# Patent

## Title
Optical beam translation device and method utilizing a pivoting optical fiber

## Abstract

An alignment device and method for delivering a light beam to an optical application, such as an optical trap having a pair of lenses with overlapping focal regions for trapping a particle therein. The alignment device includes a light source for generating a beam of light, a support member, an optical fiber, a collimating lens, and actuators. The optical fiber includes an input end for receiving the beam of light, and a generally rigid portion extending from the support member and terminating in a delivery end for emitting the beam of light. The collimating lens collimates the emitted beam of light. The actuators exert forces on the generally rigid portion such that it pivots about a pivot point of the optical fiber at the support member. The collimated beam of light pivots about an optical pivot point as the optical fiber pivots about the pivot point.

## Background
This application claims the benefit of U.S. Provisional Application No. 60/504,067, filed Sep. 19, 2003.


GOVERNMENT GRANT
This invention was made with Government support under grant (Contract) No. GM-32543 awarded by the NIH and grant nos.: MBC-9118482 and DBI-9732140 awarded by the NSF. The Government has certain rights to this invention.


FIELD OF THE INVENTION
The present invention relates to optical particle trapping, and more particularly to a device and method for trapping and manipulating tiny objects using laser light, and measuring minute forces imparted on these objects both in transverse and longitudinal directions.
BACKGROUND OF THE INVENTION
Devices for optically trapping small particles are better known as “optical traps” or “optical tweezers”. The technique relies on the forces created by one or more laser beams that are refracted by a microscopic object in order to trap, levitate and move that object. By focusing a laser beam though a microscope objective lens down to a very small spot (focal region), particles with high indices of refraction, such as glass, plastic, or oil droplets, are attracted to the intense regions of the beam and can be permanently trapped at the beam's focal region. Biologists are considerably interested in optical traps because minute forces can be measured with sub-picoNewton accuracy on the trapped object. Since such small forces are not accessible by conventional techniques such as scanning-force-microscopy, optical traps have become a major investigation tool in biology.
One (preferred) method to measure such forces includes capturing and analyzing the light after interacting with the particle and computing the change in momentum flux of the light due to interaction with the particle. Capturing all the light exiting the optical trap can be difficult, given that a single-beam trap needs highly marginal rays in order to trap efficiently, but even a high numerical-aperture (NA) lens may not accept all these rays when they have interacted with the particle and are deflected farther off the optic axis. In such a case, it can be difficult to capture and analyze all the light leaving the optical trap. Therefore, to address this issue, dual beam optical traps have been developed. Conventional counter-propagating beam optical traps have been used to trap particles, and measure extremely small transverse forces imparted on those particles. See for example, “Optical tweezers system measuring the change in light momentum flux”, Rev. Sci. Instrum., Vol. 73, No. 6, June 2002. Dual-beam traps are also better than single-beam traps for trapping particles with higher refractive indices.
One issue with optical traps is the alignment of the single or counter-propagating beams, so that the focal region(s) of the lens(es) are properly aligned with the sample (and each other for dual beam devices). For optical tweezers, two different methods are commonly used to move a laser-beam focus relative to samples in the objective focal plane: (1) move the sample chamber relative to the fixed beam-focus until the particle comes to the beam and is captured, or (2) translate the beam focus relative to the fixed sample chamber by changing the entrance angle of the laser beam into the back of the objective lens. The 2nd method has advantage of faster response time, as required for constant-position feedback that cancels Brownian motion in the trap. Beam-steering can be accomplished by several different methods, such as moving the lens, using a galvanometer to move a steering mirror, using an optic modulator to move the beam, translating the end of an optical fiber, etc. See for example, Svoboda and Block, Annu. Rev. Biophys. Biomol. Struct. v.23, pp. 247-285, FIG. 2 (1994).
Each of the conventional beam alignment techniques has its drawbacks. Moving the sample or lens is too slow to cancel Brownian motion. The galvanometer-mirror method is too large and complex. The acousto-optic modulator method is too large and complex, and has low light-transmission efficiency. Translating the delivery end of an optical fiber has potential advantage of simplicity, speed and high light efficiency, but suffers from an effect where the steered beam does not remain fixed at the back-focal-plane (BFP) of the objective lens. A beam steering method that does pivot about the BFP is described by Allersma et al. Biophys. J. v.74, pp. 1074-1085, FIG. 1B (1998). Unfortunately, that system uses the moving-lens “telescope” method, so the frequency response is lower than that required for Brownian-force noise cancellation.
There is a need for an optical alignment system and method, ideal for optical trap systems, that ensures and maintains the optical alignment of a light beam incident on an optical element such as focusing lens, while changing the incident angle of the light beam on that lens.
SUMMARY OF THE INVENTION
The present invention is an alignment device ideal for aligning optical systems such as optical traps. The alignment device includes a support member, an optical fiber having a generally rigid portion extending from the support member and terminating in a delivery end for emitting a beam of light, a lens for collimating the emitted beam of light, and at least one actuator for exerting a force on the generally rigid portion such that the generally rigid portion pivots about a pivot point of the optical fiber at the support member.
Another aspect of the present invention is an alignment device for delivering a light beam to an optical trap having a pair of lenses with overlapping focal regions for trapping a particle therein, where the alignment device includes a light source for generating a beam of light, a support member, an optical fiber having an input end for receiving the beam of light and a generally rigid portion extending from the support member and terminating in a delivery end for emitting the beam of light, a lens for collimating the emitted beam of light, and at least one actuator for exerting a force on the generally rigid portion such that the generally rigid portion pivots about a pivot point of the optical fiber at the support member.
One more aspect of the present invention is a method of delivering and aligning a beam of light, the method including emitting a beam of light from a delivery end of an optical fiber wherein the optical fiber includes a generally rigid portion that extends from a support member and terminates in the delivery end, collimating the emitted beam of light, and exerting a force on the generally rigid portion such that the generally rigid portion pivots about a pivot point of the optical fiber at the support member.
Other objects and features of the present invention will become apparent by a review of the specification, claims and appended figures.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram illustrating a particle trapped in an optical trap.
FIG. 2 is a schematic diagram illustrating the position sensor and circuitry for analyzing the light exiting the optical trap.
FIG. 3 is a diagram illustrating the counter-propagating beam optical trap.
FIG. 4 is a diagram illustrating the profile detector.
FIG. 5 is a diagram illustrating a first technique for aligning the optical trap.
FIG. 6A is a diagram illustrating the technique for aligning the optical trap according to the present invention, by deflecting the optical fiber that delivers the laser beam to the optical trap.
FIG. 6B is a diagram illustrating how the detector surface is disposed at a conjugate to the pivot point of the optical fiber.
FIG. 7A is a side view of the deflecting optical fiber beam alignment technique using piezo actuators to align the laser beams in the optical trap.
FIG. 7B is an end view of the deflecting optical fiber beam alignment technique using piezo actuators to align the laser beams in the optical trap.
FIG. 8 is a side view of an alternate embodiment of the deflecting optical fiber beam alignment technique of the present invention.
FIG. 9 is a side view of a miniaturized and enclosed version of the counter-propagating beam optical trap.
FIG. 10 is a diagram illustrating use of pixel-array detectors and digital signal processor in force-measuring optical trap apparatus.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention is a method and system for aligning an optical beam, and is described in the context of optical traps. Single beam and dual beam optical traps are first disclosed (which are the subject of co-pending U.S. patent application Ser. No. 10/943,716 filed concurrently herewith), followed by the disclosure of the beam alignment device and method of the present invention.
Optical Traps
A ray of light can be thought of as a directed stream of photons, which carries with it a momentum flux dP/dt=nW/c, where W is the power (Watts) carried by the ray, c is the speed of light and n is the refractive index of the surrounding buffer. In an optical trap containing a pair of objective lenses 2 and a particle 4 held therebetween in a trap region defined by the focal regions of the lenses, a particular ray[i] may be deflected by interaction with the particle 4 through angles θi, φi relative to the optic axis of the trap, as shown in FIG. 1. The reaction force felt by the trapped particle due to that ray is given by:

Fi=dPi/dt=(nWi/c)[i sin θi cos φi +j sin θi sin φi+k(1−cos φi)].  (1)

To compute forces on a trapped particle with many rays passing nearby, it is sufficient to analyze the power of all rays entering and leaving the vicinity of the trap and sum over them according to Eqn. 1, with the sign convention such that an un-deflected ray cancels its flux contribution when it exits. Experimentally, such analysis can be performed by collecting the exiting rays with another lens opposite the trapping lens. If that collection lens is a coma-free objective lens (similar to the trap lens), and if it is placed so the trap focus is also the focus of the collection lens, then a particular version of the Abbe sine condition holds for rays that strike the collection lens. According to this rule, a ray coming from the focus and inclined at an angle θi to the optic axis will emanate from the back principal plane parallel to the optic axis at a radial distance r from that axis given by

ri=n sin θiRL  (2)

where RL is the focal length of the collection lens. Combining Eqns. (1) and (2) in x-y coordinates (x=r cos φ and y=r sin φ) and summing over all rays gives an expression for the force on the particle in terms of the spatial intensity distributions W(x,y)enter and W(x,y)exit of light entering and exiting the lenses.

Fx=(1/RLc)([ΣWixi]enter−[ΣWixi]exit)  (3a)

Fy=(1/RLc)([ΣWiyi]enter−[ΣWiyi]exit)  (3b)

Fz=(n/c){[ΣWisqrt(1−(ri/nRL)2)]enter −[ΣWisqrt(1−(rinRL)2)]exit}  (3c)

The distance-weighted sums of the light intensity, Σ Wixi and Σ Wyyi, are called the “power deflections”. These moments of the spatial intensity distribution can be measured by projecting the light exiting from the collection lens onto a position-sensitive photo-detector (PSD), also known as a power deflection detector. Such detectors are different from quadrant detectors since they comprise one continuous diode (i.e. a power deflection sensor/detector) 6, not four. They can be thought of as a planar PIN junction photodiode sandwiched between two plate resistors, as shown in FIG. 2. When a light ray strikes a particular point on the detector 6, it liberates holes and electrons in the reverse-biased diode layer that electrically connects the two planar resistors at that point. For each axis (x,y), the resulting current (which is proportional to ray power Wi) is divided between the two electrodes 8 at opposite edges of a resistor layer depending on the distances to each electrode from where the ray strikes. The currents from all rays striking the PSD are thus weighted by distance from the edges and summed in a linear fashion. An op-amp circuit 10 such as the one illustrated in FIG. 2 takes the 4 current signals (two into the top PSD layer and two out of the bottom) and converts them into separate signals for x- and y-distance-averaged intensities. Thus, power deflection is a measure of the powers and off-axis distances of all the light rays forming the light beam. Power deflection of the light beam increases if the overall light beam power uniformly increases and/or if the overall light beam shifts position in the positive direction, and vice versa.
The signals from a PSD amplifier (FIG. 2) are given by

X=ΨΣWici/RD  (4a)

Y=ΨΣWiyi/RD  (4b)

where Ψ is the power responsivity of the PSD photo-diode, RD is the half-width of the square PSD detector area, xi and yi are the x and y components of the ray positions, and Wi is the power of each of those rays.

The x and y components of transverse force are given by combining Eqns. 3 and 4:

Fx=ΔXRD/cΨRL  (5a)

Fy=ΔYRD/cΨRL  (5b)

where ΔX and ΔY represent changes in the signals from the power deflection detector induced by the X and Y components of the force applied to the particle.

The signals from a PSD detector can be used directly as the x and y force components on a trapped particle, provided the input light momentum is first nulled. That is, the PSD is pre-positioned, with no object in the trap, such that the X and Y outputs are zero. For a symmetrical input beam, this act puts the detector on the optic axis. For an asymmetric input beam, nulling the detector shifts the zero-angle reference such that the incoming light flux has zero transverse (x,y) momentum in that frame. When a particle is trapped, only the output distribution changes, not the input. Even then, the output distribution remains symmetrical (null outputs) until external forces Fx and Fy are applied to the trapped particle.
A problem for the light-force sensor derives from the necessity to collect all the exiting light to calculate the force. A single-beam optical trap can apply strong radial (x,y) trapping forces, but rather weak axial (z) forces. Unless the beam is highly convergent and includes the full set of marginal rays from a high NA objective lens, the particle may escape out the back (exit) side of a trap due to a reflection or light scattering forces on the particle. Thus, to recover all the exiting light, such a high NA trap requires a high NA collection lens. However, if an external force acts on the particle, then the output rays from the trap will be deflected even farther off axis than the input rays. For larger particle displacements, even the highest NA objectives available may not collect those exiting marginal rays. Therefore, it is preferable (but not necessary) to utilize the light-momentum method using a dual beam optical trap, instead of a single beam optical trap, as detailed below.
It is possible, however, to trap particles with lower NA optics by using counter-propagating laser beams that converge through opposing lenses to a common focus (i.e. common focal region). Thus the reflected or scattering light force is balanced and the axial escape route is blocked. Such an instrument, a dual counter-propagating beam optical trap, has been reduced to practice and is shown schematically in FIG. 3. Vertically polarized light beams from separate diode lasers 12 (e.g. 835 nm light, at 200 mW, from SDL 5431 lasers) are sent through polarizing beam splitters 18, quarter wave plates 16, and objective lenses 2 (e.g. Nikon 60× plan-Apo-water NA 1.2), 50 that the light beams are circularly polarized as they encounter particle 4. The exiting light beams are collected by opposite objective lenses 2, become horizontally polarized at the opposite quarter wave plates 16, are deflected down by polarizing beam splitters 18, and are split into a pair of beams (preferably equally) by non-polarizing beam splitters 20. The first of the pair of beams are directed to power deflection detectors 22 (which measure transverse momentum of the beams) and the second of the pair of beams are directed to power concentration detectors 24 (which measure longitudinal momentum of the beams). The particle is preferably contained in a fluid chamber 26 formed by two coverslips separated by heat-sealed parafilm strips.
The high NA objective lenses 2 have the ability to focus/collect high-angle rays, but the laser beams which enter them are kept small in diameter, thus under-filling the back apertures. Therefore the trapping rays form a narrow cone (low NA beam) and the most marginal of these rays can be collected by the opposite lens 2, even when those rays are deflected outside the initial set of low inclination angles by the application of an external force to the particle 4. In this instrument, the transverse forces from the two beams add together, and hence the signals from power deflection detectors 22 must be summed to give the x and y components of transverse force on the trapped particle:

Fx=(ΔX1+ΔX2)RD/cΨRL  (6a)

Fy=(ΔY1+ΔY2)RD/cΨRL  (6b)

where ΔX1 and ΔX2 represent changes in the signals from the first and second detectors respectively induced by the X component of the force applied to the particle, and ΔY1 and ΔY2 represent changes in the signals from the first and second detectors respectively induced by the Y component of the force applied to the particle.

To obtain the longitudinal force along the optic axis, Fz, a different type of detector is utilized, namely one that measures the power concentration of the incident beam. The power concentration is a measure of cross-sectional distribution of the power within the beam. As the power of the light beam is concentrated more toward the center of the beam, its power concentration is greater. Conversely, as the beam power distribution is more spread out away from the center of the beam, its power concentration is less. Thus, for example, a power concentration detector produces a signal that increases or decreases as the power distribution within the beam becomes more concentrated toward the center of the beam, and vice versa. One example of a power concentration detector is one in which the distance-weight (sensitivity) falls off from the optic axis according to Eq. 3c, for example as sqrt (1−(r/nRL)2). Such response is obtained by a power concentration detector 24 having an attenuator 28 with a circular transmission profile, placed over a planar photodiode 30, as illustrated in FIG. 4. The circular transmission profile T is sqrt (1−(r/nRL)2), where r is now the radial distance from the center of the attenuator. One such profile generated numerically as pixels is illustrated in FIG. 4.
If the attenuator 28 is constructed so its pattern radius is nRL, then the detector response to light rayi of intensity Wi that falls a distance ri from the pattern center will be

Z=Ψ′ΣWisqrt(1−(ri/nRL)2)  (7)

where Ψ′ is the responsivity of the planar photo-diode. By combining equations (3c) and (7), the force signal Fz is proportional (by a known factor) to the difference between the signals from the two opposing axial power concentration photo-detector signals, namely,

Fz=(n/c)(ΔZ1−ΔZ2)/Ψ′.  (8)

where ΔZ1 and ΔZ2 represent the changes in the signals from the two power concentration detectors resulting from longitudinal force on the trapped particle.

In practice, to compensate for differences in laser powers and sensitivities of the axial detector, the difference signal (ΔZ1−ΔZ2) is preferably nulled, by addition of an arbitrary offset, before any particle enters the trap. The signals from detectors 22/24 are preferably sent to a processor 14, which calculates particle forces and displacements utilizing the above described equations. Processor 14 could be a stand alone device, or a personal computer running appropriate software.
An advantage of the above described transverse light-force sensor is that calibration depends only on constant factors such as RL and c that do not change with experimental conditions. Force is obtained from the conservation of linear momentum of light as measured in the far field. Thus the measurement of force becomes independent of trap/bead details such as shape and size of the particle and refractive indices. Unfortunately, for the above described axial force sensor, its calibration changes with the refractive index of the fluid buffer surrounding the particle. For instance, adding 1 molar NaCl to water inside the fluid chamber changes its index from 1.334 to 1.343. Such a −1% correction could simply be applied to the values in Eq. 8, except that the circular-profile attenuator is constructed with a particular radius suitable for water (Eq. 7). For typical rays, where r/nRL<0.5, the residual z-force error will be very small, i.e. less than 1⁄4 percent.
Due to changes in room temperature or humidity and its effect on many optical parts, an optical trap with dual counter-propagating beams requires constant alignment in order to keep the foci (focal regions) of the counter-propagating beams coincident. Such alignment involves moving one trap focus to lie on top of the other. To move a focus, either the beam angle must be steered as it enters the back of the objective lens, or else the whole objective lens must be moved. FIG. 5 illustrates a solution of the latter type, where optical trap of FIG. 4 is modified so that one of the objective lenses 2 is movable with a piezo-actuated x-y-z stage 32 to overlap the foci. Other modifications include the addition of second polarizing beam splitters 34 and relay lenses 36. If a particle has been trapped, this means the foci of the two counter-propagating beams are close enough to maintain the trap, and there is insufficient external forces on the particle to break the particle free. But if the foci are slightly misaligned, then the trap beams will exert force on each other (trade momentum) via their common interaction with the particle.
While an external transverse force on the trapped particle deflects both exiting beams in the same direction, a transverse misalignment of the foci causes the exit beams to be deflected in opposite directions. In this case, information to correct the alignment error (by moving the objective lens) may be derived from the differential force signals. Whereas the Fx is proportional to the sum of PSD signals ΔX1+ΔX2, the x-axis alignment error is proportional to their difference, namely ΔX1−ΔX2. To control transverse alignment, an instrument computer uses a proportional-integrative-differential (PID) feedback algorithm to move the piezo stage based on readings from the transverse force sensors of power deflection detectors 22. Here the x-axis error signal is ΔX1−ΔX2 and the y-axis error signal is ΔY1−ΔY2.
Foci may also be misaligned along the optic axis, that is, they may form short of each other or past each other along the z-axis. In the former case (falling short), the two beams pull each other forward via their common interaction with the trapped particle, and increase both their forward momenta. Thus both beams get smaller (more concentrated) about the optic axis, increasing their transmission through the patterned attenuators (axial-force sensors). In the latter case (foci formed past each other), the beams retard each other and their exit angles widen, decreasing their transmission through the patterned attenuators. An axial-alignment error signal can be derived from comparison of current axial sensor outputs with a particle in the trap, (Z1+Z2)full, to that of a previous measurement when the trap was empty, (Z1+Z2)empty. However the “empty” measurement is not current and would need to change if the laser power changes with time. Therefore it is best to normalize the ΔZ signals by their respective laser powers, as measured by the power deflection detector “sum” outputs (see FIG. 2). Then, the improved z-axis error signal becomes:

z−error=(Z1/Sum1+Z2/Sum2)full−(Z1/Sum1+Z 2/Sum2)empty.

This axial error signal is processed by the computer's PID algorithm and fed back to the z-axis piezo of the objective XYZ stage 32. Alternately, if an optical fiber is used to deliver the laser beam to the lens 2, the distance between the delivery end of the optical fiber and the lens 2 can be adjusted based on the error signal to align the foci of the two beams. Such a system corrects temperature drift in the axial alignment of the foci.

The above described counter-propagating-beam laser optical trap utilizes specialized photometric sensors placed in (or referenced to) the back focal planes of objective lenses to measure changes in the spatial distribution of light intensity there, changes caused by some action on the trapped particle. The beam trap manipulates micron-sized refracting particles while simultaneously measuring external forces on that particle via changes in the momentum of the trapping light. The above described beam trap can measure pico-Newton external forces of the particle in all three orthogonal axes.
For example, as illustrated in FIG. 3, a molecule 40 can be attached between particle 4 and a pipette 42, to examine its mechanical properties. As the pipette 42 is moved to exert mechanical stresses on the molecule, the force exerted in the molecule can be measured by the optical trap. All three force components (Fx, Fy, Fz) on the trapped particle, and thus on the molecule attached thereto, can be measured. Calibrations for both transverse and axial measurements are immune to changes in focus sharpness, particle size/shape/index, or laser power, and both can be used for alignment of dual trap beam foci, either against transverse errors or longitudinal errors. Calibration of the transverse force sensor is immune to changes in refractive index of buffer liquid, whereas longitudinal sensor calibration is affected slightly.
Beam Alignment Device and Method
FIG. 6A illustrates beam alignment via pivoting an optical fiber according to the present invention. Instead of moving one of the beams by moving one of the objective lenses 2, the beam is transversely moved in the trap (or in any other application) by moving the light beam before it reaches the objective lens 2 using an actuator assembly 44 that bends an optical fiber about a pivot point (see FIGS. 7A and 7B). Specifically, the optical output of the laser diode 12 is coupled into a low-mass optical fiber 46, which has a generally rigid portion that is moved (driven) with actuators (e.g. piezo-electric devices) to achieve a high frequency response (>2 kHz). The delivery end 62 of the optical fiber 46 is positioned one focal-length (F) away from a positive lens 48 so as to produce collimated light which enters the back of an infinity-corrected microscope objective lens 2. The optical fiber 46 is held at a pivot point X (farther from the lens) by a plate, block or other rigid member 52, such that the optical fiber pivots about that point (with a bend length BL) when the actuators move.
Pivot-point X is a conjugate focal point (through the positive lens 48) to a point at the center of the objective lens' back focal plane (BFP), which is a plane perpendicular to the optic axis at back focus of the lens. Pivoting the optical fiber in this manner actually tilts the optical fiber delivery end 62 away from the center of lenses 2 and 48. Yet, this movement causes the angle of light entering the objective lens 2 to change (thus steering the trap focus transversely) while the beam remains stationary at the BFP of the objective lens 2 (i.e. the beam rotates about the BFP of lens 2). Thus, the light beam pivots about an optical pivot point P (at the BFP) as the optical fiber pivots about it mechanical pivot point X. The advantage of this configuration is that it provides a faster response time in translating the beam on the far side of lens 2, as required for constant-position feedback that cancels Brownian motion in the optical trap.
Calibration stability for the optical trap derives from accurate measurement of light-momentum flux irrespective of changes in particle size, refractive index or trap position. The relay lenses 36 are used to make the calibration particularly immune to changes in trap position. The expression in Equations 3(a-c) are accurate provided that the rays in FIG. 1 between the right-hand lens 2 and the detector surface are collimated and on-axis. In practice, however, rays coming out of a lens are seldom perfectly collimated or centered. Indeed for a steered trap shown in FIG. 6A, the rays entering and leaving the lenses are deliberately made off-axis. The problem of transferring the luminance pattern (intensity distribution) from the lens 2 to the detectors 22/24 would be exacerbated by a large distance between the lens and detectors because the pattern wanders further off axis with distance or grows larger/smaller depending on collimation errors. The ideal place to put the detector to eliminate such effects is at the Back-Focal Plane (BFP) of the lens 2. At that location, changes in trap position relative to the optic axis will not affect the rendering of angle distributions Eq. 1 into spatial distributions on the detectors (Equations 3). Unfortunately the BFP is generally located somewhere inside of a typical microscope objective lens. To effectively place the detectors 22/24 inside such a lens, a relay lens 36 is used to project the BFP onto the surface of the detectors. That is, the detector surfaces of detectors 22/24 are disposed at a conjugate focal plane to the BFP of the objective lens 2 through a separate relay lens 36.
A particular example of a conjugate-plane arrangement that gives null sensitivity to trap movement is illustrated in FIG. 6B. Here the fiber's pivot-point X is conjugate to the BFP1 (back focal plane of the first, left-hand, objective lens 2). The light beam from the fiber end does not translate at BFP1, but rather pivots around the optic axis at the BFP1 as the fiber is pivoted. Meanwhile, the optical beam at the optical trap (at the objective lens focus) translates in the object-focal plane in order to manipulate trapped particles. The two objective lenses 2 are placed so their object focal planes OFP's are coincident. Therefore, the BFP2 (back focal plane of the second, right-hand, objective lens 2) becomes conjugate to the BFP1 and also conjugate to pivot-point X. Thus the beam of light does not translate at the BFP2, but instead pivots around the optic axis there. In this example, a relay lens 36 of focal length A is placed half way between the BFP2 and the surface of one of the detectors 22/24. A distance of 2A (double the focal length A) is left on both sides of the relay lens 36 (between BFP2 and the relay lens 36, and between the relay lens 36 and detector 22/24). The BFP2 is therefore imaged onto the detector surface with unity magnification. The detector surface becomes conjugate to BFP2, and thus to BFP1, and thus to pivot-point X. The light beam does not translate at the detector surface when the optical fiber is pivoted and the optical trap is moved. Once the detector 22/24 is centered on the optic axis of the light beam, the force signal remains null regardless of trap movement if nothing is in the trap to deflect the light beam. In practice, the light beam is split (as shown in FIG. 5) so that the surfaces of both detector 22 and detector 24 are conjugate to the pivot-point X.
FIGS. 7A and 7B illustrates an actuator assembly 44 of the present invention. The optical fiber 46 is pivoted by placing its delivery end inside a thin metal tube 50 that is clamped or otherwise fixed by plate or block 52. The optical fiber 46 is preferably cemented to the tube 50 at its distal end so it moves with the tube-end 54. The optical fiber emits light outward from the tube-end 54 (preferably the tube end and fiber distal end are adjacent or even coincident). The portions of tube 50 and optical fiber 46 therein extending from plate/block 52 together form a generally rigid portion of the optical fiber, and plate/block 52 serves as a support member for pivoting this rigid portion. Electrical signals are supplied to piezo stack actuators 56 (such as NEC Corp. AE0203D08), which exert forces on and deflect the tube 50 (and optical fiber 46 therein). Two such actuators 56 preferably act on a hard spherical enlargement 58 (“ball pivot”) of the tube 50, and are arranged at right angles so as to give orthogonal bending deflections and thus steer the laser-trap beam focus in both transverse dimensions of the object focal plane. Placing the ball pivot 58 close to the pivot point X and far from the tube's distal end amplifies the movement of the tube end 54. Thus a piezo stack that moves a short distance can cause the optical fiber delivery end to move a large distance. Z-axis adjustment can be implemented by moving the entire piezo actuator assembly 44 (along with lens 2) via a stage or a third piezo actuator.
FIG. 8 illustrates an alternate embodiment of the actuator assembly 44 of the present invention. Depending on the focal length of the collimating lens 48 and the distance to the BFP, pivot point X may need to be rather close (e.g. <1 cm) to the delivery end 62 of the optical fiber 46. Therefore, considering the large size of the actuators 56 and spherical enlargement 58, the actuator assembly 44 can be configured as illustrated in FIG. 8, where the optical fiber 46 pivots nearer its output end 62 (i.e. pivot point X is close to the fiber delivery end). With this configuration, actuators 56 push/pull on and bend an outer tube 60 (which concentrically surrounds tube 50). The outer tube 60 preferably includes a pivot screen 64 disposed at its distal end, which is an electro-formed metal screen having small square holes. The glass optical fiber 46 extends out of tube 50 and passes through one of these holes and rests in the square corner of that hole. Nearby, the optical fiber 46 is clamped or otherwise secured inside tube 50, which does not move. Sufficient clearance exists between tubes 50/60 such that the outer tube 60 can bend from the actuator pressure (i.e. pivot about pivot point Y), while the inner tube 50 remains straight. Thus, in this embodiment, it is the inner tube 50 serves as the support member for the generally rigid portion of the fiber, and the generally rigid portion of the optical fiber is that portion of optical fiber 46 extending out of inner tube 50. This portion of the optical fiber is generally rigid by either sufficient reinforcement (separate tube or plastic sheathing) or small enough in length relative to its inherent stiffness, such that it generally does not bend under the weight of gravity as it pivots. Outer tube 60 is affixed to support member 52 and pivots about pivot point Y, which induces the generally rigid portion of optical fiber 46 to pivot about pivot point X as the optical fiber is deflected by the movement of the pivot screen 64. This configuration has two levels of distance-amplification over the normal actuator movement: one level where the distal end of the outer tube 60 moves farther than the actuators 56, and another level where the output-end 62 of the optical fiber 46 moves farther than the pivot screen 64 (at end of the outer tube 60).
Additional details regarding the optical beam trap usable in conjunction with the beam alignment device and method of the present invention will now be discussed. FIG. 9 illustrates an embodiment that allows for more precise force/distance measurements that are not hindered by floor vibration, acoustic noise, and room temperature changes. A large apparatus on an optical table is especially difficult to isolate from vibrations if it sits on a floor that people walk on. Air-leg supports on such tables can transmit and even amplify low-frequency floor vibrations (below 5 Hz). Large metal tables also undergo large dimensional changes when the room temperature changes. A steel table 1-meter wide can expand over 10,000 nanometers for each 1-degree C. rise in room temperature. By reducing the optical trap apparatus in size, it becomes practical to enclose all optical elements in a temperature-controlled metallic shield (to prevent temperature induced dimensional changes, exclude dust particles and block audible room noise). Likewise, it becomes possible to hang the apparatus from the ceiling by an elastic cord or spring and thus better isolate it from building/floor vibrations, down to a lower frequency cutoff than an optical table (<1 Hz).
Thus, the above described counter-propagating-beam laser optical trap can be miniaturized by making five changes: (1) All lens and prism components are reduced to minimum size consistent with laser-beam diameter. (2) All free-air optical paths are reduced to a minimum length. (3) The optical breadboard-table is replaced by a custom-machined optical rail. (4) Many parts in the laser conditioning optics (namely the heating/cooling diode laser mount with collimating lens and Faraday isolator and anamorphic prism and astigmatism correction lens and spatial filter input lens and pinhole filter and spatial filter output lens) are replaced with by single small component, that is, a “butterfly mount” temperature-controlled diode laser coupled to single-mode optical fiber. (5) Finally, the assembled optical components are enclosed in an aluminum housing with attached heaters (thermostatically controlled to maintain constant housing temperature). Two additional improvements can include: placing the objective lenses and fluid chamber level with or below the optical components so that if a fluid leak occurs then the salt-buffers will drip downward away from the optics, and employing the above described object-focal plane, piezo-electric driven optical beam translators for independent translation of the laser-trap foci.
Consistent with the above described miniaturization, optical trap of FIG. 9 includes a housing 70 (preferably made of aluminum), the temperature of which is controlled by one or more thermostatic heaters 72. The optical components are mounted to an optical rail 74, with the objective lenses 2, the prism/lens assemblies 76 (which includes the beam splitters 18, quarter wave plates 16, etc.), the piezo actuator assemblies 44, the detectors 22/24 and the laser diodes 12 mounted even with or above the fluid chamber 26. A CCD camera 78 and visible light source 80 can be included for capturing images of the particles through the optical chain of objective lenses. An attachment ring 84 and cords 86 (e.g. vibration dampening elastic or bungee type chords) are used to suspend the housing 70.
While longitudinal momentum measurements are more conveniently measured using an optical trap with counter-propagating beams as described above and shown in FIGS. 3-5 and 9, it should be noted that it is possible to perform such measurements using an optical trap with a single beam, as now explained below.
An external force on a trapped particle registers as a change in the light momentum entering vs. leaving the trap. Therefore it is important to know both the light intensity distribution going into the trap and coming out, to make a valid force measurement. For transverse forces, this task is simplified by moving the power deflection detectors 22 to a position that is centered on the undeflected beam. This adjustment is made with lasers 12 running but no particle in the trap. More specifically, the power deflection detectors 22 measure only the light exiting the trap, not entering it, so they perform only half of the integration required in Equations 3. This problem is solved by aligning the detectors on the optic axis so that, when no particle is present in the trap, the output beams are centered on the detectors and the difference signals vanish. The light entering the trap carries no transverse momentum in this frame of reference and need not be considered even after a particle has been introduced. Only the exiting light is affected by interaction with the particle.
However there is no way to move a power concentration detector as shown in FIG. 3 so as to null its output when the laser is on and no particle is in the trap. For axial forces, Eq. 3(C) also must be “differenced” in order to give the proper Z-axis force. The signals for each power concentration detector should be performed in 2 steps as follows: measure a signal value Zinitial with no particle in the trap, and then measure a signal value Zfinal with an object in the trap, and take the difference ΔZ=Zfinal−Zinitial. If this ΔZ=0, then no external force is acting on the beam of light detected by that particular PSD. Accordingly, Eq. (7) can be modified to read:

Z=Ψ′{[ΣWisqrt(1−(ri/nRL)2) ]final−[ΣWisqrt(1−(ri/nRL)2)]initial}  (10)

and the corrected form of Eq. 8 for a single-beam trap might seem to be simply

Fz=(n/c)(ΔZ)/Ψ′.  (11)

Unfortunately, a further consideration complicates force measurements in a single-beam trap (or for a dual-beam where the laser powers are different). Most trapped particles, such as plastic or silica beads, are not anti-reflection coated. Therefore a small Fresnel reflection develops at their dielectric/water interface. This reflection of the trapping beam creates a pressure on a trapped particle that moves it forward in the trap (away from the laser source). At some equilibrium position, the forward force is balanced by a refraction force. Here the forward momentum of the transmitted light is increased by concentrating the rays near the optic axis, just enough to balance the momentum kick from the reflected light. Placing a particle in a single-beam trap will cause it to settle slightly forward in the trap and increase Zfinal over Zinitial, even though there is no external force on the particle.

There are several possible techniques to deal with this false Z-force component of the detector signal: First, use a dual-beam optical trap with two counter-propagating beams of equal power, so the particle remains in the center of the trap. Second, make differential measurements where Zinitial is determined from a trapped particle but it is known that the external force on that particle is zero. Then, apply the external force and measure Zfinal. Such a technique may be inconvenient to use in practice. Third, use a single beam, but use two power deflection detectors 22 and two power concentration detectors 24 in a similar manner as shown in FIG. 3 (i.e. essentially omit one of the lasers 12 from the configuration of this figure). This third technique is now explained in more detail.
The detectors 22/24 of FIG. 3 measure the transmitted light from the opposite-side laser. However, with the arrangement of the quarter-wave plates 16, any reflected light from a particle is collected by the near-side objective lens 2 and directed back into the near-side detectors 22/24. The reflected light is therefore correctly counted as momentum flux to compute force. Thus, by omitting one of the lasers from the configuration of FIG. 3, one set of detectors 22/24 is used to measure the transmitted light and the other set of detectors 22/24 is used to measure the reflected light. To measure Z-force in such a configuration, the Zinitial signal is first obtained for both transmitted and reflected light with no particle in the trap. Then, a particle is trapped that is subject to an arbitrary external force, where the Zfinal signal is measured for both the transmitted and reflected light according to:

Ztransmitted=Ztransmitted-final−Ztransmitted-initial  (12a)

Zreflected=Zreflected-final−Zreflected-initial  (12b)

Thus, the force signal Fz is:

Fz=(n/c)(ΔZtransmitted−ΔZreflected)/Ψ′.  (13)

This is physically the same measurement as that of the dual-beam optical trap according to Eq. 8.

It should be noted that each set of detectors 22/24 can be combined into a single detector that measures both transverse and longitudinal momentum of the light beam. More specifically, the power deflection detector 22, the power concentration detector 24 and the beam splitter 20 can be replaced with a single detector 90 as shown in FIG. 10. Detector 90 includes a 2-dimensional array of light-sensitive elements (pixels) with an appropriate electronic read-out interface. The pixel intensities could be read into a computer or control circuit where calculation of forces are made numerically by weighting the individual pixel intensities by their distances from the optic axis, and combining them according to Eq. 3. Alternately, the pixel intensities could be processed locally (on the detector chip) to extract moments of the pixel-intensity distribution. In using detector 90, Wi would be the light intensity at a specific pixel, the distance xi would correspond to the x-coordinate of that pixel (relative to center=0), the distance yi would be its y-coordinate, and its radius would be given by ri=sqrt (xi2+yi2). A CCD television camera and frame-grabber would suffice for collecting such data, especially if the frequency response (including exposure, readout and computation time) exceeds 5000 Hz in order to cancel Brownian motion inside the trap. Newly developed high-speed cameras and frame grabbers are now available (see for example EPIX, Inc, http://www.epixcorp.com/products/pixci_c13sd.htm). The signal processor 100 would then receive digital data from two such camera/frame-grabber combinations. A new class of digital PSD (also called “profile sensor”) is available that promises both low cost and high speed in a pixel-array detector. These detectors pre-process the pixel data on the same chip as the pixel array so as to reduce the amount of serial data that needs to be sent to the computer, i.e., the frame-grabber-processor function is “built-in” (see for example, Hamamatsu (Solid State Division) Profile Sensor S9132 Preliminary Data Sheet January, 2004; and “High Speed Digital CMOS 2D Optical Position Sensitive Detector” by Massari et al. at the European Solid State Circuit Conference (ESSCIRC) in 2002, available online at http://www.itc.it/soi_publications/pub/43.pdf).
It is to be understood that the present invention is not limited to the embodiment(s) described above and illustrated herein, but encompasses any and all variations falling within the scope of the appended claims. For example, beam alignment via a pivoting optical fiber as described herein is not limited to optical trap applications. As used herein, collimating lenses or lenses that collimate simply make a diverging or converging light beam more collimated, and do not necessarily make the resulting light beam perfectly collimated. Therefore, as used herein, a collimated beam is one that is less diverging/converging than it was before passing through a collimating lens. A single lens could include a plurality of lenses, and vice versa. While actuators 56 are preferably piezo-electric devices, they could be any conventional mechanical device for moving or applying force onto the optical fiber. The generally rigid portions of optical fiber 46 between the pivot point X and the optical fiber output end 62 need not necessarily be straight, but should be sufficiently rigid to preserve the exit angle of the beam relative to the optical fiber as the optical fiber pivots. The portion of optical fiber 46 between the pivot point X and the optical fiber output end 62 need not be straight, but should be rigid to preserve the exit angle of the beam from the optical fiber. The screen 64 could be replaced by a ledge, an eyelet, a constricted end, or simply omitted altogether (should the end of outer tube 60 sufficiently control the rigid portion of the optical fiber).
It should be further noted that a single laser device could produce the pair of counter-propagating light beams (e.g. by using a beam splitter), instead of two light sources shown in FIG. 3. For the above described equations and the single or dual beam device of FIG. 3, one in the art will appreciate that if the focal lengths RL of the collection lenses are unequal, or the power responsitivities Ψ of the power deflection detectors 22 are unequal, or the power responsitivities Ψ′ of the power concentration detectors 22 are unequal, or the half-width of the square area RD of the power deflection detectors 22 are unequal, then the equations discussed above can be expanded accordingly. For example, equation 6a (Fx=(ΔX1+ΔX2) RD/c ΨRL) is a short hand expression for Fx=ΔX1RD1/cΨ1RL2+ΔX2RD2/cΨ2RL1, and equation 6b (Fy=(ΔY1+ΔY2) RD/c ΨRL) is a short hand expression for Fy=ΔY1RD1/cΨ1RL2+ΔY2RD2/cΨ2RL1, to accommodate any unequal characteristics of the first and second lenses 2, first and second power deflection detectors 20, and first and second power concentration detectors 24. For differing focal length objective lenses, the patterned attenuators 28 may need to be different as well. Lastly, if the above described detectors are not nulled by centering them on the beam, then nulling can be performed by subtracting from the signals that portion of the signal that exists caused by the non-centered beam (i.e. measure signal using light beam without particle in trap, or from particle in trap with no forces thereon).

## Claims

1. An alignment comprising:
a support member;
an optical fiber having a generally rigid portion extending from the support member and terminating in a delivery end for emitting a beam of light;
a lens for collimating the emitted beam of light; and
at least one actuator for exerting a force on the generally rigid portion such that the generally rigid portion pivots about a pivot point of the optical fiber at the support member;
wherein the support member is a first tube member concentrically disposed around the optical fiber, the alignment device further comprising:
a second tube member concentrically disposed around the first tube member and engaged with the generally rigid portion of the optical fiber.

2. The alignment device of claim 1, wherein the second tube member includes a spherical enlargement, and wherein the at least one actuator exerts the force on the spherical enlargement to pivot the generally rigid portion.

3. The alignment device of claim 1, wherein the second tube includes a screen member having a plurality of holes, and wherein the optical fiber extends through one of the plurality of holes.

4. An alignment device for delivering a light beam to an optical trap having a pair of lenses with overlapping focal regions for trapping a particle therein, the alignment device comprising:
a light source for generating a beam of light;
a support member;
an optical fiber comprising:
an input end for receiving the beam of light, and
a generally rigid portion extending from the support member and terminating in a delivery end for emitting the beam of light;

a lens for collimating the emitted beam of light; and
at least one actuator for exerting a force on the generally rigid portion such that the generally rigid portion pivots about a pivot point of the optical fiber at the support member;
wherein the support member is a first tube member concentrically disposed around the optical fiber, the alignment device further comprising:
a second tube member concentrically disposed around the first tube member and engaged with the generally rigid portion of the optical fiber.

5. The alignment device of claim 4, wherein the second tube member includes a spherical enlargement, and wherein the at least one actuator exerts the force on the spherical enlargement to pivot the generally rigid portion.

6. The alignment device of claim 4, wherein the second tube includes a screen member having a plurality of holes, and wherein the optical fiber extends through one of the plurality of holes.

7. A method of delivering and aligning a beam of light, the method comprising:
emitting abeam of light from a delivery end of an optical fiber, wherein the optical fiber includes a generally rigid portion that extends from a support member and terminates in the delivery end;
collimating the emitted beam of light;
exerting a force on the generally rigid portion such that the generally rigid portion pivots about a pivot point of the optical fiber at the support member;
wherein the collimated beam of light pivots about an optical pivot point as the optical fiber pivots about the pivot point;
focusing the collimated beam of light using a second lens having a back focal plane disposed at the optical pivot point;
collimating the focused beam of light using a third lens;
focusing the beam of light from the third lens using a relay lens; and
measuring a light momentum of the beam of light from the relay lens using a detector, wherein the detector has a detection surface disposed at a conjugate to the pivot point.

8. A method of delivering and aligning a beam of light, the method comprising:
emitting a beam of light from a delivery end of an optical fiber, wherein the optical fiber includes a generally rigid portion tat extends from a support member and terminates in the delivery end;
collimating the emitted beam of light; and
exerting a force on the generally rigid portion such tat the generally rigid portion pivots about a pivot point of the optical fiber at the support member;
wherein:
the support member is a first tube member concentrically disposed around the optical fiber;
a second tube member is concentrically disposed around the first tube member and is engaged with the generally rigid portion of the optical fiber; and


the exerting of the force includes exerting the force on the second tube member.