A Microfluidic-based Hydrodynamic Trap for Single Particles

The ability to confine and manipulate single particles in free solution is a key enabling technology for fundamental and applied science. Methods for particle trapping based on optical, magnetic, electrokinetic, and acoustic techniques have led to major advancements in physics and biology ranging from the molecular to cellular level. In this article, we introduce a new microfluidic-based technique for particle trapping and manipulation based solely on hydrodynamic fluid flow. Using this method, we demonstrate trapping of micro- and nano-scale particles in aqueous solutions for long time scales. The hydrodynamic trap consists of an integrated microfluidic device with a cross-slot channel geometry where two opposing laminar streams converge, thereby generating a planar extensional flow with a fluid stagnation point (zero-velocity point). In this device, particles are confined at the trap center by active control of the flow field to maintain particle position at the fluid stagnation point. In this manner, particles are effectively trapped in free solution using a feedback control algorithm implemented with a custom-built LabVIEW code. The control algorithm consists of image acquisition for a particle in the microfluidic device, followed by particle tracking, determination of particle centroid position, and active adjustment of fluid flow by regulating the pressure applied to an on-chip pneumatic valve using a pressure regulator. In this way, the on-chip dynamic metering valve functions to regulate the relative flow rates in the outlet channels, thereby enabling fine-scale control of stagnation point position and particle trapping. The microfluidic-based hydrodynamic trap exhibits several advantages as a method for particle trapping. Hydrodynamic trapping is possible for any arbitrary particle without specific requirements on the physical or chemical properties of the trapped object. In addition, hydrodynamic trapping enables confinement of a "single" target object in concentrated or crowded particle suspensions, which is difficult using alternative force field-based trapping methods. The hydrodynamic trap is user-friendly, straightforward to implement and may be added to existing microfluidic devices to facilitate trapping and long-time analysis of particles. Overall, the hydrodynamic trap is a new platform for confinement, micromanipulation, and observation of particles without surface immobilization and eliminates the need for potentially perturbative optical, magnetic, and electric fields in the free-solution trapping of small particles.Download video file.^{(62M, mov)}     

Fano Resonance-Assisted Plasmonic Trapping of Nanoparticles

Plasmonic optical trapping is widely applied in the field of bioscience, microfluidics, and quantum optics. It can play a vital role to extend optical manipulation tools from micrometer to nanometer scale level. Currently, it is a challenge to obtain the highly stable optical trapping with low power and less damage. In this paper, we propose Fano resonance-assisted self-induced back-action (FASIBA) method, through which a single 40-nm gold particle can be trapped in hole-slit nano-aperture milled on metallic film. It is used to achieve ultra-accurate positioning of nanoparticle, metallic nanostructures at wide infrared wavelength range, quite effectively and evidently. The stable plasmonic trapping is achieved by tuning the transmission wavelengths and modifications of nanoslit, indicating that the depth of potential well can be increased from minus 8KT to 12KT, with the input power of 10⁹ W/m². This can be attributed to great modifications in Fano resonance transmissions according to self-induced back-action (SIBA) theory. The results are basically helpful to facilitate the trapping with lower power and less damage to the objects, which enables new scenario for the treatment of undesirable spread of a single nanoscale creature, such as virus.     

Utilization of Plasmonic and Photonic Crystal Nanostructures for Enhanced Micro- and Nanoparticle Manipulation

A method to manipulate the position and orientation of submicron particles nondestructively would be an incredibly useful tool for basic biological research. Perhaps the most widely used physical force to achieve noninvasive manipulation of small particles has been dielectrophoresis(DEP).¹ However, DEP on its own lacks the versatility and precision that are desired when manipulating cells since it is traditionally done with stationary electrodes. Optical tweezers, which utilize a three dimensional electromagnetic field gradient to exert forces on small particles, achieve this desired versatility and precision.² However, a major drawback of this approach is the high radiation intensity required to achieve the necessary force to trap a particle which can damage biological samples.³ A solution that allows trapping and sorting with lower optical intensities are optoelectronic tweezers (OET) but OET''s have limitations with fine manipulation of small particles; being DEP-based technology also puts constraint on the property of the solution.^4,5This video article will describe two methods that decrease the intensity of the radiation needed for optical manipulation of living cells and also describe a method for orientation control. The first method is plasmonic tweezers which use a random gold nanoparticle (AuNP) array as a substrate for the sample as shown in Figure 1. The AuNP array converts the incident photons into localized surface plasmons (LSP) which consist of resonant dipole moments that radiate and generate a patterned radiation field with a large gradient in the cell solution. Initial work on surface plasmon enhanced trapping by Righini et al and our own modeling have shown the fields generated by the plasmonic substrate reduce the initial intensity required by enhancing the gradient field that traps the particle.^6,7,8 The plasmonic approach allows for fine orientation control of ellipsoidal particles and cells with low optical intensities because of more efficient optical energy conversion into mechanical energy and a dipole-dependent radiation field. These fields are shown in figure 2 and the low trapping intensities are detailed in figures 4 and 5. The main problems with plasmonic tweezers are that the LSP''s generate a considerable amount of heat and the trapping is only two dimensional. This heat generates convective flows and thermophoresis which can be powerful enough to expel submicron particles from the trap.^9,10 The second approach that we will describe is utilizing periodic dielectric nanostructures to scatter incident light very efficiently into diffraction modes, as shown in figure 6.¹¹ Ideally, one would make this structure out of a dielectric material to avoid the same heating problems experienced with the plasmonic tweezers but in our approach an aluminum-coated diffraction grating is used as a one-dimensional periodic dielectric nanostructure. Although it is not a semiconductor, it did not experience significant heating and effectively trapped small particles with low trapping intensities, as shown in figure 7. Alignment of particles with the grating substrate conceptually validates the proposition that a 2-D photonic crystal could allow precise rotation of non-spherical micron sized particles.¹⁰ The efficiencies of these optical traps are increased due to the enhanced fields produced by the nanostructures described in this paper.Download video file.^{(57M, mov)}     

Strong and High-Precision Manipulation of Nanoparticle with Graphene-Coated Fiber Systems

Two kinds of graphene-coated fiber systems are proposed and studied for optical trapping. Their plasmonic modes in uniform environment and close to the substrate are studied in the finite element method. The optical forces exerted on dielectric nanoparticle by these systems are calculated by standalone waveguide approximation. It is found that for the dielectric particle with diameter of 1 nm, the maximal optical forces generated by certain modes are more than 10⁷ fN/W whereas their force ranges are only one to several nanometers. These results may have important applications in strong and high-precision optical tweezers.

     

Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime

We calculate the forces of single-beam gradient radiation pressure laser traps, also called “optical tweezers,” on micron-sized dielectric spheres in the ray optics regime. This serves as a simple model system for describing laser trapping and manipulation of living cells and organelles within cells. The gradient and scattering forces are defined for beams of complex shape in the ray-optics limit. Forces are calculated over the entire cross-section of the sphere using TEM₀₀ and TEM₀₁^* mode input intensity profiles and spheres of varying index of refraction. Strong uniform traps are possible with force variations less than a factor of 2 over the sphere cross-section. For a laser power of 10 mW and a relative index of refraction of 1.2 we compute trapping forces as high as ~ 1.2 × 10^-6 dynes in the weakest (backward) direction of the gradient trap. It is shown that good trapping requires high convergence beams from a high numerical aperture objective. A comparison is given of traps made using bright field or differential interference contrast optics and phase contrast optics.     

Characterization of photodamage to escherichia coli in optical traps

Optical tweezers (infrared laser-based optical traps) have emerged as a powerful tool in molecular and cell biology. However, their usefulness has been limited, particularly in vivo, by the potential for damage to specimens resulting from the trapping laser. Relatively little is known about the origin of this phenomenon. Here we employed a wavelength-tunable optical trap in which the microscope objective transmission was fully characterized throughout the near infrared, in conjunction with a sensitive, rotating bacterial cell assay. Single cells of Escherichia coli were tethered to a glass coverslip by means of a single flagellum: such cells rotate at rates proportional to their transmembrane proton potential (. J. Mol. Biol. 138:541-561). Monitoring the rotation rates of cells subjected to laser illumination permits a rapid and quantitative measure of their metabolic state. Employing this assay, we characterized photodamage throughout the near-infrared region favored for optical trapping (790-1064 nm). The action spectrum for photodamage exhibits minima at 830 and 970 nm, and maxima at 870 and 930 nm. Damage was reduced to background levels under anaerobic conditions, implicating oxygen in the photodamage pathway. The intensity dependence for photodamage was linear, supporting a single-photon process. These findings may help guide the selection of lasers and experimental protocols best suited for optical trapping work.     

Optical Manipulation of Dielectric Nanoparticles with Au Micro-racetrack Resonator by Constructive Interference of Surface Plasmon Waves

We design a gold micro-racetrack resonator (Au-MRR) which can tightly trap and drive the dielectric nanoparticle to rotate around the circuit of racetrack with an adjustable velocity. Since the surface plasmon waves can be excited and obey the resonance condition of the Au-MRR, the optics force can be strengthened observably due to the resonance. The optical forces applied on dielectric nanoparticle are discussed by utilizing the Maxwell’s stress tensor integration with a numerical finite element method. The depth of longitudinal trapping potential well in the Au-MRR is four times as large as that of a straight waveguide. At the same level of input power, the velocity of particle with radius of 50 nm driven by optical forces on Au-MRR is 200 times larger than that on a straight waveguide. Further, we explore the motion behavior of single nanoparticle lies on different position of Au-MRR, which can provide the details to trap and manipulate multiple nanoparticles and predict their trace of movement. This optimum geometry of Au-MRR allows further enhancement of the optical forces which is expected to realize all-optical on-chip manipulation of nanoparticles, biomolecules, and many other nanomanipulation applications.     

Single beam optical trapping integrated in a confocal microscope for biological applications.

Confocal microscopy is very useful in biology because of its three dimensional imaging capacities and has proven to be an excellent tool to study the 3D organization of, for instance, cell structures. This property of confocal microscopy makes it also very suitable for observation during guidance of the three dimensional manipulation of single cells or cell elements. Therefore we decided to integrate a confocal microscope and a single beam optical manipulator into a single instrument. The advantage of optical manipulation over mechanical techniques is that it is non-invasive and therefore may be applied on living (micro-) organisms and cells. The creation of an effective single beam optical trap requires the use of a high numerical aperture (N.A.) objective to focus the laser beam. In this paper we briefly discuss the vertical or axial force exerted on a sphere in a single beam trap. The axial force on a sphere placed on the optical axis, caused by reflection and refraction, is calculated applying a electromagnetic vector diffraction theory to determine the field distribution in the focal region. One of the results is that the particle also experiences a vertical trapping force towards the focusing lens when it is in the strongly convergent part of the field in addition to the known negative signed trapping force in the divergent part of the field. Further we describe an instrumental approach to realize optical trapping in which the optical trap position is controlled by moving the focusing objective only.(ABSTRACT TRUNCATED AT 250 WORDS)     

An automated two-dimensional optical force clamp for single molecule studies

We constructed a next-generation optical trapping instrument to study the motility of single motor proteins, such as kinesin moving along a microtubule. The instrument can be operated as a two-dimensional force clamp, applying loads of fixed magnitude and direction to motor-coated microscopic beads moving in vitro. Flexibility and automation in experimental design are achieved by computer control of both the trap position, via acousto-optic deflectors, and the sample position, using a three-dimensional piezo stage. Each measurement is preceded by an initialization sequence, which includes adjustment of bead height relative to the coverslip using a variant of optical force microscopy (to +/-4 nm), a two-dimensional raster scan to calibrate position detector response, and adjustment of bead lateral position relative to the microtubule substrate (to +/-3 nm). During motor-driven movement, both the trap and stage are moved dynamically to apply constant force while keeping the trapped bead within the calibrated range of the detector. We present details of force clamp operation and preliminary data showing kinesin motor movement subject to diagonal and forward loads.     

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc ²) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initial particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.     

Precision Surface-Coupled Optical-Trapping Assay with One-Basepair Resolution

The most commonly used optical-trapping assays are coupled to surfaces, yet such assays lack atomic-scale (∼0.1 nm) spatial resolution due to drift between the surface and trap. We used active stabilization techniques to minimize surface motion to 0.1 nm in three dimensions and decrease multiple types of trap laser noise (pointing, intensity, mode, and polarization). As a result, we achieved nearly the thermal limit (<0.05 nm) of bead detection over a broad range of trap stiffness (k_T = 0.05-0.5 pN/nm) and frequency (Δf = 0.03-100 Hz). We next demonstrated sensitivity to one-basepair (0.34-nm) steps along DNA in a surface-coupled assay at moderate force (6 pN). Moreover, basepair stability was achieved immediately after substantial (3.4 pN) changes in force. Active intensity stabilization also led to enhanced force precision (∼0.01%) that resolved 0.1-pN force-induced changes in DNA hairpin unfolding dynamics. This work brings the benefit of atomic-scale resolution, currently limited to dual-beam trapping assays, along with enhanced force precision to the widely used, surface-coupled optical-trapping assay.     

Single-molecule manipulation of macromolecules on GUV or SUV membranes using optical tweezers

Despite their wide applications in soluble macromolecules, optical tweezers have rarely been used to characterize the dynamics of membrane proteins, mainly due to the lack of model membranes compatible with optical trapping. Here, we examined optical trapping and mechanical properties of two potential model membranes, giant and small unilamellar vesicles (GUVs and SUVs, respectively) for studies of membrane protein dynamics. We found that optical tweezers can stably trap GUVs containing iodixanol with controlled membrane tension. The trapped GUVs with high membrane tension can serve as a force sensor to accurately detect reversible folding of a DNA hairpin or membrane binding of synaptotagmin-1 C2AB domain attached to the GUV. We also observed that SUVs are rigid enough to resist large pulling forces and are suitable for detecting protein conformational changes induced by force. Our methodologies may facilitate single-molecule manipulation studies of membrane proteins using optical tweezers.     

Characterization and luminescence properties of CaMgSi2O6:Eu2+ blue phosphor

A blue CaMgSi₂O₆:Eu²⁺ phosphor was prepared by the solid‐state reaction method and the phosphor characterized in terms of crystal structure, particle size, photoluminescence (PL), thermoluminescence (TL) and mechanoluminescence (ML) properties using X‐ray diffraction (XRD), transmission electron microscopy (TEM), PL spectroscopy, TLD reader and ML impact technique. The XRD result shows that phosphor is formed in a single phase and has a monoclinic structure with the space group C2/c. Furthermore, the PL excitation spectra of Eu²⁺‐doped CaMgSi₂O₆ phosphor showed a strong band peak at 356 nm and the PL emission spectrum has a peak at 450 nm. The depths and frequency factors of trap centers were calculated using the TL glow curve by deconvolution method in which the trap depths were found to be 0.48 and 0.61 eV. The formation of CaMgSi₂O₆:Eu²⁺ phosphor was confirmed by Fourier transform infrared spectroscopy. The ML intensity increased linearly with the impact velocity of the piston used to deform the phosphor. It was shown that the local piezoelectricity‐induced electron bombardment model is responsible for the ML emission. Finally, the optical properties of CaMgSi₂O₆:Eu²⁺ phosphors are discussed. Copyright © 2015 John Wiley & Sons, Ltd.     

Small‐plot studies comparing pheromone and juice baits for mass‐trapping invasive Synanthedon myopaeformis in Canada

Recent introduction of Synanthedon myopaeformis (Borkhausen) (Lepidoptera: Sesiidae) into organic apple‐growing areas of Canada has stimulated research on semiochemical‐based management of this European pest. Replicated, small‐plot (0.16 ha) experiments were conducted to compare sex pheromone, 3Z,13Z‐octadecadienyl acetate (10 mg), Concord grape juice (300 ml), or their combination, as mass‐trapping lures at trap densities equivalent to 12.5, 25, 50, and 100 traps ha^?1. Total numbers of male and female moths removed from test plots increased significantly with trap density in all juice‐based mass‐trapping experiments. In pheromone mass‐trapping experiments, however, total catches of males did not increase significantly as trap densities were increased and catches appeared to plateau with 25–50 traps ha^?1. With pheromone‐based mass‐trapping, significantly fewer males were caught in pheromone‐baited assessment traps at the centre of each mass‐trapping plot than in identical traps in untreated plots. This reduction is indicative of significant trap interference or trap ‘shut‐down’. Increasing the density of juice‐based mass‐trapping had no effect on catches of male or female moths in juice‐baited assessment traps, indicating a short range of attraction and lack of interference between juice traps. Pheromone‐ and juice‐based mass trapping removed similar numbers of males at each trap density tested, respectively, but summed catches of males and females were greatest with juice baits. Combining pheromone and juice into a single mass‐trapping treatment (50 traps ha^?1) did not significantly increase catches of males or females relative to either treatment alone. If a practical bisexual mass‐trapping system is going to be developed for S. myopaeformis, then identification of volatile kairomones in Concord grape juice may be useful.     

Removal trapping to control Artioposthia triangulata

Removal trapping was used to try and reduce numbers of the predatory planarian Artioposthia triangulata in polythene tunnels on a nursery and a grass field. Ten months of trapping in the tunnels failed to have any impact upon flatworm numbers but weekly catches reduced over a period of 12 weeks' trapping in grassland. The calculated residual population in the grassland (40 ha^-1) was small in comparison with that estimated from formalin sampling (940 × 1288 ha^-1). A separate field study examined the effect of trap density on catch by spacing traps at 2.5, 5, 10 and 20 m intervals. This showed that the numbers of planarians caught was inversely related to the logarithm of trap spacing. It is concluded that removal trapping is too demanding of resources to be a viable control option for this pest in commercial and agricultural situations.     

Development of Whispering Gallery Mode Polymeric Micro-optical Electric Field Sensors

Optical modes of dielectric micro-cavities have received significant attention in recent years for their potential in a broad range of applications. The optical modes are frequently referred to as "whispering gallery modes" (WGM) or "morphology dependent resonances" (MDR) and exhibit high optical quality factors. Some proposed applications of micro-cavity optical resonators are in spectroscopy¹, micro-cavity laser technology², optical communications^3-6 as well as sensor technology. The WGM-based sensor applications include those in biology⁷, trace gas detection⁸, and impurity detection in liquids⁹. Mechanical sensors based on microsphere resonators have also been proposed, including those for force^10,11, pressure¹², acceleration¹³ and wall shear stress¹⁴. In the present, we demonstrate a WGM-based electric field sensor, which builds on our previous studies^15,16. A candidate application of this sensor is in the detection of neuronal action potential.The electric field sensor is based on polymeric multi-layered dielectric microspheres. The external electric field induces surface and body forces on the spheres (electrostriction effect) leading to elastic deformation. This change in the morphology of the spheres, leads to shifts in the WGM. The electric field-induced WGM shifts are interrogated by exciting the optical modes of the spheres by laser light. Light from a distributed feedback (DFB) laser (nominal wavelength of ~ 1.3 μm) is side-coupled into the microspheres using a tapered section of a single mode optical fiber. The base material of the spheres is polydimethylsiloxane (PDMS). Three microsphere geometries are used: (1) PDMS sphere with a 60:1 volumetric ratio of base-to-curing agent mixture, (2) multi layer sphere with 60:1 PDMS core, in order to increase the dielectric constant of the sphere, a middle layer of 60:1 PDMS that is mixed with varying amounts (2% to 10% by volume) of barium titanate and an outer layer of 60:1 PDMS and (3) solid silica sphere coated with a thin layer of uncured PDMS base. In each type of sensor, laser light from the tapered fiber is coupled into the outermost layer that provides high optical quality factor WGM (Q ~ 10⁶). The microspheres are poled for several hours at electric fields of ~ 1 MV/m to increase their sensitivity to electric field.     

Label‐free differentiation of human immunodeficiency virus‐1 infected from uninfected cells using transmission measurement

Transmission measurement has been perceived as a potential candidate for label‐free investigation of biological material. It is a real‐time, label‐free and non‐invasive optical detection technique that has found wide applications in pharmaceutical industry as well as the biological and medical fields. Combining transmission measurement with optical trapping has emerged as a powerful tool allowing stable sample trapping, while also facilitating transmittance data analysis. In this study, a near‐infrared laser beam emitting at a wavelength of 1064 nm was used for both optical trapping and transmission measurement investigation of human immunodeficiency virus 1 (HIV‐1) infected and uninfected TZM‐bl cells. The measurements of the transmittance intensity of individual cells in solution were carried out using a home built optical trapping system combined with laser transmission setup using a single beam gradient trap. Transmittance spectral intensity patterns revealed significant differences between the HIV‐1 infected and uninfected cells. This result suggests that the transmittance data analysis technique used in this study has the potential to differentiate between infected and uninfected TZM‐bl cells without the use of labels. The results obtained in this study could pave a way into developing an HIV‐1 label‐free diagnostic tool with possible applications at the point of care .     

Plasmonic Optical Trapping in Biologically Relevant Media

We present plasmonic optical trapping of micron-sized particles in biologically relevant buffer media with varying ionic strength. The media consist of 3 cell-growth solutions and 2 buffers and are specifically chosen due to their widespread use and applicability to breast-cancer and angiogenesis studies. High-precision rheological measurements on the buffer media reveal that, in all cases excluding the 8.0 pH Stain medium, the fluids exhibit Newtonian behavior, thereby enabling straightforward measurements of optical trap stiffness from power-spectral particle displacement data. Using stiffness as a trapping performance metric, we find that for all media under consideration the plasmonic nanotweezers generate optical forces 3–4x a conventional optical trap. Further, plasmonic trap stiffness values are comparable to those of an identical water-only system, indicating that the performance of a plasmonic nanotweezer is not degraded by the biological media. These results pave the way for future biological applications utilizing plasmonic optical traps.     

How varying pest and trap densities affect Tribolium castaneum capture in pheromone traps

The red flour beetle, Tribolium castaneum (Herbst) (Coleoptera: Tenebrionidae), is an important insect pest in food processing facilities. Pheromone trapping is frequently used to monitor red flour beetle populations in structures; however, the optimal trap density and the relationship between trap captures and beetle density is not known. Two experiments were performed concurrently in environmentally controlled 30‐m² walk‐in chambers to determine the relationship between aggregation pheromone trap captures of red flour beetles and beetle and trap number. In one experiment, beetle density was kept constant at 200 individuals per chamber while trap number was varied from 1 to 8, and in the other experiment trap number remained constant at one per chamber while beetle density varied from 20 to 800 individuals. Results indicated that approximately one out of 23 red flour beetles were captured in a trap. Number of beetles captured in traps increased significantly as beetle density increased; however, the proportion of beetles captured remained consistent across beetle densities with a mean of 4.7 ± 0.6% of individuals captured. Trap captures varied significantly with trap placement within experimental chambers, indicating that subtle differences in the trapping environment can influence trap captures. Data suggested that trap densities of 0.07–0.10 m^?2 (2–3 traps per chamber) would maximize trap capture, whereas a trap density of 0.13 m^?2 (four traps per chamber) would maximize the predictive ability of a trapping equation estimating beetle density from trap captures. Results provide information needed to more thoroughly explore how environmental factors might influence red flour beetle trap capture in the absence of changes in beetle density. Further understanding of these relationships will allow for more accurate assessments of absolute beetle density from pheromone trap capture data.     

Detection of forces and displacements along the axial direction in an optical trap

We present measurements of the forces on, and displacements of, an optically trapped bead along the propagation direction of the trapping laser beam (the axial direction). In a typical experimental configuration, the bead is trapped in an aqueous solution using an oil-immersion, high-numerical-aperture objective. This refractive index mismatch complicates axial calibrations due to both a shift of the trap center along the axial direction and spherical aberrations. In this work, a known DNA template was unzipped along the axial direction and its characteristic unzipping force-extension data were used to determine 1), the location of the trap center along the axial direction; 2), the axial displacement of the bead from the trap center; and 3), the axial force exerted on the bead. These axial calibrations were obtained for trap center locations up to approximately 4 microm into the aqueous solution and with axial bead displacements up to approximately 600 nm from the trap center. In particular, the axial trap stiffness decreased substantially when the trap was located further into the aqueous solution. This approach, together with conventional lateral calibrations, results in a more versatile optical trapping instrument that is accurately calibrated in all three dimensions.