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Algorithms

Holographic optical tweezers (HOTs) offer several advantages over other alternative methods for generating multiple optical traps, such as unique manipulation capabilities, but suffer a main limitation: the holographic optical elements displayed on the modulator are difficult to calculate.

Every different arrangement of traps requires a specific and complicated diffraction pattern that takes time to compute. Although modulators are refreshed at DVI frame rates (60 Hz) and are thus capable of choreographying quick positional changes of a set of optical traps, this is frequently achieved only through pre-computed sequences of holograms (see Figure 1).

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Figure 1. Latex microspheres (3 micron in size) are manipulated by an array of holographic optical traps

Video-rate computation of holograms is however possible by use of the supercomputing capabilities of modern graphic-processing units (GPUs) included in most PC video cards, but tricking them into computing non-graphic algorithms has been difficult so far. An alternative route is to use simplified algorithms and regular CPU power although at the expense of a lower optical performance.  
Real-time computation of holograms enables in the end a live user interaction with the samples and therefore results in much more convenient and powerful experimental systems. We have used the latter approach with excellent results in our HOT setups. To that end, we have written software (publicly available here) that permits the interactive trapping of microscopic particle through a windows user interface (Figure 2).

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Figure 2. HOLOTRAP Interactive manipulation of several latex microspheres

The HOLOTRAP software incorporates two different algorithms, the well-known "lenses and gratings" and our own "random mask encoding" method. The lenses and gratings algorithm is slower than the random mask method and may produce visible spurious "ghost" traps, especially for symmetric arrangements. On the other hand, the random mask method is less efficient wasting energy as a random background "noise", being appropriate to quickly generate a small number of traps.

The random mask algorithm divides the spatial light modulator into as many subdomains 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 subdomain (see Figure 3). Random subdomains give good, well-shaped optical traps.

Figure 3. A divide-and-conquer strategy is the basis of hologram computation

A video sequence showing real-time generation of holograms by clicking and dragging with a mouse is shown in Figure 4.

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  Figure 4. Fast hologram generation of three optical traps