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Holographic microscopy of holographically trapped three-dimensional structures

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Abstract

Holographic optical trapping uses forces exerted by computer-generated holograms to organize microscopic materials into three-dimensional structures. In a complementary manner, holographic video microscopy uses real-time recordings of in-line holograms to create time-resolved volumetric images of three-dimensional microstructures. The combination is exceptionally effective for organizing, inspecting and analyzing soft-matter systems.

©2007 Optical Society of America

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Supplementary Material (1)

Media 1: GIF (3004 KB)     

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Figures (4)

Fig. 1.
Fig. 1. Combined dynamic holographic optical trapping and holographic video microscopy system.
Fig. 2.
Fig. 2. Holographic imaging of a three-dimensional configuration of holographically trapped colloidal spheres. (a) Conventional bright-field image of five colloidal spheres trapped in the xy plane. Scale bar indicates 5 μm. (b) The pattern is rotated around the y axis by 45°. (c) Bright-field image of the rotated pattern, as seen in the xy plane. (d) Coherent image of the same structure, as seen in the xy plane. (e) Holographic reconstruction of an xz slice through the tilted pattern. Circles denote the intended particle coordinates. [Media 1]
Fig. 3.
Fig. 3. Axial structure of the light field scattered by a colloidal sphere. (a) Hologram recorded in the xy plane of a single sphere trapped at z = 17 μm above the focal plane.(b) Real part of the scattered field reconstructed from (a). (c) Hologram recorded with sphere at z = 0. (d) Axial section of the scattering field obtained by translating the particle past the focal plane in Δz = 0.122 μm steps. (e) Equivalent reconstruction using conventional illumination. Scale bar indicates 5 μm. (f) Axial intensity profiles from (b) and (d) demonstrating accuracy of the axial reconstruction.
Fig. 4.
Fig. 4. Resolution limits for occluded objects. (a) Hologram of the holographically organized structure rotated to 90°, with 4 spheres arranged along the optical axis. Scale bar indicates 5 μm. (b) Holographic reconstruction of ∣v(r, z)∣ in the yz plane. (c) The same section through ∣ℑ{v(r, z)}∣2. (d) Axial traces through ∣ℑ{v(r, z)}∣2 showing positions of axially stacked spheres compared with individual sphere (filled red trace).

Equations (8)

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h z ( r ) = 1 2 π z e ikR R ,
I ( r ) = a ( r ) 2 + 2 { a * ( u h z ) } + u h z 2 .
b ( r ) = I ( r ) a ( r ) 2 a ( r ) 2 { a * ( u h z ) } a ( r ) 2 { u h z }
B ( q ) b ( r ) exp ( iq r ) d 2 r U ( q ) H z ( q ) + U * ( q ) H z * ( q ) ,
H z ( q ) = exp ( ikz [ 1 ( λq 2 πn ) 2 ] 1 2 )
B ( q ) H z ' ( q ) U ( q ) H z z ' ( q ) + U * ( q ) H z z ' ( q ) .
v ( r , z ) v ( r , z ) exp ( ( r , z ) )
= 1 4 π 2 B ( q ) H z ( q ) exp ( iq r ) d 2 q .
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