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The three sets of LED flashes are synchronized, so all cameras record each colored shadow projected by the opaque particles at the same instant. This is done for each of the three colors to record the three instants onto the same image frame. Due to their especially large pixel-count, four Nokia Lumia smartphone cameras are selected to observe the volume of interest from four different angles. The pixel pitch-size is 1. The lens system has a fixed aperture of f 2. The images are saved automatically in DNG RAW format, before the default commercially supplied color-interpolations of the pixel-arrays are performed.

The small pixel size in the sensor compromises the sensitivity to illumination. However, this is overcome by using high-power LEDs as a light source and registering shadows rather than the scattered light or fluorescence from particles, typically employed in PIV. This decreases significantly the illumination intensity requirements. The control settings of the four cameras are synchronized using simultaneous html commands transmitted through a local wireless network from a PC.

These commands set the exposure time, white balance, gain, ISO and then control the triggering time. The ISO is set to minimizing noise in the sensor. In order to minimize any misalignment or movement of the individual cameras, a stiff customized 3D-printed holder made of polylactic acid PLA was fabricated in-house.

This holder enabled a firm attachment of the smartphones to a geared tripod-head for fine positioning and angle adjustments. The geometry and the position of the cameras are illustrated in Fig. The cameras view the flow through 3 adjacent windows of the octagonal tank. Here we have not used fluid-filled prisms to minimize the distortions of light-rays going through the air-plexiglass interface Such setup could improve results in future work.

In order to test our technique, a vortex ring is produced and observed as it travels up inside an octagonal water tank, through the field of view of the four cameras. The bottom side of this container is sealed from the water and it is connected by a hose to an air flow controller that is operated in pulsed mode. The flexible membrane is enclosed at the top by a 3D printed cap with a smaller circular centered hole of 60 mm in diameter.

The duration and pressure level of the air pulse, delivered into the chamber, can be regulated and is synchronized with the LEDs via a digital delay generator DG from Stanford Research.

The air pulse drives the membrane upwards pressurizing the chamber and forcing the water to pass through the reduced cross section in the cap, accelerating the flow and finally separating the boundary layer to generate the vortex ring, as explained in Fig. As expected, increasing the pressure of the air pulse gives more impulse to the membrane and produces a faster translation and rotation of the vortex ring.

We selected two pressure levels, of 2. Schematic drawing of the vortex ring generator. Pulsed air is introduced into the enclosed bottom chamber, pushing a latex membrane to force out a fraction of the fluid in the chamber through a circular orifice, thus creating a vortex ring. The liquid inside the chamber has been pre-seeded with black micro-spheres. The material density of the particles in traditional PIV systems should be nearly neutrally buoyant to follow the fluid motion.

Simultaneously, opaque particles are necessary to block the light from the camera sensors and obtain sharper shadows in the recorded images.

To reduce the density differences between the particles and the fluid, we use a sodium chloride aqueous solution as the working fluid, to make the particles follow better the fluid motions. This allows slow particle sedimentation between experiments without significantly affecting their flow-tracing properties. This reduces the number of defocused particles that add noise in the captured images. The particles are stirred in the chamber within the cylinder on top of the latex membrane, allowing them to be captured by the vortex ring, tracing the flow field once the air is pulsed.

In this way, out-of-focus particles can be minimized, improving the image quality for our demonstration. A schematic of this procedure is illustrated in Fig. Then, the light passes through a curved diffuser made of a white polyester sheet, distributing the light more uniformly throughout the camera view, as illustrated in Fig. The duration of the illumination faces the common trade-off between sufficient intensity and the need to freeze the instantaneous location of the particles.

The pulses are synchronized and activated by a digital delay generator. The time delays between the three different LED color pulses was adjusted for the strength of the vortex rings, i. We highlight that much smaller time steps can be achieved by the lighting and camera system, being only constrained by the velocity of the flow and the vortex generation system. Using multi-color illumination can cause systematic bias in the position of the particles recorded in the different colors, due to differences in the diffraction through the transparent walls of the tank.

The amount of this diffraction varies slightly with the wavelength of the light. Detailed study of this effect has been carried out by McPhail et al. Further discussion about this bias error will be addressed in a later section. In order to reconstruct the 3D position of the multitude of tracer particles, it is crucial to obtain a high-quality calibration from in-situ images from all four cameras. For this purpose, we use a typical dotted bi-planar calibration target shown in Fig. This calibration intends to correct any distortion arising from the imperfect lenses and diffraction due to non-perpendicular viewing angles through the tank walls.

Significant pincushion distortions are visible at the edges of the calibration target in Fig. This original calibration is subsequently improved with the self-calibration algorithm described in a later section Image of the calibration target type 22 from LaVision viewed from two angles. The image shows the optical distortions produced by the lens and by the angled view through the Plexiglas walls. Once the cameras are triggered and the vortex ring is generated, the two or three color-coded lights are flashed in a sequence to produce shadows of the particles at different times, t 1 and t 2 as well as t 3.

We obtained a pair or triplet of images of each particle in a single frame, as shown in Fig. Note that the order of the colors of the dots is reversed from that of the illumination, i. This is because the particle at t 1 blocks the red light and moves before the blue light fills in the shadow. For two-color cases we use the blue and red flashes to minimize cross-talk between them, as these wavelengths are the most separated of the three colors. However, getting sufficient energy in the blue LED can be a challenge Cross-contamination will of course depend both on the spectral content of the illuminating light and the shape of the band-pass filter in the Bayer matrix on the sensor.

This greatly facilitated the separation of color channels without any pre-processing of the images, as is clearly shown in Fig.

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The captured image is separated in its RGB channels red b , green c , and blue d. For a second implementation of the technique, of primary focus herein, we exploited all three color-channels on the sensors of the cameras, by using a three color LED illumination. Each color of the LED light was pulsed separately, e. All three flashes occur within the same exposure time of the cameras, capturing three different spatial positions of each particle. The particle-color denoting each time step on the sensor is detected as the corresponding negative color in the RGB color space, as depicted in Fig.

From this diagram, we observe the yellow pixels in Fig. Similarly, the cyan and magenta pixels in Fig. The RGB color space represented in Cartesian coordinates. The white dashed arrows link the corresponding negative colors that are captured in the images.

Schematic representation of the color time-coding approach used for the CMOS sensors. As the particle travels, the colored lights are flashed at different times, leaving their corresponding shadowed pixels recorded in the camera sensor. The final result is an image of the negative colors for each time step, i. Using multi-color illumination introduces a bias error to the particle locations, which arises from the slightly different refraction of the three wavelengths of light, when they pass through the thick plexiglass wall of the tank. Furthermore, color crosstalk between the RGB channels due to mismatch of the emission bandwidth of the LED lights and the transmission spectra of the Bayer filter array used in the camera sensor, can negatively affect the results.

These effects were studied in great detail by McPhail et al. In order to quantify the above sources of systematic error, we use a glass calibration plate which contains regular arrays of differently sized black dots. This target is placed inside the water-tank at the location of the vortex ring. Separate images are then captured by flashing the background diffusers with a single color at a time, allowing us to quantify the shift in the position of the dots due to chromatic aberration and to quantify the crosstalk between the color channels, as is depicted in Fig.

Images of the dotted calibration glass slide inside the water-tank, back-illuminated by red a , green b or blue c LED flashes. The middle column images are magnified sections of the dots corresponding to the white square in panel a. On the right column we show the corresponding RGB intensity histograms. From the histograms in Fig. McPhail et al. This allows us to reconstruct the three particle fields and calculate the two 3D displacement-vector fields, between the green and red flash, as well as between the red and blue. Without chromatic aberrations, no displacement of particles should be observed.

However, it is clear from the images in Fig. The images are then loaded and processed by the tomographic PIV algorithm with the same parameters as for the moving particles. This chromatic-aberration shift is primarily related to the angle of viewing through the wall and is therefore a slowly varying function over the image area and should remain fixed throughout the experiments, if the cameras are not moved.

Example of these displacement fields are shown in Supplementary Fig. The magnitude of this effect is also different between green-red vs red-blue particle fields. The final velocity fields are corrected by subtracting these error velocity fields from their corresponding final velocity fields. One can clearly see the vertical shifting of the colored shadows, due to the chromatic aberrations. When estimating the particles per pixel density it is important to keep in mind the relatively large size of the particles used in our setup. Using a color sensor one needs more pixels to effectively pin down the particle center, than is required for a regular monochrome PIV sensor setup.

Additionally one can obtain the source density N s , i. Reducing the particle size makes it possible to increase the particle per pixel density N , while keeping the source density N s constant. For this technique we estimate that the lower limit of each particle size is 4 pixels to avoid false color due to pixel binning, which can arise from the interpolation of the Bayer filter array, as previously mentioned. The single channel concentration in ppp is relatively low compared to traditional tomographic PIV, but is necessary to separate the particles for each color channel without devising too much overlap that may affect the color separation and low quality reconstruction.

The maximum particle displacement between the flash instants was approximately 15 pixels, as measured in the fastest regions around the vortex core. As observed in Fig. This inhomogeneous background in the picture occurs due to the different locations of each of the LEDs behind the projection lens and a slight unbalance in the intensity of each colored light.

Owing to the fixed camera lenses, with constant focal length and aperture, the depth of focus is also fixed. These inflexible optics in addition to the size of our tank, limits the accessible region of interest ROI. Considering that most of the commercial cameras used for PIV have a typical resolution of 4 Mpx or less, for configurations where the full image resolution of the smartphones can be used, the 40 Mpx would be almost ten times larger than the specialized equipment.

We first show, in Fig. Each of these images is then interpolated using the demosaic method proposed by Malvar et al. Steps for preprocessing of the raw image file, showing the same region as in Fig. The effects of the inhomogeneous background-color intensities can be minimized with additional image pre-processing steps in the following manner. First, we record several images of the same 3-color pulse-lighted background without any particles in the field of view. We use these images to subsequently normalize the background and intensities of the particle shadows.

We do this by treating the background RAW image-files in the same way of separation and demosaic interpolation as the particle images, thus, obtaining the background reference frames for each color. Taking the local average background for each color and inverting the color intensities of both, the averaged background and particle images, allow us to subtract their intensities, resulting in a more uniform background and enhancing the particle signals.

The threshold is strict, but real particles have a much higher intensity than the background at this point, Fig. The pixel intensity curves for the processing steps of the images are explained in Fig. For comparison, the color intensities are plotted on the right side, along cuts through the image, marked by the dashed line. Once the images for all four cameras are pre-processed and split up into the separate color channels, they are imported, together with the calibration images, into the commercially available software Davis 8.

Other algorithms for 3D reconstructions and cross-correlations have been published, but adapting them for efficient computing is a challenge in its own right. Any current Tomo-PIV system will therefore bear the cost of this software, irrespective of the hardware. The initial calibration is carried out on all 17 shifted images of the calibration plate, the error is shown in Fig. We use a third order polynomial for the fit model. We note that cameras 1 and 4, view the calibration target from a much larger angle than the cameras at the center. However, this is greatly improved by subsequently performing a self-calibration, where the reconstructed particles are triangulated and used directly to correct the calibrations via disparity maps Log-in to view content.

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