Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor

Fully angularly resolved 3D microrheology with optical tweezers

Microrheology with optical tweezers (MOT) is an all-optical technique that allows the user to investigate a materials' viscoelastic properties at microscopic scales, and is particularly useful for those materials that feature complex microstructures, such as biological samples. MOT is increasingly being employed alongside 3D imaging systems and particle tracking methods to generate maps showing not only how properties may vary between different points in a sample but also how at a single point the viscoelastic properties may vary with direction. However, due to the diffraction limited shape of focussed beams, optical traps are inherently anisotropic in 3D. This can result in a significant overestimation of the fluids' viscosity in certain directions. As such, the rheological properties can only be accurately probed along directions parallel or perpendicular to the axis of trap beam propagation. In this work, a new analytical method is demonstrated to overcome this potential artefact. This is achieved by performing principal component analysis on 3D MOT data to characterise the trap, and then identify the frequency range over which trap anisotropy influences the data. This approach is initially applied to simulated data for a Newtonian fluid where the trap anisotropy induced maximum error in viscosity is reduced from ~ 150% to less than 6%. The effectiveness of the method is corroborated by experimental MOT measurements performed with water and gelatine solutions, thus confirming that the microrheology of a fluid can be extracted reliably across a wide frequency range and in any arbitrary direction. This work opens the door to fully spatially and angularly resolved 3D mapping of the rheological properties of soft materials over a broad frequency range.

Fast and robust calibration method of liquid-crystal spatial light modulator based on polarization multiplexing

We propose a fast and robust method for calibrating Spatial Light Modulators (SLMs) based on polarization phase-shifting interferometry. Our method effectively calibrates the SLM by addressing both the static aberration and nonlinear phase response, utilizing specially designed gray images loaded sequentially onto the SLM. Notably, we introduce a novel kinoform that effectively eliminates the influence of tilt phase shift between two shots of the polarization camera. This results in a highly accurate phase aberration map and phase modulation curve with exceptional stability, making it an ideal method to calibrate the SLM with exceptional efficiency and precision in real applications.

Positioning Accuracy in Holographic Optical Traps

Spatial light modulators (SLMs) have been widely used to achieve dynamic control of optical traps. Often, holographic optical tweezers have been presumed to provide nanometer or sub-nanometer positioning accuracy. It is known that some features concerning the digitalized structure of SLMs cause a loss in steering efficiency of the optical trap, but their effect on trap positioning accuracy has been scarcely analyzed. On the one hand, the SLM look-up-table, which we found to depend on laser power, produces positioning deviations when the trap is moved at the micron scale. On the other hand, phase quantization, which makes linear phase gratings become phase staircase profiles, leads to unexpected local errors in the steering angle. We have tracked optically trapped microspheres with sub-nanometer accuracy to study the effects on trap positioning, which can be as high as 2 nm in certain cases. We have also implemented a correction strategy that enabled the reduction of errors down to 0.3 nm.

Aberration-corrected three-dimensional non-inertial scanning for femtosecond lasers

Large aberrations are induced by non-collimated light when the convergence or divergence of the incident beam on the back-pupil plane of the objective lens is adjusted for 3D non-inertial scanning. These aberrations significantly degrade the focus quality and decrease the peak intensity of the femtosecond laser focal spot. Here, we describe an aberration-corrected 3D non-inertial scanning method for femtosecond lasers based on a digital micromirror device (DMD) that is used for both beam scanning and aberration correction. An imaging setup is used to detect the focal spot in the 3D space, and an iterative optimization algorithm is used to optimize the focal spot. We demonstrate the application of our proposed approach in two-photon imaging. With correction for the 200-µm out-of-focal plane, the optical axial resolution improves from 7.67 to 3.25 µm, and the intensity of the fluorescence signal exhibits an almost fivefold improvement when a 40× objective lens is used. This aberration-corrected 3D non-inertial scanning method for femtosecond lasers offers a new approach for a variety of potential applications, including nonlinear optical imaging, microfabrication, and optical storage.

Microparticle Manipulation and Imaging through a Self-Calibrated Liquid Crystal on Silicon Display

We present in this paper a revision of three different methods we conceived in the framework of liquid crystal on silicon (LCoS) display optimization and application. We preliminarily demonstrate an LCoS self-calibration technique, from which we can perform a complete LCoS characterization. In particular, two important characteristics of LCoS displays are retrieved by using self-addressed digital holograms. On the one hand, we determine its phase-voltage curve by using the interference pattern generated by a digital two-sectorial split-lens configuration. On the other hand, the LCoS surface profile is also determined by using a self-addressed dynamic micro-lens array pattern. Second, the implementation of microparticle manipulation through optical traps created by an LCoS display is demonstrated. Finally, an LCoS display based inline (IL) holographic imaging system is described. By using the LCoS display to implement a double-sideband filter configuration, this inline architecture demonstrates the advantage of obtaining dynamic holographic imaging of microparticles independently of their spatial positions by avoiding the non-desired conjugate images.

Complex beam shaping based on an equivalent q-plate system and analysis of its properties using digital holography polarization imaging

In this study, we generate various complex beams carrying angular momentum (AM) by using a programmable beam shaping system to mimic typical q-plates. When a circularly polarized wave is incident onto the system, the emerging beam reverses its spin handedness and obtains a spatial phase factor. This phase factor can be engineered by designing a computer-generated hologram (CGH) and applying it to a spatial light modulator (SLM) to produce a beam with controllable spatially distributed orbital angular momentum (OAM) density. To determine the properties of the generated fields, we combine digital holography (DH) with the beam shaping system to yield visualizations of the beam intensity, phase, and AM distributions over the transverse plane at different propagation distances. Comparisons of the theoretically and experimentally obtained results show good qualitative agreement. This study advances our understanding and interpretation of AM characteristics produced by a programmable q-plate-like system.

Exact Theory of Optical Tweezers and Its Application to Absolute Calibration

Optical tweezers have become a powerful tool for basic and applied research in cell biology. Here, we describe an experimentally verified theory for the trapping forces generated by optical tweezers based on first principles that allows absolute calibration. For pedagogical reasons, the steps that led to the development of the theory over the past 15 years are outlined. The results are applicable to a broad range of microsphere radii, from the Rayleigh regime to the ray optics one, for different polarizations and trapping heights, including all commonly employed parameter domains. Protocols for implementing absolute calibration are given, explaining how to measure all required experimental parameters, and including a link to an applet for stiffness calculations.

Backplane aberration calibration of spatial light modulators using a phase-retrieval algorithm

The calibration and correction of backplane aberration of a liquid-crystal spatial light modulator (LCSLM) are important for its proper functioning. To simplify the calibration procedurally, we study a random-illumination-phase-retrieval-based method. Our method improves the convergence of the phase-retrieval-based calibration and reduces the calibration complexity. However, the cross talk of the LCSLM deteriorates the calibration performance. We determined the relationship between the probability density function of the random phases and the light-intensity pattern and proposed an algorithm to compensate for the cross talk. We conducted a series of simulations to test the performance of the above-mentioned algorithms. The results show that our algorithms are effective and outperform other methods.

Highly uniform holographic microtrap arrays for single atom trapping using a feedback optimization of in-trap fluorescence measurements

We report on the novel optimization method to realize highly uniform microtrap arrays for single atom trapping with a spatial light modulator (SLM). This method consists of two iterative feedback loops with the measurements of both diffracted light intensities and in-trap fluorescence intensities from each microtrap. By applying this method to the single ⁸⁷Rb atom trapping, we can reduce the variance of trap depths from 20.8% to 1.7% for 4 × 4 square arrays and less than 4% for various arrays with up to 62 sites. The detection error of individual single atoms is also reduced from 1.7% to 0.0054% on average.

Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects

In this paper, we present a kind of dual-mode photosensitive arrays (DMPAs) constructed by hybrid integration a liquid crystal microlens array (LCMLA) driven electrically and a CMOS sensor array, which can be used to measure both the conventional intensity images and corresponding wavefronts of objects. We utilize liquid crystal materials to shape the microlens array with the electrically tunable focal length. Through switching the voltage signal on and off, the wavefronts and the intensity images can be acquired through the DMPAs, sequentially. We use white light to obtain the object's wavefronts for avoiding losing important wavefront information. We separate the white light wavefronts with a large number of spectral components and then experimentally compare them with single spectral wavefronts of typical red, green and blue lasers, respectively. Then we mix the red, green and blue wavefronts to a composite wavefront containing more optical information of the object.

Reducing aberration effect of Fourier transform lens by modifying Fourier spectrum of diffractive optical element in beam shaping optical system

In general, Fourier transform lenses are considered as ideal in the design algorithms of diffractive optical elements (DOEs). However, the inherent aberrations of a real Fourier transform lens disturb the far field pattern. The difference between the generated pattern and the expected design will impact the system performance. Therefore, a method for modifying the Fourier spectrum of DOEs without introducing other optical elements to reduce the aberration effect of the Fourier transform lens is proposed. By applying this method, beam shaping performance is improved markedly for the optical system with a real Fourier transform lens. The experiments carried out with a commercial Fourier transform lens give evidence for this method. The method is capable of reducing the system complexity as well as improving its performance.

Toward optical-tweezers-based force microscopy for airborne microparticles

Optical tweezers have found widespread application in biological and colloidal physics for the measurement of pN forces over nanometer to micrometer length scales. Similar aerosol-phase measurements of interparticle force have not been reported in spite of the potential to better resolve particle coagulation kinetics. Various refractive index mismatches in the beam path as well as the need to explicitly account for gravity and inertial particle motion provide a number of challenges that must be overcome to make such measurements tractable. In this regard, we demonstrate schemes by which the particle position and trap stiffness may be unambiguously measured using bright-field microscopy with resolution comparable with analogous condensed-phase measurements. Moreover, some of the challenges of working with highly dynamic aqueous particles are introduced and exploited to observe size-dependent phenomena in aerosol optical tweezers. Notably, when combined with cavity-enhanced Raman spectroscopy, this provides a unique opportunity to explore trapping forces over a continuum of particle size and refractive index. It is expected that the methods developed will provide a basis for the measurement of pairwise interaction forces in aerosol optical tweezers while providing a probe of fundamental airborne particle trapping dynamics.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Optical trapping and binding

The phenomenon of light's momentum was first observed in the laboratory at the beginning of the twentieth century, and its potential for manipulating microscopic particles was demonstrated by Ashkin some 70 years later. Since that initial demonstration, and the seminal 1986 paper where a single-beam gradient-force trap was realized, optical trapping has been exploited as both a rich example of physical phenomena and a powerful tool for sensitive measurement. This review outlines the underlying theory of optical traps, and explores many of the physical observations that have been made in such systems. These phenomena include 'optical binding', where trapped objects interact with one another through the trapping light field. We also discuss a number of the applications of 'optical tweezers' across the physical and life sciences, as well as covering some of the issues involved in constructing and using such a tool.

Simultaneous rotation, orientation and displacement control of birefringent microparticles in holographic optical tweezers

We report the experimental implementation of a new method for generating multiple dynamical optical tweezers, where each one of them is generated with an independent linear polarization state with arbitrary orientation. This also allows an independent simultaneous polarization-rotation control. The laser beam, both for generating multiple traps and polarization control, has been modulated using a single reflective nematic liquid crystal with parallel alignment. We present experimental results of controlled displacement, orientation and rotation of birefringent particles. In addition, a simple method for estimating and canceling out the primary astigmatism present in the system is presented.

Determination of wavefront structure for a Hartmann wavefront sensor using a phase-retrieval method

We apply a phase retrieval algorithm to the intensity pattern of a Hartmann wavefront sensor to measure with enhanced accuracy the phase structure of a Hartmann hole array. It is shown that the rms wavefront error achieved by phase reconstruction is one order of magnitude smaller than the one obtained from a typical centroid algorithm. Experimental results are consistent with a phase measurement performed independently using a Shack-Hartmann wavefront sensor.

Characterization of holographically generated beams via phase retrieval based on Wigner distribution projections

In this work, we propose a robust and versatile approach for the characterization of the complex field amplitude of holographically generated coherent-scalar paraxial beams. For this purpose we apply an iterative algorithm that allows recovering the phase of the generated beam from the measurement of its Wigner distribution projections. Its performance is analyzed for beams of different symmetry: Laguerre-Gaussian, Hermite-Gaussian and spiral ones, which are obtained experimentally by a computer generated hologram (CGH) implemented on a programmable spatial light modulator (SLM). Using the same method we also study the quality of their holographic recording on a highly efficient photopolymerizable glass. The proposed approach is useful for the creation of adaptive CGH that takes into account the peculiarities of the SLM, as well as for the quality control of the holographic data storage.

Microparticle movements in optical funnels and pods

Three-dimensional microparticle movements induced by laser beams with a funnel- and tubular pod-like structure, in the neighbourhood of the focal plane of an optical trapping setup, are experimentally studied. The funnel and pod beams constructed as coherent superpositions of helical Laguerre-Gaussian modes are synthesized by a computer generated hologram using a phase-only spatial light modulator. Particle tracking is achieved by in-line holography method which allows an accurate position measurement. It is experimentally demonstrated that the trapped particle follows different trajectories depending on the orbital angular momentum density of the beam. In particular applying the proposed pod beam the particle rotates in opposite directions during its movement in the optical trap. Possible applications of these single-beam traps for volumetric optical particle manipulation are discussed.

Single-plane multiple speckle pattern phase retrieval using a deformable mirror

A design for a single-plane multiple speckle pattern phase retrieval technique using a deformable mirror (DM) is analyzed within the formalism of complex ABCD-matrices, facilitating its use in conjunction with dynamic wavefronts. The variable focal length DM positioned at a Fourier plane of a lens comprises the adaptive optical (AO) system that replaces the time-consuming axial displacements in the conventional free-space multiple plane setup. Compared with a spatial light modulator, a DM has a smooth continuous surface which avoids pixelation, pixel cross-talk and non-planarity issues. The calculated distances for the proposed AO-system are evaluated experimentally using the conventional free-space phase retrieval setup. Two distance ranges are investigated depending on whether the measurement planes satisfy the Nyquist detector sampling condition or not. It is shown numerically and experimentally that speckle patterns measured at the non-Nyquist range still yield good reconstructions. A DM with a surface height of 25 microns and an aperture diameter of 5.2 mm may be used to reconstruct spherical phase patterns with 50-micron fringe spacing.