OTSLM toolbox for structured light methods

We present a new Matlab toolbox for generating phase and amplitude patterns for digital micro-mirror device (DMD) and liquid crystal (LC) based spatial light modulators (SLMs). This toolbox consists of a collection of algorithms commonly used for generating patterns for these devices with a focus on optical tweezers beam shaping applications. In addition to the algorithms provided, we have put together a range of user interfaces for simplifying the use of these patterns. The toolbox currently has functionality to generate patterns which can be saved as an image or displayed on a device/screen using the supplied interface. We have only implemented interfaces for the devices our group currently uses but we believe that extending the code we provide to other devices should be fairly straightforward. The range of algorithms included in the toolbox is not exhaustive. However, by making the toolbox open sources and available on GitHub we hope that other researchers working with these devices will contribute their patterns/algorithms to the toolbox. Program summary: Program Title: OTSLM Toolbox for Structured Light Methods Program Files doi: http://dx.doi.org/10.17632/8sc66m9r7s.1 Licensing provisions: GPLv3 Programming language: Matlab Nature of problem: There are many algorithms for generating computer controlled holograms however the code and descriptions for these algorithms is often provided as supplementary material to research publications which use these methods, and in some cases only the description is provided without code to reproduce the pattern. Furthermore, implementation of these algorithms can be a time consuming task. Even for simple patterns with simple analytical expressions for the far-field phase or amplitude, such as the Laguerre-Gaussian and Hermite-Gaussian beams, time is often wasted by researchers having to re-implement and test these patterns. Existing libraries for generation of SLM patterns focus on specific tasks, methods of pattern generation, or target specific hardware. These libraries are not general purpose or easily modifiable for general use by researchers working with computer controlled holograms in fields such as beam shaping and optical tweezers. Solution method: We have assembled a toolbox containing many methods commonly used with these devices. The number of methods available makes assembling a complete toolbox impossible, instead we have focused on putting together a general collection of methods, in the form of an open source toolbox, with the hope that other researchers will contribute patterns/algorithms they use. The toolbox currently includes a range of simple and iterative methods for beam shaping and steering as well as some of the methods our group currently uses for SLM control, calibration, imaging and optical tweezers beam shaping. To make the tools we have developed easy to use, we have tried to maintain a consistent well documented interface to each of the functions and provided graphical user interfaces to many of the simpler functions enabling code-free pattern generation. Additional comments: Some of the features require the Optical Tweezers Toolbox [1], in particular, the non-paraxial beam visualisation and optimisation routines. Certain functions require components from other Matlab packages such as the image acquisition toolbox, these can be licensed and installed from Mathworks. There is also interest from the authors in providing a Python version that requires no proprietary components depending on interest from the community. A public repository for the toolbox is available on GitHub [2]. References [1] Optical Tweezers Toolbox (Version 1), https://github.com/ilent2/ott, (2019). [2] OTSLM, https://github.com/ilent2/otslm, (2019)

Visual guide to optical tweezers

It is common to introduce optical tweezers using either geometric optics for large particles or the Rayleigh approximation for very small particles. These approaches are successful at conveying the key ideas behind optical tweezers in their respective regimes. However, they are insufficient for modelling particles of intermediate size and large particles with small features. For this, a full field approach provides greater insight into the mechanisms involved in trapping. The advances in computational capability over the last decade have led to better modelling and understanding of optical tweezers. Problems that were previously difficult to model computationally can now be solved using a variety of methods on modern systems. These advances in computational power allow for full field solutions to be visualised, leading to increased understanding of the fields and behaviour in various scenarios. In this paper we describe the operation of optical tweezers using full field simulations calculated using the finite difference time domain method. We use these simulations to visually illustrate various situations relevant to optical tweezers, from the basic operation of optical tweezers, to engineered particles and evanescent fields

Understanding particle trajectories by mapping optical force vortices

Vortices can be found in many types of fields, from fluid velocity fields to optical fields. In optical manipulation, we are interested in the optical force field arising from the interaction between the beam and the particle. There are several mechanisms that can lead to circulation of particles around an optical trap including transfer of angular momentum from the beam to the particle or oscillations due to a lack of damping in the dynamical system. Understanding of the creation and behaviour of vortices occurring in optical fields can provide means for creating interesting rotational dynamics for particles held in structured light fields. Here, we describe the mechanisms that can lead to circulation in an optical trap. In particular we describe how the force field vortices can be found in different trapping configurations and we discuss the relationship between force vortices, optical vortices and Brownian vortices

Machine learning reveals complex behaviours in optically trapped particles

Since their invention in the 1980s, optical tweezers have found a wide range of applications, from biophotonics and mechanobiology to microscopy and optomechanics. Simulations of the motion of microscopic particles held by optical tweezers are often required to explore complex phenomena and to interpret experimental data. For the sake of computational efficiency, these simulations usually model the optical tweezers as an harmonic potential. However, more physically-accurate optical-scattering models are required to accurately model more onerous systems; this is especially true for optical traps generated with complex fields. Although accurate, these models tend to be prohibitively slow for problems with more than one or two degrees of freedom (DoF), which has limited their broad adoption. Here, we demonstrate that machine learning permits one to combine the speed of the harmonic model with the accuracy of optical-scattering models. Specifically, we show that a neural network can be trained to rapidly and accurately predict the optical forces acting on a microscopic particle. We demonstrate the utility of this approach on two phenomena that are prohibitively slow to accurately simulate otherwise: the escape dynamics of swelling microparticles in an optical trap, and the rotation rates of particles in a superposition of beams with opposite orbital angular momenta. Thanks to its high speed and accuracy, this method can greatly enhance the range of phenomena that can be efficiently simulated and studied

Orientation of swimming cells with annular beam optical tweezers

Optical tweezers are a versatile tool that can be used to manipulate small particles including both motile and non-motile bacteria and cells. The orientation of a non-spherical particle within a beam depends on the shape of the particle and the shape of the light field. By using multiple beams, sculpted light fields or dynamically changing beams, it is possible to control the orientation of certain particles. In this paper we discuss the orientation of the rod-shaped bacteria Escherichia coli (E. coli) using dynamically shifting annular beam optical tweezers. We begin with examples of different beams used for the orientation of rod-shaped particles. We discuss the differences between orientation of motile and non-motile particles, and explore annular beams and the circumstances when they may be beneficial for manipulation of non-spherical particles or cells. Using simulations we map out the trajectory the E. coli takes. Estimating the trap stiffness along the trajectory gives us an insight into how stable an intermediate rotation is with respect to the desired orientation. Using this method, we predict and experimentally verify the change in the orientation of motile E. coli from vertical to near-horizontal with only one intermediate step. The method is not specific to exploring the orientation of particles and could be easily extended to quantify the stability of an arbitrary particle trajectory

Swimming force and behavior of optically trapped micro-organisms

We demonstrate how optical tweezers combined with a three-dimensional force detection system and high-speed camera are used to study the swimming force and behavior of trapped micro-organisms. By utilizing position sensitive detection, we measure the motility force of trapped particles, regardless of orientation. This has the advantage of not requiring complex beam shaping or microfluidic controls for aligning trapped particles in a particular orientation, leading to unambiguous measurements of the propulsive force at any time. Correlating the direct force measurements with position data from a high-speed camera enables us to determine changes in the particle’s behavior. We demonstrate our technique by measuring the swimming force and observing distinctions between swimming and tumbling modes of the Escherichia coli (E. coli) strain MC4100. Our method shows promise for application in future studies of trappable but otherwise arbitrary-shaped biological swimmers and other active matter

Optical force measurements illuminate dynamics of Escherichia coli in viscous media

Escherichia coli and many other bacteria swim through media with the use of flagella, which are deformable helical propellers. When the viscosity of media is increased, a peculiar phenomenon can be observed in which the organism's motility appears to improve. This improvement in the cell's swimming speed has previously been explained by modified versions of resistive force theory (RFT) which accounts for the interaction between flagella and molecules associated with the viscosity increase. Using optical tweezers, we measure the swimming force of individual E. coli in solutions of varying viscosity. By using probe-free force measurements, we are able to quantitatively validate and compare RFT and proposed modifications to the theory. We find that the force produced by the flagellum remains relatively constant even when the viscosity of the medium increases by approximately two orders of magnitude, contrary to predictions of RFT and variants. We conclude that the observed swimming forces can be explained by allowing the flagella geometry to deform as the viscosity of the surrounding medium is increased

Theory and practice of simulation of optical tweezers

Computational modelling has made many useful contributions to the field of optical tweezers. One aspect in which it can be applied is the simulation of the dynamics of particles in optical tweezers. This can be useful for systems with many degrees of freedom, and for the simulation of experiments. While modelling of the optical force is a prerequisite for simulation of the motion of particles in optical traps, non-optical forces must also be included; the most important are usually Brownian motion and viscous drag. We discuss some applications and examples of such simulations. We review the theory and practical principles of simulation of optical tweezers, including the choice of method of calculation of optical force, numerical solution of the equations of motion of the particle, and finish with a discussion of a range of open problems