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Research Papers

Using GPUs for Realtime Prediction of Optical Forces on Microsphere Ensembles

[+] Author and Article Information
Sujal Bista

Institute for Advanced Computer Studies,
Department of Computer Science,
University of Maryland,
College Park, MD 20742
e-mail: sujal@cs.umd.edu

Sagar Chowdhury

Research Assistant
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: sagar353@umd.edu

Satyandra K. Gupta

Professor
Fellow of ASME
Institute for Systems Research,
Department of Mechanical Engineering,
University of Maryland,
College Park, MD 20742
e-mail: skgupta@umd.edu

Amitabh Varshney

Professor
Institute for Advanced Computer Studies,
Department of Computer Science,
University of Maryland,
College Park, MD 20742
e-mail: varshney@cs.umd.edu

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received February 2, 2013; final manuscript received February 19, 2013; published online April 25, 2013. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 13(3), 031002 (Apr 25, 2013) (10 pages) Paper No: JCISE-13-1017; doi: 10.1115/1.4023862 History: Received February 02, 2013; Revised February 19, 2013

Laser beams can be used to create optical traps that can hold and transport small particles. Optical trapping has been used in a number of applications ranging from prototyping at the microscale to biological cell manipulation. Successfully using optical tweezers requires predicting optical forces on the particle being trapped and transported. Reasonably accurate theory and computational models exist for predicting optical forces on a single particle in the close vicinity of a Gaussian laser beam. However, in practice the workspace includes multiple particles that are manipulated using individual optical traps. It has been experimentally shown that the presence of a particle can cast a shadow on a nearby particle and hence affect the optical forces acting on it. Computing optical forces in the presence of shadows in real-time is not feasible on CPUs. In this paper, we introduce a ray-tracing-based application optimized for GPUs to calculate forces exerted by the laser beams on microparticle ensembles in an optical tweezers system. When evaluating the force exerted by a laser beam on 32 interacting particles, our GPU-based approach is able to get a 66-fold speed up compared to a single core CPU implementation of traditional Ashkin's approach and a 10-fold speedup over the single core CPU-based implementation of our approach.

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Figures

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Fig. 1

In an optical tweezer setup, a Gaussian laser beam is converged by a convex lens (objective lens of a microscope) to a focal point which is used for trapping microparticles. To create multiple optical traps, the laser beam is split into multiple-beams using a diffraction grating. Diagram courtesy of [8].

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Fig. 2

An illustration of the optical tweezers system. A laser beam with a Gaussian-based intensity distribution is converged into a focal point with the help of a convex lens. The figure shows laser beam trapping microparticles at the focal point.

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Fig. 3

When an optical trap is placed close to a microparticle, it pulls the particle towards the focal point. The images above captured using the imaging device in the optical tweezers system show a microparticle moving into a trap.

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Fig. 4

Diagram showing the simplified ray-optics model for calculating the force. The incident ray is diverted from its original path when it interacts with the microparticle. This causes the ray to change its momentum. When the ray changes momentum due to the microparticle, equal and opposite force is applied to the microparticle.

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Fig. 5

An overview of the GPU pipeline. The properties of the laser and the 3D grid are saved into the constant GPU memory, whereas the properties of the particles and the 3D grid cells are saved in the global GPU memory. These are used by the first GPU kernel that performs ray-object intersection and force per ray calculation. The output is written to a large global memory array. We then perform a parallel-prefix sum at the output. As the parallel-prefix sum adds up all the components together, segmentation/final force calculation kernel finds the proper segment boundaries for each component and subtracts necessary amount from the boundaries to compute the final result.

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Fig. 6

Pictorial view of the matrices that map discretized representation of incident ray angles to the force applied to the microparticle, the direction of the transmitted ray, and the position of the transmitted ray. The mapping is highly coherent which allows NMF to efficiently factorize each component of the matrix into two compact sized outer product matrices. Value of m used in our experiments is 4.

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Fig. 7

The final force contribution for each particle is calculated by subtracting values from the segment boundaries of an array that contains the result of the parallel-prefix sum. In this figure, we show how the final value of the scattering force is computed for a particle.

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Fig. 8

Here we show the time taken to compute the force exerted by a laser beam containing 32 rays 5000 times on a varying number of particles. We compare brute-force GPU ray tracing against GPU ray tracing with a 3D grid. As the number of particles increases, the use of a 3D grid data structure shows a clear advantage.

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Fig. 9

An illustration of the shadowing phenomenon. (a) shows the focal point of three laser beams at location (0.0,0.0,0.0), (-1.0,7.5,0.0), and (-1.0,2.5,0.0). (b) shows the movement of a single particle from (0.0,-4.0,0.0) to (0.0,0.0,0.0). (c) shows the movement of same particle when second particle is present at location (-1.0,5.5,0.0). Finally, (d) shows the difference in force experienced by the first bead caused by the shadowing phenomenon.

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Fig. 10

An illustration of the shadowing phenomenon similar to the previous figure. (a) shows the movement of a single particle from (-4.0,0.0,0.0) to (0.0,0.0,0.0). (b) shows the movement of same particle when second particle is present at location (-1.0,5.5,0.0). Finally, (c) shows the difference in force experienced by the first bead caused by the shadowing phenomenon.

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Fig. 11

Here we show the arrangement of the microparticles in the upward and downward configuration

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Fig. 12

Downward configuration with spacing 2.5 μm between the lower microparticles and laser moving with the velocity 22.4 μm/s. The two beads are trapped as the laser moves. The top row shows the captured video and the bottom row shows the simulated result.

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Fig. 13

Downward configuration with spacing 4.0 μm between lower two microparticles and laser moving with the velocity 22.4 μm/s. Only one bead is trapped as the laser moves. The top row shows the captured video and the bottom row shows the simulated result.

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Fig. 14

Here we show the comparison between the force calculated using our method and the force computed using stiffness. Here the focal point of the laser is located at (0.0,0.0,0.0) and we compute force by placing the microparticle along the Y-axis. Both forces are similar. The force computed using stiffness is an approximation but we validate our result since the stiffness value computed by Singer et al. [32] is calibrated.

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