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Abstract
Complex diffusive scattering media pose significant challenges for light focusing as well as optical imaging to be implemented in practice. Recently, it has been demonstrated that the wavefront shaping technique can be applied to realize focusing and imaging through scattering medium. Here we report dynamic optical manipulation of particles through turbid media by employing the interleaved segment wavefront correction method, which is an improved genetic algorithm providing faster convergence speed and higher peak to background ratio. Manipulating micro-beads behind a scattering medium along both one and two dimensional predesigned trajectories in real time has been successfully demonstrated.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Focusing and imaging inside or behind turbid media, ranging from biology to atmospheric science, has always been a great challenge. This is due to the fact that scattering media such as biological tissues and atmosphere scatter light randomly and thus decrease the imaging quality dramatically. To address this issue, techniques such as adaptive optics have been developed to improve the imaging quality through the turbulent media [1–3]. However, such adaptive optical approaches are inefficient for highly turbid media, where the distribution of the light is severely disturbed during its propagation, leading to a speckle pattern in the imaging plane. To obtain a perfect focused spot or extract valid information behind a highly inhomogeneous medium, much efforts have been paid, and indeed imaging through scattering medium has been successfully achieved [4–8]. As an effective method, wavefront shaping technique provides a non-invasive tool for imaging through scattering medium, and improves the resolution and penetration depth fantastically [3,9]. Thanks to the novel optoelectronic device, namely spatial light modulator (SLM), the distortion of the wavefront can be quantified and compensated precisely. With the utilization of complex phase modulation, in situ aberration measurement and correction can be implemented to eliminate the scattering effects, which makes imaging through highly turbid and diffusive media possible [10]. Especially, in the field of biomedical optics, imaging depth and imaging quality have been limited by the scattering effect. To address this issue, wavefront shaping techniques relying on guide stars have been developed. So far, variety of guide stars including fluorescence, nonlinear particles, and photoacoustic feedback have been successfully applied to biomedical imaging. In particular, by using of nonlinear photoacoustic signal as a guide star enables controlling light in an entire volume [11]. The method not only improves the imaging contrast and resolution [12], but also achieves multi-focus focusing at the same time, which enables focusing and imaging inside or behind scattering media in three dimensions [13]. Recently, combining wavefront shaping with optical manipulations has been also verified, indicating the possibility of optical trapping through turbid media [14]. For optical manipulation, a tightly focused laser beam is highly desirable, and any imperfection could impact the trapping performance. Although researchers have demonstrated that the scattered light fields could be directly used for particle manipulation [15–17], which may relax the requirements of setup and sample preparations, such speckle “optical tweezers” suffer from limited optical power and less control over the particle motions. It has been shown that, based on the phase only SLM and an iterative optimization, the scrambled speckle can be refocused through the scattering medium [18–22]. Not only refocusing a point source but also imaging an object via the so-called “memory effect” [23] through a scattering medium have been demonstrated. Such recollection of scattered light is enabled by the algorithm that can dynamically adjust the wavefront. As a parallel optimal algorithm, genetic algorithm (GA) controls a large number of segments simultaneously, and has been widely used to yield a sharp focus through turbid media. In practice, the intensity of the refocused point relies on the dynamic range of the optical detector, and also the optimization speed is jeopardized by the relative large number of the segments. The aforementioned two shortcomings handicap the application of GA in particle manipulation through scattering media. In this report, we propose and demonstrate the application of an improved GA, named as interleaved segment correction (ISC) method [24], for optical manipulation, which provides fast convergence speed and high peak to background ratio (PBR) in comparison to the traditional GA. With the ISC method, we first construct tightly refocused light spots through a scattering medium, and then set the spots move through predesigned trajectories by utilizing the memory effect. With the refocused spots, capturing and manipulating micro-beads behind a scattering medium along both one and two dimensional trajectories are demonstrated.
2. Methods
2.1 Principle of interleaved segment correction (ISC) method
One of the efficient strategies for refocusing light through turbid media is the wavefront shaping method. In this work, we utilize the ISC method [24], which is an improved version of the traditional GA. The principle of the ISC can be explicitly explained as follows. Behind the turbid medium, according to the Huygens–Fresnel principle, the scattering field at the target is the coherent superposition of all wavelets, which can be expressed as:
where An and φn are the amplitude and phase of the n-th mode wavelets. tmn is the transmission matrix which describes the scattering property of medium. If the phase of each wavelet can be modulated by the SLM such that all wavelets are coherently superimposed at the target, the distorted light should be refocused after passing through the scattering medium. To achieve such coherent superposition, the incident wavefront is divided into a number of units whose phases can be accurately controlled by the SLM. By setting the intensity from the pixels of the CCD as a feedback, the focusing of the scattered light can be improved continuously through the iterations.In this work, we divide the pixel array of the SLM into 180 × 180 segments, and each segment contains 6 × 6 pixels, as shown in Fig. 1(a). All the 180 × 180 segments are divided into 9 interleaved groups [Fig. 1(b)], and each group consists of 60 × 60 segments. Instead of optimizing the 180 × 180 segments altogether in convention GA, we perform the GA for each group independently. For this case, 9 corrected phases will be acquired [Fig. 1(c)]. Then the final correction phase is obtained by merging the 9 independent correction phases [Fig. 1(d)]. Note that during the calculation of the correction phase of a specific segment, the phases of all other segments are maintained at zero. And the SLM can be divided into much more segments if higher correcting accuracy is required. However, for a larger number of segments, the parallel search feature of GA will be decreased, resulting a slower convergence of the algorithm. To achieve a reasonable tradeoff between the efficiency and optimizing quality, here we use 9 interleaved groups for correcting the wavefront distortion. In comparison to the traditional GA, the ISC method has the advantages of fast convergence speed and high peak to background ratio. Furthermore, the ISC method can significantly reduce the dynamic range requirement of the detector.
Fig. 1 Principle of the interleaved segment correction (ISC) method. (a) The pixel array of an SLM is divided into 180 × 180 segments, and each segment contains 6 × 6 pixels; (b) All segments are divided into nine interleaved groups, as marked by the numbers; (c) Each individual section is optimized in sequence, the optimized phase in each segment is labeled with different colors; (d) Final correction phase, which is obtained by merging the 9 independent correction phases.
2.2 Experimental setup
Figure 2 illustrates our experimental setup for demonstrations of refocusing of the scattered light and particle manipulation behind a scattering medium. A laser beam (λ = 532 nm) is first expanded through a reversed telescope (L1, f = 50 mm; L2, f = 150 mm), and then guided by a triangle reflector (M2) onto the SLM (1920 × 1080 pixels, pixel size 8μm, PLUTO Vis, HoloEye Inc., Germany). The SLM was relayed to the back aperture of the objective (Obj 1, 20X, NA = 0.6, Edmund Inc., USA) by a 4f-system (L3, f = 200 mm; L4, f = 200 mm). The scattering medium (S, cover glass coated with a thin layer of milk) is placed 3 mm in front of the Obj1. The optimized phase is loaded on the SLM to compensate the distortions and refocus the scattered light. Another objective (Obj2, 20X, NA = 0.45, Nikon Inc., Japan) along with a lens (L5, f = 200 mm) serve as an imaging system to obtain the information of the speckle field and provide feedback to the ISC method through a CCD camera (1280 × 960pixels, pixel size 3.75μm, 8 bit, DMK 23U445, The Imaging Source Inc., Germany). For the particle manipulation, we place a cuvette containing silica beads with diameter of 3 µm behind the scattering medium, and the manipulation process is also monitored through the Obj2, L5, and the CCD camera. The LED is used to provide illumination for monitoring the particle manipulation, and it is turned off during the refocusing optimization of the scattered light.
Fig. 2 Experimental setup for demonstrations of refocusing of the scattered light and particle manipulation behind a scattering medium. L: Lens, M: Mirror, SLM: Spatial light modulator, Obj: Objective lens, BS: Beam splitter, F: Filter. The inset displays the scattering medium S (cover glass coated with a thin layer of milk) and the cuvette containing particles (silica beads with diameter of 3 µm).
3. Experimental results
In order to evaluate the quality of the refocused scattering light for optical trapping, we start with a simple case, which is refocusing the random speckle to a single spot. As shown in Fig. 3, when the laser beam passed through the milk-coated cover glass without any correction, the scattered light represents a typical speckle pattern [Fig. 3(a)]. After the correction phase [Fig. 3(c)], which is obtained after about 900 optimization iterations, is loaded into the SLM, a tightly focused beam can be achieved [Fig. 3(b)]. The sharp focused spot has a PBR about 1910, which should be able to trap micro-beads. (Note that the PBR is defined and calculated through the ratio of the intensity of the refocused spot to the average intensity of the background.) To verify this, we place the cuvette containing silica beads at the focal spot behind the scattering medium, and monitor the particle trapping process. The results are depicted in Figs. 3(f)-3(i), and the corresponding video is provided in the supplementary information (see Visualization 1). From the results, we can see that a particle is captured when it moves to the focal point, and eventually moves to a stable position corresponding to the reshaped beam. Actually, refocusing the speckle into multiple spots with the proposed method is also feasible. As an example, we generate three points behind the scattering medium simultaneously. The space between the two adjacent points was set to be about 8 µm. The results are displayed in Figs. 3(d) and 3(e), where the three focal points originated from the speckle are shown in Fig. 3(d), and the corresponding optimized correction phase is shown in Fig. 3(e). In Fig. 3(d), the three focused spots have PBR values of 592, 674 and 680 from left to right, respectively. Figure 3(j) displays the multiple particle trapping results with the refocused multi-spot. This concludes that the proposed ISC method indeed can be used for optical manipulation behind a scattering medium.
Fig. 3 Experimental results for refocusing scattered light and trapping particles through a scattering medium by using the ISC method. (a) The speckles behind the scattering medium without phase correction; (b) Refocused scattered light with a correction phase after 900 optimization iteration; (c) The optimized phase pattern; (d) Refocusing 3 points simultaneously through the scattering medium; (e) The corresponding optimized phase pattern for refocusing the scattering light into 3 spots; (f)-(i) Trapping a bead through scattering medium by using the refocused beam, where the white triangle marks the focal point of the recollected scattered light (see Visualization 1); (j) Capturing three beads simultaneously through the scattering medium (Scale bar: 10 µm).
As well known, holographic optical tweezers can be used not only for particle trapping, but also for manipulation along different trajectories. Next, we shall demonstrate that the ISC method can be combined with holographic optical tweezers to manipulate micro particles behind scattering media along various predefined trajectories. Such manipulations are enabled by the optical memory effect of the random scattering media, which ensures that the wavefront correction method remains valid for tilted and even shifted optical scattering fields [22]. In order to achieve particle manipulation behind a scattering medium, on the top of the optimal correction phase [e.g., Fig. 3(c)], we add a blazed grating phase, the period of which is determined by
By adjusting the parameters k1 and k2, the period of the grating which defines the position of the focused point can be changed at ease. Therefore, the trapped particles can be manipulated along different trajectories. By setting k2 = 0 and continually changing k1, the corresponding results are shown in Fig. 4, which depicts the time resolved particle motion, and the dotted and solid circles marks the starting and the current position of the particle at that moment along the direction marked by the white dashed arrow. The corresponding video is shown in supplementary information (see Visualization 2). As can be seen from the results, we have successfully achieved particle manipulations behind a scattering medium along one dimension with a distance larger than 20 microns.Fig. 4 Experimental results of manipulating a silica bead through a scattering media in a one dimensional trajectory. (a)-(e) display the time resolved particle manipulation process (see Visualization 2), where the dotted and solid circles indicate the starting and current positions of the silica bead, and the dashed arrow points the particle moving direction. (Scale bar: 10 µm).
Similarly, by changing the phase map loaded in the SLM with a two dimensional blazed grating phase, the movement of the focused point and thus the trajectory of the trapped particle can be to precisely controlled in real time. Figure 5 shows the corresponding experimental results, in which Figs. 5(a)-5(e) and Figs. 5(f)-5(j) illustrate particle manipulations along a square and a circular trajectory, respectively. For the circular trajectory case, the radius of the motion is about 10 microns, and for the squared one, the motion length at each side is about 10 microns. The corresponding video is shown in supplementary information (see Visualization 3 and Visualization 4). The experimental results clearly demonstrate the feasibility of the holographic particle manipulations behind scattering media with the ISC method. The approach can be readily extended to particle manipulation along an arbitrary predesigned trajectories. We point out that, in the proposed method, not only the correction of the wavefront distortion due to scattering can be achieved, but also the spherical aberration of the optical system can be eliminated in the optimization process.
Fig. 5 Experimental results of manipulating silica beads through a scattering media along two dimensional trajectories. (a)-(e) and (f)-(j) display the time resolved particle motion along a rectangular and circular trajectory(see Visualization 3 and Visualization 4), respectively. The white arrow indicates the moving direction of the trapped bead, and the dotted line traces the trajectory of the bead. (Scale bar: 10 µm).
4. Discussion
Since the particle manipulations reported here are greatly depending on the memory effect of the scattering medium, it is necessary to evaluate the effective range of the memory effect in our experiment. By changing the period of the blazed grating overlaid on the optimal phase, we measure the intensity of the spot at different positions, which is plotted in Fig. 6(a). The normalized focusing intensity as a function of the distance away from the central optical axis is shown in Fig. 6(b). The blue dots represent experimental data points, whereas the red line is the fitting curve by using the theory formula [25,26]:
where is the focusing intensity, k0 is wave vector, θ is the angle difference from the original position, and L is the effective thickness. It can be seen that the intensity of the focal spot decreases as it moves away from the original position. Although the intensity is lower at a relative long distance from the origin, the profile of the focused point is still well preserved due to the memory effect. From the data shown in Fig. 6(b), we can calculate the full-width at half-maximum (FWHM) of the curve to be about 45 μm. In our experiment, the focal point is shifted within 20 microns, and therefore the performance of particle manipulation is not much influenced by the range of the memory effect. From Eq. (3), we can see that the memory effect of the scattering medium mainly depends on the factors of the wave vector and the effective thickness of the scattering medium. Therefore, for a specific scattering medium, the memory effect is definitive, which is not affected by the imaging objective and the speckle grain size. We point out that the discrepancy between the experimental data and the fitting curve is mainly due to the thickness non-uniformity of the scattering medium, which was prepared manually in our experiment.Fig. 6 Experimental evaluation of the range of the memory effect. (a) Focused scattering light at different blazed grating phase; (b) The normalized light intensity of the focal point corresponding to (a) as a function of the distance shifted from the central position.
In this study, there are two ways to generate multiple points behind the scattering medium. One easy and quick way is to use the GA algorithm to generate a multi-focusing hologram (CGH method), and then superimpose it to the optimized phase. Although the multiple focal points can be easily generated, the approach relies on the memory effect, which will suffer from the non-uniform peak intensity, as shown in Fig. 6. For this reason, in our experiment, we have directly optimized multiple focal points with the ISC method, as shown in Figs. 3(d), 3(e) and 3(j). We set the intensity of three points as the target on the CCD, rather than a single point, and the calculation of the fitness value I was determined by Equation (4).
where I1, I2, and I3 represent the light intensity on each focal point. The comparison of the multi-point results from the two different schemes is shown in Fig. 7. From the intensity profiles plotted in Fig. 7 (c), one can easily see that the intensity uniformity of the multiple focal points from direct optimization is much better from CGH approach due to the absence of memory effect.Fig. 7 Comparison of two different approaches for generating multiple focal points behind the scattering medium. (a) Result by superimposing a multi-focusing phase hologram and the optimized phase (CGH); (b) Result by directly optimizing multiple focal points with the ISC method (3 Points); (c) Intensity profiles along the white dashed lines in (a) and (b).
5. Conclusion
We have demonstrated particle manipulations through scattering media by employing the ISC method. With the refocused scattering light, capturing and manipulating micro particles behind a scattering medium in both one and two dimensions have been successfully realized in real time. Further using SLMs with high refreshing rate and high efficiency algorithms, our approach may be applied for dynamic turbid media. Our method may find important applications in biomedical imaging and other related fields.
Funding
National Natural Science Foundation of China (NSFC) (11574389, 61705256, 11704405 and 81427802)
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