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Optical tweezers using a diode laser Robert S. Afzal and E. Brian Treaty Candela Laser Corporation, Wayland, Massachusetts 01778 (Received 22 October 1991; accepted for publication 16 December 1991) Simple modifications were made to a commercial microscope to enable injection of light from a diode laser, and demonstrate optical tweezers action. The basic properties of microscope I optics are presented together with discussion of principles to be followed in arranging the external optics for achieving useful tweezers. Procedures using a single-mode diode laser along with experimental results are presented in enough detail to permit readers to make their own system for trapping and manipulating single cells. It is surprisingly easy to demonstrate tweezers action once some basic concepts are understood. I. INTRODUCTION Optical tweezers’ are a device used to manipulate small objects such as biological cells using a focused laser beam. The single beam gradient force trap was originally demonstrated by Ashkin and co-workers2 In its most common form, optical tweezers apparatus consists of a laser beam introduced into a microscope and focused by the objective into the object plane. Objects are trapped near the focus of the beam and can be manipulated by moving the laser beam. Once a laboratory curiosity, optical tweezers are gaining acceptance as a useful laboratory instrument. Optical tweezers have been used in various fields of biophysics and biotechnology. Aside from simple uses such as holding one cell or organelle and moving it relative to the other cells, tweezers have been used to make precise force measurements on the compliance of bacterial flagellae3 and other biological motors.4 Tweezers have also been incorporated in cellular surgery and fusion experiments,5 as well as in automated cell counters and sorting apparatus.6 Further applications await the invention and development of suitable techniques by a cadre of researchers with optical tweezers available to them. To date, most tweezers incorporate Nd:YAG, or an argon-ion laser for the trapping beam, which tend to be large and expensive laboratory devices. The use of diode lasers for trapping7 not only provides a cost cutting advantage, but the mechanical support can be smaller and lighter, making it easier to move and set up the instrument. This will hopefully make this apparatus more accessible to a larger number of potential users. In this article we describe how to construct a simple tweezer device based on commercially available parts and provide the reader with a working knowledge so that modifications and customization of this basic design can be made. In the second section we describe the microscope, provide a simplified theory and discuss the requirements for beam steering in order to understand how to couple the laser beam effectively into the microscope. The third section discusses the trapping requirements of the laser beam used. Section IV describes the diode laser used and how to power the diode. Section V describes how to couple the beam into the microscope and presents some results from our own experiments. 2157 II. THE MICROSCOPE A. Description The microscope used in this work is the Nikon Diaphot TMD. This is an inverted microscope with the objective lens below the stage, but the regular type (overhead) can also be used. It has three auxiliary ports-the video output port, the epi-fluorescence attachment port, and the 35 mm camera port. The video accessory is very important, in that we made more adjustments and measurements while looking at the video display than while looking through the eyepieces. Laser beams were injected through the epi-fluorescence port. The video camera, a Sony XC57, has some sensitivity in the IR so the location and symmetry of the laser beam (where it intersects the glass-water interface below the object plane) are readily checked. The microscope objective used was a 100X oil immersion (CFN Plan Achromat, N.A. 1.25, working distance 0.16 mm, focal length 1.71 mm). (Better visibility is available by using phase contrast.) The regular eyepieces ( 10 X CFWN) were modified by attaching infrared blocking BG 18 glass filters to their lower ends for eye protection, supplied by Grayco Optics. The epi-fluorescence attachment (without the exciting lamp) comprises a focusing lens (f-160 mm) and an adjustable iris in the field diaphragm plane. The epi-fluorescence dichroic filter assembly was modified by replacing the filter glass with a visible-IR dichroic supplied by CVI, and the laser beam was injected through the epi-fluorescence port, sometimes with the epi-fluorescence attachment plus an external eyepiece, and sometimes without. The dichroic was the only specially coated optical element* in the microscope. We used a video adapter with relay lens in conjunction with a Sony XC-57 camera for video monitoring and a Tektronix oscilloscope camera to record pictures of the TV monitor, and a Nikon 35 mm camera to take color or black and white photographs. The various ports referred to are depicted in Fig. 1. B. Simple theory of microscope The microscope manufacturers do not supply optical diagrams or other details relevant to the design of their instruments. Fortunately, one can work out all the details Rev. Sci. Instrum. 63 (4), April 1992 0034-6746/92/042157-07$02.00 @copyright, 1992 American Institute of Physics 2157 Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or see http://rsi.aip.org/rsi/copyright.jsp Inverted Microscope FIG. 2. Simplified optics of objective and eyepiece.The spots at A and B are minimum in size when the back aperture is filled. The eyepoint is located at the image of the objective back aperture formed by the eyepiece. Light beams passing through A ’ and B’ are in different directions if the back aperture is filled in both cases.The planes (A, B) and (A’ and B’) are conjugate, as are the eyepoint and the objective back aperture. Foc”sin~ K m %I( , smge - ini sample -we I I LA / EY&Yan&d "lew Of m* stqp Back Of m* Ob~tlve and *,ccllYe oQp?cl~ve/-- FIG. 1. Schematic of typical inverted microscope showing where laser beam is injected. necessary for injecting a laser beam for trapping by noting the following simple facts and approximations: ( 1) The microscope objective is designed to form its image at a distance of 160 m m from its back aperture plane which is approximately at the position of its back focal plane. A beam injected into this back aperture with a divergent radius of curvature of 160 m m (i.e., approximately collimated) will focus to a point in the object plane. The illuminated spot at this point will have minimum size if the injected beam fills the back aperture. To move a spot of minimum size across the object plane requires that the approximately collimated beam at the back aperture be steered in angle while always filling the aperture. Moving a point source (from a focused laser beam for example) in the objective image plane (at the 160 m m position) will cause motion of the spot in the object plane, but its size and intensity will vary unless the beam from the point source always fills the back aperture. (See Fig. 2.) (2) Various planes in the microscope are sequentially imaged to one another and are said to be conjugate. There are two important sets of conjugate planes: the field planes containing the object (specimen) plane, and the aperture planes containing the back aperture of the objective. (The complex light amplitudes in these two sets are approximately Fourier transforms of each other.) A “collimated” laser beam at any aperture plane appears at the back aperture of the objective and its position and steering there are related to its position and steering at the other aperture planes through simple imaging in conjunction with Abbe’s 2158 Rev. Sci. Instrum., Vol. 63, No. 4, April 1992 sine condition. lo (B earn diam.~sine of half-angle is preserved. ) (3) The optical train from the objective out through the epi-fluorescence attachment can be seen from Fig. 1 and contains the following components. There is a negative lens near the objective that moves the image at 160 m m to infinity. A dichroic reflector at 45” couples the beam to the epi-fluorescence attachment. It is thus sitting in a collimated beam. The first element encountered in the attachment is a positive lens that undoes the collimation and allows the image to form in the field aperture plane of the attachment. The lens focal length is about 160 mm. An external eyepiece can be used outside the epi-fluorescence attachment to examine the specimen in the object plane. The conjugate to the objective back aperture (imaged by the eyepiece, in conjunction with the positive-negative lens pair enclosing the collimated portion of the beam) is called the eyepoint. The eyepoint also identifies the position of the Gaussian beam waist of a laser beam injected into the microscope that is focused on the object plane. (This is because the “waist” identifies the minimum in the beam diameter, which occurs at each aperture plane.) This eyepoint is a good place to locate a steering mirror for injecting a laser beam. (See Fig. 3.) (4) For purposes of elementary calculation, ignore the presence of the positive and negative lens pair forming the collimator and simply assume that the image plane is 160 m m behind the objective back aperture. An example will Eyepiece Laser Seam .. \ FIG. 3. Rotation of mirror located at eyepoint accomplishes the beam control illustrated in Fig. 2. Optical tweezers Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp 2158 make this clear. We want to inject a Gaussian beam with spot size (l/e” intensity radius) 2.5 mm into the back aperture of the objective” using a 10X eyepiece outside the field stop of the epi-fluorescence attachment. The 10 Xeyepiece has a focal length of 25 cm/lo. Its distance from the back aperture is then (16 + 2.5) cm. The eyepoint location is l/( l/2.5-1/18.5), or 2.89 cm outside the eyepiece. The image of the 6-mm-diam back aperture of the objective has a diameter of 2.89/18.5 times 6 mm, or 0.94 mm. A Gaussian beam running backward from the objective starts with converging wavefront radius 160 mm and spot size 2.5 mm at a wavelength of say, 842 nm. It propagates 18.5 cm, then encounters a 2.5 cm lens and forms a waist computed to be 2.89 cm beyond the lens (eyepiece). The computed waist size (radius) at the eyepoint is then calculated to be 0.39 mm. The half confocal parameter of this input beam (i.e., the distance from the waist at which the Gaussian beam area is double that at the waist) is 55 cm, so there is no need to try to locate the waist exactly and place it at the eyepoint; although the steering mirror should be located accurately there. With the epi-fluorescence tube removed, a collimated beam with waist 2.5 mm injected into the epi-fluorescence port does essentially the same thing, but without the ease of steerability. This beam encounters first the dichroic beam splitter, then the negative lens, and then the back of the objective. C . Verification of the beam steering requirements Looking into the microscope eyepiece one sees the circular field of the specimen plane. The. eye’s pupil is located at the eyepoint. An injected beam is to be rotated about a point in this eyepoint plane (outside the epi-fluorescence attachment) so as to access any point in the circular field of the specimen. It is easy to verify the steering requirements and measure the mirror scan needed. Measurements were made with a green He-Ne laser. Using a 10 cm focal length lens we focused the beam onto the field diaphragm plane of the fluorescence attachment. The lens was mounted on a micrometer driven stage so as to move the focussed spot sideways in the field plane. The object used in the object plane of the microscope was a 0.1 mm scale from a viewing loupe (Edmund Scientific). Two different objectives were used in the microscope: IOX and 40 X . Motion in the object plane is reduced from that in the field diaphragm plane by the objective magnification. We measured this factor to be 11.05 for the 10 X objective and 42.7 for the 40X objective. This means that the specified magnification are approximate. The field of view through the regular oculars is 1.9 mm wide using the 10X objective and 0.5 mm with the 40x. The field number for these oculars is nominally 20, which when divided by the objective magnification gives the size of the field of view in millimeters. Using the 10X eyepiece, a mirror was mounted on a rotating stage with the axis passing through the eyepoint. As the mirror was rotated, observations were made of the illumination at the location of the objective back aperture.12 If the axis of the rotating stage, arranged to be in the mirror plane, is not in the eyepoint plane, rotation causes the green laser spot to 2159 Diameter Of Object Fteld Negative L?“S Dtchrotc Attachment FIG. 4. Straightened-out version of the optical train between the object plane and the beam steering mirror behind the eyepieces.A beam steering of 46”going into the eyepieceproduces a 7.2”steering at the back aperture of the objective, and this in turn moves the laser spot across the diameter of the object field. move off center at the objective back aperture; observation through the oculars of a ground glass slide in the object plane shows the point of green light fading as it moves t away from the center of the field, eventually disappearing before reaching the visual boundary if the offset is large enough. With the mirror correctly situated at the eye point, the intensity of the green spot is maintained all the way to the visual boundary. By rotating the mirror in the eyepoint plane about an axis normal to the plane of incidence and viewing the HeNe spot in the object plane, one measures the required angular motion of the mirror. For example, with the 10X objective, and a 10x eyepiece behind the field diaphragm plane, we measured 12.06”/mm for the mirror, or 24.12”/ mm for the beam at the eyepoint. Thus, to cover the 1.9 mm field requires 46“ of beam steering (23” of mirror rotation). Similarly, with the 40 X objective we found 49.4”/ mm for the mirror steering and 23.25” to cover the 0.5 mm field. Thus with either objective, we require roughly 46” of beam steering to cover the visual field, independently of the magnification of the objective. The corresponding angle at the back aperture of the objective is 7.2“. (See Fig. 4.) (This independence is not surprising since the angular field observed through the oculars does not depend on which objective is in use.) The required mirror motion is half of this for the rotation axis described above, and higher for other rotation axes. It is easier to inject a large collimated beam into the fluorescence port than to connect the epi-fluorescence attachment, with an extra eyepiece and then introduce the correct Gaussian beam waist at the eyepoint. The approach is satisfactory if one chooses to move the microscope stage for bringing particles into the beam. However, it is difficult to move the stage as smoothly as one can move the laser beam. If one wants maximum power delivered to the object plane or wants to move the focal spot while maintaining constant power, the epi-fluorescence attachment plus eyepiece are recommended. If less than maximum power is satisfactory, lateral translation of the final lens of the collimator will provide some angular scan, and it is necessary to overfill the back aperture of the objective to keep it illuminated as the beam scans. III. TRAPPING REQUIREMENTS The trapping force2 is proportional to laser power for constant beam parameters. This is basically because the Rev. Sci. Instrum., Vol. 63, No. 4, April 1992 Optical tweezers 2159 Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp forces are of the type pgrad E. Ashkin and co-workers2+” have carefully distinguished amongst pressure (due to reflection and absorption), and the gradient forces (due to refraction), and radiometer forces due to thermal gradients. (Optical trapping occurs where the net gradient and radiation pressure balance each other.) The forces tend to be perpendicular to the particle surface, which is readily understood by considering particles large enough that the optical field near the surface is separable into incident, reflected and refracted componentsi The continuity of phase along the surface expressed as the conservation of the tangential component of k vector leads to the laws of reflection and refraction. Then the relation between k vector and momentum (multiplication by Plan&s constant in the photon picture, for example) tells us that there is no tangential momentum transfer; and so the forces are normal to the surface. Laser light that has been injected through the back aperture of the objective can be pictured in the object plane as a set of rays filling a cone, but because of the finite spot size at the apex, a set of Poynting vector flow lines would be more appropriate. A particle that is small compared to the spot, and located close to its center sees a roughly parallel set of flow lines and will be propelled through the focal point without trapping. A larger particle can experience the gradient forces and be trapped. Clearly the gradients are greater for larger N.A. With a N.A. of 1.25 the cone (semivertical) angle is 70” in water while for N.A. of 0.85 it is 40”. We have observed that polystyrene spheres of 2 and 3 pm can be trapped with an objective having N.A. 0.85 (the 60xCF plan achromat with corrector) but 1 pm particles cannot (i.e., at a power level of the order of 10 mW), whereas the 1 ,um particles can be trapped using the N.A. 1.25 objective. With the latter objective, a minimum section of the back aperture has to be filled before the 1 ,um particles get trapped; otherwise, they are pulled into the central part of the field and propelled out roughly vertically. The samples are usually enclosed between a slide and cover with a ring of grease forming the containing walls. If the focus is raised so as to approach the slide, there is a possibility of trapping against the barrier formed by the slide. This type of trapping has been observed. Rays that pass close to the center of a spherical particle produce momentum kicks due to refraction that are almost equal and opposite as shown in Fig 5, which also shows how rays further from the center produce momentum changes with a resultant backward component. In a cone of rays, those close to the axis therefore contribute little to the trapping, but much to the radiation pressure (associated with reflection and absorption) and heating. (Particle trapping involves a balancing of the refractive or gradient forces and the radiation pressure.) Heating should also be minimized in order to reduce any adverse effects of the laser light on living cells. For this reason, Ashkin and Dziedzic” recommended using a laser with a wavelength in the range of 0.8-1.8 pm. Too long a wavelength will be absorbed by water. Diode lasers are readily available in the wavelength range 0.80-0.85 pm. It is surprisingly easy to trap larger particles (-5-10 2160 Rev. Sci, Instrum., Vol. 63, No. 4, April 1992 Force Incident Rays Incident Rays (b) FIG. 5. Illustrates how rays near the edges of the beam can produce backwards directed gradient forces while those near the center cannot. The forces in each area are the resultants of the normal forces at the points of refraction on each ray. pm) such as yeast cells. Smaller particles (- 1 pm) present more of a challenge and force one to check the beam propagation at various stations in the optical train, Trapping can be readily achieved by removing the fluorescence attachment and injecting a collimated beam directly onto the dichroic beam splitter. Verification of trapping can be made by moving the stage and observing all objects move relative to the trapped object. Moving the stage is all right for coarse motion but for fine control or for making precise measurements, moving the laser beam is desirable and more sophistication in the optical train is needed. The approach we have followed is to add the fluorescence attachment and lOXocular, and place a movable mirror at the eyepoint of the ocular as in Fig. 3. Finally, since the particle is trapped beyond the laser focus, and the trapped particle is to be observed in focus visually, the laser beam has to be slightly convergent in the region of the dichroic beam splitter in order for the trapped particle to be brought into focus. (Note also that dispersion in the objective increases this requirement.) IV. DIODE LASER DESCRIPTION Diode lasers can be procured as single-mode or multimode devices. The multimode versions have higher power and lower unit cost (per watt) and they are useful for pumping solid state lasers, which may then be used for optical tweezers. So far we have not found them useful directly for optical tweezers. The single-mode laser, aithough having less power, is more suitable for tweezers. Diode lasers have a larger beam divergence transverse to the junction than along it. For example, the SDL-5412Hl (Spectra Diode Labs 100 mW single mode) has FWHM beam divergence angles of 30” and lo”. The emitting junction dimensions are 1 by 3 pm, and in each of the two transverse directions propagation follows regular Gaussian mode optics behavior.16 The equivalent waist positions are different for the two directions, exhibiting astigmatism. By Optical tweezers Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp 2160 imaging the diode output with magnification using a high N.A. collimating lens, one can fmd the vertical waist then move the diode with a micrometer drive to bring the imaged horizontal waist to the same position. The difference in micrometer readings is then a measure of the astigma- tism. A typical value is 15 ,um for the single-mode diode laser. Upon collimation (Melles-Griot No. 06-GLC 001 collimator) the two divergences are in proportion to the junction dimensions, so an anamorphic prism pair (MellesGriot No. 06 GPA 004) is used to expand the beam (3 X ) F~~f-b’ws L ..-5K 1 2N2222 5 Lamp "1, :~ i + 12” 47 OP400 FIG. 6. Circuit diagrams for (a) powering the laser diode, (b) its thermoelectric cooler, and (c) the photddiode for measuring output power. All capacitor units are PF and the OP4OO’swere powered by a + and - 12 V dc level. PHOTODIODE Inside Diode Laser 2161 2161 Optical tweezers Rev. Sci. Instrum., Vol. 63, No. 4, April 1992 Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp and thereby reduce its divergence in the junction direction. (The diode laser output is polarized parallel to the junction and so the first surface encountered by the beam in the expander is at Brewster’s angle.) Thus, one obtains a collimated, roughly circular, Gaussian beam (with some astigmatism). This beam can be examined with a Reticon array or a Spiricon laser beam analyzer.17 The wavelength is typically 840 nm. The diode with its protective circuitry can be mounted into a small package and mounted alongside the other optical elements, and fed through a short cable from its power supply. Figure 6 shows a suitable circuit diagram for powering the diode, Manufacturers’ recommended handling procedures must be followed to avoid damage to the diode from electrostatic discharge. V. EXPERlMENTAL CONFIGURATION Microscope Objactiw Epi-!aoreocencs Attachment II I 10x Eye Piece Colllmafor Eye Point \ 0-m \ 4:l Telescope Rotating Mirror $ / \ \ Ansmorphlc Prism Pair FIG. 7. System optical layout for making force measurements. 2162 Rev. Sci. Instrum., 4.0=10*’ 3.5 *Ias i60 3.0 r1 o-7 140 2.5 11 O-7 120 2.0 “I o-7 100 1.5.10“ 80 I,0 *to-7 60 3.5 4 4.5 5 5.5 6 6.5 Incident Laser Power (mw) FIG. 8. Measurement of trapping force on 2 p latex spheresas a function of laser power at 842 nm wavelength, using Ashkin’s viscous drag method. AND RESULTS Before getting involved in the development of a complicated optical train, it is very convenient and easy to demonstrate trapping simply by removing the epi-fluorescence attachment and injecting the circularized laser beam from the diode into the microscope onto the dichroic reflecting the beam through the objective. Confirmation of trapping is easily done by slowly moving the translation stage and observing all objects in the field of view move relative to the trapped object. This allows the user to gain a feeling for the optical trapping phenomenon and the forces involved. In order to beam steer for the purpose of moving the trapped object to a desired location or to make more quantitative force measurements utilizing the viscous forces, for example, a more involved optical train needs to be developed. For these purposes, the epi-fluorescence attachment without the UV lamp was inserted into the back end of the microscope. As stated earlier in this report, the epi-fluorescence attachment and a 10X eyepiece projects the image of the back aperture of the objective to the eye point. Based on the Gaussian beam calculation, a beam of about 0.8 mm diameter at the eyepoint will just fill the back aperture of the microscope objective. To achieve this we used a 4:1 telescope to reduce the beam diameter from z 3 to -0.7 mm. We used two positive lenses, f = 10 cm and f = 2.5 cm to form the telescope. Location of the laser spot in the video field of view is determined by adjusting the objective focus and observing the formation of a bright i-l I-J- , 180 Vol. 63, No. 4, April 1992 Diode Laser spot on the video monitor. The spot is formed when light reflected from the glass-water interface is imaged onto the CCD array of the camera. Changing the separation between the lenses in the telescope allows the trapped particle to be brought into and out of focus in the object plane. Since objects at the eyepoint are imaged to the back aperture of the objective a gimbal mounted mirror placed at the eye point can then steer the beam across the field of view without steering off the back aperture of the objective. The reader may then choose to beam steer by moving the gimbal mirror by hand, by motor driven gears or by galvanometers depending on the application desired. To quantify our trapping capability we performed trapping force measurements on 2 pm latex spheres. Measurement of the trapping force by the usual method13 of finding the maximum speed that the particle can be held against the viscous force (the 67rav of Stokes’ law) requires that the focus remain good and uniform as it is moved over the field. In our experiment we used a rotating mirror with a=14” wedge placed at the eyepoint (Fig. 7), As the mirror rotated, the beam traced out an ellipse of 55 and 45 ,um major and minor axes in the object plane. We could then determine the speed at which a particle was released from the trap by measuring the angular velocity of the motor. Maximizing the force with the available laser power from the diode mostly involves minimizing the optical losses (especially by vignetting). Figure 8 shows a graph of trapping force vs laser power. Power levels were measured at the back of the objective by placing an object with an opening the same size as the back aperture where the objectives screw in. We used optics and equipment that were available to us cheaply and quickly. Therefore. Gptical losses in the optical path could be greatly reduced by using specially coated lenses and mirrors if higher trapping forces are desired using the same laser. We would encourage the interested reader to build and experiment with optical tweezers, paying proper attention to eye safety, and verify how easy it is to trap and move particles. Once built, various improvements can be added for beam scanning, computer driven manipulation, a beam rotator (dove prism) for rotating ceils, and so on. Optical tweezers Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp 2162 ACKNOWLEDGMENTS We thank Mr. Zhengliang Lu for setting up the diode laser assembly; Dr. S. M. Block of the Rowland Institute of Science for introducing us to the subject; Dr. Horace Furumoto for his interest, encouragement, and support; and the National Science Foundation for funding this work, under Small Business Innovation Research Grant No. ISI9060563. ’For a comprehensivereview, see S. M. Block, Noninvasive Techniques in Cell Biology (Wiley, New York, 1990), Chap. 15, pp. 375-602. The term “optical tweezers”was coined by A. Ashkin and J. M. Dziedzic in their article in Science 235, 1517 ( 1987). ‘A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, Opt. Lett. 11, 288 (1986). ?I. M. Block, D. F. Blair, and H. C. Berg, Nature 338, 514 (1989). *S. M. Block, L. S. B. Goldstein, and B. 3. Schnapp, Nature 348, 348 (1990); A. Ashkin, K. Schtitze, J. M. Dziedzic, U. Euteneuer, and M. Schliwa, Nature 348, 346 ( 1990). ‘R. W. Steubing, S. Cheung, W. H. Wright, Y. Numajiri, and M. W. Bems, Cytometry 12, 505 (1991). ‘T. N. Buican, M. Smyth, H. A. Crissman, G. C. Salzman, C. C. Stewart, and J. C!. Martin, Appl. Opt. 26, 53 11 ( 1987). ‘S. Sato, M. Ohyumi, H. Shibata, H. Inaba, and Y. Ogawa, Opt. Lett. 16, 2163 282 (1991). The diode that we used had a wavelength of 0.84 pm. ‘The fluorescence attachment comes with a dichroic filter that reflects shorter wavelengths from the exciter and transmits the visible ftuorescence. The optical element should be replaced by another dichroic that reflects the infrared laser light and transmits the visible. Ours was fabricated by CVI. Some infrared still passesthrough the filter from the sample, and this is useful for alignment using the video system, but eye protection filters have to be added to the eyepieces. ‘See, for example, S. Inou6, video Microscopy (Plenum, New York, 1986). IoF. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1951). “The 2.5 mm radius is arbitrary. The back aperture of the objective is about 6 mm. If the spot is too small there is no trapping, while too big a spot over fills the aperture and causes circular fringes around the central spot in the object plane, which represent wasted light. “It is easy to remove the objective and place a sheet of translucent material at the position of the back aperture. 13A. Ashkin, Phys. Rev. Lett. 24, 156 (1970). 14W. H. Wright, G. J. Sonek, Y. Tadir, and M. W. Berns, IEEE J. Quantum Electrons 26, 2148 (1990). “A. Ashkin and J. M. Dziedzic, U. S. Patent No. 4 893 886 (16 January 1990). 16H. Kogelnik, Bell Syst. Tech. J. 44, 455 (1965). 17Theseunits are available from EG&G and Spiricon, Inc., respectively. Optical tweezers Rev. Sci. Instrum., Vol. 63, No. 4, April 1992 2163 Downloaded 30 Oct 2006 to 129.64.54.11. Redistribution subject to AIP license or copyright, see http://rsi.aip.org/rsi/copyright.jsp