Imaging-based flow measurement techniques, like particle image velocimetry (PIV), are vulnerable to time-varying distortions like refractive index inhomogeneities or fluctuating phase boundaries. Such distortions strongly increase the velocity error, as the position assignment of the tracer particles and the decrease of image contrast exhibit significant uncertainties. We demonstrate that wavefront shaping based on spatially distributed guide stars has the potential to significantly reduce the measurement uncertainty. Proof of concept experiments show an improvement by more than one order of magnitude. Possible applications for the wavefront shaping PIV range from measurements in jets and film flows to biomedical applications.
© 2016 Optical Society of America
Optical measurement techniques are to date the key to basic and applied investigations in fluid mechanics. Especially particle image velocimetry (PIV) and particle tracking velocimetry (PTV) are widely employed, as they enable non-invasive flow field measurements over a large viewing window [1–7]. Both PIV and PTV use particles to track the flow behavior. A thin light sheet illuminates the flow and a camera located perpendicularly to the light sheet acquires subsequent images at known times. While in PTV the movement of single particles is tracked, PIV analyses the particle displacement using the cross-correlation between the images. Both approaches at the end allow determining the flow velocity. Depth information can be obtained by scanning the illumination light sheet. In contrast, in micro PIV (µPIV) a large area of the flow is illuminated at once and depth information is provided by the depth-sectioning capabilities of a microscope objective. All of these techniques require accurate knowledge of the measurement volume to allocate the detected particle at the correct 3D coordinate [1–7]. However, optical distortions, e.g. due to refractive index fluctuations, introduced by temperature, pressure or concentration gradients, lead to an uncertain position assignment and to low-contrast particle images, which is accompanied by a strong increase of the position uncertainty, resulting in an increased velocity error.
While static distortions are deterministic and can be corrected easily via calibration measurements or additional data analysis [8, 9], the correction of time-varying distortions is elaborate. However, such wavefront distortions appear in a huge variety of applications. Volumetric distortions consist of a varying, inhomogeneous refractive index over an extended volume. These commonly appear as temperature gradients, e.g. in combustion or flame measurements [10, 11], as pressure gradients, e.g. in compression and expansion fronts or shock waves in compressible fluids  and as concentration gradients, e.g. in mixtures of gases, biological fluids or in electrolysis cells [13, 14]. Besides, there are also several applications, where the distortion is introduced by a fluctuating phase boundary, as occurring at water channels with an open surface , at multi-phase flows, such as bubble swarms in water , at flows behind complex-shaped interfaces, e.g. in levitated droplets , at flows alongside a phase boundary  or at film flows, such as a thin fluid film running down an inclined surface , just to name some examples. However, despite their broad spreading, the correction of time-varying distortions and their influence on PIV measurements have not been discussed in literature in detail [12, 20]. Software-based correction employing measurements with background oriented schlieren (BOS) was proposed . However, BOS is just usable for compensation of transparent distortions and has never been used for µPIV.
Adaptive optics (AO) originally known from astronomy , has the great potential to clear up information-containing light of any distorting effect. Adaptive optical setups employ spatial light modulators (SLM), like deformable mirrors (DM) or liquid crystal on silicon (LCoS) SLM. The greatest challenge for AO-correction is finding an appropriate phase or amplitude mask that compensates for the distortions. The approach to this task strongly depends on the desired application and the nature of the distortion, i.e. the structure, spatial frequency content and the amplitude. Generally, sensor-less and sensor-based approaches are distinguished. Sensor-less approaches are based on iterative optimization of the displayed mask. The iterations have to be fast enough, so that the corrected measurement can be performed in real time. Hence, for iterative AO mainly deformable mirrors are used, as these offer sufficient response times [22, 23]. But, DMs commonly just have a small number of pixels, with a relatively large pixel size, which limits the correctable spatial frequency content of the distortion and the overall applicability. Sensor-based approaches typically consist of an adaptive optical element, a sensor for measuring the distortions and a control unit that calculates the control parameters for the adaptive element. Hence, the AO system represents a closed-loop feed-forward control for the optical measurement system.
Digital optical phase conjugation (DOPC), a prominent sensor-based AO technique [24–26], has proved that adaptive optics has the potential to widen the applicability of several optical techniques. For example, DOPC enabled focusing light deep into highly scattering media, which was a milestone for biomedical imaging, as it was long thought that scattering is a fundamental limit. Furthermore, DOPC enabled focusing through highly scattering media by overcoming the diffusion barrier of scattered photons [27, 28]. The key for DOPC was carefully shaping the wavefronts incident on the sample using an SLM, employing LCoS technique, which exhibits a high spatial resolution. The knowledge about how to shape the wavefronts comes from reference light, named beacon or guide star, which is modulated by the distortion and enables recording a fingerprint of the acting distortion .
A variety of guide star approaches have been proposed up to now. But most of them have drawbacks as they are either based on invasively locating beads inside the sample that act as reference beacons  or, in case of ultrasound-based acoustooptic guide stars, require multiple optical/acoustic accesses and sophisticated setups . To be usable in flow measurements, guide stars should be non-invasive, like the TRACK (Time Reversal by Analysis of Changing wavefronts from Kinetic targets) approach, which uses the movement of particles themselves as guide stars . However, most of the guide star techniques aim at creating a focus inside a medium and are thus not appropriate for PIV because imaging-based flow field measurements require correction of an extended optical path that transfers the image.
Recently, we started analyzing distortion correction of aberrations in flow measurements based on laser Doppler velocimetry (LDV) [32–35]. The Fresnel guide star (FGS) technique was introduced and it was demonstrated, that just one optical access is enough to correct for the influence of a fluctuating air-water interface, as the analysis of the Fresnel reflex at the phase boundary contains all required information . However, the described approach is not usable for imaging-based techniques like PIV, as here spatially distributed information has to be obtained.
In this paper, we introduce a spatially distributed guide star technique for correction of µPIV measurements through phase boundaries and thin phase objects. We apply a sensor-based approach based on digital holography for phase sensing and a liquid crystal spatial light modulator for phase actuation. This technique can be categorized according to the guide star interaction with the distortion into transmission (TGS) and Fresnel guide star (FGS). We present a thorough experimental and theoretical characterization and analysis of the correction performance and describe the current technological and fundamental limitations of the techniques. Although, the approach can be used for both illumination and detection paths, we will concentrate on the correction of the detection path, as this is the most crucial part of a µPIV setup, as used here for experimental validation. Section 2 describes the proposed guide star techniques and reveals the theoretical framework. The setup for the TGS and experimental data are presented in Section 3. Section 4 contains the description of the FGS setup as well, as experimental and simulated data. Section 5 discusses the results and the limitations and gives an overview of possibilities to extend the approaches to correct volumetric, multi-layered distortions.
2. Concept of distributed guide stars
Most guide star-based techniques aim at focusing light into or through scattering or spatially diffusing medium. To be able to correct two-dimensional images, like occurring in PIV, a spatially resolved guide star has to be used, to track the optical path length change within the detection path. A reference status has to be defined priorly and the spatial light modulator is applied to compensate for the distorting changes and to reconstruct the reference status. The first challenge is finding an appropriate reference status, as in many real life applications there is no turn-on key for the aberrations, as in Lab environments. As here we discuss the influence of fluctuating phase boundaries, using time-averaging of the changing distortion may be one usable solution to find a reference. A general case is sketched in Fig. 1. A single phase boundary is located between the detecting setup and the measurement location, marked as depth-of-interest (DOI). The right part of Fig. 1 depicts a dislocated phase boundary. To enable correction, this optical path length change has to be traced.
In general, there are two possible guide star configurations. When the guide star interacts with the distortion as the sample light does, i.e. in transmission (Fig. 2), we call the guide star Transmission Guide Star (TGS). When the guide star interacts with the distortion from the opposite side as the sample light does, i.e. in reflection, we call the guide star Fresnel Guide Star (FGS). As here we give a general introduction, we at first neglect differences in propagation angles between sample light and guide stars.
Using the TGS for the example of Fig. 1, the reference phase and the distorted phase are obtained. The phase difference can be given as , where n1 and n2 are the refractive indices of the two media and d3(x,y) is the spatially distributed displacement of the boundary. If now the SLM is located in the detection path and the phase conjugate is displayed on the SLM, i.e. , the reference situation is reproduced and the measurement can be performed aberration-free, although the distortion is still present. The usage of the FGS is trickier, as the FGS measures the profile change from the opposite side of the phase boundary, as shown in Fig. 2(b). While the TGS directly measures the correct path length changes, the FGS just measures the surface change. Applying the FGS to measure the reference and the aberration one obtains for the reference and for the aberration. The factor 2 comes from the reflection geometry. As the influence of the distortion on the sample light is unchanged, no matter which guide star is used, the phase error to be corrected is still . The phase difference for the FGS amounts to .
As the Fresnel guide star just propagates in the medium with refractive index n1, the refractive index n2 has to be known to compensate for the phase distortion of the transmitting light correctly. Furthermore, in contrast to TGS it is not the phase conjugate that has to be displayed on the SLM, but the measured phase weighted by the phase factor cφ. Additionally, the double-passing of the path, due to reflection geometry has to be taken into account. We obtain Eq. (1):
3. Experiments using a transmission guide star
The µPIV setup used is sketched in Fig. 3. The test object is a straight micro channel with a square cross section (length of channel sidewall 500 µm) and a total channel length of about 25 mm. The entrance length of the flow was about 10 mm, ensuring a fully developed laminar flow with constant velocity. A 530 nm high power LED is used to illuminate a part of the micro channel in CW mode. Polystyrol particles of 3 µm diameter suspended in de-ionized water are used as tracer particles. A Nemesys syringe pump drives a constant flow of 0.01 µl/s. Light from the depth of interest (DOI) within the micro channel is collected using a microscope objective (20x, NA = 0.4). The depth of correlation, which defines the spatial resolution in axial direction, can be estimated to be approximately 30 μm . The field of view is approximately 600 x 600 µm, which means that the whole micro channel width is imaged. The sample light (red) is directed towards the LCoS SLM (HoloEye PLUTO) and imaged on the PIV camera. After a reference measurement, a distortion is located between the micro channel and the SLM. Now the sample light transmits through the distortion. The optical path length change induced by the distortion is traced by off-axis digital holography. A beam splitter is used to split the beam of a 532 nm laser into the object beam, which in this case is the TGS (green), and a reference beam (violet). The object beam path of the adaptive correction has partly a common path with the measurement path, so that the TGS passes the aberration exactly as the sample light does. The diameter of the laser beam used as the TGS is approximately 1 cm. The SLM, located in the object beam path, is imaged on a digital camera (Holo Cam in Fig. 3), where the guide star interferes with the reference beam, recording an off-axis digital hologram. The polarizing optics are necessary to fit the SLM polarization and to enable flexible control of the intensity ratios in both arms. The digital camera used for wavefront sensing has a pixel size of 4.4 µm, while the pixel size of the SLM amounts to 8 µm. As common in DOPC setups, the alignment between SLM and the wavefront sensing camera is very crucial . We employ the direct access of the SLM to the holography camera and display a calibration-rectangle on the SLM. This allows mapping the SLM pixels to the camera pixels. After recording the hologram and the reconstruction, the phase information is interpolated to the SLM pixel size. The phase information of the TGS, is reconstructed using the angular spectrum method . To correctly shape the wavefront, the recorded transmission guide star phase is conjugated and displayed on the SLM to correct for the distortions. The reference, distorted and the corrected measurements are performed subsequently.
3.2. Experimental results
At first, an undisturbed µPIV reference measurement is performed. An exemplary image is depicted in Fig. 4 on the left. Particles can easily be identified and the corresponding flow velocity profile in Fig. 5 shows a near parabolic velocity profile.
We now introduce a static distortion into the measurement path. In this example, the distortion is a translucent foil with a thickness of about 500 µm. The transmittance of the foil is approximately 80% and the transmitted light is scattered at an angle of 2°. As can be seen in the middle part of Fig. 4, the foil strongly blurs the particle images. The contrast and signal-to-noise ratio in the distorted image is decreased, and no particles are visible. This leads to a reduced cross-correlation peak, as is exemplarily depicted in Fig. 6. Despite the blurred image, the correlation-based evaluation of the particle displacement still enables evaluating this distorted measurement. The resulting flow profile is depicted in Fig. 5(a). As can be seen, the foil induces a reduction of the flow velocity, a slight deformation and a change of the smooth parabolic reference profile to a wavy distorted profile.
The velocity error, i.e. the deviation to the reference, is in the range of 25% [Fig. 5(b)]. The TGS samples the integral optical path length changes due to the distortion and the phase conjugate of the measured phase is displayed on the SLM. An exemplary image of the corrected measurement is plotted in Fig. 4 on the right. The particles are clearly visible again, however the contrast of the particles is still reduced. The corrected profile on the left of Fig. 5 (blue) is in very good agreement with the reference. The averaged velocity error is reduced to about 1%. The residual error can be explained by the non-ideal phase correction and by differences in the interaction angle between the guide star or the sample light and the aberration.
The impact of the distortion on the flow profile is explained in Fig. 7. The depth of interest (DOI) in all measurements is aligned to the middle of the micro channel, at which the local flow velocity is maximal. If now a distortion is inserted in the beam path, like e.g. a defocus aberration, this leads to an optical path length change, which dislocates the depth of measurement (DOM) from the DOI. As in µPIV a large volume of the micro channel is illuminated, a measurement can still be performed. However, the DOM shift will lead to measurements at the wrong axial position. This can be observed in a decrease of the flow velocity in the profiles in comparison to the reference measurement. Hence, this dislocation leads to an erroneous position assignment, which strongly increases the measurement uncertainty. Using the spatially resolved guide star the impact of the distortion on the measurement is detected and conjugated, so that the DOM shifts back to the DOI. If the distortion in the beam path consists of a rough phase boundary or a thin, rough phase-object, the resulting phase is speckled. This can be understood as local fluctuations of the measurement depth, which can also be observed in the wavy distorted flow profile in Fig. 5(a). The conjugated measured phase displayed on the SLM is depicted in Fig. 8. As can be seen, approximately 70% of the SLM pixels are used for correction.
The presented results prove that wavefront shaping using a TGS is appropriate to clear up distorted PIV measurements. If for example dispersion effects can be neglected, different wavelengths could be used for TGS and the sample light, or the TGS could excite fluorescence. This would enable to separate both beams and would allow for online correction. However, the TGS requires two optical accesses and a common path to the sample light. This limits the applicability of TGS for PIV at very low concentrations or PTV applications. Hence, it is beneficial to use the Fresnel guide star, which just requires one optical access, as it applies the Fresnel reflex at the distortion and does not depend on the particle concentration. This will be discussed in the next section.
4. Experiments using a Fresnel guide star
The µPIV setup using the FGS is sketched in Fig. 9. The only difference to the TGS setup of Fig. 3 is that now a quarter-wave plate combined with a polarizing beam-splitter (PBS) is used to split the beams. The PBS directs the laser light towards the distortion, where it is reflected. Due to the commonly reduced reflectivity of transparent or translucent media, the polarizing optics is required to split the intensities in the object and reference arms as required. Another half-wave plate is used to tune the polarization in the reference path to the polarization state of the object beam path. As described in section 2, the FGS is usable for measurements of phase boundaries. As a proof of principle, we use the convex part of a plano-convex lens with focal length of f = 500 mm as distortion. The flow in this measurement was set at 0.025 µl/s. The procedure for the measurements is the same as for the TGS. At first, a reference measurement is conducted without the distortion. Afterwards the distortion is introduced and a distorted and a corrected measurement are performed.
4.2. Experimental results
In order to enable tracking of the distortion with one optical access, the influence of the distortion on the transmitting light has to be corrected by measuring the reflection at the phase boundary, which in our example is the convex lens. However, as the FGS light does not pass the medium as the sample light does, the influence of the refractive index step at the boundary is not included in the measured phase. Hence, the refractive index has to be known or at least estimated to enable correction. In our example we use a BK-7 lens from Thorlabs, which has a refractive index of . The phase factor can be calculated as . In other words: the FGS measures approximately the fourfold curvature compared to the acting aberration that distorts the sample light. In our setup, this results in a too high spatial frequency content of the holograms which prohibited adequate spectral separation. Hence, we chose phase-shifting digital holography for phase reconstruction  as it uses the whole spatial bandwidth of the camera. The SLM was used to shift the phase of the object beam to acquire four phase shifted holograms. The resulting wrapped phase is unwrapped, weighted by the phase factor and interpolated to the SLM pixel size. Note, that in the case of FGS it is not the conjugate phase, but the weighted measured phase that has to be displayed for correction. The plano-convex lens is located in the object beam path slightly tilted, to obtain a spatial separation of the Fresnel reflex on the convex boundary and the flat backside of the lens. The distorted flow profile plotted in Fig. 10(a) shows the expected behaviour. The introduction of the defocus aberration into the setup leads to a shift of the DOM from the DOI in axial direction as described in the last section (Fig. 7). In addition, as the plano-convex lens is tilted, the shift of the DOM varies over the field of view resulting in a skewed lateral velocity profile. Reliable measurements are not possible for this case. The resulting velocity error reaches up to several ten percent [Fig. 10(b)]. Using the FGS for correction allows shifting the DOM back to the DOI, which reduces the average velocity error down to an acceptable level of about 3-4%. However, there is still a deformation of the corrected flow profile visible that results in slightly increased velocity errors near the micro channel walls. These errors are due to the imperfect phase correction, resulting due to the angle differences between the FGS beam and the sample light. Nevertheless, the correction using the FGS with just one optical access worked sufficiently good.
However, the major drawback of the FGS is that the refractive indices have to be known to weight the measured phase difference with the phase factor. In order to test the influence of mismatched phase factor, we replaced the micro channel by an USAF test chart and performed the measurement with the lens-distortion again. Exemplary results for different refractive index deviations are plotted in Fig. 11.
As can be seen, correction with a wrong phase factor results in a residual defocus error. We use the cross-correlation between the reference and corrected images with different phase factor deviations to quantify the quality of the correction with mismatched phase factors. The result is plotted in Fig. 12. The maximum of the correlation coefficient corresponds to the theoretically calculated phase factor. With increasing mismatch, the correlation coefficient drops nearly symmetrically. In this example, all wrongly chosen refractive indices lead still to an improvement of the measurement compared to the correlation coefficient obtained by using the distorted image. However, other distortions may be more vulnerable to such errors which could even lead to an increased measurement error when an erroneous correction is applied.
The residual defocus occurring for a refractive index deviation leads to a too small or too large shift of the DOM. For the PIV measurement this means, that the measurements are performed at the wrong axial position. Flow profiles are shown in Fig. 13(a) for a variety of refractive index deviations. The mean velocity error is smaller than 10% for a refractive index mismatch of ~5% [Fig. 13(b)]. This underlines the necessity to accurately estimate the refractive index. If an estimation is not possible, a combination of FGS with refractometry could be applied to measure the refractive indexes.
However, correction of a strong distortion, given by a rough phase boundary, using the FGS approach is more challenging. As described, FGS requires unwrapping and weighting of the measured phase. But light interaction with a rough surface will form a speckle field, where the phase relation between different speckles may not be known, complicating the unwrapping procedures. Consequently, for correct determination of the optical path length in such case, unwrapping has to be circumvented. One solution might be the use of two wavelength interferometry (TWI), that offers synthetic wavelengths with increased 2π unambiguity range [41, 42]. Exemplary simulated data are shown in Fig. 14 to visualize a possible procedure using TWI. A rough phase boundary between BK7 and air with maximum surface amplitude of 3 µm was simulated. To offer an adequate resolution we choose a synthetic wavelength of Λ≈16 µm, using λ1 = 532 nm and λ2 = 515 nm. The FGS with synthetic wavelength measures the optical path length change induced by the rough phase boundary in reflection [Fig. 14(a)]. The path length information is now weighted by the phase factor and used to calculate the correction map for the transmitting sample light of 532 nm [Fig. 14(c)]. After correction, the path length change induced by the rough phase boundary is compensated as plotted in Fig. 14(d). However, in experiments the speckles have to be adequately sampled both in lateral dimension and by the synthetic wavelength. This means, that the magnification of the rough surface has to be adjusted, so that each speckle corresponds to enough pixels, as wrapping has to be used. The synthetic wavelength and magnification thus have to be tuneable or a priori knowledge of the distortion properties is required.
Wavefront shaping guided by the TGS and FGS approaches improved the performance of µPIV in the presented proof-of-principle experiments by reducing the velocity uncertainty by more than one magnitude. However, there are limitations for both approaches. The main drawback of the presented setups is the LCoS spatial light modulator that limits the usage of the approaches to slowly varying distortions. However, the spatially distributed guide star techniques are not limited to LCoS SLMs and digital holography but may be implemented with other faster light modulators and sensors using e.g. ferroelectric modulators. The choice of the adaptive optical approach requires a priori knowledge of the distortion, in terms of occurring spatial frequencies, amplitudes and optical accesses.
The TGS is usable when two optical accesses are present and low particle concentrations are used, because enough guide star light has to pass the measurement volume without being affected by the particles. Refractive index distributions e.g. occurring for concentration or temperature gradients and fluctuating phase boundaries can be compensated using the TGS.
One advantage of TGS is, that correction is achieved by displaying the conjugate of the measured phase. The situation for FGS is more complicated, as the measured phase has to be weighted to enable correction. This requires unwrapping the phase, which can be challenging for rough samples and requires more sophisticated approaches based on TWI. As the profile of a disturbing phase boundary is measured in reflection, any profilometric technique may theoretically be used to measure the surface information.
For multilayered phase boundaries more sophisticated setups based on tomographic phase acquisition are required, as otherwise reflections at upper layers may disturb the phase measurement. This can be, for example, achieved using illumination with short coherence length or with a swept laser as described in [43–46]. The Fresnel reflex at the desired phase boundary can be selected by appropriately locating the coherence gate. The backscattered light interrogates the upper layers and enables recording the integral path length information. The FGS correction can be then performed for the selected layer. Both presented guide star techniques are not limited to flow measurements but may be applied in different biomedical as well as process engineering applications.
Imaging-based flow measurement techniques require accurate position assignment of the tracer particles. However, fluctuating phase boundaries or distortions located between the measurement volume and the camera lead to increased positioning and consequently to velocity errors. We show that wavefront shaping techniques based on spatially distributed guide stars have the potential to reduce these measurement errors. Two techniques are introduced and proof-of-concept experiments are presented. Both transmission and Fresnel guide stars proved to be adequate to compensate the impact of the distortion, enabling measurements through translucent media or disturbing phase boundaries. The measurement errors of the velocity were successfully reduced from several ten percent down to ≤ 3%. Especially the FGS has high potential, as it just requires one optical access. It is the nature of the distortion that enforces a certain approach for the adaptive system and hence leads to distortion specific limitations that are caused by the current technological limitations of spatial light modulators, like pixel size, pixel number or achievable frame rates. However, the expected technological progress will boost the achievable performances of digital optoelectronic devices, overcoming current limitations in the future.
Funding by a Reinhart Koselleck project (CZ 55/30) of German Research Foundation (DFG) and partial funding by the Leibniz Association within the Joint Initiative for research and innovation (SAW-2014-IFW-1) are gratefully acknowledged.
References and links
1. J. G. Santiago, S. T. Wereley, C. D. Meinhart, D. J. Beebe, and R. J. Adrian, “A particle image velocimetry system for microfluidics,” Exp. Fluids 25(4), 316–319 (1998). [CrossRef]
2. A. Ronald and J. Westerweel, Particle Image Velocimetry (Cambridge University, 2010).
3. M. Raffel, C. E. Willert, S. Wereley, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide, 2nd ed. (Springer, 2007).
4. J. Westerweel, G. E. Elsinga, and R. J. Adrian, “Particle image velocimetry for complex and turbulent flows,” Annu. Rev. Fluid Mech. 45(1), 409–436 (2013). [CrossRef]
5. J. Westerweel, “Fundamentals of digital particle image velocimetry,” Meas. Sci. Technol. 8(12), 1379–1392 (1997). [CrossRef]
6. H. G. Maas, A. Gruen, and D. Papantoniou, “Particle tracking velocimetry in three-dimensional flows,” Exp. Fluids 15(2), 133–146 (1993). [CrossRef]
7. A. A. Adamczyk and L. Rimai, “2D particle tracking velocimetry (PTV): Technique and image processing algorithms,” Exp. Fluids 6(6), 373–380 (1988). [CrossRef]
8. D. Reuss, L. David, M. Megerle, and V. Sick, “Particle-image velocimetry measurement errors when imaging through a transparent engine cylinder,” Meas. Sci. Technol. 13(7), 1029–1035 (2012). [CrossRef]
9. G. Minor, P. Oshkai, and N. Djilali, “Optical distortion correction for liquid droplet visualization using the ray tracing method: further considerations,” Meas. Sci. Technol. 18(11), L23–L28 (2007). [CrossRef]
10. B. Böhm, C. Heeger, R. L. Gordon, and A. Dreizler, “New perspectives on turbulent combustion: Multi-parameter high-speed planar laser diagnostics,” Flow Turbul. Combus. 86(3), 313–341 (2010). [CrossRef]
11. C. Willert, C. Hassa, G. Stockhausen, M. Jarius, M. Voges, and J. Klinner, “Combined PIV and DGV applied to a pressurized gas turbine combustion facility,” Meas. Sci. Technol. 17(7), 1670–1679 (2006). [CrossRef]
12. G. E. Elsinga, B. W. van Oudheusden, and F. Scarano, “Evaluation of aero-optical distortion effects in PIV,” Exp. Fluids 39(2), 246–256 (2005). [CrossRef]
13. T. Weier, C. Cierpka, J. Hüller, and G. Gerbeth, “Velocity measurements and concentration field visualizations in copper electrolysis under the influence of Lorentz forces and buoyancy,” Magnetohydrodynamics 42, 379–387 (2006).
14. J. König, K. Tschulik, L. Büttner, M. Uhlemann, and J. Czarske, “Analysis of the electrolyte convection inside the concentration boundary layer during structured electrodeposition of copper in high magnetic gradient fields,” Anal. Chem. 85(6), 3087–3094 (2013). [CrossRef] [PubMed]
15. G. Gomit, L. Chatellier, D. Calluaud, and D. Laurent, “Free surface measurement by stereorefraction,” Exp. Fluids 54(6), 1540 (2013). [CrossRef]
16. E. Schleicher, M. J. da Silva, S. Thiele, A. Li, E. Wollrab, and U. Hampel, “Design of an optical tomograph for the investigation of single- and two-phase pipe flows,” Meas. Sci. Technol. 19(9), 094006 (2008). [CrossRef]
17. Y. Abe, Y. Yamamoto, D. Hyuga, K. Aoki, and A. Fujiwara, “Interfacial stability and internal flow of a levitated droplet,” Microgravity Sci. Technol. 19(3-4), 33–34 (2007). [CrossRef]
18. A. E. Hosoi and J. W. Bush, “Evaporative instabilities in climbing films,” J. Fluid Mech. 442, 217–239 (2001). [CrossRef]
19. S. Kalliadasis, C. Ruyer-Quil, B. Scheid, and M. G. Velarde, Falling Liquid Films (Springer, 2012).
20. R. Schlüßler, J. Czarske, and A. Fischer, “Uncertainty of flow velocity measurements due to refractive index fluctuations,” Opt. Lasers Eng. 54, 93–104 (2014). [CrossRef]
21. R. Tyson, Principles of Adaptive Optics (CRC Press, 2010).
22. I. M. Vellekoop, A. Lagendijk, and A. Mosk, “Exploiting disorder for perfect focusing,” Nat. Photonics 4, 320–322 (2010).
23. M. J. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014). [CrossRef]
25. Y. M. Wang, B. Judkewitz, C. A. Dimarzio, and C. Yang, “Deep-tissue focal fluorescence imaging with digitally time-reversed ultrasound-encoded light,” Nat. Commun. 3, 928 (2012). [CrossRef] [PubMed]
26. J. W. Czarske, D. Haufe, N. Koukourakis, and L. Büttner, “Transmission of independent signals through a multimode fiber using digital optical phase conjugation,” Opt. Express 24(13), 15128–15136 (2016). [CrossRef] [PubMed]
27. D. Wang, E. H. Zhou, J. Brake, H. Ruan, M. Jang, and C. Yang, “Focusing through dynamic tissue with millisecond digital optical phase conjugation,” Optica 2(8), 728–735 (2015). [CrossRef] [PubMed]
32. J. Czarske and H. Müller, “Two-dimensional directional fiber-optic laser Doppler anemometer based on heterodyning by means of a chirp frequency modulated Nd:YAG miniature ring laser,” Opt. Commun. 132(5), 421–426 (1996). [CrossRef]
34. J. König, A. Voigt, L. Büttner, and J. Czarske, “Precise micro flow rate measurements by a laser Doppler velocity profile sensor with time division multiplexing,” Meas. Sci. Technol. 21(7), 074005 (2010). [CrossRef]
35. L. Büttner, C. Leithold, and J. Czarske, “Interferometric velocity measurements through a fluctuating gas-liquid interface employing adaptive optics,” Opt. Express 21(25), 30653–30663 (2013). [CrossRef] [PubMed]
36. H. Radner, L. Büttner, and J. Czarske, “Interferometric velocity measurements through a fluctuating phase boundary using two Fresnel guide stars,” Opt. Lett. 40(16), 3766–3769 (2015). [CrossRef] [PubMed]
37. M. G. Olsen and R. J. Adrian, “Out-of-focus effects on particle image visibility and correlation in microscopic particle image velocimetry,” Exp. Fluids 29(7), S166–S174 (2000). [CrossRef]
38. M. Jang, H. Ruan, H. Zhou, B. Judkewitz, and C. Yang, “Method for auto-alignment of digital optical phase conjugation systems based on digital propagation,” Opt. Express 22(12), 14054–14071 (2014). [CrossRef] [PubMed]
39. N. Koukourakis, T. Abdelwahab, M. Y. Li, H. Höpfner, Y. W. Lai, E. Darakis, C. Brenner, N. C. Gerhardt, and M. R. Hofmann, “Photorefractive two-wave mixing for image amplification in digital holography,” Opt. Express 19(22), 22004–22023 (2011). [CrossRef] [PubMed]
43. N. Koukourakis, V. Jaedicke, A. Adinda-Ougba, S. Goebel, H. Wiethoff, H. Höpfner, N. C. Gerhardt, and M. R. Hofmann, “Depth-filtered digital holography,” Opt. Express 20(20), 22636–22648 (2012). [CrossRef] [PubMed]