An adaptive system identification approach to optical trap calibration.

A method of adaptive system identification for the modeling of an optical trap's system dynamics is presented. The system dynamics can be used to locate the corner frequency for trapping stiffness calibration using the power spectral method. The method is based on an adaptive least-mean-square (LMS) algorithm, which adjusts weights of a tapped delay line filter using a gradient descent method. The identified model is the inverse of the high order finite impulse response (FIR) filter. The model order is reduced using balanced model reduction, giving the corner frequency which can be used to calibrate the trapping stiffness. This method has an advantage over other techniques in that it is quick, does not explicitly require operator interaction, and can be acquired in real time. It is also a necessary step for an adaptive controller that can automatically update the controller for changes in the trap (e.g., power fluctuations) and for particles of different sizes and refractive indices.

Three-dimensional parallel holographic micropatterning using a spatial light modulator.

We present a micropatterning method for the automatic transfer and arbitrary positioning of computer-generated three-dimensional structures within a substrate. The Gerchberg-Saxton algorithm and an electrically addressed spatial light modulator (SLM) are used to create and display phase holograms, respectively. A holographic approach to light manipulation enables arbitrary and efficient parallel photo-patterning. Multiple pyramidal microstructures were created simultaneously in a photosensitive adhesive. A scanning electron microscope was used to confirm successful replication of the desired microscale structures.

Controlled rotation of birefringent particles in an optical trap.

Optical traps have been used in a multitude of applications requiring the sensing and application of forces. However, optical traps also have the ability to accurately apply and sense torques. Birefringent particles experience a torque when trapped in elliptically polarized light. By measuring the frequency content of the exiting beam, the rotational rates can be set up in a feedback loop and actively controlled. Here we describe an optical trap with feedback torque control to maintain constant rotational rates despite the introduction of an increased drag on the particle. As a result, this research has the potential to advance the understanding of rotary motor proteins such as F1 ATPase.

Adaptive disturbance rejection in an optical trap.

This article presents a method for characterizing the system dynamics of a trapped particle in real-time and designing a controller to minimize disturbances to the particle's position. Specifically, adaptive system identification is used to determine the trap characteristics and the actuator transfer function describing the mirror voltage to trap position path. Using an internal model control scheme combined with a filtered-x least-mean-square algorithm, adaptive control was used to create a controller that minimizes a frequency weighted mean-squared-error. The dynamics associated with multiple particle sizes and materials were experimentally determined under different power levels, each case resulting in different system dynamics and demonstrating positive control results. The adaptive system identification and the controller presented automate the process of system identification and control design, enabling the automation of optical trap controller design.

Aberration correction in holographic optical tweezers.

Holographic or diffractive optical components are widely implemented using spatial light modulators within optical tweezers to form multiple, and/or modified traps. We show that by further modifying the hologram design to account for residual aberrations, the fidelity of the focused beams can be significantly improved, quantified by a spot sharpness metric. However, the impact this improvement has on the quality of the optical trap depends upon the particle size. For particle diameters on the order of 1 microm, aberration correction can improve the trap performance metric, which is the ratio of the mean square displacement of a corrected trap to an uncorrected trap, in excess of 25%, but for larger particles the trap performance is not unduly affected by the aberrations typically encountered in commercial spatial light modulators.

Aberration correction in holographic optical tweezers.

Holographic or diffractive optical components are widely implemented using spatial light modulators within optical tweezers to form multiple, and/or modified traps. We show that by further modifying the hologram design to account for residual aberrations, the fidelity of the focused beams can be significantly improved, quantified by a spot sharpness metric. However, the impact this improvement has on the quality of the optical trap depends upon the particle size. For particle diameters on the order of 1 microm, aberration correction can improve the trap performance metric, which is the ratio of the mean square displacement of a corrected trap to an uncorrected trap, in excess of 25%, but for larger particles the trap performance is not unduly affected by the aberrations typically encountered in commercial spatial light modulators.

3D interferometric optical tweezers using a single spatial light modulator.

Hexagonal arrays of micron sized silica beads have been trapped in three-dimensions within an optical lattice formed by the interference of multiple plane-waves. The optical lattice design with sharply peaked intensity gradients produces a stronger trapping force than the traditionally sinusoidal intensity distributions of other interferometric systems. The plane waves were generated using a single, phase-only, spatial light modulator (SLM), sited near a Talbot image plane of the traps. Compared to conventional optical tweezers, where the traps are formed in the Fourier-plane of the SLM, this approach may offer an advantage in the creation of large periodic array structures. This method of pattern formation may also be applicable to trapping arrays of atoms.

Servo control of an optical trap.

A versatile optical trap has been constructed to control the position of trapped objects and ultimately to apply specified forces using feedback control. While the design, development, and use of optical traps has been extensive and feedback control has played a critical role in pushing the state of the art, few comprehensive examinations of feedback control of optical traps have been undertaken. Furthermore, as the requirements are pushed to ever smaller distances and forces, the performance of optical traps reaches limits. It is well understood that feedback control can result in both positive and negative effects in controlled systems. We give an analysis of the trapping limits as well as introducing an optical trap with a feedback control scheme that dramatically improves an optical trap's sensitivity at low frequencies.

Interactive approach to optical tweezers control.

We have developed software with an interactive user interface that can be used to generate phase holograms for use with spatial light modulators. The program utilizes different hologram design techniques, allowing the user to select an appropriate algorithm. The program can be used to generate multiple beams and can be used for beam steering. We see a major application of the program to be in optical tweezers to control the position, number, and type of optical traps.