N 1. Time points are determined by the

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1 upplemena Mehods Geneaon of scan sgnals In hs secon we descbe n deal how scan sgnals fo 3D scannng wee geneaed. can geneaon was done n hee seps: Fs, he dve sgnal fo he peo-focusng elemen was geneaed o poduce he nended -vbaon of he mcoscope objecve. econd, a ajeco was defned ehe based on an analcal funcon o b poducng a smooh lne passng hough peseleced posons n 3D space (use-defned mode. In he las sep, a new se of fnal scan pons along he pedefned ajeco was defned assung equdsan 3D spacng. Geneaon of -scan sgnal. A snusodal funcon was used fo connuous acceleaon of he mcoscope objecve along he opcal as. The nended vbaon of he objecve was defned as O ( = A sn π F ( wh amplude A, fequenc F and =,..., N. Tme pons ae deemned b he chosen pel dwell me Δ = and he oal numbe of pels pe ccle N s gven b N = /( F. Because of he nea of he peo-focusng elemen plus Δ objecve load he acual -poson of he objecve n geneal does no accuael mach he mposed dve sgnals. Fo a snusodal moon, a fequenc-dependen amplude educon and phase shf esul, whch need o be coeced (upplemena Fg.. We heefoe mposed he followng coeced dve sgnal o he peo-elemen O ( = A sn(π F ϕ (, co co co wh phase shf ϕ co and coeced amplude A co = A /θ, whee θ s he amplude educon faco. Noe ha fo an vbaon fequenc θ and ϕ co mus be newl deemned. We deemned θ and ϕ co fom a smulaneous measuemen of he dve sgnal and he acual poson sgnal. A H, amplude educon was onl aound 5% fo he 4. Coecon was elable up o H. A hghe fequences he amplude educon could no be full coeced fo because of he lmed ange of he conol eleconcs (upplemena Fg. b.

2 Analcal scan paens. A smple mehod o defne a 3D scan paen s o use an analcal mahemacal funcon. We used hs appoach o geneae spal, squaespal o Lssajous scan paens. These paens wee fs compued n a wodmensonal plane o pe-defne he ajeco. The -movemen of he objecve was consdeed lae when calculang he fnal scan pons (see below. Fo spal o squae-spal mode he -componens and of pons,, (whee s a wocomponen veco wee calculaed n one-degee seps as, s π = s sn 8 and, s π = s cos 8 wh =,...,( s and <. pal dens and ccula wee adjused b vang s and. s s he oal numbe of degees fo he spal oaon, hus he basc paen conans s/36 spals. Tpcal values of s wee o 4. Fo =, a ccula spal paen esuls. Loweng leads o a successvel moe squae-spal paen, whch mgh be useful fo lng lage volumes n a space-fllng manne. Tpcal values of wee. o. Fo a Lssajous-pe basc paen he -componens and wee calculaed as π f π f, = sn and, = sn (4 K K wh =,..., ( K. f and f denoe he fequences n and ( f > f and,, (3 f f =. Fo one Lssajous-paen ccle he numbe of peods n - and - decon hus ae gven b K / and K / f, especvel. Tpcal values wee 4 - f fo fequences and - fo K. The basc scan paens wee hen concaenaed o oban a cean numbe of paen eaons pe peod of he objecve's -movemen (pcall o 4 paen eaons. In spal mode, successve spals wee moed o each ohe dung one half ccle of he objecve s oscllaon (n spal-n spal-ou manne so ha a smooh anson fom one spal o he ne was ensued. To mpove volume coveage a 8 -phase jump was appled a he lowe and uppe lms of he - movemen so ha he laeal mama of -scannng fo downwad and upwad movemen of he objecve wee neleaved.

3 3 Use-defned scan paen. Alenavel, we mplemened a use-defned mode, n whch mulple pons (e.g. cell somaa wee pe-seleced fom a pevousl acqued efeence mage sack. Fom hese pe-seleced pons a connuous smooh 3D ajeco was obaned b nseon of addonal pons as descbed n he followng. Fs, all pe-seleced pons I whn each wo-dmensonal mage plane fom he efeence sack wee soed clockwse (upplemena Fg. a. Then, he mamum dsance beween pons n -decon was deemned and pons above half of hs dsance n -decon wee soed fom lef o gh accodng o he - componen, pons n he lowe half fom gh o lef. In ode o educe he lengh of he fnal scan lne, pons wee fuhe eaanged. Fo each pon (sang wh pon he shoes pah o he hd-ne pon was deemned fo he wo possble odes of he nemedae pons, whch wee e-odeed f necessa. Afe defnon of he pon ode, a smooh scan lne was geneaed b eavel nseng new pons and (upplemena Fg. b and c. In he fs ound, wo addonal pons pons I, I and I wh = I, j accodng o e e,, α ; e e α ΔI κ = I I / κ and = / and, j, wee geneaed fo hee consecuve = I e e, α (5 e e α ΔI κ = I I / κ whee κ s a faco = / deemnng he numbe of pons o be nseed beween neghboung I (pcall we used κ =. e = ΔI / ΔI and e = ΔI / ΔI ae he un vecos beween he consdeed pons. In he ne ound (j =,,κ fuhe pons and wee nseed bu now consdeng he angles (, j, j,, j and (, j,, j,, j, especvel (upplemena Fg. c. Usng hs algohm a smooh ajeco whou shap edges was obaned ha ncluded all pe-seleced pons.,, j, j Equdsan 3D pel dsbuon. Afe pe-defnon of he scan ajeco n wo dmensons he -vbaon of he objecve had o be consdeed. can geneaon and fluoescence acquson wee done wh a fed, pe-defned pel dwell me Δ (pcall Δ = μs. To elae fluoescence nens values fom dffeen pels o each ohe adjacen scan pons should be spaced equdsanl n 3D. Because a

4 4 connuous snusodal wavefom was used fo he objecve s moon n -decon he speed of -movemen changes dung he vbaon ccle, necessang a coecon of he -dsances. Effecvel hs foced us o ecalculae he ene 3D ajeco, so ha he newl defned scan pons had equdsan 3D spacng (upplemena Fg. 3. To calculae he equed 3D pel spacng fo a gven scan paen we fs calculaed he oal lengh L of he pe-defned ajeco (conssng of he se of pons fo one vbaon ccle n he -pojecon: L N = =, whee = (,, (,, (6 The mean pel dsance n -dmenson heefoe s d = L / N. Accodng o equaon ( he mean focus change n -decon s gven b equed 3D pel spacng d s compued fom hese wo vaables as d = A N. The / d = d d (7 We ne geneaed a new se of scan pons (hee-componen vecos along he pe-defned ajeco ha wee equdsanl spaced n 3D wh spacng d. To hs end one has o eale ha he dsance beween wo pels n he -plane wll be a funcon of he acual phase of he -oscllaon ccle O ( accodng o d ( = d ΔO ( (8 whee Δ ( = O ( O (. We saed wh he fs new pon, whch was se O equal o :, =,, =, = O, ( The -pojecon s of he dsance o he ne pon was calculaed as s = = ( (,,,, (9 ( and compaed o he equed dsance epeaed fo he ne pons unl s k > d (. If s < ( he calculaon was d ( wh k d =. The ne pel sk k was hen nseed on he lne beween k and a he poson ha elded he

5 5 coec dsance d ( beween he scan pons and (upplemena Fg. 3b. The eac -coodnaes wee calculaed as, = N β M,, = N β M,, = O ( Δ wh wo-componen vecos N k, ( = and M = k k. The faco β s obaned b solvng he quadac equaon ( N M = β ( d eldng β = d ( M ( N M N M N M (3 M Takng no accoun he objecve s dsplacemen n he -decon (ΔO ( he 3D dsance beween and equals d. The above algohm was eavel epeaed usng he followng geneal equaons, = N β M,, = N β M,, = O ( Δ wh N = k,, M = k k and he faco β deemned as gven n equaon (4 (3. Fo he analcal scan paens hs pocedue was epeaed unl he ene ajeco was flled wh he new se of pons, now equdsanl spaced n 3D. In use-defned mode, scan pons wee equall dsbued fo all segmens n mage planes of he efeence sack ha conaned pe-seleced pons (upplemena Fg. 3d. An eo was euned when he me equed o scan one segmen eceeded he me fo he objecve o each he ne plane. The nepolaon neval ΔT beween he las scan pon n one plane (coespondng o he objecve s - poson o he fs scan pon n he ne plane conanng pe-seleced pons (poson s gven b ΔT = O ( O ( (5

6 6 whee O ( s he nvese funcon of (.Thus he numbe of equed O nepolaon pels s N I = ΔT / Δ. Inepolang scan pons wee equall dsbued along he smooh pe-defned ajeco wh he above descbed algohm. Dependng on he nepolaon neval and he phase of he vbaon ccle hs mehod esuled n ehe acceleaed o slowed-down scannng unl he -poson of he ne mage plane was eached and he ne elevan segmen was scanned (upplemena Fg. 3e. Auomac lase nens adjusmen We assumed an eponenal deca of he ecaon lgh nens wh deph. To coec fo hs deca he sgnal appled o he ockel s cell fo lase nens adjusmen was modulaed accodng o O ( λ I( = I e (6 whee I denoes he lase nens a O (. We used -5 μm fo he scaeng lengh λ of nea-nfaed lgh n neococal ssue, and μm fo he bead es sample. Refeences. Klenfeld, D., Ma,.., Helmchen, F. & Denk, W. Flucuaons and smulusnduced changes n blood flow obseved n ndvdual capllaes n laes hough 4 of a neocoe. oc. Nal. Acad. c. UA 95, (998.. Ohem, M., Beauepae, E., Chagneau, E., Me, J. & Chapak,. Twophoon mcoscop n ban ssue: paamees nfluencng he magng deph. J. Neuosc. Meh., 9-37 (.

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( )

5-1. We apply Newton s second law (specifically, Eq. 5-2). F = ma = ma sin 20.0 = 1.0 kg 2.00 m/s sin 20.0 = 0.684N. ( ) ( ) 5-1. We apply Newon s second law (specfcally, Eq. 5-). (a) We fnd he componen of he foce s ( ) ( ) F = ma = ma cos 0.0 = 1.00kg.00m/s cos 0.0 = 1.88N. (b) The y componen of he foce s ( ) ( ) F = ma = ma