Transient Response In Ultra-high Speed Liquid Lenses
HomeSearchCollectionsJournalsAboutContact usMy IOPscienceTransient response in ultra-high speed liquid lensesThis article has been downloaded from IOPscience. Please scroll down to see the full text article.2013 J. Phys. D: Appl. Phys. 46 5102)View the table of contents for this issue, or go to the journal homepage for moreDownload details:IP Address: 128.112.36.203The article was downloaded on 24/01/2013 at 14:30Please note that terms and conditions apply.
IOP PUBLISHINGJOURNAL OF PHYSICS D: APPLIED PHYSICSJ. Phys. D: Appl. Phys. 46 (2013) 075102 (7pp)doi:10.1088/0022-3727/46/7/075102Transient response in ultra-high speedliquid lensesM Duocastella and C B ArnoldDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ, 08544, USAE-mail: cbarnold@princeton.eduReceived 15 September 2012, in final form 29 November 2012Published 23 January 2013Online at stacks.iop.org/JPhysD/46/075102AbstractLiquid lenses are appealing for applications requiring adaptive control of the focal length, butcurrent methods depend on factors such as liquid inertia that limit their response time to tens ofmilliseconds. A tunable acoustic gradient index (TAG) lens uses sound energy to radiallyexcite a fluid-filled cylindrical cavity and produce a continuous change in refractive powerthat, at steady state, enables rapid selection of the focal length on time scales shorter than 1 µs.However, the time to reach steady state is a crucial parameter that is not fully understood. Herewe characterize the dynamics of the TAG lens at the initial moments of operation as a functionof frequency. Based on this understanding, we develop a model of the lens transients whichincorporates driving frequency, fluid speed of sound and viscosity, and we show that is in goodagreement with the experimental results providing a method to predict the lens behaviour atany given time.(Some figures may appear in colour only in the online journal)lens is in a continuous state of changing focus, and a fastspeed camera or synchronized pulsed illumination enablesone to capture images at different focal planes [15–18]. Anexample of this type of device is the tunable acoustic gradientindex of refraction (TAG) lens, an acoustically driven opticalelement [19]. In the TAG lens, a fluid-filled cylindrical cavityis acoustically excited causing a periodic standing wave inthe fluid, and consequently, a periodic change in the indexof refraction due to density modulations [20]. Since theexcitation signal can have frequencies up to the MHz range,the focal-scanning rate at steady state can also be of that order,significantly faster than other methods [18].In previous work, the theory behind the TAG lensoperation was developed for the steady-state regime [20], andthe feasibility for using the device for imaging [18, 21, 22]and materials processing [23] was demonstrated. Here, weanalyse transients in the lens behaviour as it approaches thesteady state as a function of frequency. Based on these results,we find the time to reach steady state primarily depends onthe mechanical properties of the filling fluid as well as thefrequency of the driving signal. We present experimentalcharacterization of this effect and develop a model to describethe temporal evolution of standing waves within the TAGlens, which is in good agreement with the experimentalresults.1. IntroductionIn several fields, including high-speed three-dimensionalmicroscopy [1], flow cytometry [2] or laser materialsprocessing [3], there exists a demand for adaptive lensescapable of changing focus at high speeds. The conventionalapproach of mechanically moving an ensemble of opticalelements to achieve a user tunable focal length is inherentlylimited by the slow response time of the physical actuation.This has spurred research for faster and more robustalternatives, particularly liquid lenses [4], which can takeadvantage of a number of mechanisms to change the focus.Successful implementations have demonstrated the changingcurvature of an interface between two immiscible fluids usingelectrowetting [5, 6], acoustic radiation force [7, 8], stimuliresponsive hydrogels [9], or adjusting the flow conditions [10];the modulation of the surface profile of an encapsulated liquiddroplet [11] by means of electrostatic [12] or pneumatic [13]forces; or the generation of a refractive index change withina liquid through the controlled diffusion of solutes [14]. Inmany conditions, such approaches provide ample performancewith response times of tens of milliseconds and focal-scanningrates below the kHz range. A much faster focusing mechanismcan be achieved using oscillating liquid lenses [15]. Insteadof waiting for the lens to reach a fixed focus condition, the0022-3727/13/075102 07 33.001 2013 IOP Publishing LtdPrinted in the UK & the USA
J. Phys. D: Appl. Phys. 46 (2013) 075102(a)M Duocastella and C B Arnold(b)beam expanderRF signal (S2)TAGlensWavefrontsignal generatorRF signal(S2)wavefrontresponse10 mscontrollabledelay time15 ns(S1)Laser pulse(S3)timeFigure 1. Experimental setup. (a) Scheme of the setup used to characterize the transient behaviour of the TAG lens. (b) Temporal diagramof the different signals involved in the synchronization system.2. Experimental setupWe use a TAG lens (TAG Optics Inc., TL2-B-355V) with aninner diameter of 16 mm and a length of 20 mm. We drivethe lens with a function generator (Syscomp, WGM-201) thatproduces a sinusoidal signal between 500 kHz and 1 MHz andan ac voltage of 20 V peak to peak. The lens filling fluidis silicone oil with a viscosity of 100 centistokes, a staticrefractive index of 1.403 and a speed of sound of 1000 m s 1 .The characterization setup for the TAG lens is schematizedin figure 1(a). We use a pulse generator (Stanford Research,DG-535) triggered by a computer to control the delay timebetween laser pulses from a Nd : YVO4 laser (15 ns duration,355 nm wavelength, M 2 1.3) and the RF signal that drivesthe TAG. We analyse the laser beam 1 cm after passing throughthe lens using a Shack–Hartmann wavefront sensor (ThorlabsWFS 150 C). The beam is expanded prior to the lens entranceto ensure a flat wavefront and we set an electronic aperture forthe wavefront analysis of 1 mm. In this set of experiments, thedelay times used are presented in figure 1(b). We increment thetime separation between the RF signal and the laser pulses insteps of 0.1 and 0.5 µs enabling data acquisition with sufficienttemporal resolution.Figure 2. Determination of the TAG lens resonances. Impedancespectroscopy measurement of the lens where each peak correspondsto a lens resonant frequency.the first moments of operation presented in figure 3(a) revealsa first change in optical power at 8 µs. We define this timeas τ , which corresponds to the time an acoustic wave takesto travel from the piezoelectric to the lens centre. After thistime, the lens optical power oscillates at the same frequencyas the driving signal, with the TAG continuously changingbetween a converging and a diverging lens [18]. Notably, theamplitude of the oscillation periodically increases every 2 τuntil, at 1.6 ms, the optical power variation is below 5%, asshown in figure 3(b). At this point, we consider that a standingwave is formed and that steady state is reached. The analysis ofthe frequency components of TAG transient computed with afast Fourier transform (FFT) algorithm presented in figure 3(c)reveals a single frequency component at 582 kHz.For off-resonance conditions, we present two frequencies,586.5 and 595.5 kHz, separated, respectively, by 3.5 and12.5 kHz from the closest resonance at 582 kHz. We canobserve in figures 4(a) and (d) common trends with the TAGbehaviour on resonance. In particular, in both cases the lensrefractive power oscillates with varying amplitude until atabout 1.6 ms it stabilizes reaching steady state. In addition,the first change in refractive power also occurs at 1 τ and isfollowed by periodic changes in amplitude every 2 τ . However,3. Study of the lens transient behaviourThe optical performance of the TAG lens critically depends onthe driving frequency selected [20]. Two different scenarioscan be distinguished: when the driving frequency correspondsto a resonance of the lens, and the off-resonance case. Ingeneral, working on resonance is preferred since it enablesrefractive powers about 2 orders of magnitude higher thanoff-resonance [20]. In this experiment, we measure the TAGresonances using impedance spectroscopy (Solartron 1260A).The plot of impedance versus frequency is presented in figure 2.The well-defined peaks in the plot, with approximatelyconstant spacing between each other, indicate the presenceof resonances in piezoelectrics, and consequently, in the TAGlens.We first characterize the transient behaviour of the TAGwhen driven on resonance. In particular, we select the 582 kHzresonance. The evolution of the lens refractive power over2
J. Phys. D: Appl. Phys. 46 (2013) 075102(a)M Duocastella and C B Arnold(b)normalized timetransient behaviorsteady-state5311.0100.55normalized time00-0.5-5-1.0-1005101520253035400time (µs)(c)0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8time (ms)(d)6experimentmodel582Amplitude (a.u.)510normalized time45302-510500-105506006500700frequency (kHz)0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8time (ms)Figure 3. Transient behaviour of the TAG on resonance conditions, at a frequency of 582 kHz. (a) Experimental values of the TAG lensoptical power at the first moments of operation. In the upper horizontal axis, time has been normalized by τ , being the time an acoustic wavetakes to propagate from the piezoelectric to the lens centre. (b) Measured temporal evolution of the TAG lens optical power until reachingsteady state. The inset corresponds to a detail of the first moments of the lens operation where time has been normalized by τ . (c) Frequencycomponents of the signals corresponding to (b) and (d). (d) Model that predicts the TAG optical power evolution over time.in this case the amplitude does not monotonically increase, asobserved on resonance, but it is periodically modulated. Theperiod of the amplitude modulation at 586.5 kHz is 0.28 mswhereas at 595.5 kHz the period is 0.08 ms. Such periodicity(T ) follows the simple relationship:T 1, f behaviour [20]. Accordingly, the density fluctuations in thelens fluid obey the damped wave equation: 2 (cs2 ρ ν ρ 2ρ) 2 0, t t(2)where cs is the fluid speed of sound and ν 7/4µ, withµ being the kinematic viscosity. The force imparted by thepiezoelectric walls to the fluid can be written as the followingNeumann boundary condition: ρ ρ0 vA ωcs2ρ 0 vA ω 2 ν sin(ωt) cos(ωt), (3) r r r0ν 2 ω2 cs4ν 2 ω2 cs4(1)where f is the separation of the driving frequency from itsclosest resonance. Another relevant aspect that is worth notingis the decrease in the TAG refractive power as one movesfurther from resonance, in good agreement with experimentsat steady state [20]. Concerning the signal analysis in thefrequency domain, we can observe in figure 4(c) that for the586.5 kHz case there are two frequency components. Themost intense one corresponds to the driving frequency, whereasthe other one corresponds to the closest resonance frequency.For the 595.5 kHz case, the signal presents several frequencypeaks (figure 4(f )). The most intense one corresponds to thedriving frequency, wheres the other peaks can be related to theremaining resonance frequencies (see figure 2).where r0 is the lens radius, ρ0 is the static density, vA is thevelocity of the piezoelectric wall and ω is the driving frequency.We can expand the solution to the above equation as a sum ofeigenfunctions:ρ(r, t) r(Asin(ωt) Bcos(ωt)) km t 22 νkmt/222 Cm sinJ0 (km r) e4c ν km2m 1 km t 22 Dm cos4c ν 2 km2 Em sin(ωt) Fm cos(ωt)(4)4. Modelling the lens transientsWe can describe the TAG lens transients using the linearacoustic model that successfully predicted the lens steady-state3
J. Phys. D: Appl. Phys. 46 (2013) 075102(a)transient behaviourM Duocastella and C B Arnoldsteady-sate(b)(c)steady-satetransient 1.0-1.0-1.5-1.500.20.40.60.81.01.21.41.6A mplitude 0650700frequency (kHz)(e)steady-satetransient behaviour0.8-1.01.20.15experimentmodelA mplitude (a.u.)transient behaviour1.0tim e ( ms )tim e ( ms )(d)0.80.50.100.05000.20.40.6tim e ( ms )0.81.01.21.41.61.8500550tim e ( ms )600650700frequency (kHz)Figure 4. Transient behaviour of the TAG off-resonance. Experimental (a) and modelled (b) evolution of the lens optical power at afrequency of 586.5 kHz (3.5 kHz away from resonance). (c) Representation of both experimental data and model in the frequency domain.The signals present two frequency components, which correspond to the driving frequency and the closest resonance at 582 kHz.Experimental (d) and modelled (e) evolution of the lens optical power at a frequency of 595.5 kHz (12.5 kHz away from resonance). Thecorresponding representation of the signals in the frequency domain reveal a higher peak at the driving frequency and a series of smallerpeaks at the closest resonant frequencies.where km xm /r0 is the location of the mth zero of J1 (x) 0,and the coefficients are given byA B ρ(r,t) t 0 rDm ρ0 vA ωcs2ν 2 ω2 cs4ρ0 vA ω2 ν 2 2ν ω cs4 0, we obtain 2B(5)Cm (6) 2ρ0 vA ωEm r02 J02 (km r0 ) 2 4 k (c ω2 ν 2 ) cs2 ω2 2 r0 m s 2 2ωJ0 (km r)r 2 drν ω cs40 r022 2 (ω cs km )J0 (km r) dr2rω2 2cs2 km2 r0ω2 0 0 J0 (km r)r 2 dr km0 J0 (km r) drν 2 ω2 cs4.2 ) k 4 (ν 2 ω2 c4 )ω2 (ω2 2cs2 kmmsdr Fm(9)22km ν 2 km r02 2ωA 0 J0 (km r)r 2 dr νkmDm ωEm . 2r02 J02 (km r0 )4cs2(10)Since the experimental measurements are taken at thevicinity of the lens centre r 0, and for low viscosityfluids where ν cs2 /ω, the only terms that will contributesignificantly to the final solution are Dm and Fm , whichyields to0 1222 242 24 ω (ω 2cs km ) km (ν ω cs ) 2ρ0 vA ω2 νFm r02 J02 (km r0 )r020 J0 (km r)rr02 J02 (km r0 )(7)ρ(0, t) e νkm t/2 Dm cos(km cs t) Fm cos(ωt) . (11)2m 1The relative small changes in the fluid density comparedwith the static density enable one to use a linearized versionof the Lorentz–Lorenz equation that relates fluid density withrefractive index [24]. Therefore, the temporal evolution of thefluid refractive index (n), and consequently, the lens opticalpower (P ), will be proportional to (11)(8)Note the comparison with [20]. The only undeterminedcoefficients are Cm and Dm , which depend on the initialboundary conditions.Considering ρ(r, 0) 0 andP n ρ P Cρ4(12)
J. Phys. D: Appl. Phys. 46 (2013) 075102(a)M Duocastella and C B Arnold(b)normalized tim e(c)normalized tim e1 3 5 7 9 11 13 15 17 19 21 232 25 27 9 311 3 5 7 9 11 13 15 17 19 21 232 25 27 9 311.00.50.500-0.5-0.5-1.0-1.0experimentmode section 40.20A mplitude m e ( ms )0.100.150.200.25600tim e ( ms )700800900frequency (kHz)Figure 5. Prediction with the TAG lens model. (a) Temporal evolution of the TAG at a frequency of 680 kHz as computed using the modeldescribed in section 4. (b) Experimental data obtained at 680 kHz, in good agreement with the predicted behaviour. (c) The correspondingrepresentation of (a) and (b) in the frequency domain confirms the good agreement between model and experiment.with C being the proportionality constant between density andoptical power.The numerical computation of (11) for the resonant andoff-resonant cases experimentally analysed are presented infigures 3(d), 4(b) and 4(e). We only use C as a fittingparameter. Note, though, that it is possible to derive thefundamental terms in C as done in prior work [20].We can observe in all cases a very good agreement betweenmodel and experiment. Notably, the model describes thecontinuous oscillation of the TAG optical power, the changes inthe oscillation amplitude every 2 τ as well as the time to reachsteady state. In addition, the plots of the computed transientsand experimental data in the frequency domain presented infigures 2(d), 3(c) and 3(f ) reveal that both signals have thesame frequency components. Therefore, the model not onlyprovides good visual agreement but quantitatively reproducesthe experiment.The capability of the model to predict the lens transientsis analysed in figure 5. We first compute the temporalresponse of the lens at a frequency of 680 kHz (figure 5(a)).Theapparently random signal obtained presents the same trends aspreviously described, including the change in amplitude every2 τ . By collecting the experimental data at this frequency weshow in figure 5(b) that the experiment follows the behaviourpredicted by the model. Model and experiment also have thesame frequency components, as presented in figure 5(c). Weconclude that the model can be used to predict transients giventhe dimensions of the lens and the properties of the fillingfluid. The capability to predict the lens transient enables oneto operate the lens prior to reaching steady state. In fact, themodel opens the door to the selection of user-defined transientswhich can be used to shape light in order to induce uniqueeffects on materials.frequency of the driving signal travel back and forth interferingwith each other (figure 6). In this way, the first change in theTAG optical power occurs when the first wave, generated atthe piezoelectric, reaches our detector placed at the centre ofthe lens (time 1 τ ). This wave continues propagating towardsthe piezoelectric, reaching it at 2 τ . At this moment, the waveinterferes with an incoming new wave. The resulting wavepropagates to the centre of the lens, arriving at this point at3 τ . Since this resulting wave has a different amplitude thanthe first wave, we observe a change in refractive power. Thisprocess is repeated successively, producing variations in theamplitude of the lens power every 2 τ . On resonance, thesuccessive interferences are constructive, and the waves addup to produce a monotonic increase in the amplitude. Offresonance, interferences are partially constructive (or partiallydestructive), and the additive process between waves is lessefficient and is time dependent. As a result, a periodicmodulation in the amplitude is observed and the final refractivepower is lower than on resonance. Since the fluid has a certainviscosity, waves suffer losses in successive roundtrips due toviscous damping. Such damping ultimately balances out thegain injected in the cavity through the driving signal, leadingto steady state.According to this interpretation, we can write the equationcorresponding to the additive process of cylindrical waves atthe vicinity of the lens centre as5. Additional interpretation of the lens transientswhere φ is the phase shift between waves and γ is thedamping factor. On resonance, waves will add up and weassume a 0 phase shift. Off resonance, the phase shiftis 2τ ω. By rewriting ω ωresonance ω, where ωexpresses the proximity to resonance, we obtain φ 2τ ω.Notably, (13) with this value of φ corresponds to a wave withperiodicity T 2π/ ω 1/ f , in good agreement withρ(0, t) i(t) γ m sin ( ωt mφ) ,m 0 0,i(t) 1, .The solution found in (11) represents the temporal evolutionof the TAG lens as a Fourier–Bessel expansion with timedependent coefficients. A more intuitive interpretation ofthe observed transient behaviour consists in considering theTAG lens as a cylindrical resonator in which waves with the5for 1 t 3τfor 3τ t 5τ(13)
J. Phys. D: Appl. Phys. 46 (2013) 075102M Duocastella and C B Arnoldt 1τt 0piezoelectri csound wavesfluidt 2τt 3τFigure 6. Scheme of the model based on considering the TAG as a resonator. Cylindrical waves travel back and forth in the TAG, interferingwith each other and producing periodic changes in the lens optical power every 2 τ .(a)(b)6model section 4model section 5Amplitude (a.u.)Amplitude (a.u.)5model section 4model section 50.204320.150.100.05105000550600650700600frequency (kHz)700800900frequency (kHz)Figure 7. Comparison between the two models that described the TAG lens temporal evolution. Plot of the frequency components of thelens transient at (a) resonance conditions, at 582 kHz; and (b) off-resonance conditions, at 680 kHz. Note in both cases the good agreementbetween models.the empirical relationship described in (1). Concerning thedamping factor, we assume the classical attenuation coefficientfor acoustic waves [25], which in this particular case can bewritten asAssuming that steady state is reached when amplitudechanges between consecutive waves are below 5%, and usingelementary algebra, yields toAl 1 Al cs2 ln(0.05) γ l 0.05 tsteady state .A0ω2 ν2γ e 2τ ν ω2cs(14)(16)with 2 τ being the time delay between successive a wave.The calculation of (13) is in good agreement withexperiment and with the model described in section 4, as canbe observed in figure 7 for both resonance and off-resonanceconditions. In addition, the model allows further insights aboutthe TAG transient behaviour and in particular about the time toreach steady state. Using (13), the amplitude (A) of a travellingwave after l roundtrips can be rewritten asAl A0l γ i.According to this equation, the time to reach steady state for theexperimental conditions analysed in figure 3 is 1.3 ms, which isin close agreement with the measured value. In addition, (16)also unveils strategies to reduce the lens transient time. Thisincludes driving the lens at higher frequencies, or using fluidswith higher viscosities or lower speeds of sound. In any of thesemethods the number of cavity roundtrips that acoustic wavesexperience is reduced, which can result in loss of optical power.In order to compensate for this effect, one can increase thegain per roundtrip by increasing the power of the lens drivingsignal.(15)i 06
J. Phys. D: Appl. Phys. 46 (2013) 075102M Duocastella and C B Arnold[8] Koyama D, Isago R and Nakamura K 2010 Compact,high-speed variable-focus liquid lens using acousticradiation force Opt. Express 18 25158–69[9] Dong L, Agarwal A K, Beebe D J and Jiang H 2006 Adaptiveliquid microlenses activated by stimuli-responsivehydrogels Nature 442 551–4[10] Mao X, Waldeisen J R, Juluri B K and Huang T J 2007Hydrodynamically tunable optofluidic cylindrical microlensLab Chip 7 1303–8[11] Song W, Vasdekis A E and Psaltis D 2012 Elastomer basedtunable optofluidic devices Lab Chip 12 3590–7[12] Binh-Khiem N, Matsumoto K and Shimoyama I 2008Polymer thin film deposited on liquid for varifocalencapsulated liquid lenses Appl. Phys. Lett.93 124101[13] Chronis N, Liu G, Jeong K H and Lee L 2003 Tunableliquid-filled microlens array integrated with microfluidicnetwork Opt. Express 11 2370–8[14] Mao X, Lin S S, Lapsley M I, Shi J, Juluri B K andHuang T J 2009 Tunable liquid gradient refractive index(l-grin) lens with two degrees of freedom Lab Chip9 2050–8[15] McLeod E, Hopkins A B and Arnold C B 2006 Multiscalebessel beams generated by a tunable acoustic gradient indexof refraction lens Opt. Lett. 31 3155–7[16] Lopez C A and Hirsa A H 2008 Fast focusing using apinned-contact oscillating liquid lens Nature Photon.2 610–3[17] Stan C A 2008 Liquid optics: oscillating lenses focus fastNature Photon. 2 595–6[18] Mermillod-Blondin A, McLeod E and Arnold C B 2008High-speed varifocal imaging with a tunable acousticgradient index of refraction lens Opt. Lett. 33 2146–8[19] McLeod E and Arnold C B 2008 Optical analysis oftime-averaged multiscale bessel beams generated by atunable acoustic gradient index of refraction lens Appl. Opt.47 3609–18[20] McLeod E and Arnold C B 2007 Mechanics and refractivepower optimization of tunable acoustic gradient lensesJ. Appl. Phys. 102 033104[21] Olivier N, Mermillod-Blondin A, Arnold C B andBeaurepaire E 2009 Two-photon microscopy withsimultaneous standard and extended depth of fieldusing a tunable acoustic gradient-index lens Opt. Lett.34 1684–6[22] Duocastella M, Sun B and Arnold C B 2012 Simultaneousimaging of multiple focal planes for three-dimensionalmicroscopy using ultra-high-speed adaptive opticsJ. Biomed. Opt. 17 050505[23] Mermillod-Blondin A, McLeod E and Arnold C B 2008Dynamic pulsed-beam shaping using a tag lens in the nearUv Appl. Phys. A 93 231–4[24] Born M and Wolf E 2003 Principles of Optics:Electromagnetic Theory of Propagation, Interference andDiffraction of Light (Cambridge: Cambridge UniversityPress)[25] Pierce A D 1989 Acoustics an Introduction to its PhysicalPrinciples and Applications (Woodbury NY: AcousticalSociety of America)6. ConclusionUnder the conditions studied in this paper we havedemonstrated that the TAG lens can reach steady state in a 1 mstime-scale. Once in steady state, using pulsed illuminationit is possible to select between different focal lengths intime scales below 1 µs. The duration of the lens transientresponse depends on the driving frequency as well as onthe properties of the filling fluid including speed of soundand viscosity. The lens temporal behaviour also dependsstrongly on the driving frequency. On resonance, the lensoptical power monotonically increases, whereas off resonanceit can periodically vary or even present apparently randomforms. Two robust models have been used to describe the lenstransients that are in good agreement with all the experimentalconditions analysed. The models enable one to predict thetime to reach steady state as well as to determine the lensoptical power at any given time prior to reaching steady state.This makes possible to operate the lens during transients. Byappropriately selecting a particular temporal evolution of thelens optical power one could shape light in a fast and controlledway, with important applications in relevant areas such as laserprocessing or microscopy.AcknowledgmentsThe authors acknowledge financial support from AFOSR.In addition, we acknowledge Christian Theriault from TAGOptics Inc. for providing the lens.References[1] Yang L, Raighne A M, McCabe E M, Dunbar L A andScharf T 2005 Confocal microscopy usingvariable-focal-length microlenses and an optical fiberbundle Appl. Opt. 44 5928–36[2] Gerstner A O, Laffers W and Tárnok A 2009 Clinicalapplications of slide-based cytometry: an updateJ. Biophoton. 2 463–9[3] Kuwano R, Tokunaga T, Otani Y and Umeda N 2005 Liquidpressure varifocus lens Opt. Rev. 12 405–8[4] Graham-Rowe D 2006 Liquid lenses make a splash NaturePhoton. sample 2–4[5] Kuiper S and Hendriks B H W 2004 Variable-focus liquid lensfor miniature cameras Appl. Phys. Lett. 85 1128–30[6] Miccio L, Finizio A, Grilli S, Vespini V, Paturzo M,De Nicola S and Pietro Ferraro 2009 Tunable liquidmicrolens arrays in electrode-less configuration and theiraccurate characterization by interference microscopy Opt.Express 17 2487–99[7] Oku H and Ishikawa M 2009 High-speed liquid lens with 2 msresponse and 80.3 nm root-mean-square wavefront errorAppl. Phys. Lett. 94 2211087
beam expander Laser Wavefront signal (S1) RF signal (S2) Laser pulse (S3) wavefront response pulse generator controllable delay time 15 ns time 10 ms (a) (b) RF signal (S2) (S1) (S3) TAG lens wavefront sensor Figure 1. Experimental setup. (a) Scheme of the setup used to characterize the
steady state response, that is (6.1) The transient response is present in the short period of time immediately after the system is turned on. If the system is asymptotically stable, the transient response disappears, which theoretically can be recorded as "! (6.2) However, if the system is unstable, the transient response will increase veryFile Size: 306KBPage Count: 29Explore furtherSteady State vs. Transient State in System Design and .resources.pcb.cadence.comTransient and Steady State Response in a Control System .www.electrical4u.comConcept of Transient State and Steady State - Electrical .electricalbaba.comChapter 5 Transient Analysis - CAUcau.ac.krTransient Response First and Second Order System .electricalacademia.comRecommended to you b
behringer ultra-curve pro dsp 24 a/d- d/a dsp ultra-curve pro ultra- curve pro 1.1 behringer ultra-curve pro 24 ad/da 24 dsp ultra-curve pro dsp8024 smd (surface mounted device) iso9000 ultra-curve pro 1.2 ultra-curve pro ultra-curve pro 19 2u 10 ultra-curve pro ultra-curve pro iec . 7 ultra-curve pro dsp8024 .
Transient and Steady-State Response Analysis 4.1 Transient Response and Steady-State Response The time response of a control system consists of two parts: the transient response and the steady-state response. By transient response, we mean t
47 117493 SCREW, mach, hex washer hd 2 48 BOX, control 276868 Ultra 395/495 1 15D313 Ultra 595 1 49 CONTROL, board, 110V 1 246379 Ultra 395/495 1 248179 Ultra 595 1 50 276882 COVER, control 1 51 15K393 LABEL, control, Graco 1 56 CORD, power 1 15J743 Ultra 395/495, Stand 1 15D029 Ultra 595, L
exponential, the forced response will also be of that form. The forced response is the steady state response and the natural response is the transient response. To find the complete response of a circuit, Find the initial conditions by examining the steady state before the disturbance at t 0. Calculate the forced response after the disturbance.File Size: 773KB
Typically users of pipe stress analysis programs also use PIPENET Transient module. High stresses in piping systems, vibrations and movements can occur because of hydraulic transient forces. One of the powerful and important features of PIPENET Transient module is its capability of calculating the force-time history under hydraulic transient .
age response changes from one steady state initial state! to another steady state. The transition from an initial state to steady state occurs within a region and the response in this region is called the transient response. Hence, the complete response of a system consists of two parts: the transient response
TABLE OF CONTENTS: XPRESS ULTRA FIELD TERMINATION CONNECTORS SC Xpress Ultra Fiber Connectors Page 2 LC Xpress Ultra Fiber Connectors Page 3 ST Xpress Ultra Fiber Connectors Page 3 CLEANING & INSPECTION Optical Connector Contamination Pages 5 - 6 Xpress Ultra Cleaner Pages 7 - 8 Xpress Ultra Cleaner Replaceable Cartridge Page 8 Xpress Ultra
