n a n o s ec o n d p u l s e d l as er at 720 n m w av e l en g t h . T h e O A s ig n a l s d e t e c te d b y t h e a rr a y e l e m e n ts w e r e d i gi t iz ed a t 4 0 me g as a m p l e s p e r s e co n d f o r a t im e w in d o w o f 4 9 4 s a mp l e s d e l ay e d b y 2 0  s w i t h r e s p e c t t o t h e l a s e r p u l s e . T h e c o l l e c te d s i g n al s w e r e b a n d - p as s f i l t e r ed b et w e en 0 . 5 - 8 M H z t o re m o v e l o w - f r eq u e n c y o ff s e ts an d hi g h - fr e qu e n cy n o i s e . A c l u s t er o f a c o us ti c s c at t e r er s w e r e r a n d o ml y d i s t ri b u t e d al o n g a c ir c u l a r r i n g co a x i a l l y -a l i gn e d w it h t h e a r ra y . S p ec i fi c al l y , ~ 3 0 0 b o ro s i l ic a t e c ap i l l ar y g l a s s t u b in g s w it h i n s i d e a n d o ut s i d e d i am e t e r s o f 0 .8 6 an d 1 . 5 0 m m r es p e ct i v el y ( W ar n e r I n s t ru m e n t s L LC , H a md e n , U SA ) w e r e d is tr i b u t e d a l o n g a n a n n u l us w it h 1 6 m m r ad i u s a n d 20 m m t h i c k n e s s . Th e c u s to m -m a d e a r ra y ( I ma s o n ic s S a S , Vo r a y , F r an c e ) h as a r a d i u s o f 4 0 m m an d c o n s i s ts o f 51 2 e l e m en t s w it h 5 M H z ce n t ra l f r e qu e n cy a n d > 8 0 % d e t e ct i o n ba n d w id t h . Th e d i m en s i o n s o f t h e e l em e n t s ar e 0 . 3 7 x 1 5 mm 2 . F i gu r e 1 : A c o u s ti c s c at t e r in g o f o p t o a co u s t ic w a v e s . ( a) L ay - o u t o f t h e ex p e ri m e n ta l s y s t e m . T A – t r an s d u c e r a r ra y , U S – u l tr a s o u n d s c at t e r er s , F B – f ib e r b u n d l e , L B – l as er be a m, O A – o p ti c al a b so r b e rs , U W – u l t r a s o u n d w av e s . ( b) C o l l e c t e d o p to a c o u s t i c s i gn a l s w i t h n o s c at t e r er s i n t h e p ro p a g at i n g p at h , r el at i v e l y l o w an d h i g h d en s i t y o f s c at t e r er s . ( c ) S c at t er e d w a v e d i re c t i v i ty f o r a n in d iv id u a l s ca t t e re r l o c a te d at a d is ta n c e o f 1 6 . 2 5 m m f r o m a p o i n t a bs o r be r . (d ) Ra t io o f t h e t o t a l d e te c t e d OA s i g n a l e n e r g y w i th a n d w i t h o u t s c at t er e r s in t h e p r o p a g at i n g p a th v e rs u s d is t an c e o f th e ab s o r bi n g m ic r o s p h er e f r o m t h e c e n t er o f t h e t ra n s d u ce r a r ra y . Th e s i g n a l e n er g y i s i n t eg r at e d o v e r a l l t ra n s d u ce r el e m e n t s an d t i m e i n s t a n ts . T he e f fe c t s o f ac o u s t i c s ca t t e ri n g i n t h e c ol l ec t ed O A s ig n a l s a r e i l l u s t r at e d i n F ig . 1 b . F o r a s in gl e 100  m d i am e t e r m i cr o s p h er e a bs o r b e r ( C o s p h er i c L LC , S a n t a B ar b ar a , US A ), t he s i g n a l d et e c t ed by o n e o f th e a r ra y e l e me n t s w i t h n o s c at t e r er s i n t h e p r o p ag a t i n g p at h i s p l o t t ed a t t h e to p . A s e xp e c t ed , t h e g e n e ra t ed s ig n a l is c o n f i n e d i n ti m e t o a s ho r t i n t er v a l co r re s p o n d i n g to  t 1 ~ 1 /B W c e n te r ed a t t = d / c , w h er e B W is th e d et e ct i o n b a n d w i d t h , d is t h e d is ta n c e b et w e en t h e s p h er e a n d t h e s e n s o r an d c i s t h e sp e e d o f s o un d . T h e o t h e r t w o p l o t s s h o w t h e d e te c t e d s ig n a l w h e n a co u s t ic s ca t t e re r s a re p r e s en t (F i g. 1 a ) . F o r t h e re l a ti v e l y l o w s ca t t e ri n g d en s i t y o f 3 s c a t t e re r s / cm 2 t h e s ig n a l e x te n d s i n t i m e o v e r  t 2 ~ 5  s , y e t t h e p ar t c o rr e s p o n d in g to d ir e ct p r o p a g at i o n r e m ai n s d o mi n a n t a n d c o n t ai n s m o s t o f t h e u s ea b l e i n f o r ma t io n f o r im a ge r ec o n s t r u c t i o n . N o t e al s o s o me e a rl y ar r iv i n g r es p o n s es a s c r ib e d t o a d i re c t a c o u s t i c p r o p ag a ti o n t h r o u gh g l as s h a v i n g s p e ed o f s o u n d s ig n i f ic a n t l y h i g h e r t h a n w a t er . T h e s ig n a l d e t ec t e d i n t he p r e s e n c e o f d e n s e l y d i s t r i bu t e d 12 s c at t e r er s / cm 2 e x hi b it s a c o m p l e x p at t e r n s p a nn i n g  t 3 ~ 10  s a n d h a s n o d o m i n a n t p e a ks . I n t h is c as e, t h e l o c at i o n o f t h e p o i nt a bs o r b er i s e n c o d e d a l o n g t h e e n t ir e r ec o r d e d i n t e rv a l , t h u s a n y g iv en d i s t r i b u t i o n o f o p t i c al a bs o r b e r s ca n i n p r i n c ip l e b e c o mp r e s s e d in to a s i n gl e w av ef o r m . W e n e x t m e as u r ed t h e d i r ec t iv i t y p a t t e rn f o r a n in d i v i d u a l s c at t e r er b y p l a c in g a n ab s o r bi n g m ic r o s p h e r e at t h e c e n t er o f t h e t ra n s d u c er a rr a y an d a g l a ss t u b i n g a t a d i s t a n c e o f 1 6 . 2 5 m m f r o m i t . T h e r e l at i v e a mp l i t u d e o f t h e s c a t t er e d w a v e f o r d if f e r en t a n g l es w as e s t im a t e d b y m ea s u ri n g t h e d i ff er e n c e b et w e en th e O A s i gn a l s co l l ec t e d b y a l l t h e a rr a y e l em en ts w it h a n d w i th o u t t h e t u bi n g i n t h e p ro p ag a t i n g p at h . I t i s s ho w n t ha t t h e s c at t e r ed w av e s h av e a d o m i n a n t f o r w ar d p r o p a g at i on c o m p o n en t . T h is is e x p e c t e d c o n s i d e r in g t h a t t h e e ff e c ti v e d i m en s i o n o f e ac h s ca t t e re r c o r r e s p o n d s t o ~5  a (  a b ei n g t h e a co u s t ic w a v e l e n g t h a t t h e ce n t ra l f r eq u e n c y o f t h e d et e c t io n ar r ay ) , w h i c h fa l l s i n t o t h e M ie s ca t t e ri n g r e g im e . F o r w a r d p r o p a g at i o n i s es s e n t i al t o m in i m i z e t h e l o s s o f e n e r g y d u e t o t r an s m i s s io n t h ro u g h t h e s c a tt e r i n g m ed i u m. F i g . 1 d s h ow s t he r a t io o f t h e t o t al d et e c t ed O A s i g n al e n e r gy f o r a l l a r ra y el em e n t s w it h (E ) a n d w it h o u t (E 0 ) s ca t t e re r s p r e s en t in t h e p r o p a g at i n g p at h . F o r o u r d et e c t io n c on f ig u r at i o n ap p r o x i ma t el y 10% o f t h e O A s ig n a l e n er g y i s p r es er v e d a f t e r a d d in g s ca t t e r in g. T h is v a l u e i s i n cr e as e d f o r OA s o u r c es l o c a te d a w a y fr o m t h e a rr a y ’ s c e n t er , s u g g es ti n g t h at c y l i n d ri c al f o c u s i n g o f t h e d et e ct i o n el e m e n t s c o n t r i b u te s t o t h e e n er g y co l l ec t i o n ef f i ci e n c y . I m ag e r e co n s t ru c t io n i n t h e p r es en c e o f ac o u s ti c s c at t e r in g im p l ie s e s ta b l is h i n g a m o d el l in k i n g th e i n i t ia l O A p r e s s ur e (p r o p o r ti o n al t o t h e o p ti c al a b s o r p ti o n ) t o t h e c ol l e ct e d p r e ss u r e w a v e f o r ms . S i mi l a r l y t o t h e t i me - d o ma i n m o d el -b a s ed O A r e co n s t ru c t io n ap p r o ac h es [ 1 0 ,1 1 ] , o n e ma y as s u m e t h at t h e ab s o r be d en e r g y i s c o n fi n e d w it h i n t h e r e g io n o f i n t er e s t (R O I ) a n d t h at th e a c qu i r e d O A s ig n a ls  󰇛   󰇜 c o rr e s p o n d to a l i n e ar s up e r p o s i t io n o f t h e s i g n al s   󰇛  󰇜 f o r ea c h p i x e l b el o n gi n g to t h e i m ag e gr i d c o v e r in g s u c h R O I , i . e. ,  󰇛   󰇜       󰇛  󰇜  , ( 1 ) w h er e   i s t h e a b s o rb e d o p ti c al e n e r gy f o r th e i -t h p i x el . F o r u l t r as o u n d w a v e s p r o p a g at i n g t h r o u g h a un i fo r m n o n - s c at t er i n g m ed i u m,   󰇛  󰇜 c an b e e s t im a t ed f r o m t h e O A fo rw ar d m o d e l , e . g . b y i n t er p o l a t in g l i gh t ab s o r p t io n v al u es b et w e en t h e p ix e l p o s i ti o ns [ 1 1 ] . W h en ac o u s t i c s c a t t e r in g t ak e s pl a c e, p h ys i c al m o d el l in g o f   󰇛  󰇜 i mp l i es a c cu r a t e k n o w l ed g e o f t he po s i t io n , s h a p e a n d ac o us t i c p r o p e r ti e s o f t h e s c at t e r er s , w h ic h m ay t ur n t o o co m p l ic a t e d . I ns t e ad ,   󰇛  󰇜 ca n b e e x p e r im en t a l l y me a s u r e d b y m o v i n g a n O A s o u r c e a cr o s s a g r id o f p o in t s a n d c ol l e ct i n g t h e c o r re s po n d i n g r es p o n s e s . F o r t h i s p u r p os e , a 1 0 0  m p ol y e t h y l e n e m ic r o s p h er e w as s c a n n e d w it h 75  m s te p s i n t he h o r iz o n ta l an d v er t ic a l d ir e c t io n s o v er a R O I o f 4 . 5 x 4 .5 mm 2 . F o r t h e e x p e r im e n t a l l y m ea s u re d s i g n a l s , E q . (1 ) r ep r e s e n t s a l i n e ar m o d e l t h a t ca n b e e xp re s s e d in a m at r ix fo r m v i a      , ( 2 ) w h er e p i s a c ol u m n v ec t o r co n t ai n i n g t h e s i g n a l ( s ) f o r a s e t o f p o s it i o n s a n d in s t an t s a n d H i s a v e c t o r c o n t a in i n g t h e a bs o r b e d e n e rg y i n ea c h p i x e l o f t h e s c an n i n g g r id . T h e c o l u mn s o f m a tr i x M p r ep r e s e n t t h e s i g n al ( s ) fo r ea c h p o s i t io n o f t h e s ca n n ed p a r t i c l e. M o re g en e r al l y , t h e mo d e l i n Eq . (2 ) ca n b e ex p a n d e d in to      , ( 3 ) w h er e s r e p r es e n t s a n y l i n ea r c o mb i n a t i o n o f s i g n a l s i n c l ud e d i n m at r ix M s . T he p er f o rm a n c e o f t h e m o d el i n E q . ( 3 ) f o r i m ag e r ec o n s t r u c t i o n fr o m a re d u ce d n um b e r o f s i g n al s w as f ir s t t e s te d b y c o n s i d e r in g a s p a r s e d i s t ri b u t i o n o f a b s o r b e rs . F o r t h is , t h e m ic r o s p h er e w a s s ca n n ed a t r a n d o m g ri d po i n t s w it h i n t he R OI n o t i n c l u d e d in th e ca l i b r a ti o n gr i d an d t h e s i g n al s w e re ad d e d u p . A d d i t io n a l l y , t h e O A s i g n a l s f r o m a l l t r an s d u ce r e l em e n t s w e re s u p er i mp o s e d t o fo r m a u n i q u e t i m e- r e s o l v ed s i g n a l ex p r es s e d in a v e c t o r f o r m a s s m . I m a ge r ec o n s t r u c t i o n w a s ba s e d up o n nu m er i ca l i n v e r s io n o f E q . ( 3 ), i .e . ,      󰇝                   󰇞 , ( 4 ) w h er e t h e p ar a me t er  a l l o w s w ei g h t in g t h e r eg u l ar i z at i o n t e r m      , w i t h L b ei n g a n a rb i t r ar y m a tr i x . Th e re c o n s t ru c t io n r es ul t s f o r a n in d i v i d u al m i c ro s p h er e , t ak i n g L a s t h e i d en t i t y m a t r i x , in d i c at e t h a t i t w a s p os s i b l e t o a c cu r a t e l y r ec o n s t r u c t an i m ag e o f a p o i n t a b s o rb e r w i th a n O A w av e fo r m d et e c t ed at a s in gl e p o s i t io n (F i g . 2 a ) . Th e fu l l - w i d t h a t h al f ma x i mu m (F W H M ) o f t h e r e c o n s t ru c t ed s p h e r e w h e n u s in g t h e L 2 n o rm i s ~ 1 5 0  m , a s in d i ca t ed in t h e p ro f i l e i n F i g. 2 b , w h ic h m at c h e s t h e e x p e c te d i n - p l a n e s p a ti a l r e s ol ut i o n o f t h e a rr a y f o r t h e s c a tt e r i n g -f r ee c a s e [ 1 2 ] . Th e p ro f i l e i n F i g. 2b f o r t he L 1 n o rm r eg u l a r iz a t io n h a s a s i g n i f ic a n t l y lo w e r F W H M . Th i s i s a t t r ib u t ed to t h e s p a r s it y c o n d it i o n an d m us t n o t n ec e s s ar i l y b e as c r ib e d t o th e a ch i ev ab l e r es o l u t io n , al t h o u g h L 1 -b a s ed re g u l a r iz at i o n h as be e n s h o w n to en h a n c e t h e s p a t ia l r es o l u t io n b e y o n d t h e ac o us ti c d i f fr a c t i o n b ar r ie r [ 1 3 ] . Ac c u ra t e r ec o n s t ru c t io n s ar e s i mi l a r l y r en d e r e d w h e n m u l t ip l e m i c r o s p h e re s a r e p re s e n t i n t h e R O I ( F i g s . 2 c a n d 2 d ), y et r e s u l t i n g i n h i g h er n o i s e l e v e l s d ue t o r ed u c ed s p ar s i t y i n t h e i ma g e s w h ic h h a mp e r s i m a ge r e co n s t ru c t io n fr o m a s i n g l e w a v e fo r m . F i gu r e 2 : E x p e r im e n t al v al i d at i o n o f t h e s c a tt e r i n g m e d i at e d s i n gl e d e t ec t o r o p t o ac o u s t i c to mo g r ap h y . ( a ) Op to a c o u st i c i m ag e s o f a m ic r o s p h er e r e co n s t ru c t ed w it h a s in g l e d e te c t e d w av e f o r m . ( b) O n e- d i m en s i o n a l p r o fi l e s a l o n g t h e r ec o n s t r u c te d im a g e s s h o w n in (a ) . I m ag e s r e co n s t r u c t e d f o r 2 an d 3 m ic r o s p h er e s a re s h o w n in (c ) an d ( d ) , r e s p e c ti v e l y . T h e y el l ow ar r o w s i n d ic a t e t h e po s i t i o n o f t h e s p h er e s . R ed an d bl u e s qu a r e s c o r r es p o n d to in v er s i o n s d on e w it h e it h e r L 2 o r L 1 n o r m (l = 2 o r l = 1 i n E q . ( 4 )) . Sc a l eb a rs – 1 m m. T he i ma g in g p e r fo r ma n c e o f th e s u g g e s te d a p p r o a c h w a s fu r t h er t es te d b y im a g in g a w i l d- t y p e z eb r af i s h l a r v a 5 d p f p o st m or t e m . I m a ge r ec o n s t r u c t i o n w a s p e r fo r m ed c o n s id e r i n g a to t al v a ri a ti o n r eg u l a r iz a t io n t er m , i . e. , E q. ( 4 ) w a s m o d i f ie d t o       󰇝               󰇛󰇜 󰇞 . ( 5 ) R ec o n s t r u c t i o n ma d e f r o m a s i g n al c o r r e s p o n d i n g to t he s u m o f al l 5 1 2 s i gn al s o f t h e a r ra y re n d er s t h e fi s h i n t h e c o r re c t p o s i t io n , a l t h o u g h it s s ha p e i s d is t o r te d ( F ig . 3 a ) . Cl ea r l y , th e im a g e q u al it y i mp r o v es w h e n r ec o n s t r u c ti n g w it h 1 6 s i g n a l s co r re s p o n d i n g t o t h e s u m o f a l t er n a ti n g ch a n n e ls o f t h e a r r a y (F i g . 3b ) . A s a r ef e r en c e , F i g. 3 c s h o ws t h e im a g e r e co n s t r u c t ed w it h al l t h e 5 12 a r r a y el em e n t s w i th n o s ca t t e re r s i n t h e ul t r as o u n d p r o p a g at i n g p at h a n d F i g. 3 a s h ow s a b r i g h t f ie l d m i c r o s c o p ic i m a ge o f t h e l ar v a , w h er e r e l a t i v e l y l a rg e l i g h t a bs o r b i n g s t ru c t u r es a re l ab e l l e d . F o r t h e re c o n s t r u c t io n o f t he im a g e i n F i g . 3c , a c o n v en t i o n a l m o d el - m at r ix M s w a s b ui l t a s d e s cr i be d e l s e w h e r e [ 1 4] . E v e n t ho u g h t he r e fe r en c e im a g e e x h i b it s t h e b e s t r ec o n s t r u c t i o n q u al it y , m os t s tr u c tu r e s c a n b e cl e ar l y i d en t i f ie d i n i ma g e s re c o n s t ru c t ed w i t h a s ig n i fi c an t l y l o w er n u mb e r o f s ig n a l s . F i gu r e 3 : I m ag i n g o f 5 d a y s - po s t - f e rt i l iz a t io n z eb r af i s h l ar v a p o st m o r t e m . (a ) O p t o a c o us t i c i ma g e o f t h e l ar v a o b t ai n e d w it h a s in gl e i n t eg r a t ed w a v e fo r m . ( b ) Op t o a c o u s t i c im a g e o f t h e l a r v a o b t ai n e d f ro m 1 6 i n d i v i d u al s ig n a l s . ( c ) O p to ac o u s ti c i m a ge o f t h e l a r v a o b t ai n e d w i th al l 5 1 2 s i g n a l s fr o m th e t r a ns d u c e r a rr a y w i t h no ac o us t i c s c at t e r in g i n t h e ul t r a s o u n d p r op a ga t in g p at h . (d ) B ri g h t f i el d m ic r o s c o p y i m ag e o f th e l a rv a . E – e y e s , Y S S – y o l k s ac s t ri p e , V S – v e n t ra l s t ri p , D S – d o rs a l s t r i p e , C V – ca u d al v ei n . S c a l e ba r s – 1 mm . M i n i m iz a t i o n o f t h e a m o u n t o f d a t a re q u i r ed f o r O A i m a g e f o r ma t io n ma y co n t r i bu t e t o re d u c in g co s t s o r , a l te r n at i v e l y , s p e e d i n g u p a c q u i s i t io n s . H er e in , w e ha v e d em o n s t r at e d t h e b a s ic fe a s ib il it y t o “ p h y s i c al l y ” e n c od e t h e o p t ic a l a b s o r p t io n d i s t r ib u t i o n i n a d e fi n e d R O I b y c ap i t al i z in g o n t h e c o mp l e x p r o p ag a t i o n o f u l t ra s o u n d w a v e s i n a s c at t e r in g me d i u m . W h il e s e v e ra l t i m e- of - fl i g ht r ea d in g s ar e n o rm a l l y r eq u i r ed t o t r i l a te r at e p o s it i o n o f a g i v e n O A s o u r c e, t h is i n f o r ma t io n c an al t e r n at i v e l y b e c a rr i ed v i a m u l t i p l e a c o u s t i c s ca t t e ri n g e v e n t s . T hu s , t h e s u g ge s t ed ap p r o ac h r e p r es en t s a s o rt o f c o mp r e s s e d d at a a cq u i s i ti o n m et h o d o l o g y . I n a c o n v e n t io n a l O A i m ag i n g s c en ar i o , t em p o r a l r e s o l u ti o n i s u l t im a te l y l i mi t ed b y t h e t i me i t t a k es f o r a l l t h e g en e r at ed s ig n a l s t o l e a v e t h e R O I . W h i l e t h i s u l ti m at e l i mi t i s u n at t a i n a bl e w it h t h e s u gg e s te d a p p r o ac h d u e t o t h e e x t e n d e d a cq u i s i ti o n w in d o w c au s e d by mu l t i p l e s c at t e r in g e v e n t s , s u c h w i n d o w i s m u c h s h o r t er t h a n t h a t r eq u i r ed f o r a l t er n a ti v e a p p r o a ch e s u s in g ac o u s ti c re f l e ct o r s [ 8 ] . A p o t en t i a l d r a w ba c k o f t h e s ug g e s t ed me t h o d o l o g y i s t h e l i mi t ed d a t a s p a r s it y , w h ic h is e s s en t i a l f o r h i gh q u a l i ty O A i ma g e r ec o n s t r u c t i o n . W e h a v e s h o w n t h at a s i n gl e a bs o r b e r c a n be v er y a cc u r a t e l y r ec o n s t r u c te d w i t h a s in g l e w a v e f o r m , w h i c h tu r n s m o r e c h a l l e n g in g f o r mu l t ip l e so ur c e s . Y et , in d i v i d u al f l ow in g a b so r b e rs ha v e b ee n p r e v i o u s l y u s ed in l o ca l iz a t i o n O A t o m o g ra p h y ( L OT ) to br e ak t h r o u g h t h e a co us t ic d i f fr a ct i o n b ar r ie r [ 1 5 ,1 6 ] . Th e r e fo r e , c o mp r e s s e d a cq u i s i ti o n o f s i g n al s m a y f i n d a p p l i c ab i l it y f o r s u p e r -r e s o l u t i o n i ma g in g o f v a s c u l a r s t ru c t u r es . F u r t h e rm o r e, an a l te r n at i v e m e th o d b as ed o n a pl a s ti c a co u s ti c m as k p l a ce d in fr o n t o f an ul t r a s o u n d s e n s o r h a s b e en r ec e n tl y s u g g es te d f o r c o m p r es s e d ac q u i s it i o n o f s i gn a l s an d r ec o n s tr u c t i o n o f s p a r s e im a g es i n p u l s e- e ch o u l tr a s o u n d [ 1 7 ] . A d i s t r i bu t i o n o f a c o u s t ic s ca t t e re r s s i mi l a r t o t h e o n e e m p l o y e d h e r e c an t h u s s e r v e t h e s a m e p u rp o s e w h i l e a l s o f a c il it a ti n g h y br i d iz a t i o n o f u l tr a s o n o g ra p h y w it h O A i m ag i n g . O v e r al l , t h e d e m o n s t ra t ed f e a s ib i l i t y t o f o r m a n i m a ge w i t h a s i n gl e O A w a v e f o r m p a v e s a w ay to th e d e v e lo p m e n t o f f as t e r an d af f o r d a bl e OA i m ag i n g s y s t e ms . A c kn o wl e d g m e n t s T hi s s t u d y w as p ar t ia l l y s u p po r t e d by t h e E u r o p ea n R e s e a rc h C o u n c il C on s o l id a t o r g r a n t ER C - 2015 -C o G - 682379. R e f e r en c e s [ 1 ] B e ar d , P a u l . " B io m e d i c al p h o t o a co u s t ic im a gi n g ." I n t e rf a c e f o c u s 1 . 4 (2 0 1 1 ): 6 0 2 - 6 31 . [ 2 ] T a r u t t i s , Ad r i a n , an d V a s i l i s N tz i ac h r i s to s . " A d v a n c e s i n re a l - t im e m u l t is p e c t ra l o p t o a co u s t ic im a g in g a n d i t s a p pl i ca t io n s . " Na t u r e P h o t o n i c s 9 . 4 ( 2 0 1 5 ) : 21 9 . [ 3 ] D e á n - B e n , X . L . , e t al . " A d v a n c ed o p t o a co u s ti c m et h o d s fo r m u l t is c a l e i ma g in g o f i n v i v o d y n a m ic s . " C h e mi c al S o ci e ty R ev i e w s 4 6 . 8 ( 2 0 1 7 ) : 2 1 5 8 - 2198. [ 4 ] W an g , L i h o n g V . , an d J u n j i e Y ao . " A p r ac t ic a l gu i d e t o p h o t o ac o u s t i c t o m o g ra p h y i n th e l i fe s c i en c e s . " N a tu r e m et h o d s 1 3 .8 ( 2 0 1 6 ) : 6 2 7 . [ 5 ] D ea n - B e n , X . L u i s , e t a l . " S t at i s t i ca l a p p r o a ch fo r o p t o a co u s ti c i ma g e r ec o n s t ru c t io n i n t h e p r e s e n c e o f s t ro n g ac o u s t i c h e t er o g en e i t ie s . " I EE E T r an s a ct i o n s o n M ed i c a l I ma g in g 3 0 . 2 ( 2 0 1 1 ) : 401 - 408. [ 6 ] P o u d el , J o e m in i , e t a l . " M i ti g at i o n o f ar t i f a ct s d u e t o i s ol at e d a co u s t ic h e t er o g en e i t ie s i n p ho t o ac o u s t i c c o m p u t e d t o mo g r a p h y us in g a v ar i ab l e d at a t r u n ca t io n - ba s e d r e co n s t r uc t i o n m e t h o d . " J o u r n a l o f b io m e d i c a l o p t ic s 2 2 .4 ( 2 0 17 ) : 0 4 1 0 18 . [ 7 ] D e á n - B e n , X o s é L u is , V a s i l i s N tz i a ch r i s t o s , a n d D a n ie l R az a n s k y . " A r t e f a ct r e d u ct i o n i n o p t o a c o us t ic t o mo g r ap h i c im a g in g by e s t i ma t in g t h e d i s t r ib u t io n o f a c o us t ic s c at t e r er s . " J o u r n al o f b i o m e d i ca l o p t i cs 1 7 . 1 1 ( 2 0 1 2 ): 1 1 0 5 0 4 . [ 8 ] C o x , B e n j a mi n T. , S i mo n R . A r r i d g e, a n d Pa u l C . B e a r d . " P h o to a c o u s t i c t o m o g r a p h y w it h a l im i t e d -a p e r tu r e p l an a r s e n s o r a n d a re v e r be r a n t c av i t y . " I n v e rs e P r o b l em s 2 3 . 6 ( 2 0 0 7 ) : S 95 . [ 9 ] H u an g , B in , e t a l . "I m p r o v i n g l i mi t ed - v i ew p ho to a c o u s t i c t o mo g r ap h y w i t h an a c o u s ti c r ef l e c t o r ." J o u rn a l o f bi o m e d i ca l o p t i cs 1 8 . 1 1 ( 2 0 1 3 ): 1 1 0 5 0 5 . [ 10 ] Pa l t au f , Gu e n t h er , e t a l . " I t er a t i v e r e co n s t r uc t i o n a l go ri t h m f o r o p t o a c o us t i c i ma g in g . " T h e J o u rn a l o f th e A c o u s t i c al S o c ie t y o f A me r i c a 1 1 2 . 4 ( 2 0 0 2 ) : 1 5 3 6 -1 5 44 . [ 11 ] Ro s e n t h al , Am i r, D a n i e l R a z a n s k y , an d V a s il i s N t z ia c hr i s t o s . " F as t s e m i- a n a l y t ic a l m o d e l -b a s ed ac o u s ti c in v e rs io n fo r qu a n t i ta t iv e o p t o a c o us t i c to m o gr a p hy ." I E E E t ra n s a c t i o n s o n m e d i c al i m ag i n g 29 . 6 ( 2 0 1 0 ) : 1 2 7 5 - 1285. [ 12 ] M e r č e p , E l en a , e t a l . " Tr a n s m is s i o n– r e fl e c t io n o p t o a co u s ti c u l t r as o u n d ( T RO P US ) c o mp ut e d t o m o g r a p h y o f s ma l l an i m a l s . " L i g h t : S c i en c e & A p p l ic a t i o n s 8 .1 ( 2 0 1 9 ) : 1 8 . [ 1 3 ] E g o l f, D a v i d M . , R y a n K W C h e e, a n d Ro g e r J. Z e mp . " S pa r s i ty - b as ed r ec o n s t r u c ti o n fo r s up e r- r e s o l v ed l im i t ed - v ie w p ho t o a c o us t ic c o mp u t ed t o mo g r ap h y d ee p in a s c at t e r in g m e d i um . " O p t i cs l e t t e rs 4 3 . 1 0 ( 2 0 1 8 ): 2 2 21 - 2224. [ 1 4 ] D e a n - B e n , X . L u ís , V as i l i s N tz i a ch r i s t o s , a n d D a n i el Ra z a n s k y . " A c ce l e ra t io n o f o p t o a c o us ti c mo d e l - ba s e d r ec o n s t r u c t i o n u s in g a n g u l a r im a g e d i s c r e ti z a t i o n . " I E E E T ra n s a c ti o n s o n me d i c al i ma g in g 3 1 . 5 ( 2 0 1 2 ) : 1 1 5 4 - 1162. [ 1 5 ] Vi l o v , Se r g e y , B a s t ie n A r n a l , a n d E mm a n u el B os s y . " O v e r c o m i n g t h e a c o u s ti c d if fr a ct i o n l i m it i n p h o t o a co u s t ic i m a gi n g b y t h e l o c a l iz a t io n o f f lo w i n g a b s o rb e rs ." O p t i c s l e t t er s 4 2 . 2 1 ( 2 0 1 7 ): 4379 - 4382. [ 1 6 ] D ea n -B en , X. L u í s , a n d D an i e l Ra z a n s k y . " L o ca l i z a ti o n o p t o a c o us t i c t o mo g r ap h y . " L i g h t : S ci e n c e & A p p l ic a ti o n s 7 . 4 ( 2 0 1 8 ): 18004. [ 1 7 ] Kr u i z i n g a, Pi e t e r , e t al . " Co m p re s s iv e 3D u l t r a s o un d im a gi n g u s in g a s in gl e s e n s o r . " S ci e n c e ad v a n c es 3 . 1 2 (2 0 1 7 ): e 1 7 0 1 4 2 3 .