Parameters of multi-convex lens array and the recording system for dusty plasma experiment with the CMOS camera D810.
The integral photography technique has an advantage in which instantaneous three-dimensional (3D) information of objects can be estimated from a single-exposure picture obtained from a single viewing port. Recently, the technique has come into use for scientific research in diverse fields and has been applied to observe fine particles floating in plasma. The principle of integral photography technique and a design of a light-field camera for dusty plasma experiments are reported. The important parameters of the system, dependences of the size of the imaging area, and the spatial resolution on the number of lenses, pitch, and focal length of the lens array are calculated. Designed recording and reconstruction system is tested with target particles located on known positions and found that it works well in the range of dusty plasma experiment. By applying the integral photography technique to the obtained experimental image array, the 3D positions of dust particles floating in an RF plasma are identified.
- dusty plasma
- integral photography
- three-dimensional reconstruction
- particle measurements
- plenoptic camera
Fine particles immersed in plasma are charged up negatively, show three-dimensional (3D) motion, and form 3D-ordered state, i.e., Coulomb crystal [1, 2, 3, 4, 5]. Diagnostic methods for 3D information about the positions of fine particles in a plasma have therefore been widely researched. Among the various dusty plasma experiments, 90° separated two CCD cameras with helping 3D computed tomographic reconstruction  and stereoscopic [7, 8] are widely used to determine the 3D position of each fine particle . They require two or more detectors; however, the locations and numbers of observation ports are considerably restricted in many plasma experiment devices. Planar laser scanning technique can obtain the 3D information of particles with one CCD camera [10, 11], but it requires a little while to scan across the wide field of view. In-line holographic techniques  and two-color gradient methods [13, 14] can obtain 3D position of dust particles from a single-exposed photograph taken from a direction; however, these methods require a 12 bit or higher dynamic range sensors. It is required that a technique can acquire the 3D information of a dusty plasma with a single-exposed photograph taken from one viewing port with a conventional dynamic range sensor.
The “integral photography technique”  is known as a principle used in naked eye 3D display and in commercial refocus cameras. Such refocus camera is also called as “plenoptic camera” or “light-field camera.” It provides 3D imaging technologies based on a small lens array or a pinhole array to capture light rays from slightly different directions. This technique has an advantage in which instantaneous 3D information of objects can be estimated from a single-exposure picture obtained from a single viewing port.
Recently, the integral photography technique has come into use for scientific research in diverse fields. Example applications are particle tracking for velocimetry [16, 17, 18, 19], microscopy measurement [20, 21], spray imaging , etc. In the research filed of plasma, 3D reconstructions of positions of particles levitating in a plasma have been demonstrated using commercial light-field Lytro cameras , and the time evolution of dusty plasmas has been measured using a commercial light-field Raytrix camera . An open-ended plenoptic camera, which is constructed with a lens array and a typical reflex CMOS camera, obtained the 3D positions of dust particles in a radio-frequency (RF) plasma [25, 26]. Dual-filter plenoptic imaging system has been applied to observe lithium pellets in a high-temperature plasma .
In this chapter, the principle, design, and experimental results of the integral photography technique for 3D imaging of dusty plasmas will be presented.
2. Principle of the integral photography analysis
Figure 1 shows a schematic of recording and 3D reconstruction system with integral photography for dusty plasma experiment. A small lens array is placed in front of the particles levitating in a plasma to obtain an array of projected image. The rays emerging from 3D objects, i.e., scattering light rays from dusts pass through the small lens array and are captured on a sensor device. A 3D spatial point of object that is a position of a dust particle should be projected to two-dimensional (2D) image points (
2.1 Recording system for dusty plasma experiments
In this section, it is shown how to design a recording system for dusty plasma experiments. Figure 2 shows a schematic of relationship among lens array, detector, and imaging area on the recording system. The Cartesian (
The considerable parameters of the lens array are the number of lenses, lens pitch, and focal length. In the following discussion, we deal only with convex lens array. The focal length
In order to make an efficient recording system, the configuration of the CMOS sensor must be considered. The number of lenses in the array should be a multiple of the aspect ratio of the CMOS sensor. In addition, the lens pitch must take into account the size of the imaging area. After passing through the lens, rays are projected onto the sensor directly. If we assume that rays from a given dust particle are projected onto all elemental images, the limit of the imaging area is calculated using straight lines passing through the center of the outermost lens
and through pixels on the edges of the sensor area corresponding to the outermost lens
In the same manner, the limits for the
An uncertainty in the reconstructed image will be attributed to the spatial resolution of an elemental image on CMOS sensor . The length
and along the
The above equation indicates that the large ratio of distances
2.2 Reconstruction of 3D position of light source
To extract the positions of projected particles (
Using the observed elemental image array, the 3D image of particle distribution is reconstructed in the computer. The light path arriving at the point (
where is the center of the (
A target light source should locate on where
3. Experimental setup and results
3.1 Estimation of measurement parameters for a dusty plasma experiment
In order to determine the parameters of multi-convex lens array for a dusty plasma experiment, we adjusted the side of the imaging area and
|35 mm (convex)|
|9 × 6|
|Size of a lens||2.2 × 2.2 mm2|
|Pixels per lens||818 × 818 pixels|
|Working area on ||∼24 mm2|
|Working range of ||55–143 mm|
A picture of the designed lens array using acrylic plastic is shown in Figure 4. The rim around the periphery facilitates the holding of the array. Figure 5 shows a sample image obtained with the designed lens array system. The object appears as a single green circle with ∼1 mm of diameter which is located on
3.2 Reconstruction of known target light sources
Developed recording and reconstruction system has been tested using target light sources located on known positions. In this test experiment, the typical exposure time of the camera is 1/400 s. The elemental image array obtained with the system was stored in a computer as 10 bits of data. In addition to the position (
In Figure 6, the 3D positions of the known target and reconstructed particles are marked by open squares and closed circles, respectively. In this test experiment, the optical axis is set along the
3.3 Apply to dusty plasma experiment
Finally, the developed system is applied to a dusty plasma comprising monodiverse polymer spheres (diameter = 6.5 μm) floating in a horizontal, parallel-plate RF plasma. Figures 7 and 8 show a photograph and schematic of the experimental setup. A piezoelectric vibrator is contained in an RF electrode as the injector of fine particles into a plasma. A grounded counter electrode is positioned at the upper side of the 13.56-MHz-powered electrode at the distance of 14 mm. Fine particles levitate in the plasma generated between the electrodes. A solid-state laser, which radiates light of 532 nm in wavelength, 4 mm in diameter, and ∼10 mW in radiation power, was used in our experiment to observe fine particles in the plasma using scattered laser light.
The lens array and the CMOS sensor were located at a side port of the chamber with a distance of
4. Expected future of the integral photography technique for plasma measurement
The integral photography technique has great potential of versatile applications for plasma measurement. With the help of Mie-scattering ellipsometry technique [31, 32], it would bring information about the size of particles in addition to six-dimensional information about position and velocity. Combined with intrinsic fluorescence spectroscopy , specification of dust’s materials will be available not only for standard polymer but also for unusual target such as microorganisms [34, 35]. Moreover, deconvolution techniques [36, 37] will extend the integral photography to determine 3D distribution of spatially continuous light sources . 3D information of bremsstrahlung emissivity distribution should be obtained with pinhole ultraviolet or soft X-ray detector [39, 40, 41], instead of lenslet array for visible light.
It is still unclear how many dust particles can be counted by the system using the integral photography technique because many parameters trade off against each other. Well-designed optical and recording systems are required to identify the 3D positions for a large number of particles. The defocusing effect of objects is another considerable problem. The effect makes the positions of objects on sensor difficult to identify, and uncertainties in the reconstructed image may increase. In order to avoid such a problem, some commercial light-field cameras mount different
The integral photography technique is useful for 3D observation of dusty plasmas. This technique has an advantage in which instantaneous 3D information of objects can be estimated from a single-exposure picture obtained from a single viewing port. The principle of integral photography technique and its analytical method has been explained in detail. A design of a light-field camera for dusty plasma experiments has been reported. The important parameters of the system, dependences of the size of the imaging area, and the spatial resolution on the number of lenses, pitch, and focal length of the lens array are calculated. Then, the recording and reconstruction system has been tested with target particles located on known positions and found that it works well in the range of dusty plasma experiment. By applying the integral photography technique to the obtained experimental image array, the 3D positions of dust particles floating in an RF plasma are identified.
The author appreciates Prof. Y. Hayashi and Prof. Y. Awatsuji of Kyoto Institute of Technology for fruitful suggestions from the perspective of researches for the dusty plasma and the integral photography technique, respectively. The author also thanks Prof. S. Masamune of Chubu University and Prof. H. Himura of Kyoto Institute of Technology for the comments on this study. Finally, the author would like to thank Mr. K. Tokunaga of Kyoto Institute of Technology for experimental assistance. This research is partly supported by JSPS KAKENHI Grant Numbers 15K05364, 18K18750, and 24244094.