1. Introduction

Aerosol particles larger than approximately one µm in size constitute a category of natural and manmade particulates known as the coarse-mode aerosol (CMA). Common types of CMA particles include mineral dust (MD) and biologic particles, like pollen. The ability to characterize CMA particles is important for agriculture, climate science, and manufacturing processes [1–3]. For example, MD represents the largest component, by mass, of aerosols in continental regions and is an important mechanism for the transport of nutrients to land and marine ecosystems [2,4,5]. Dust in the atmosphere scatters and absorbs sunlight and can nucleate cloud droplets, all leading to radiative forcing effects on the climate [6,7]. Dust also reduces visibility, which impacts aviation [8]. To best understand the impact of CMA particles in most applications, basic information such as particle size, shape, and number concentrations are needed [9,10].

Due to the (optically) large size of CMA particles, especially MD, high quality characterization of particle size and shape is achieved by microscopy of collected samples [11]. Such characterization is far more challenging, however, when the particles are in aerosol form and sample collection is either not practical or not possible. An example where this is the case is in measuring the particle transport flux of a flowing MD aerosol [3]. Moreover, extended working-distance microscopy is often not feasible as the volume considered may not be large enough to capture the aerosol dynamics.

This article demonstrates how flowing MD aerosol particles can be imaged in-air within a sensing volume of approximately one cm$^{3}$ in a time dependent manner. This is done with digital in-line holography (DIH) to render quasi-3D representations of individual particles in the 3D sensing volume in time steps of approximately 10 ms to create a video of the flowing particles. The approach has been applied by others, e.g., to spray droplets [12] and is similar to digital holographic particle image velocimetry (PIV) and particle tracking; see the thorough review by [13].

The focus here, however, is on characterizing the morphology of the individual particles rather than using them, e.g., as tracers to characterize a supporting fluid’s flow as is often the case in PIV. More importantly, MD particles are highly nonspherical in shape and their morphology is difficult to resolve. Here, we resolve MD particle images well in two of the three spatial dimensions with an approximate resolution in the third (axial) dimension. Thus, the work stands out among most PIV and DIH volumetric measurements, which either investigate spherical particles or assume the particles are spherical when they may not be. Lastly, the absence of a microscope objective gives the approach a large working distance, $\sim 10$ cm, in an open-path configuration suggesting a relatively straightforward extension to measurements in applied contexts.

Figure 1 shows the experimental arrangement used for time-series imaging of flowing MD particles. The optical train begins with a 49.5 mW solid-state laser source (Coherent OBIS FP-445-LX) emitting $\tau =300$ ns pulses at a wavelength of $\lambda =445$ nm propagating along the negative $z$-axis. The beam is focused by lens L1 ($f=30$ mm) to a $50\,\mu \textrm {m}$ diameter pinhole (PH) serving as a spatial filter to improve the beam profile. Next, the beam is expanded by lens L2 ($f=-50$ mm) and collimated by L3 ($f=400$ mm) to a final diameter of approximately 25 mm.

 

Fig. 1. Experimental arrangement to observe a settling MD aerosol with DIH. Particles are aerosolized by a sieve above a test box where they then flow through a laser beam as they settle. Pulses of light illuminate the moving particles, giving a series of digital holograms that yield particle images via Eq. (1).

Download Full Size | PDF

The collimated beam passes through a plexiglass “test box” $10\times 10\times 10$ cm in size via windows (W) to illuminate a CCD sensor (FLIR, GS3-U3-123S6M) with an array of $4096\times 3000$ pixels, each $3.45\,\mu \textrm {m}\times 3.45\,\mu \textrm {m}$ in size. The sensor surface defines the $x-y$ plane through the origin. Mineral dust is aerosolized into the box using a sieve to mechanically disperse a dried-powder sample of MD. A rectangular slot at the top of the test box restrains the particles to enter the beam below over approximately a one cm segment along the $z$-axis. Thus, this segment of the beam defines the sensing volume over which particles may be imaged (below). The falling particles pass through the beam and collect onto the box floor. While in the beam, each particle scatters a small portion of the light, forming an object wave, see Fig. 1. The remainder of the beam constitutes the reference wave, which interferes with the object waves of all particles in the beam to produce a fringe pattern across the sensor; this pattern constitutes the digital hologram.

To observe particle dynamics, a series of $N$ holograms are captured in sequence. The sensor is placed in global shutter mode at its maximum frame-rate of 103 frames per second and outputs a sequence of TTL pulses indicating the integration time ($\sim 0.01\,\textrm {ms}$) of each frame’s exposure. This signal is passed to a digital delay generator to form a sequence of trigger pulses for the laser such that the trigger pulses are delayed by $3\,\mu \textrm {s}$ relative to the beginning of each exposure. In this way, the sensor is guaranteed to be integrating during the arrival of each $300$ ns laser pulse.

Each exposure is a "raw" hologram, $I^{\textrm {holo}}_{n}(x_{i},y_{j})$ where $n\in [1,N]$ and the coordinates $(x_{i},y_{j})$ denote each pixel in a hologram. Following acquisition of $N$ raw holograms, an identical sequence is measured without particles present, thus providing $N$ "reference" exposures $I^{\textrm {ref}}_{n}(x_{i},y_{j})$. Then, the difference between each raw and reference measurement is taken to form $N$ contrast holograms as $I^{\textrm {con}}_{n}(x_{i},y_{j})=I^{\textrm {holo}}_{n}(x_{i},y_{j})-I^{\textrm {ref}}_{n}(x_{i},y_{j})$. This subtraction cancels stray light in the holograms due to dust that has fixed to the optics and effects due to the Gaussian beam-profile, resulting in improved particle-image quality [14]. An example of a single contrast hologram is shown in Fig. 2(a). As explained in [15], DIH suffers from aliasing effects due to the limited resolution of the pixel array. Here, the Nyquist condition that the particle must be separated from the sensor by $z>N_{\textrm {pix}}\Delta x/\lambda$ is not satisfied and image replicas can occur [15]. To resolve this, we perform a linear interpolation of the holograms and re-sample them at twice the resolution. While this does not improve the image resolution it does eliminate image replicas. Note that these image replicas are not the same as twin images, which are always present to some extend in DIH, see [16].

 

Fig. 2. Approximate 3D shapes of flowing MD aerosol particles using the arrangement of Fig. 1. Equation (1) is used with a hologram $I^{\textrm {con}}_{n}$ to generate particle-image reconstructions in 121 image layers stacked along the $z$-axis producing the streak-like structures in (a). In (b) is the appearance of the reconstructions in several layers for the particle circled in (a). In (c) is the particle hull obtained from all perimeters, which is re-scaled along the $z$-axis by $\alpha$ to give the contracted hull in (d) where $\alpha \ell _{z}\sim 75\,\mu \textrm {m}$. A 3D surface is then obtained from the contracted hull in (e). Repeating the process for all streaks yields the final 3D distribution of MD particles in (f). Note that the hologram is shown at $z=89$ mm for illustration, but is in reality located at $z=0$, i.e., the sensor surface.

Download Full Size | PDF

For each $I^{\textrm {con}}_{n}$, an image of the particles present in the beam during the $n^{\textrm {th}}$ laser pulse can be computationally reconstructed. The process is well documented and follows scalar diffraction theory [17,18]. First, $I^{\textrm {con}}_{n}$ is envisioned as a transmission diffraction grating in the plane $S_{\textrm {h}}:(x,y,z=0)$ through which a plane wave diffracts to form a complex-valued wave $K$ in a parallel image-plane $S_{\textrm {im}}:(x,y,z=\textrm {const.})$. This plane wave is an approximation for the laser beam but travels in the opposite direction, i.e., along the positive $z$-axis, recall Fig. 1. One of several ways to do this is by evaluating the Fresnel diffraction integral in the form of a convolution [18],

To image the particles in 3D throughout the one cm segment of the beam, Eq. (1) is repeatedly evaluated for 121 steps in $z$ along this segment of the beam. The process yields a collection of image layers, which when stacked together represent a 3D image field in the sensing volume, i.e., the beam segment, and is shown in Fig. 2(a). Each particle appears in the image-stack volume as a gray-level streak along the $z$-axis. In Fig. 2(a), a specific particle’s streak is indicated by a red circle in a single layer in the image stack. Figure 2(b) shows this same particle’s image as one moves from the first layer to the last. The image is clearly in-focus at layer 60 whereas it progressively blurs for subsequent layers in either direction. By defining a threshold gray-level $I_{\textrm {gr}}$ of $I_{\textrm {gr}}=20$%, where 0% represents white and 100% represents black, the image of each particle in a given layer can be binarized whether the image is well-focused or not. Doing so defines a perimeter for the image (similar to the boundary line of [19,20]), which is also shown in Fig. 2(b) in red. Notice that as the particle image blurs in layers away from the best-focus layer (60), the perimeter shrinks in size. This occurs because, generally, the gray-level density of the image spreads as it blurs. Once the image blurs to the point that all gray levels fall below $I_{\textrm {gr}}$, no further perimeters are generated. Collecting all the perimeters for a given particle streak in Fig. 2(a) forms a skeleton, or hull, see Fig. 2(c), and serves as the basis for a quasi-3D representation particle.

At this stage, the length of a given hull extends along the $z$-axis, i.e., the axial direction, for a distance that is clearly much greater than the true axial length of the particle. The reason for this is due to the well-known difference in image resolution between the axial and lateral directions ($x$ and $y$ axes) in DIH. If NA is the numerical aperture of the sensor with respect to a given particle, which is always less than one here, the axial resolution is poorer than the lateral resolution by a factor of $1/\textrm {NA}$. Moreover, given that the MD particles are opaque to the laser light, it is questionable whether the axial length of a particle could ever be determined with DIH as its obscured side would appear not to affect the hologram fringe pattern.

Work by [21] considers simulated and measured in-line holograms to investigate how reasonable it may be to describe the axial extent of a particle from stacked perimeter curves like Fig. 2(c). While it is clear from [21] that an accurate representation of the length is not possible at the same level as representation of the particle’s lateral size and shape, the study does find that reasonable estimates for the axial length are possible in some cases. Here, we build on [21] to develop a method where the the axial length of a particle may be systematically estimated from the axial length of its hull [e.g., $\ell _{z}$ in Fig. 2(c)] in combination with the well-resolved cross sectional area of the particle image in its best-focus image layer. The method is based on the following calibration measurement.

Using 50 µm diameter polymer microspheres (Cospheric GPMS-098 45-53 µm) dispersed by the sieve into the test box, an image stack for the sensing volume similar to Fig. 2(a) is generated. Particle hulls are then formed where the axial length of the hulls is $\ell _{z}$ as in Fig. 2(c). A particle radius $R$ is determined by equating the area $A_{\textrm {p}}$ of the particle image in the best-focus image layer to the cross sectional area of a sphere, i.e., $R=\sqrt {A_{\textrm {p}}/\pi }$. Then, a scale factor $\alpha$ is defined that contracts the axial hull-length to be that of the diameter of the spherical particle, i.e, $\alpha =2R/\ell _{z}$. The result is a new hull that shows an approximate 3D representation for a sphere with a degree of shape distortion in the form of tapering of the shape along the axial direction; this is shown in Fig. 5 in [21]. When this method is applied to Fig. 2(c), the result is the contracted hull in Fig. 2(d) and serves as a mesh for the final representation of the 3D particle shape in Fig. 2(e). Notice that because $\alpha$ is determined by the particle-image area in the best-focus image layer, smaller (larger) particles will result in smaller (larger) contraction of the hull’s axial length.

We emphasize that this method to define an axial extent for a particle is only an approximation and there is no guarantee that high aspect-ratio particle, e.g., needle or disk-like shapes, could be reasonably represented. However, given that the MD particles are dispersed through a sieve, the likelihood that such extreme aspect ratio particles are present is low. This claim is supported by the fact that a falling high aspect-ratio particle may tumble as it falls through the beam, and thus, would reveal its shape character in some of the $N$ holograms of the videos. No particles of this character are observed.

The final axial location of a particle represented in this manner is determined by the $z$-coordinate of the best-focus image layer, which is automatically found for each particle-image streak using the auto-focus process of [22]. Meanwhile, the lateral location of a particle is determined by the location of the particle image in the layers, i.e., the image streak shown in Fig. 2(a). Note that for a given image layer where a given particle may be well focused, the other particles’ images are generally not in focus. Figure 2(a) shows this property by the blue arrows, which indicate the axial location of the best-focus image layer for each particle’s image-streak. The end product is shown in Fig. 2(f) where the 3D particle reconstructions are shown in the sensing volume and the blue dashed lines illustrate the varying axial locations of the particles.

All of the discussion relating to Fig. 2 concerns a single contrast hologram from a single exposure of the sensor. Repeating this reconstruction process for each of the $N$ holograms generates a video of the flowing aerosol. Figure 3(a) shows four still-frames from the video in Visualization 1. Two particles are identified by red and blue arrows, which can be tracked as they fall via the time-stamps shown. Note that the downward direction is the negative $x$-axis, consistent with Fig. 1.

 

Fig. 3. Time sequence from a video of a settling MD aerosol imaged with digital holography. The images in (a)-(d) show the first four frames in the video of Visualization 1, where MD is aerosolized by a sieve with openings of $43.2\,\mu$m in the arrangement of Fig. 1. Two specific particles are identified by the red and blue arrows. The vertical direction is along the positive $x$-axis. In (e) and (f) are shown microscope images of the MD particles that pass through this sieve, (e), and the larger sieve used in Fig. 2, (f). Polymer microspheres $50\,\mu$m in diameter are placed in the field of view in these images for reference.

Download Full Size | PDF

Figure 3(b) and (c) show microscope images of the MD particles after being passed through two sieves. In Fig. 3(b) the sieve size is $43.2\,\mu$m, which is the sieve used in the measurements for this figure and the corresponding video, Visualization 1. Particles passed through a larger sieve, of size $104.1\,\mu$m, are shown in Fig. 3(c), which corresponds to the sieve used in Fig. 2. In both cases, the $50\,\mu$m diameter polymer microspheres are added to the sieved sample when imaged by the microscope to provide a size reference.

The frame rate of the sensor equates to approximately 10 ms between hologram acquisitions and allows one to estimate aspects of the particle dynamics. For example, the two particles tagged by arrows in Fig. 3(a) fall together and cover a distance of approximately 3.5 mm in 29 ms and they appear to cover the same distance during each time step shown. This implies that the particles have reached a terminal velocity by of approximately $v_{\textrm {exp}}\simeq 0.12 \,\textrm {m}/\textrm {s}$. If the air in the test box is assumed to be still, a particle’s terminal velocity is the same as its settling velocity, $v_{\textrm {s}}$, which can be calculated for particles of simple shapes, namely spheres, from Stokes’s law [23]. However, the MD particles here are highly nonspherical and it is difficult to calculate $v_{\textrm {s}}$ for such shapes. We thus compare $v_{\textrm {exp}}$ to an approximate calculation for $v_{\textrm {s}}$ assuming that the particles are composed of silica, which is common for MD.

The settling velocities for certain nonspherical particles are estimated in [23] by introducing a shape factor $\chi$ as a correction to the settling velocity for a spherical particle of radius $R$. Using the $\chi$-value for sand of $1.57$ as an approximation for the particle-shape characteristics in Fig. 3(a), the settling velocity is $v_{\textrm {s}}=\rho _{\textrm {p}} g R^{2}/(72\mu \chi )$, where $\rho _{\textrm {p}}$ is the density of the particle material (2196 $\textrm {kg}/\textrm {m}^{3}$ for silica [24]), $g$ is the acceleration of gravity, and µ is the dynamic viscosity of air at STP ($1.758\times 10^{-5}\,\textrm {Pa}\,\textrm {s}$ [24]). The sphere-equivalent radii (based on $A_{\textrm {p}}$ from the above) of the particles in Fig. 3(a) are $R_{\textrm {r}}\simeq 47\,\mu$m for the red-arrow particle and $R_{\textrm {b}}\simeq 45\,\mu$m for the blue arrow, leading to settling velocities of $v_{\textrm {s}}\simeq 0.38\,\textrm {m}/\textrm {s}$ and $v_{\textrm {s}}\simeq 0.35\,\textrm {m}/\textrm {s}$, respectively. Given the multiple approximations made, it is difficult to account for the discrepancy between the values for $v_{\textrm {s}}$ and $v_{\textrm {exp}}$, although agreement is found to within a factor of three.

Other useful information about the MD aerosols can be obtained. For example, the sphere-equivalent radii of the particles in a video provide an estimate for variability in size in the aerosol, i.e., a size distribution. Figure 4 shows the distributions for the particles observed in two videos, where the MD is aerosolized either through the $43.2\,\mu$m-opening sieve or the $104.1\,\mu$m-opening sieve. The distributions show a Gaussian-like character with mean values close to the sieve-opening sizes. While particles smaller than the sieve openings trivially pass through the sieve, Fig. 4 reveals that some particles larger than the opening also pass through highlighting the problematic aspect of representing irregular-shaped particles by sphere-equivalent radii.

 

Fig. 4. Sphere-equivalent radii $R_{\textrm {sp}}$ size distributions for MD aerosols produced by $43.2\,\mu$m-opening or $104.1\,\mu$m-opening sieves. The particle radii are determined from the holographically derived approximation for the 3D particle shape as in Fig. 2.

Download Full Size | PDF

2. Conclusion

We have shown that digital in-line holography is capable of imaging a flowing mineral dust aerosol with sufficient speed to form videos of the particle flow. This is done for multiple particles within approximately a one centimeter portion of a laser beam. A novel aspect of this work is the development of a hull, or 3D skeleton, of each nonspherical particle derived from the holographic image. These hulls provide an approximate representation of the 3D shape of the particles from a relatively simple optical arrangement.