Multi-functional optical tweezers using computer-generated holograms

Transcription

1 PRE-PUBLICATION Optics Communications 000 (2000) 000±000 Multi-functional optical tweezers using computer-generated holograms J. Liesener *, M. Reicherter, T. Haist, H.J. Tiziani Institut fur Technische Optik, Universitat Stuttgart, Pfa enwaldring 9, D Stuttgart, Germany Received 17 July 2000; accepted 6 September 2000 Abstract Optical tweezers are capable of trapping microscopic particles by photon momentum transfer. The use of dynamic computer-generated holograms for beam shaping allows a high exibility in terms of trap characteristics and features. We use a liquid crystal display (LCD) to display the holograms. E ciency losses caused by the periodic electrode structure of the LCD have been clearly reduced by use of an optically addressed spatial light modulator. We realized multiple traps, which can hold and move at least seven silica spheres independently in real time. We also demonstrate the controllability of trapped particles in three dimensions without the need for mechanical elements in the setup. Ó 2000 Elsevier Science B.V. All rights reserved. 1. Introduction The ability to manipulate micrometer-sized particles with laser beams has led to applications, mainly in biological elds. Early works of Ashkin et al. in 1970 [1] and in the 1980s [2] served as seeds for this technique now known as optical tweezers. Therein ray optics and photon momentum considerations were used to show that, roughly speaking, a high-index particle n particle > n medium is attracted by the beam focus if the parameters are chosen appropriately. In experimental works of several authors [3±8] di erent setups have been realized showing the usability of optical tweezers for manipulation and investigation purposes. Normally a trapped particle is moved by motion of a microscope stage. Alternatively adjustable mirrors or accousto-optical modulators can be used to steer the beam and thus the trapped particle [9]. Such setups become quite complicated if three-dimensional steering or multiple trapping is desired [10]. In Ref. [11] we have presented a holographic tweezer setup in which computer-generated holograms written on a liquid crystal display (LCD) have been used to control the number, positions, and shapes of optical traps in two dimensions. The basic setup is brie y explained in Section 2. We extend this method to the full three-dimensional manipulation of multiple objects as shown in Section 3. In Section 4 we present a modi ed setup with an optically and an electrically addressed LCD in order to improve the di raction e ciency considerably and hence much more laser power is available for the hologram reconstruction. * Corresponding author. Fax: address: liesener@ito.uni-stuttgart.de (J. Liesener) /00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S (00)

2 2 J. Liesener et al. / Optics Communications 000 (2000) 000± Basic tweezer setup The basic experimental setup of the tweezer is shown in Fig. 1. Its central element is the LCD which is controlled by a personal computer. It displays the Fourier holograms which are read out by a collimated 1 W Ar -laser (Spectra Physics 165) at a wavelength of 488 nm. The beam is then coupled into the microscope setup by a dichroic mirror (DM). The beam diameter is reduced to t the 2 mm aperture of the water immersion microscope objective, MO (Zeiss Achroplan 100/ 1.0 W). The hologram reconstruction in the focal plane of the MO forms the trap. This is where the particles are trapped for manipulation. The illumination from below with a white light source is used for imaging the particles onto the CCD camera (Sony XC±55). The strong backscattered laser light is ltered out by an interference lter. The twisted nematic LCD (Epson) with VGA resolution ( pixels) was removed from a data projector (InFocus LitePro 580). It has a ll factor of 44% and a pixel pitch of 42 lm. The active area has a size of 26:9 20:2 mm 2. By removing the polarizers on both sides of the LCD panel the LCD no longer acts as an amplitude modulator, as originally desired. The phase shifting properties can be optimized for maximum di raction e ciency by the choice of the input Fig. 1. Optical tweezer setup containing an LCD for holographic beam shaping. polarization. A phase shift of 1.6p can be accomplished at 488 nm by the LCD used. The computation of Fourier holograms is straightforward for manipulation in two dimensions. In this case the reconstruction is just the Fourier transform of the hologram. Therefore a central spot, capable of trapping a high index particle, is generated if the hologram consists of a uniform phase U. A lateral displacement of this trap can be achieved if the hologram is chosen to be a blazed grating: U x; y ˆ 2p x 2p y mod 2p 1 K x K y K x and K y are the fringe periods in the x and y direction. For light modulators with a maximum phase shift below 2p, as in our case, the e ciency is reduced and part of the intensity remains in the central (zeroth order) spot. Multiple traps can be realized by summing up the complex functions e iuj x;y and then calculating the argument of that complex function:! X U x; y ˆarg e iu j x;y 2 j By considering only the phase of the complex sum, trap intensity variations can occur. The behavior is complex and not yet studied thoroughly by us. However, these variations did not appear hindering in our experiments. We also employed more complex elds like doughnuts [11] which have advantages in some applications. The keyboard is used to control the tweezer features like the number of traps, their positions, and their shapes. Fig. 2 shows the simultaneous trapping of seven 1 lm silica spheres which have been precisely arranged in a V-shape. Each of the trapped particles can be moved independently by the user. Among the spheres two appear larger because the corresponding traps hold two particles on top of each other. The computation of one hologram with a personal computer (Pentium III 600) takes less than 1 s for seven simultaneous traps.

3 J. Liesener et al. / Optics Communications 000 (2000) 000±000 3 Fig. 2. Seven silica spheres, positioned precisely in a V-shape. The 1-lm-sized particles can be moved independently. 3. Three-dimensional trapping By no means is one limited to a manipulation in just one plane. By adding a lens term to the blazed gratings the beam focus can be shifted up and down parallel to the optical axis: U x; y ˆ 2p x 2p y C x 2 y 2 mod 2p 3 K x K y C controls the axial position of the trap. The appearance of a typical hologram is depicted in Fig. 3. It is a hologram for three laterally and axially displaced traps which lls the entire LCD panel. Fig. 4 shows an experiment that demonstrates the controllability in three dimensions. To our knowledge this is the rst time that full three-dimensional particle manipulation with a single beam optical trap was accomplished without moving parts. Two equivalent silica spheres, again of 1 lm diameter, are trapped. By changing the hologram, one of the spheres is pushed out of the observation plane and therefore appears blurred and bigger. After being moved to the left the sphere is shifted back into the observation plane on the other side of the stationary sphere. 4. Improved setup using an optically addressed liquid crystal display For the practical use of optical tweezers and holographic applications in general it is often desirable to have maximum laser power available in the hologram reconstruction. The setup of Fig. 1, however, leads to some loss of laser power caused by the LCD structure. The loss can be traced back to two major limiting factors: First, about 56% of the laser power is

4 4 J. Liesener et al. / Optics Communications 000 (2000) 000±000 Fig. 3. Phase hologram for three laterally and axially displaced traps. Fig. 4. Manipulation in three dimensions. One of the 1 lm particles (a) is pushed out of the observation plane (b). It is passed over to the other side of the the stationary particle (c±e) and shifted back into the observation plane (f).

5 J. Liesener et al. / Optics Communications 000 (2000) 000±000 5 blocked by the mask structure surrounding each pixel which also de nes the ll factor of 44%. Second, the periodic structure of the LCD acts as an optical grating which de ects 56% of the remaining power into side orders. Only the central di raction order of the LCD can be used for the hologram reconstruction. Considering further re- ection and absorption losses, only 15% of the original laser power is available for the hologram reconstruction. Those are general limitations whenever LCDs are used in holography. We overcome the described losses for the most part by use of an additional optically addressed liquid crystal display (OALCD). The basic optical tweezer setup (Fig. 1) is modi ed by replacing the LCD by a low-pass lter setup, as shown in Fig. 5. The OALCD (Jenoptik SLM-O30) has one planar-nematic liquid crystal layer of 30 mm in diameter. A dielectric mirror between the liquid crystal and the photoconductor layer prevents the read light from addressing the photoconductor and allows a read out in re ection. A 2p phase shift of the reading light at 488 nm has been achieved with a writing light intensity of 0.5 mw/ cm 2 at 633 nm. A resolution of 25 line pairs/mm can be accomplished with the element. As before, an Ar -laser at 488 nm was used to read out the hologram information, this time however in re- ection. A HeNe laser at 633 nm illuminates the LCD. Fig. 6 illustrates how the hologram information is transferred from the LCD to the OALCD in a 4f Fig. 6. The hologram information is transferred from the LCD to the OALCD. The phase disribution is rst displayed by the LCD, encoded as an intensity distribution. After a low-pass ltering process, the hologram information is converted back into a phase distribution by the OALCD. setup. The coherent imaging system contains an aperture for low-pass ltering purposes, located in the Fourier plane of the imaging lens. The di raction orders due to the LCD pixel structure appear as equally spaced copies of the Fourier-transformed hologram in the Fourier plane of the imaging lens. By blocking those side orders, the information about the LCD pixel structure gets completely lost, leaving the hologram information only. Fig. 7 demonstrates how the LCD pixel structure of the write light gradually vanishes when the aperture diameter is reduced. In this example a blazed grating has been written on the LCD. Di raction loss is reduced because the resulting hologram ± displayed on the OALCD ± is not pixelated any more and additionally the e ective ll factor now is 100%. Minor sources of losses are the limited re ectivity of the broad-band dielectric mirror in the OALCD and some absorption loss in the ITO layer [12]. The OALCD re ects 85% of the reading light at 488 nm. In order to quantify the improvement obtained by the OALCD, we measured the di raction e ciency, de ned as the ratio of the power in the rst di raction order of a blazed grating to the input laser power. For the unmodi ed setup it is 9.5%. This reduced value as opposed to the 15% from above is due to the imperfect polarization and phase shift properties of the LCD. With the combination of the electrically and the optically addressed LCD we considerably improved di raction e ciency by a factor of nearly 6±53%. Fig. 5. Optical tweezer setup containing the low-pass ltering setup.

6 6 J. Liesener et al. / Optics Communications 000 (2000) 000±000 Fig. 7. The e ect of low-pass ltering. (a) The aperture is wide open, the LCD pixel structure is clearly visible. (b) The central ve di raction orders pass the partly closed aperture, the pixel structure appears blurred. (c) Only the central di raction order passes the aperture, the pixel structure is completely vanished. 5. Conclusion The versatility of optical tweezers using computer-generated holograms displayed on an LCD has been demonstrated. The technique quali es for a wide range of applications. We demonstrated the ability to trap and manipulate multiple particles independently in three dimensions without mechanical elements. In terms of hologram reconstruction e ciency a clear improvement has been accomplished by use of an additional, OALCD. The e ciency was raised by a factor of almost 6 compared to a single electrically addressed LCD. Acknowledgements We thank the Deutsche Forschungsgemeinschaft for the nancial support. References [1] A. Ashkin, Phys. Rev. Lett. 24 (4) (1970) 156±159. [2] A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm, S. Chu, Opt. Lett. 11 (1986) 288±290. [3] Y. Tadir, W.H. Wright, O. Vafa, T. Ord, R.H. Asch, M.W. Berns, Fertil. Steril. 53 (1990) 944±947. [4] M.D. Wang, H. Yin, R. Landick, J. Gelles, S.M. Block, Biophys. J. 72 (1997) 1335±1346. [5] S.C. Kuo, M.P. Sheetz, Science 260 (1993) 232±234. [6] P.C. Mogensen, J. Gluckstad, Opt. Commun. 175 (2000) 75±81. [7] P.J.H. Bronkhorst, G.J. Steekstra, J. Grimbergen, E.J. Nijhof, J.J. Sixma, G.J. Brakenho, Biophys. J. 69 (1995) 1666±1673. [8] K.T. Gahagan, G.A. Swartzlander, Opt. Lett. 21 (1996) 827±829. [9] R.M. Simmons, J.T. Finer, S. Chu, J. Spudich, Biophys. J. 70 (4) (1996) 1813±1822. [10] E. Fallman, O. Axner, Appl. Opt. 36 (10) (1997) 2107± [11] M. Reicherter, T. Haist, E.U. Wagemann, H.J. Tiziani, Opt. Lett. 24 (1999) 608±610. [12] M. Gilo, R. Dahan, N. Croitoru, Opt. Eng. 38 (1999) 953± 957.