Optically trapped particle dynamic responses under varying frequency sinusoidal stimulus

Tan Xu, Qingchuan Zhang, Shangquan Wu, Zhaoxiang Jiang, Xiaoping Wu

Optical tweezers have become indispensable and powerful micro-manipulation tools and acute force probes in biomedical fields. Therefore, calibrating the optical trap is essential for precise force measurements in biomolecular interactions. Currently, however, mainstream calibration methods mainly focus on analyzing nanometer level Brownian motions of trapped particles. There is thus an urgent need to investigate trapped particle dynamic processes in slightly large range to address practical situations for the biological application of optical tweezers. This paper proposes a varying frequency sinusoidal excitation method to probe trapped particle responses and develops a mathematical model to extract trap stiffness. Experimental results revealed that the proposed method achieved significantly lower relative error ( < 5%) even when particle size or laser power varied, and that the excitation frequency didn’t have much impact on trap stiffness. Thanks to its simplicity, effectiveness and robustness, our method provides an ideal candidate for further picoNewton force measurement studies for dynamic interactions in biomedical applications.

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Axial displacement calibration and tracking of optically trapped beads

Guoteng Ma, Chunguang Hu, Shuai Li, Xiaoqin Gao, Hongbin Li, Xiaotang Hu

High-precision axial displacement tracking of trapped beads is an indispensable feature of optical tweezers in advanced single-molecule studies. Here, we demonstrate an alternative method that enables axial calibration and tracking to be carried out on the same sample to avoid unnecessary errors. This method works by applying a dynamic force balance on a bead trapped between a piezoelectrically driven glass slide and an optical trap; in this configuration, the bead can be stopped precisely in different positions and imaged by a camera. A simple gradient algorithm is used to process the images into calibration data. After optimization of the calibration method and samples, our method exhibited better than 5 nm experimental axial resolution, with a measurement range of +/-500 nm around the objective focus at video speed. Moreover, for the first time, the deviation of the focusing plane in dual-trap optical tweezers was measured. We confirmed the axial deviation between two optical traps in our setup to be ~10 nm, corresponding to a force spectroscopy gage error of ~1 pN. This approach offers a favorable solution for in-use setup updating, as it can be seamlessly integrated into any optical tweezers system without requiring new hardware updates.

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Real-time measurement of three-dimensional morphology of blood cells in batches by non-orthogonal phase imaging

Hao Han, Yuanyuan Xu, Jingrong Liao, Shuangshuang Xue, Yawei Wang

In order to overcome the shortcoming of traditional tomography requires the vast amount of data and the limitation of intersection angle between two beams existed in a microscope objective to realize the real-time detection of three-dimensional (3D) morphological distribution of blood cells in batches, a method of reconstructing cell substructure with only two non-orthogonal phases is proposed in this paper. In this work, an optimized maximum entropy tomography (MET) algorithm is used for rapid 3D reconstruction which requires less phase information from non-orthogonal directions. Moreover, two phase images can be obtained simultaneously by the phase imaging system combined with flow cytometry and optical tweezers (OT). We perform simulations of two types of cell models and experiments of red blood cell (RBC), thrombocyte and lymphocyte. Results demonstrate this method is of great significance for 3D morphological analysis of blood cells in the field of clinical diagnosis or even life sciences.

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Optical trapping Rayleigh particles with a twist effect

Yao Zhang, Haoran Yan, Daomu Zhao

We theoretically and numerically investigate the focusing properties and the radiation forces produced by a focused rotating anisotropic generalized multi-Gaussian Schell model (RAGMGSM) beam. We find that for different parameters at the trapped plane, the intensity distribution would evolve into an elliptical dark hollow or elongated Gaussian beam profile. Compared to the focal plane, the trapped plane has an axial displacement due to the twist effects. Further, we demonstrate that two types of particles at different positions of the trapped plane can be trapped and rotated simultaneously by such a focused beam. Moreover, the influences of the beam index M, the coherence width δ, and the twist factor u on the radiation forces is elucidated respectively. The limits of each parameter for stability of optical trapping under a certain condition are explicitly discussed.

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Research on the special bottle beam generated by asymmetric elliptical Gaussian beams through an axicon-lens system

Zhikun Yang, Xinglei Lin, He Zhang, Yingtian Xu, Liang Jin, Yonggang Zou, Xiaohui Ma

A special bottle beam was obtained by shaping the elliptical Gaussian beam through an axicon optical system. When elliptical Gaussian beams have a different eccentricity (σ = 0, 0.3, 0.6, 0.9), the optical field distribution after axicon and the focusing lens was investigated. By comparison with a circular Gaussian beam, this asymmetry leads to the formation of a non-diffracting beam from a quasi-Bessel beam characteristic to a quasi-Mathieu beam characteristic after the incident axicon. At the same time, the bottle beams produced by the asymmetric light source incident on the axicon-lens system showed changes in the front and rear sides. In addition, the variation of the diffraction spot in the optical space region on the bottle beam axis was also analyzed. On this basis, a hollow light spot tweezer with “quasi-Pearcey beam handle” was obtained, which is expected to expand the application of particle trapping operation.

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Double-arm optical tweezer system for precise and dexterous handling of micro-objects in 3D workspace

Yoshio Tanaka

Double-arm manipulators are unfamiliar as equipment used in microscopic work in biomedical laboratories, whereas they are prevalent in factory automation and humanoids. For non-contact micromanipulation in three-dimensional (3D) workspaces, we propose and design a double-arm optical tweezer system that can easily exchange two types of end-effectors (i.e., optical landscapes for laser trapping) with a focus tunable lens and a microlens array. With a time-shared scanning approach under interactive personal computer (PC) mouse controls, the system can perform the precise and dexterous handling of micro-objects in a 3D workspace. As a proof of concept, we demonstrate the two-dimensional (2D) and 3D dexterous handling of microbeads in the motions of solving puzzle rings. We also demonstrate the precise and periodic patterning of microbeads for massive dynamic arrays. This double-arm system can be applied with versatile tools used for various non-contact micromanipulations in the biomedical field and for dynamic arrays in single cell and 3D biology.

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Trapping two types of particles using a focused partially coherent modified Bessel-Gaussian beam

Meiling Duan, Hanghang Zhang, Jinhong Li, Ke Cheng, Gao Wang, Wen Yang

Using the extended Huygens-Fresnel principle and Rayleigh scattering regime, the analytical expressions for the intensity and radiation forces of a focused partially coherent modified Bessel-Gaussian (MBG) beam have been derived, and used to study the optical trapping effect of the focused partially coherent MBG beams acting on dielectric sphere with different refractive indices. The results show that the focused partially coherent MBG beam with m = 0 cannot capture the low index of refraction particles, but can trap the high index of refraction particles. The focused partially coherent MBG beam with m ≥ 1 can trap the high index of refraction particles to a ring on the focal plane, and simultaneously capture the low index of refraction particles to z-axis. When the topological charge m increases, the radiation force decreases while the transverse trapping range increases for low and high index of refractive particles. Besides, larger the value of the spectral degree of coherence ξ is, the easier the two types of particles are trapped by the focused partially coherent MBG beam. Trapping stability is also analysed. The obtained results are useful for analysing the trapping efficiency of focused partially coherent MBG beam applied in micromanipulation and biotechnology.

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Two-laser optical tweezers with a blinking beam

Weronika Lamperska, Jan Masajada, Sławomir Drobczyński, Paweł Gusin

We report on a two-laser holographic optical tweezers setup and present its two major advantages over single-laser one. First, the trap stiffness of a weak trapping beam can be measured with a considerable accuracy. Second, a novel method of examining local viscosity of fluid is proposed. Both measurements are performed based on forcing the oscillations of a microscopic polystyrene bead placed between two optical traps. The two beams are generated by separate laser sources and therefore their trapping power can vary. Moreover, a stronger trap ‘blinks’, modulated by an electronic shutter. The blinking frequency can be precisely adjusted to the experimental conditions, which results in high accuracy of the measurements.

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Rotation of single live mammalian cells using dynamic holographic optical tweezers

Bin Cao, Laimonas Kelbauska, Samantha Chan, Rishabh M. Shetty, Dean Smith, Deirdre R. Meldrum

We report on a method for rotating single mammalian cells about an axis perpendicular to the optical system axis through the imaging plane using dynamic holographic optical tweezers (HOTs). Two optical traps are created on the opposite edges of a mammalian cell and are continuously transitioned through the imaging plane along the circumference of the cell in opposite directions, thus providing the torque to rotate the cell in a controlled fashion. The method enables a complete 360° rotation of live single mammalian cells with spherical or near-to spherical shape in 3D space, and represents a useful tool suitable for the single cell analysis field, including tomographic imaging.

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Clad photon sieve for generating localized hollow beams

Yiguang Cheng, Junmin Tong, Jiangping Zhu, Junbo Liu, Song Hu, Yu He

A novel photon sieve structure called clad photon sieve is proposed to generate localized hollow beams and its design principle and focusing properties are studied. The clad photon sieve is composed of the internal zone and external zone with pinholes being positioned on the dark zones. Pinholes in the internal zone and in the external zone give destructive interference to the focus, leading to localized hollow beams being generated on the focal plane. Focusing properties of clad photon sieve with different focal lengths, zone numbers and modulation factors are also studied by theoretical calculations, numerical simulations and experiments, showing that the central dark spot size can be controlled by the focal length and rings number, and the intensity of the central dark spot varies with different modulation factors related with the internal zone and the external zone. This photon sieve can be useful for trapping and manipulating of particles and cooling of atoms.

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Optical force on diseased blood cells: Towards the optical sorting of biological matter

Juan Sebastian Totero Gongora, Andrea Fratalocchi

By employing a series of massively parallel ab-initio simulations, we study how optical forces act on biological matter subject to morphological disease. As a representative case study, we here consider the case of Plasmodium falciparum on red blood cells (RBC) illuminated by a monochromatic plane wave. Realistic parameters for the geometry and the refractive index are then taken from published experiments. In our theoretical campaign, we study the dependence of the optical force on the disease stage for different incident wavelengths. We show that optical forces change significantly with the disease, with amplitude variation in the hundreds of pN range. Our results open up new avenues for the design of new optical systems for the treatment of human disease.

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Substrate-dependent cell elasticity measured by optical tweezers indentation

Muhammad S. Yousafzai, Fatou Ndoye, Giovanna Coceano, Joseph Niemela, Serena Bonin, Giacinto Scoles, Dan Cojoc

In the last decade, cell elasticity has been widely investigated as a potential label free indicator for cellular alteration in different diseases, cancer included. Cell elasticity can be locally measured by pulling membrane tethers, stretching or indenting the cell using optical tweezers. In this paper, we propose a simple approach to perform cell indentation at pN forces by axially moving the cell against a trapped microbead. The elastic modulus is calculated using the Hertz-model. Besides the axial component, the setup also allows us to examine the lateral cell–bead interaction. This technique has been applied to measure the local elasticity of HBL-100 cells, an immortalized human cell line, originally derived from the milk of a woman with no evidence of breast cancer lesions. In addition, we have studied the influence of substrate stiffness on cell elasticity by performing experiments on cells cultured on two substrates, bare and collagen-coated, having different stiffness. The mean value of the cell elastic modulus measured during indentation was 26±9 Pa for the bare substrate, while for the collagen-coated substrate it diminished to 19±7 Pa. The same trend was obtained for the elastic modulus measured during the retraction of the cell: 23±10 Pa and 13±7 Pa, respectively. These results show the cells adapt their stiffness to that of the substrate and demonstrate the potential of this setup for low-force probing of modifications to cell mechanics induced by the surrounding environment (e.g. extracellular matrix or other cells).

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Living cell manipulation in a microfluidic device by femtosecond optical tweezers

Yan Li, Zhongyi Guo, Shiliang Qu

We have realized cell sorting and manipulation in a fabricated microfluidic device by a self-constructed femtosecond optical tweezer efficaciously. The used microfluidic device with two micro-pools inside silica glass is fabricated by water-assisted femtosecond laser ablation and subsequent heat treatment. After the heat treatment, the diameter of the fabricated microchannels could be reduced significantly and the internal surface of the device could also be made much smoother comparatively, which was crucial for the subsequent experiments of living cell manipulation and cell sorting by using femtosecond optical tweezers because of the optical beam quality required. Our experimental results show that we can manipulate cells very easily by our self-constructed femtosecond optical tweezer, which demonstrates that the incorporation of the microfluidic device and the femtosecond optical tweezer is accessible and practical for the micromanipulation experiments, such as cell sorting and manipulation.

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Investigation on specific solutions of Gerchberg–Saxton algorithm

Pasquale Memmolo, Lisa Miccio, Francesco Merola, Antonio Paciello, Valerio Embrione, Sabato Fusco, Pietro Ferraro, Paolo Antonio Netti

The most popular method used to generate the Computer Generated Holograms (CGH) is the Gerchberg–Saxton (GS) algorithm. GS computes an approximation of the desired beam shape, and consequently, some distortions may arise. Although many algorithms have been proposed, exact methods to overcome the problem completely do not yet exist. Here we show, for the first time to best of our knowledge, that in some specific configurations exact solutions of the GS algorithm can be achieved so as to produce a limited number of light intensity spots in a clean array. The basic concept is described and both numerical as well as experimental implementations are provided.

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Simultaneous trapping of low- and high-index microparticles by using highly focused elegant Hermite-cosh-Gaussian beams

Zhirong Liu, Kaikai Huang, Daomu Zhao

The analytical expression for the propagation of elegant Hermite-cosh-Gaussian (EHCHG) beams through a paraxial ABCD optical system is derived and used to study the radiation forces produced by highly focused EHCHG beams acting on a Rayleigh dielectric particle. Owing to the characteristics of this kind of beams our analysis shows that it can be expected to simultaneously trap and manipulate dielectric spheres with low-refractive index at the focal point, and particles with high-refractive index nearby the focal point. Finally, the stability conditions for effective trapping and manipulating particles by this kind of focused beams are discussed.
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A novel video-based microsphere localization algorithm for low contrast silica particles under white light illumination

O. Ueberschär, C. Wagner, T. Stangner, C. Gutsche, F. Kremer

On the basis of a brief review of four common image recognition algorithms for microspheres made of polystyrene or melamine resin, we present a new microsphere localization method for low-contrast silica beads under white light illumination. We compare both the polystyrene and silica procedures with respect to accuracy and precision by means of an optical tweezers setup providing CMOS video microscopy capability. By that we demonstrate that our new silica algorithm achieves a relative position uncertainty of less than ±1 nm for micron-sized microspheres, significantly exceeding the precision of the other silica approaches studied. Second, we present an advancement of our single microsphere tracking method to scenarios where two polystyrene, melamine resin or silica microspheres are in close-to-contact proximity. While the majority of the analysis algorithms studied generate artefacts due to interference effects under these conditions, we show that our new approach yields accurate and precise results.

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Focusing of concentric piecewise vector Bessel–Gaussian beam

Jinsong Li, Ying Fang, Shenghua Zhou and Youxiang Ye

The focusing properties of a concentric piecewise vector Bessel–Gaussian beam are investigated in this paper. The beam consists of three portions: the center circular portion and outer annular portion are radially polarized, while the inner annular portion is generalized polarized with tunable polarized angle. Numerical simulations show that the evolution of focal pattern is altered considerably with different Bessel parameters in the Bessel term of the vector Bessel–Gaussian beam. The polarized angle also affects the focal pattern remarkably. Some interesting focal patterns may appear, such as two-peak, dark hollow focus; ring focus; spherical shell focus; cylindrical shell focus; and multi-ring-peak focus, and transverse focal switch occurs with increasing polarized angle of the inner annular portion, which may be used in optical manipulation.

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Tunable gradient force of hyperbolic-cosine–Gaussian beam with vortices

Xiumin Gao, Zhuo Li, Jian Wang, Lingling Sun and Songlin Zhuang

Gradient force plays an important role in optical tweezers technique. In this paper, the tunable gradient force in focal plane of the hyperbolic-cosine–Gaussian (ChG) beam is investigated numerically. The ChG beam contains one spiral vortex and one non-spiral vortex. Simulation results show that the gradient force distribution can be altered considerably by decentered parameters of ChG beam, topological number of the spiral vortex, and vortex parameter of the non-spiral vortex. Many novel gradient force patterns can occur, which means corresponding optical traps may come into being, including ring optical trap, multiple-point trap pattern, line optical trap, rectangle trap pattern, and rhombus trap pattern. In addition, force pattern evolution principle may also differ significantly.

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