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Dynamic Holographic Optical Tweezers
Holotrap, an interactive Java application
to generate multiple dynamic holographic optical tweezers Go to the download page
A major improvement in optical tweezers has been brought about by the introduction of holograms displayed onto spatial light modulators (SLMs). With these in the setup, the laser wavefront can be spatially modified prior to the focusing step, resulting in a completely programmable intensity landscape over the sample plane. Large arrays of optical traps, position three-dimensional control or traps with exotic properties are among the new possibilities of holographic optical tweezers.  Unfortunately, liquid crystal SLMs are notoriously unable to modulate the whole unit circle in complex space, that is, they are incapable of modifying both phase and amplitude of the incoming wavefront on an independent basis. They are constrained to modulate along one-dimensional manifolds through the complex plane, coupling phase and amplitude. Most frequently the spatial light modulator is set to a phase-only configuration. Although there is no control over the amplitude, the phase of the light beam can be changed at will. The limited modulation capabilities of SLMs lead to problems in hologram generation that prevent holographic optical tweezers from reaching their full potential. Although, given a desired array of traps, the required hologram can be easily obtained by computing an inverse Fourier transform, the result is, in general, a full complex object that cannot be accommodated on the display. Algorithms have been developed that provide solutions by constraining the hologram to be a pure phase function but still generate usable traps, but they are time consuming. Computational load makes user interaction with the sample difficult in real time so there is a clear need for faster algorithms and better displays.  The algorithm divides the spatial light modulator into as many subdomains, Ik, as traps are required so that these subdomains do not overlap and jointly cover the whole modulator area. Then, each linear phase function (or quadratic for 3D control) is displayed only on the pixels of a given Ik. (see Figure). Random Ik subdomains give good, well-shaped optical traps. Once the random masks are selected, the hologram can be directly written onto the spatial light modulator without performing any further computation. Thus, the procedure is very fast and can be easily carried out at near video-rates, therefore enabling real-time interaction with the user. Our interactive holographic optical manipulation system based on this algorithm is shown in the video below. The control software is implemented in Java and is capable of displaying holograms (512x512 pixels) at an average rate of 10-12 Hz (including aberration correction of the Holoeye SLM and compensation of the operating curve nonlinearities), using a Pentium IV HT, 3.2 Ghz, computer. Click the image to watch the video (mpeg file, 3 MB): 
The experimental set-up uses a Holoeye LC-R 2500 reflective SLM to display the computed holograms and generate the desired trap pattern at the focal plane of the objective lens. We used an oil immersion objective, 100x, NA 1.3, mounted on an adapted inverted Nikon TE2000 optical microscope, which allows both focusing the laser beam onto the sample plane and observing the sample and traps with the CCD camera through the dichroic mirror.  Click the image to watch a video trapping a single yeast cell (mpeg file, 2.2 MB):   We
carried out a complete characterization of the modulator by a technique
previously developed [2]. The characterization consists of measurements
of the amplitude and phase modulation for each grey level displayed on
the SLM. Depending on the polarization state of the input light and on
the polarizing elements placed after the display, different modulation
operating curves are obtained (one for each configuration). In order to
optimize light efficiency, we searched for a phase-only configuration.
If the modulator is placed between polarizers with their axes of
transmission oriented at -45º and 64º with respect to
the
vertical of the laboratory, we obtained the curve shown in the figure,
where the contrast is only 1:1.2 (an almost flat amplitude response)
and the maximum phase modulation is 1.98 pi (for a wavelength of 532
nm). To generate the holograms, we developed an iterative method based
on the Gershberg-Saxton algorithm [3], which allows the optimization of
the desired hologram to any complex modulation curve of the SLM.We dynamically trapped and moved several yeast cells between 5-10 µm with a 120 mW 532 nm laser. However, when trying to get the traps focused we found them severely aberrated and far from the diffraction-limited results we expected.  The following figure shows two experimental traps focused at different planes. We believe that this may be caused by the SLM panel not being completely flat but having a small optical power. When placed at 45º, this residual lens may introduce the astigmatic behaviour we observed.  We corrected this digitally, by adding this phase pattern to all the holograms.  The experimental traps after correction look much more symmetrical.  Click the image to watch a video trapping multiple yeast cells (mpeg file, 3.6 MB). Three corrected holographical optical traps are trapping yeast cells. The traps are controlled by means of the SLM:  References [1] J. E. Curtis, B. A. Koss and D. G. Grier, “Dynamic holographic optical tweezers”, Opt. Commun. 207, 169–175 (2002). [2] E. Martín-Badosa, A. Carnicer, I. Juvells, and S. Vallmitjana, “Complex modulation characterization of liquid crystal devices by interferometric data correlation”, Meas. Sci. Technol. 8, 764-772 (1997). [3] R. W. Gershberg and W. O. Saxton, Optik 35, 237-246 (1972). Download the presentation E. Martín-Badosa et al. "Generation of Holographic Optical Tweezers with Arbitrary Modulation Operating Curves" presented at Diffractive Optics 2005, September 2005, Warsaw (Poland). Related publications
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