Holographic or diffractive optical components, such as a spatial
light modulator (SLM), can be used in optical tweezers for the
creation of multiple and modified optical traps. In addition to
this, SLMs can also be used to correct for aberrations within the
optical train resulting in an improved trapping performance.
Typically an electrically addressed SLM may deviate from flatness
by up to 4λ, dominated by astigmatism due to the overall
curvature of the SLM surface. This astigmatism may be corrected by
adding the appropriate hologram to the SLM display resulting in a
dramatic improvement in the fidelity of the focussed spot. The
impact that this correction has on the performance of the optical
trap is most noticeable for small particles. For the SLM used in
this study, the improvement in trap performance for a 0.8 μm
diameter particles can be in excess of 25%. However, for 5 μm
diameter particles our results show an improvement of less than
0.5%. This dependence upon particle size is most probably
associated with the relative size of the PSF and the trapped
particle. Once the PSF is significantly smaller than the particle
diameter, further reduction brings little improvement in trap
Using feedback control, a versatile optical trap can be constructed that can be used to control either the position of trapped objects or apply specified forces. Yet, 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, it is surprising to note that 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 reach limits. It is well understood that feedback control can result in both positive and negative effects in controlled
systems. This paper discusses the performance and analytical limits that must be considered in the development and design of control systems for optical traps.
The quantitative study of displacements and forces of motor proteins and processes that occur at the microscopic level and below require a high level of sensitivity. For optical traps, two techniques for position sensing have been accepted and used quite extensively: quadrant photodiodes and an interferometric position sensing technique based on DIC imaging. While quadrant photodiodes have been studied in depth and mathematically characterized, a mathematical characterization of the interferometric position sensor has not been presented to the authors' knowledge. The interferometric position sensing method works off of the DIC imaging capabilities of a microscope. Circularly polarized light is sent into the microscope and the Wollaston prism used for DIC imaging splits the beam into its orthogonal components, displacing them by a set distance determined by the user. The distance between the axes of the beams is set so the beams overlap at the specimen plane and effectively share the trapped microsphere. A second prism then recombines the light beams and the exiting laser light's polarization is measured and related to position. In this paper we outline the mathematical characterization of a microsphere suspended in an optical trap using a DIC position sensing method. The sensitivity of this mathematical model is then compared to the QPD model. The mathematical model of a microsphere in an optical trap can serve as a calibration curve for an experimental setup.