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Fast generation of holographic optical tweezers by random mask encoding of Fourier components

Mario Montes-Usategui, Encarnación Pleguezuelos, Jordi Andilla, and Estela Martín-Badosa

Open Access Open Access

Abstract

The random mask encoding technique of multiplexing phase-only filters can be easily adapted to the generation of holographic optical tweezers. The result is a direct, non-iterative and extremely fast algorithm that can be used for computing arbitrary arrays of optical traps. Additional benefits include the possibility of modifying any existing hologram to quickly add more trapping sites and the inexistence of ghost traps or replicas.

©2006 Optical Society of America

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Figures (6)
Fig. 1.
Fig. 1. Optical setup for generating holographic optical tweezers.

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Fig. 2.
Fig. 2. Encoding two linear phases by complementary random binary masks.

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Fig. 3.
Fig. 3. (a) Binary mask, 256×256 pixels. (b) Magnitude squared of its Fourier transform in logarithmic scale.

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Fig. 4.
Fig. 4. (a) Hologram encoding an array of 4 optical traps and b) resulting traps.

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Fig. 5.
Fig. 5. New trapping site added to a Gerchberg-Saxton hologram.

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Fig. 6.
Fig. 6. (2.21 MB) Real-time, interactive manipulation of two yeast cells by means of tweezers generated with the algorithm.

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Equations (7)

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E ( x , y ) = ∫∫ R ( u , v ) e − i 2 π λf ' ( ux + vy ) dudv .
R ( u , v ) = ∑ k = 1 N e i 2 π λf ' ( x k u + y k v ) ,
E ( x , y ) = ∑ k = 1 N ∫∫ e − i 2 π λf ' [ ( x − x k ) u + ( y − y k ) v ] dudv = ∑ k = 1 N δ ( x − x k , y − y k ) .
R ( u , v ) = ∑ k = 1 N h k ( u , v ) e i 2 π λf ' ( x k u + y k v ) ,
h k ( u , v ) = { 1 iff ( u , v ) ∈ I k 0 otherwise ,
I l ∩ I m = ∅ ∀ l , m ∣ l ≠ m and ∪ k = 1 N I k = ℜ 2 .
E ( x , y ) = ∑ k = 1 N H k ( x − x k , y − y k ) ,
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