Schematic setup for digital in-line holography. A laser at and a beam expander (BE) are used to illuminate the dust particles. The interference pattern of reference and object wave is recorded with a CCD sensor. To avoid saturation of the CCD sensor, a neutral density filter (NDF) is mounted in front of the camera. Additionally, a video mircoscope (VM) in top-view position is used as a reference diagnostic.
(a) Central part of the hologram of microspheres levitated about above the electrode, i.e., in the bulk plasma region of the rf discharge. The full hologram has . To guide the eye a sketch of the hologram is plotted below (b). Other smaller ring shaped interference patterns are caused by dust particles on rf-reactor windows.
Numerical reconstruction of the hologram. Solving Eq. (1) the complex wave field is computed for planes perpendicular to the optical axis. The distance of the plane closest to the hologram is . The distance between neighboring planes is typically chosen to half a particle diameter.
Result of the numerical reconstruction of the hologram shown in Fig. 2(a). Although the reconstruction scheme uses the full hologram, the amplitude of the complex wave field is plotted just for a small fraction containing dust particles. The position of the different reconstruction planes is given with respect to , i.e., the distance from the CCD sensor is . Two particles and are marked to show that they are in focus in different planes.
Reconstruction of the complex amplitude with its (a–c) real part and (e–g) imaginary part at different reconstruction planes in a distance . The real part and the intensity of a single particle of the cluster reaches its maximum at the focal plane (d), whereas the imaginary part vanishes at the focal plane (h). This can be used to determine the depth position of particles.
Average particle positions of a 2D dust layer consisting of 9 particles. For comparison, the measurements with the DIH (○) and the top-view video microscope (∗) are overlaid. The -axis is aligned with the optical axis which is additionally indicated by an arrow.
(a) Top-view of the trajectory of a particle (10 frames). The solid line shows the results of the DIH and the dashed line those of the video microscope (b) -position of a particle in every frame. The comparison of the DIH results (-) and the video microscope (∗) shows an average displacement of . (c) Same analysis for the -position. Here, the average displacement is .
Particle arrangement of small clusters ( and ). (a, b) Inverted video microscope (top-view) images. (c, d) Average positions of the reconstructed clusters consisting of 4 (c) and 7 (d) particles. The marker size represents the root mean squared displacement of particles from their equilibrium position. For comparison, the top-view projections are shown below.
(a) Typical image of the central part of the dust cloud. Due to their rapid motion and an exposure time of , the particles are imaged as short lines. (b) Velocity distribution of the particles in the dust cloud. The dashed line is a 2D Maxwell distribution with .
(a) Particle position from a single hologram. To simplify the comparison with Fig. 9(a), just the projection into the -plane is plotted. (b) Average pair distribution from the DIH data. The function shows characteristics of finite particle arrangements in a gaseous state.
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