Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B21/00—Microscopes
  • G02B21/32—Micromanipulators structurally combined with microscopes
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
  • G02B27/62—Optical apparatus specially adapted for adjusting optical elements during the assembly of optical systems
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
  • G02B6/24—Coupling light guides
  • G02B6/26—Optical coupling means
  • G02B6/35—Optical coupling means having switching means
  • G02B6/3564—Mechanical details of the actuation mechanism associated with the moving element or mounting mechanism details
  • G02B6/3568—Mechanical details of the actuation mechanism associated with the moving element or mounting mechanism details characterised by the actuating force
  • G02B6/3578—Piezoelectric force

Definitions

• 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.
• 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.
• 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.
• 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.
• NA numerical-aperture
• 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.
• 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.
• 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.
• Figure 10 is a diagram illustrating use of pixel-array detectors and digital signal processor in force-measuring optical trap apparatus.
• 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 number 10/ filed concurrently herewith), followed by the disclosure of the beam alignment device and method of the present invention.
• W the power (Watts) carried by the ray
• c the speed of light
• n the refractive index of the surrounding buffer.
• PSD position-sensitive photo-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.
• the resulting current (which is proportional to ray power W,) 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.
• 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.
• Y ⁇ ⁇ Wyi/RD (4b)
• ⁇ is the power responsivity of the PSD photo-diode
• R n is the half-width of the square PSD detector area
• xj and yj are the x and y components of the ray positions
• Wj is the power of each of those rays.
• the x and y components of transverse force are given by combining Eqns. 3 and 4:
• F x ⁇ X R D /c ⁇ R L (5a)
• F y ⁇ Y R D /c ⁇ R L (5b)
• ⁇ X and ⁇ Y 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.
• nulling the detector shifts the zero-angle reference such that the incoming light flux has zero transverse (x,y) momentum in that frame.
• the output distribution changes, not the input. Even then, the output distribution remains symmetrical (null outputs) until external forces F x and F y 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.
• the particle may escape out the back (exit) side of a trap due to a reflection or light scattering forces on the particle.
• a high NA trap requires a high NA collection lens.
• the output rays from the trap will be deflected even farther off axis than the input rays.
• 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.
• 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 14 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.
• 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:
• ⁇ Xj and ⁇ X 2 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 ⁇ Y 2 represent changes in the signals from the first and second detectors respectively induced by the Y component of the force applied to the particle.
• F z 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.
• 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.
• 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 L ) 2 ).
• the circular transmission profile T is sqrt (1 - ( ⁇ / ⁇ R L ) 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 nR , then the detector response to light rayj of intensity Wj that falls a distance r, from the pattern center will be
• and ⁇ Z 2 represent the changes in the signals from the two power concentration detectors resulting from longitudinal force on the trapped particle.
• the difference signal ( ⁇ Zj- ⁇ Z 2 ) 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.
• 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.
• 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.
• the x-axis alignment error is proportional to their difference, namely ⁇ X
• 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.
• PID proportional-integrative-differential
• the x-axis error signal is ⁇ Xj- ⁇ X 2
• the y-axis error signal is ⁇ Y,- ⁇ Y 2 .
• 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.
• both beams pull each other forward via their common interaction with the trapped particle, and increase both their forward momenta.
• both beams get smaller (more concentrated) about the optic axis, increasing their transmission through the patterned attenuators (axial- force sensors).
• 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, (Z ⁇ +Z 2 ) ⁇ ,u, to that of a previous measurement when the trap was empty, (Z ⁇ +Z 2 ) emp ty.
• 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 ⁇ Z signals by their respective laser powers, as measured by the power deflection detector "sum” outputs (see Fig. 2).
• 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.
• 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.
• 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 (F x , F y , F z ) 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.
• 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.
• 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).
• actuators e.g. piezo-electric devices
• 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 collimating 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.
• BFP back focal plane
• Pivoting the optical fiber in this manner acftially 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).
• 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).
• BFP Back-Focal Plane
• the BFP is generally located somewhere inside of a typical microscope objective lens.
• a relay lens 36 is used to project the BFP onto the surface of the detectors.
• 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.
• the fiber's pivot-point X is conjugate to the BFPj (back focal plane of the first, left-hand, objective lens 2).
• the light beam from the fiber end does not translate at BFPj, but rather pivots around the optic axis at the BFPj as the fiber is pivoted.
• 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 BFP 2 (back focal plane of the second, right-hand, objective lens 2) becomes conjugate to the BFP
• a relay lens 36 of focal length A is placed half way between the BFP 2 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 BFP 2 and the relay lens 36, and between the relay lens 36 and detector 22/24). The BFP 2 is therefore imaged onto the detector surface with unity magnification.
• the detector surface becomes conjugate to BFP 2 , and thus to BFP
• the light beam does not translate at the detector surface when the optical fiber is pivoted and the optical trap is moved.
• the force signal remains null regardless of trap movement if nothing is in the trap to deflect the light beam.
• 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. 7 A 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.
• 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).
• 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.
• 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).
• 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.
• the optical trap apparatus 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).
• 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.
• 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
• longitudinal momentum measurements are more conveniently measured using an optical trap with counter-propagating beams as described above and shown in Figs.
• 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 Zj n ⁇ l j a
• any reflected light from a particle is collected by the near-side objective lens 2 and directed back into the nearside detectors 22/24.
• the reflected light is therefore correctly counted as momentum flux to compute force.
• one set of detectors 22/24 is used to measure the transmitted light and the other set of detectors
• the Z m , curvature a i 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 Z ⁇ nn i signal is measured for both the transmitted and reflected light according to: X't eflected ⁇ X-reflccled- ⁇ nnl ⁇ & ⁇ cflccted-imt l ( 1 •-- O
• 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.
• the pixel intensities could be processed locally (on the detector chip) to extract moments of the pixel-intensity distribution.
• Wj would be the light intensity at a specific pixel
• the distance y ⁇ would be its y-coordinate
• 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.
• 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).
• ESSCIRC European Solid State Circuit Conference
• beam alignment via a pivoting optical fiber as described herein is not limited to optical trap applications.
• 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.
• 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).
• 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.
• the focal lengths Rj. of the collection lenses are unequal, or the power responsitivities ⁇ of the power deflection detectors 22 are unequal, or the power responsitivities ⁇ ' of the power concentration detectors 22 are unequal, or the half-width of the square area RQ of the power deflection detectors 22 are unequal, then the equations discussed above can be expanded accordingly.
• the patterned attenuators 28 may need to be different as well.
• nulling can be perfonned 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).

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