Flow velocity measurements through a fluctuating free surface by means of adaptive optics

Transcription

1 Flow velocity measurements through a fluctuating free surface by means of adaptive optics Christoph Leithold 1,*, Lars Büttner 1, Jürgen W. Czarske 1 1: Laboratory for Measurement and Testing Techniques, Technische Universität Dresden, Germany * correspondent author: Jürgen W. Czarske Abstract The noninvasive investigation of flows where media of different optical density participate is often not possible. A direct measurement through free, transient surfaces will result in higher measurement uncertainties or they will hinder any measurement at all. To overcome this issue we make use of adaptive optics (AO). Dependent on the measurement system, an adaptive correction of the illumination path and/or the observation path can result in improved measurement properties. AO can therefore help to directly measure noninvasively flow velocities and flow turbulence at places that were inaccessible before. Examples of interest are convection flows at emergency core cooling, where cold water is injected into a pressurized water reactor, forming a free falling jet, as well thin film flows and biomedical flows. Interferometric velocity measurement systems are especially sensitive to wavefront distortions since the straightedge of the system - the interference pattern - is directly influenced and needs to be stabilized by AO. Interferometric measurement systems are an important tool for measuring flow velocity profiles. It is therefore of high interest to stabilize those systems in the presence of optical distorting environments. In the studied model experiment, we equipped a laser Doppler velocimeter (LDV) with AO to measure through a pumpdriven free surface. The AO system realizes both beam stabilization as well as wavefront shape control to compensate for the dynamic optical distortions. Depending on the strength of the distortion we could achieve an over-all improvement of the measurement properties that is flow velocity uncertainty, interference contrast and rate of validated signals. The largest gain in validation rate was achieved at medium distortions where it raised over 50 percentage points. We discuss the expected effects of our model distortion onto the LDV and give an outline of further advancements of the AO flow velocity measurement system. The experiments studied so far are very promising to exploit new potentials in the field of multi-phase flows. 1. Introduction Due to the presence of dynamic interfaces, the non-invasive investigation of velocity distributions in multiphase flows is a complicated task. In some cases like bubble flows, jet flows or thin film flows with sediments it s not arrangeable at all to measure through a static, optical window. A typical case of interest is a free falling jet flow at emergency core cooling. During an accident, a pressurized water reactor needs cooling and therefore cold water is injected, forming a free falling jet. It is important to understand how the thermal convection in this particular case works to reduce thermal stress in the reactor walls. Noninvasive flow measurements inside the jet could directly help to validate and improve computational fluid dynamics code. Other kinds of fluctuating interfaces between to media occur for example at fuel cells (CO 2 bubbles in water-methanol) [Burgmann2012], at levitated droplets [Abe2007], [Hyers2005] or at thin film fluid films, running down an inclined surface [O'Brien2002], [Kalliadasis2012]. A straightforward optical measurement through a moving boundary layer will result in higher uncertainties or even deteriorate the measurement. As a solution to this metrological problem, the principle of wavefront correction by means of adaptive optics (AO) seems to have a big potential. AO is predominantly known from astronomy, where it has led to a renaissance of earth-bound telescopes. Optical distortions of the light path through the atmosphere caused by turbulent flows of gas layers of different temperatures can be corrected such that the achievable resolution gets improved. AO systems for wavefront correction consist usually of a sensor for measuring the wavefront, an adaptive optical element and a control unit that reads the wavefront data and calculates the control parameters for the actuators [Hardy1998]. Besides astronomy, adaptive optics has found its way into various fields of research. In ophthalmology it has improved retina imaging [Liang1997], [Roorda2002]. Using AO - 1 -

2 with optical coherence tomography, 3D in-vivo retinal imaging is possible [Zhang2006]. In latest developments, adaptive optics has been used for deep tissue focusing to allow for imaging through highly scattering media [Tao2011], [Wang2012]. Regarding fluid velocity measurements, the velocity of erythrocytes and the retinal blood flow was measured with the help of adaptive optics [Zhong2008]. Because of the ongoing development on this field, adaptive optics (AO) systems have become commercially available as compact and easy-to-use devices. This offers a great potential for fluid flow research to face the challenges described above. The objective of this contribution is to demonstrate that adaptive optics is an appropriate tool to improve the measurement properties of flow velocity measurement techniques in environments with distortions of the optical paths. A model experiment is presented which uses laser Doppler velocimetry that is based on a Mach-Zehnder interferometer, as the measurement method and a pump driven fluctuating water surfacas as the optical distortion. The AO-system realizes both beam stabilization as well as wavefront shape control to compensate for the dynamic optical distortions. The former was done by a deformable membrane mirror which can correct for low-order Zernike terms while the beam direction was corrected by a two-axis piezo tip-tilt stage on which the mirror was mounted. Depending on the strength of the distortion we could achieve an over-all improvement of the measurement properties that is measurement uncertainty, interference contrast and rate of validated signals. In 2.1 we discuss the expected effects of the distortion onto the measurement system. Subsequently we show how we characterized our model distortion (2.2) and explain the used experimental setup (2.3). The results of the measurement system characterization are discussed in 2.4 where we also present a simple test flow velocity profile; provided by the pump nozzle originally used for driving the optical distortion (fluctuating water surface). Finally we give a brief summary and outline possible future advancements of the system. 2. Experiments 2.1 Measurement principle and preliminary considerations Laser Doppler velocimetry (LDV) is amongst the most often applied velocity measurement techniques for fluid flow research. At the basic principle, two coherent laser beams are made to intersect under a small angle 2. If a particle carried with the flow to be investigated passes through the intersection volume, it scatters light with an amplitude modulation with frequency f (t), which is given by the total derivative of the phase difference ( r, t) of the individual phases of the two partial light waves: d r 2 f ( t) ( ). (1) dt t t 0 t r r0 ( t) r r0 ( t) r r0 ( t) Where r ( ) is the particles trajectory. In a common and undisturbed LDV the phase difference is not explicitly time-dependent and equation (1) simplifies to in the direction of the gradient of and the fringe spacing: f ( t) vx ( t) / d with (t) the velocity component v x 1 d 2. (2) x In the case of plane waves this simplifies to d. (3) 2sin In paraxial approximation laser beams can be described as Gaussian beams, whose wavefront curvature lead to spatial dependent fringe spacing according to equation (2). In standard LDV system, the Gaussian laser beams are usually adjusted in such a way that the beam waists of the partial beams coincide with the point of the intersection. Consequently, the beam positions with the maximum intensity and with approximately - 2 -

3 plane wavefronts are located in the measurement volume such that the variation of the fringe spacing is minimized. In a disturbed LDV and hence both summands in (1) are explicitly time-dependent. The latter term in equation (1) is a jitter-like term. If the velocity of the passing particle is high enough, a quasi-static approach is justified. This means that the first summand in equation (1) is much larger than the second summand, but still time-dependent: A fast enough particle crossing the measurement volume will see an almost static fringe system. However, different particles passing through the beam intersection at different times may see completely different fringe systems. The fluctuating surface water wave adds a transient and spatial varying phase shift to the light wave which (after propagation to the measurement volume) directly influences the fringe spacing and therefore the straightedge of the velocity flow measurement system. Expanding the local height h(x,t) spatially into a Taylor series (or analogously into Zernike series) leads to 2 2 h( x, t) 1 h ( x, t) h( x0, t) ( x x0)tan ( t) 2 ( x x0)... 2 (4) x x x Stroke Tilt 0 Curvature with x 0 as the incident position of the laser beam and tan h/ x as the slope at this position. This allows to classify the effects in a quasi-static approach and to discuss the consequence for the measurement properties separately as follows, where the order represents the order of the spatial derivate of the height profile function: A) 0. order: Stroke of the interface. For a lift of the interface a parallel shift of the beam occurs whereas the beam direction remains constant. The consequence is a shift of the measurement volume, i.e. a dislocation of the measurement position. B) 1. order: Tilt of the interface. Due to refraction, a tilt of the interface will change the propagation direction of the beam. Going to the two-dimensional consideration, it has to be distinguished between a tilt in the plane spanned by the two partial beams x and a tilt in the direction normal to this plane y. This will result in the following effects: tilt in x-direction: A change of the beam direction will result in a different position of the beam crossing, i.e. again a dislocation of the measurement position. Moreover, it will lead to a different crossing angle and hence to a different fringe spacing according to eq. (3). Since the fringe spacing acts as the calibration constant between the measured frequency and the velocity, an unknown systematic deviation of the determined velocity occurs for a single particle. Due to the stochastic movement of the interface, this is a random error varying with time. Since usually a series of burst signals is evaluated to perform a statistical analysis of the flow, this effect increases the statistic uncertainty of the velocity measurement ( virtual turbulence ). Tilt in y-direction: A beam deflection in the y-direction normal to the plane spanned by the two beams will result in skew rays. The reduced overlap of the partial beams results in lower rate of valid burst signals. In the worst case of negligible overlap the measurement will fail completely. C) 2. order: Curvature of the interface. Due to refraction, a curvature of the interface will induce a lens effect on the beam propagation what will change the radius and the position of the beam waist. Hence, the beam waist will not coincide any longer with the crossing point of the beams. As a consequence, beams with a significant wavefront curvature will interfere in the measurement volume. For example, if the beam waists of the beams are both located before or behind the measurement volume, a fan-like interference fringe system will appear. Generally, a strong variation of the fringe spacing within the measurement volume will occur which increases the measurement uncertainty. D) Higher Orders: Distortions of the surface with high spatial frequency

4 The wavefront of the beams will be locally distorted, leading to inhomogeneities in the interference fringes. The fringe spacing can vary in all three dimensions. Similar to the topic before, the measurement uncertainty will increase. It should be noted that the extent, at which the different distortion orders appear, strongly depend on the incidence point of the beam with respect to the surface wave, i.e. to the phase of the wave. For example, if the beam passes through a maximum of the water wave, a convergent lens will mainly affect the beam, if it passes through a minimum, a divergent lens effect appears. If the beam propagates through the inflection point of the wave, mainly a beam deflection will occur. 2.2 Characterization of the optical distortion The aim of the model experiments is to enable LDV measurements through a fluctuating air-water interface. The requirements for the AO system where estimated by measuring the temporal behaviour of the free surface. We used a chromatic-confocal distance sensor (co. Micro Epsilon Optronic GmbH, Dresden/Germany) with a measurement rate of 1 khz. The Bandwidth was limited by the back reflected intensity, which is (air-water) only around 4% of the incident intensity. This sensor principle which is based on the evaluation of chromatic aberration turned out to be well suited for measuring the height of the reflecting water surface. The fluctuation of the interface was generated by a water pump, see also the description of the experimental setup in the next section. The height h of the water surface was measured as a function of time for different operation voltages of the pump. Fig. 1 shows the results in frequency domain for three different voltages as an example. As can be seen, the maximum frequency occurs for 5.9 Hz that is almost independent of the voltage. The spectrum contains frequency contents until several 10 Hz. Fig. 1 Spectra of the water surface fluctuations for three different operation voltages of the pump. Same ordinate scaling for all spectra. The phase velocity v Ph = /k and the wavelength of the surface waves can be deduced from the dispersion relation for water waves [Sommerfeld]: 2 3 k tanh( h k) gk (5) 0 where =2 f is the angular frequency and k=2 / the angular wave number of the water wave, = kg/s 2 the air-water surface tension, = 10 3 kg/m 3 the water density, g= 9.81 m/s the gravitational acceleration and h 0 = 5.2 cm the absolute water height above the bottom of the basin. Using the mean frequency of 5.9 Hz yields a phase velocity of 0.3 m/s and a wavelength of around 50 mm

5 From the preceding characterizations of the distortion the following requirements for the AO system can be deduced: A safe upper limit for the occurring frequencies can be chosen as 50 Hz. In accordance to the Nyquist- Shannon sampling theorem, the AO system should have a bandwidth of at least 100 Hz. The wavelength of the capillary wave of about 5 cm is significantly larger than the laser beam diameter when it breaks through the water surface (~ 1 mm). Consequently, for the deformable mirror a low number of actuators is sufficient since no high spatial frequencies need to be corrected. The required tilting range of the deformable mirror can be estimated from the inclination of edge of the capillary wave using: h 1 h tan (6) x v t Here, the assumption of negligible dispersion (shape conservation of the wave) were used. This yields a mean tilting angle of the water surface of 24 mrad for the highest pump voltage. Taking into account the angular magnification of the optical system of yields a required tilting range of for the mirror of 0.79 mrad. Under consideration of these specifications, an adaptive optics system from co. Flexible Optical B.V., the Netherlands, was chosen, which consists of a deformable mirror (DM) with integrated tip-tilt stage, a Hartmann-Shack wavefront sensor (HS-WFS) and a control software. The micromachined membrane DM (figure 2) had a clear aperture of 10 mm and consists of 17 actuators that are driven electrostatically. It is mounted on a two-axis piezoelectric tilt stage that allows a tilting of 1.2 mrad. The HS-WFS uses typically 8x8 elements of the microlens array. The control software is installed on a standard PC. It reads the wavefront data and drives the deformable mirror in a closed-loop operation. The bandwidth of the feedback control is 200 Hz which allows for compensating distortions with frequencies up to 100 Hz in accordance to the Nyquist-Shannon sampling theorem. Ph 2.3 Experimental Setup Fig. 2 Deformable mirror with 2D tilt function used for the model experiment A laser Doppler velocimeter was realized on a horizontally aligned optical breadboard with a solid state laser of 532 nm wavelength as the light source, see fig. 3. A prism beam splitter generates the two partial beams. The partial beams propagate through beam conditioning lenses, are directed downwards onto a water-filled basin and made to intersect by two separate mirrors M2 and M3. For this model experiment, the dynamic airwater interface will represent the optical distortion. In order to generate capillary waves with a broad spectrum and of stochastic behaviour a water pump was chosen to generate a flow in the basin and as a consequence waves at the free water surface. For the fundamental investigations intended here it is sufficient that only one beam gets affected by the distortions. Hence, the application of an AO system in only one partial beam was enough. One partial beam was directed with M1 onto the deformable mirror DM. A small incident angle ( 10 ) was chosen to avoid - 5 -

6 an elliptical beam deformation. After running through the basin the beam was split by a prism beam splitter whose reflected partial beam was directed onto the Hartman-Shack wavefront sensor to measure the beam distortions caused by the fluctuating interface. The second partial beam without wavefront correction was guided directly into the basin. A glass plate was fixed on the water surface at the beam incident point to prevent the distortion of this beam. It is necessary that the plane of the actuators that is the plane where the deformable mirror adds a spatial varying phase shift to the light wave is optically mapped onto the plane of the distortion which is the plane where the water wave adds another spatial varying phase shift to the light wave. This is obviously comprehensible when looking at the tip/tilt: If the DM were placed directly over the water wave as the last optical element, it would not be possible to keep the measurement position (position of intersecting beams) as well as the beam angle constant at the same time for an arbitrary local tilt of the water wave. To account for the needed mapping a Keplerian telescope was placed behind the DM such that the DM and the water surface are located in the input and output focal plane of the telescope, respectively. The adjustment of the beams was done in such a way that the beam intersection (i.e. the measurement position) was located underneath the basin and the second beam splitter. Here, an optical chopper with a fixed pinhole was placed which rotated with constant circumferential speed. The pinhole rotated through the measurement volume in order to generate burst signals with a well-defined Doppler frequency thus acting as a velocity reference. Fig. 3 Experimental setup: Laser Doppler velocimeter with adaptive optics system implemented in one partial beam to correct for wavefront distortions. M: mirror, BS: prism beam splitter 2.4 Results Since the distortions in the considered experiment are of random nature, a characterisation of the measurement properties and the assessment of the wavefront correction can be performed best by means of statistical evaluations. Here we chose the interference contrast, the validation rate and the frequency uncertainty as figures of merit. As derived from the considerations in section 2.1, the appearance of skewed rays will affect the beam overlap. Hence, the visibility of the interference I I max min V (7) max I I min with I max and I min as the maxium and minimum Intensities of the modulation in the burst signal, respectively, - 6 -

7 can be used as a figure of merit. A poor modulation degree will also result in a low signal-to-noise ratio (SNR) and a low fringe visibility / interference contrast V. In standard LDV systems, an SNR or fringe visibility validation is commonly employed which discards signals from the statistics whose SNR or V does not exceed a predefined threshold. Therefore, the validation rate, i.e. the ratio of valid burst signals to the total number of bursts, can be used as a measure for a fully-developed interference fringe system as well. In the experiments, 1000 burst signals generated by the moving pinhole were recorded for each voltage setting of the water pump and also for the interface at rest (water pump at 0 V) and evaluated. The results for the mean interference contrast and the mean validation rate are shown in fig. 4 left as a function of the distortion amplitude. The interference contrast for the surface at rest is about 83 %. It decreases monotonically with increasing amplitude of the distortion to about 8 % for the maximum distortion amplitude of 222 µm. If the AO system is activated, the interference contrast is improved over the whole amplitude range. The maximum improvement occurs at medium distortion amplitudes, where the interference contrast rises from 22 % to 48 %. A similar behaviour can be seen at the validation rate which is displayed in fig. 4, right. It decreases from 100 % for the undistorted case exponentially to about 8 % for the highest distortion amplitude of the about 200 µm. With the wavefront correction applied, the validation rate is improved over the whole range. Again, the maximum improvement occurs for moderate distortion amplitudes: about 50 percentage points for a distortion amplitude of about 45 µm. Obviously, higher distortion amplitudes are more difficult to compensate. Fig. 4 Interference contrast (left) and rate of valid burst signals (right) at 10 % interference contrast threshold in dependence of the mean amplitude of the distortion, with and without wavefront correction by the AO system. Moreover, the mean velocity of the moving pinhole and the standard deviation were calculated from the 1000 burst signals that were taken for each amplitude value of the distortion. The default velocity of the rotating pinhole is of v= 3.14 m/s and a relative standard deviation of is achieved for the undistorted case, which is mainly limited by the stability of the rotational frequency as well as vibrations of the optical chopper. At around 220 µm distortion amplitude, the standard deviation rises up to about 2.5%. With the active AO system the relative uncertainty can be reduced over the whole range. At mean amplitudes of distortion of around 30 µm the uncertainty could be reduced by a factor of 2. For large distortions the AO system couldn t reduce the standard deviation significantly. Assuming a fixed measurement time, the uncertainty of the mean value of the measured velocity is still significantly improved since it depends on the amount of signals measured which is then proportional to the validation rate. It is important to note that a Mach Zehnder interferometer has an intrinsic cap of the standard deviation when distorted. This is due to the fact, that the beam envelope is limited. Assuming an ideal scattering particle, the overlap of the observation volume and the beam envelopes determines the amount of detected light for each beam. Strong tip/tilts induced by the water surface will lead to beam crossings outside of the observation volume (or skew rays) and therefore they will not be detected and therefore will not increase the standard deviation. On the other hand, randomly occurring good aligned beams will be detected, reducing variance. The same argument holds for defocus and higher Zernike terms. This way the measurement system automatically selects weak distorted signals

8 Furthermore we measured flow profile of the nozzle attached to the pump. The measured mean velocity with ± standard deviation v of the measured velocity distribution is shown in fig. 5, left. It includes virtual turbulence from the measurement system as well as the turbulence from the flow itself. The effect of the AO onto the standard deviation is fairly small: The averaged standard deviation for the uncorrected case (adaptive optics off) is around 9.5% larger than for the reference measurement (both beams decoupled from the distortion by glass plate). When comparing the corrected case (adaptive optics on) with the reference this reduces to 5.7%. The measurement time was fixed. This way the different situations: uncorrected, corrected and reference contain different amounts of valid measurement signals N proportional to their different validation rates. This directly shows up when calculating the confidence interval of the mean flow velocity at each position. Assuming normal distribution we get v k k. (8) N Where k is the corresponding quantile of the student s t-distribution. 2 k with k (size of 99% probability two sided confidence interval) is shown in fig. 54, right. In the uncorrected case the mean confidence interval is 2.13 times larger compared to the reference. This reduces significantly to a factor of 1.17 in the corrected case due to the higher measurement rate. Fig. 5 Left: mean velocity value ± standard deviation of the velocity distribution Right: 99% probability ( 2 with k ) confidence interval of the mean velocity k We simulated the measurement process with the help of the measured time dependent height function (see 2.2). We used random initial conditions of the measured fluctuating water surface and calculated the time dependent fringe system. Sampling the consecutive the different fringe systems results in one burst signal. This way we account for both summands in equation (1). The spatial derivatives of the water surface up to second order where calculated out of the temporal behavior as shown in equation (2). The optical propagation was done by means of the angular spectrum (Fourier transforming Helmholtz equation in the lateral spatial coordinates). For in detail analysis of the simulation see [Büttner2013]. As a result we saw that the water surfaces tip/tilt is the most important term for the mean interference fringe visibility and hence for the validation rate. In terms of the measurement uncertainty we saw that each investigated summand (height offset, tip/tilt, curvature) only gives a small contribution smaller than 0.3% each compared to about 2.5% when all effects occur simultaneously. The strongest contribution to the uncertainty occurs, if tip/tilt and curvature appear together. More defocus range as well as more tilt angle would reduce this covariance. The implementation of an adaptive lens might be a good choice, since it offers a larger tunable range of the focal length at the cost of tuning speed compared to microelectromechanical mirrors [Koukourakis2014]

9 3. Conclusions & Outlook The experiments revealed that adaptive optics is an appropriate tool to improve the properties of fluid flow measurement techniques. In this contribution we have performed a fundamental analysis of the effects of wavefront distortions on the measurement properties of a laser Doppler velocity which is based on a Mach- Zehnder interferometer. The optical distortion was represented by an air-water interface, hence having relevance at film flows, bubble flows or jet flows. The investigations confirmed that the measurement properties can be improved for all amplitudes of the distortions when using the AO system. At a distortion amplitude of 45 µm the validation could be raised over 50 percentage points from 28 % without wavefront correction to about 83 % with correction by the AO system. As an outlook, an LDV system equipped with two AO systems (one for each partial beam) will offer a full functionality for measuring in film flows or jet flows. Using the Fresnel reflex directly at the distorting surface to drive the AO algorithm would lead to only one necessary optical access. Since often only the lower order distortions need to be corrected, a tip/tilt mirror in conjunction with an adaptive lens would be sufficient to realize a simple, cost effective measurement system. The transfer of AO technique to an interferometric profile sensor with two fringe systems would introduce a much higher spatial resolution as has been recently demonstrated again [König2013], [Neumann2013]. The rapid progress of the required components makes the employment of AO an attractive extension for fluid flow measurement techniques. Hence, AO systems have at least a good potential to become a standard tool for flow measurements in situations that were hardly accessible by measurement before. References Abe Y, Yamamoto Y, Hyuga D, Aoki K, Fujiwara A (2007) Interfacial stability and internal flow of a levitated droplet, Microgravity Science and Technology 19(3-4): Burgmann S, Blank M, Wartmann J, Heinzel A Investigation of the effect of CO2 bubbles and slugs on the performance of a DMFC by means of laser-optical flow measurements, (2012) Energy Procedia 28: Büttner L, Leithold C, Czarske J (2013) Interferometric Velocity Measurements through a fluctuating Gas- Liquid Interface employing Adaptive Optics, Optics Express Vol. 21, 25: Hardy J.W (1998) Adaptive Optics for Astronomical Telescopes, ISBN: , Oxford University Press, New York Hyers R.W (2005) Fluid flow effects in levitated droplets, Meas. Sci. Technol. 16: Kalliadasis S, Ruyer-Quil C, Scheid B, Velarde M.G, (2012) Falling Liquid Films ISBN: (Print) (Online), Springer London König J, Tschulik K, Büttner L, Uhlemann M, Czarske J (2013) Analysis of the Electrolyte Convection inside the Concentration Boundary Layer during Structured Electrodeposition of Copper in High Magnetic Gradient Fields, Analytical Chemistry, Vol. 85, 6: Koukourakis N, Finkeldey M, Stürmer M, Leithold C, Gerhardt N.C, Hofmann M.R, Wallrabe U, Czarske J, Fischer A (2014) Axial scanning in confocal microscopy employing adaptive lenses (CAL), Optics Express, Vol. 22, 5: Liang J, Williams D, Miller D (1997) Supernormal vision and high-resolution retinal imaging through adaptive optics, J. Opt. Soc. Am. A, Vol. 14, 11:

10 Neumann M, Friedrich C, Kriegseis J, Grundmann S, Czarske J (2013) Determination of the phase-resolved body force produced by a dielectric barrier discharge plasma actuator, Journal of Physics D: Applied Physics, O'Brien S.B.G, Schwartz L.W, (2002) Theory and modeling of thin film flow, Encyclopedia of Surface and Colloid Sci: Roorda A, Romero-Borja F, Donnelly W.J, Queener H, Hebert T.J, Campbell M.C.W (2002) Adaptive optics scanning laser ophthalmoscopy, Optics Express Vol. 10, 9: Sommerfeld A (1950) Mechanics of Deformable Bodies (Lectures on Theoretical Physics), Academic Press Inc. New York Tao X, Azucena O, Fu M, Zuo Y, Chen D.C, Kubby J, (2001) Adaptive optics microscopy with direct wavefront sensing using fluorescent protein guide stars, Optics Letters Vol. 36, 17: Zhang Y, Cense B, Rha J, Jonnal R, Gao W, Zawadzki R, Werner J, Jones S, Olivier S, Miller D (2006) High-speed volumetric imaging of cone photoreceptors with adaptive optics spectral-domain optical coherence tomography. Optics Express Vol. 14, 10: Zhong Z, Petrig B, Qi X, and Burns S (2008) In vivo measurement of erythrocyte velocity and retinal blood flow using adaptive optics scanning laser ophthalmoscopy. Optics Express Vol. 16, 17: