1. Introduction

The increasing frequency and magnitude of aerosol particles induced outbreaks worldwide in recent decades has aroused a huge public concern. Understanding, detection, and identification of aerosol particles at single species level in airborne environment are of utmost importance in order to mitigate the threat of airborne spread of infectious agents in both occupational and residential environments and avoid potential impacts on human health.

Optical methods principally allow for non-invasive and real-time detection of micro-sized particles by analyzing the elastically scattered light intensity [1–3]. In this approach, the optical beam intersects with an aerosol microfluidic channel, and the size of particles is determined based on the intensity of scattered light. These sensors offer the advantage of a simplified sensing configuration, and capability of simultaneous particle sizing and counting at a relatively low cost. However, these sensors have several limitations. One significant challenge arises from the fact that the scattering cross-section is influenced not only by particle size but also by the particle's refractive index, which is often unknown. As a consequence, this introduces sizing ambiguity and prevents the identification of particle composition. Furthermore, an evident drawback of this technique is its inherent inability to detect multiple objects within the sensing volume. This limitation inevitably places constraints on the dynamic range and measurement throughput.

More importantly, in many practical industrial applications that involve mixtures of particles of different materials, the primary focus is not solely on determining the size and count of the sampled particles. Instead, there is a growing interest in discerning the mass densities or refractive indices (optical densities) of these particles. The objective here is to identify and classify the type of material composition. Nevertheless, this level of characterization exceeds the capabilities of current particle sensors. The ability to identify and classify particle types based on their mass densities or refractive indices is a challenge that has yet to be fully addressed.

Especially, mass density is related to the composition of materials, potentially offering a unique parameter for particle classification, identification and purity assessment. Online monitoring of the mass density variations at single particle level gives valuable insights into the particle characteristic (e.g., efficacy of drug particles during manufacturing in pharmaceutical industry). One possible and straightforward solution is first sampling of particles using filtering, impaction, or impingement techniques [4–6], and then analyzing and inspecting the collected samples manually under a microscope by a specialized technician. This type of aerodynamic separation and microscopic analysis provide accurate particle sizing and counting, as well as recognition of particle shape and mass densities. However, this approach is labor-intensive and expensive. Furthermore, since the sampling and inspection processes are separated (i.e., the sampling is performed in the field, whereas the sample analysis is conducted in a remote laboratory), this causes significant delays in the reporting of the results and limits its application for on-site monitoring scenarios. Another approach for particle discrimination involves analyzing time-of-flight measurements to estimate the aerodynamic characteristics and mass densities of particles. This method relies on registering and analyzing the transit time of particles as they pass through a double-crest beam. However, since this technique relies on optical scattering characterizations, the irregular or non-spherical shape of particles may introduce uncertainties in the aerodynamic analysis and compromise the measurement accuracy.

Optical density or refractive index of a particle serves as an additional parameter, akin to a fingerprint, that holds significant value for particle identification. This approach has been routinely utilized in discriminating bulk materials, films, and have been extended to micro-sized particles in recent years [9–12]. For instance, Glen and Brooks have effectively employed a cloud and aerosol spectrometer with polarization ratio characterization to successfully differentiate between various types of dust particles [11]. Nonetheless, several challenges arise when attempting to adapt these techniques for the development of compact particle sensors. The transition from laboratory-scale demonstrations to compact, field-ready devices requires addressing various technical, practical, and miniaturization challenges. The need to ensure reliable and accurate measurements in real-world settings while maintaining portability and ease of use adds further complexity to the process. Overcoming these challenges will be essential to fully harness the potential of polarization-based particle classification for the development of practical and effective compact particle sensors.

As a transformative solution to overcome the limitations associated with existing particle analysis methods, we introduce a holographic imaging platform, which enables simultaneous measurement of the mass density and optical density of each individual particle. Particularly, the particles are first sampled and classified via an inertial spectrometer according to their inertia. By interrogating the particle location and size with calibrated models, particle mass density estimation and classification can be achieved. Furthermore, as will be observed in this paper, this strategy encounters challenges when dealing with particle types with similar mass densities. In order to address such scenarios, we therefore extract another independent fingerprint parameter (i.e., refractive index) of each particle in parallel. By performing Monte Carlo fitting techniques to the Lorenz-Mie theory, the refractive index of each particle can be obtained from the measured hologram. The combination of two independent parameter enables a more comprehensive and accurate characterization of particles, particularly in scenarios where discrimination based on a single parameter might be challenging due to overlapping values. An obvious improvement in classification accuracy has been achieved. Finally, a proof-of-concept prototype is developed and a customized IOS-based App is programed for the remote control of the CMOS imager and the sample image reconstruction. The platform's compact size, portability, and capability for simultaneous measurement of mass density and optical density position it as a valuable tool for remote and on-site settings. By harnessing the strengths of holography and multi-parameter characterizations, this platform holds the potential to revolutionize particle detection and analysis in various fields, providing timely and reliable insights for a diverse range of applications.

2. Experimental setup

The schematics of the holography imaging platform mainly consists of a digital in-line holography microscope and a 3D printed inertial impactor, as is shown in Fig. 1. Since there are no optical components between the sample plane and the image plane, unit optical magnification can be approximated, which guarantees rapid reconstruction of sample image over a very large field of view (e.g., ∼118mm², for IMX183 CMOS chip with an active area of ∼13.3${\times} $8.9 mm).

 

Fig. 1. (a) Schematics of the digital in-line holography platform with an inertial impactor for particle metrology and classification. (b) Illustration of the prototype design. (c) Experimental achieved prototype of the holography platform. A 3D printed block is employed to integrate all the component and modules. (d) Illustration of the home-built App interface.

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The inertial impactor is essentially composed of three parts: (a) the prismatic throat, where the particles are injected into a clean air stream and then accelerated forward by the converging walls; (b) the curvature with a 90° bend, where the particles are separated according to their inertia; (c) the deposition section, where the separation is enlarged and the particles are captured on a sticky polymer coverslip. The width ($W$) and the height ($H$) are chosen to match the active area of the CMOS imager, which is positioned under the impaction plate. The impactor is connected to and driven by a miniaturized pump (Flite4, SKC) with a throughput up to 20 L per minute. An infrared vertical-cavity surface-emitting laser (VCSEL) diode (OPV300, TT Electronics, 850 nm) illuminates the collected particles from a top position (with a distance of 5 cm) and casts an in-line hologram of the samples, which is registered by the CMOS imager with a wireless data communication unit (KS-989, Wifi connection). The schematic design of the holography platform is illustrated in Fig. 1(b), and the experimental achieved prototype is shown in Fig. 1(c). A 3D printed block is employed to integrate all the components and modules. A home-built IOS App interface (named Smart Scopy by us) is programed for the remote control of the CMOS imager and the laser diode, as well as the image reconstruction and processing. The hologram capturing and image processing are illustrated in Fig. 1(d), which will also be detailed in Section 4.2.

3. Hologram formation and reconstruction

Numerical image reconstruction from the digitally recorded holograms (by CMOS) is one of the critical parts of whole process. Reconstruction of the hologram is based on scalar diffraction theory, in which the object-scattered wavefront captured by CMOS imager is numerically calculated using different methods [7–11]. Proper selection of the reconstruction methods and numerical models, are, therefore, important in order to guarantee reconstructed image quality. In what follows, we present the methods and numerical procedures for experimental reconstruction of the captured hologram based on our practical configuration.

As illustrated in the experimental setup (Fig. 1), as well as the simplified schematics shown in Fig. 2, the VCSEL laser diode can be approximated as a point source illuminating the particles from a top position. In what follows, spherical waves are used for the derivation of expressions, in order to reconstruct the particle image and extract the phase and amplitude information.

 

Fig. 2. Schematics of digital in-line holography based on a spherical wave illumination.

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When a wave passes the object plane, the wave is partially scattered by the object, forming the object wave $\textrm{O}({X,Y} )$, meanwhile, the un-scattered part act as the reference wave $\textrm{R}({X,Y} )$. The interference pattern between the object wave and reference wave creates the so-called hologram. An object can be described by a transmission function [12,13],

Considering a spherical wave illumination, the incident wave can be described as

The wavefront distribution beyond the object can be then written as

The propagation of the exit wave from the object can be described by the Fresnel-Kirchhoff diffractive formula [12,13]:

The recorded hologram can therefore be given as

Prior to the reconstruction procedure, the object field is normalized by division with the background field $B({X,Y} )= {|{R({X,Y} )} |^2}$. We note that the background field needs to be recorded with the exact same experimental conditions (only in the absence of particles) as that of the sample hologram. The background field could also be simulated from the hologram. With such a configuration, the normalized hologram is independent on experimental conditions including intensity fluctuation of laser diode and CMOS sensitivity, which is therefore propitious to build robust and efficient platform for particle metrology, at the same time, eliminate effects of background imperfections.

Another step following normalization is subtraction of 1 in order to obtain a function oscillating around zero. Altogether, the distribution of the normalized hologram is written as

The reconstruction of a digital hologram is achieved by multiplication of the holograph with the reference wave $R({X,Y} )= \frac{{\textrm{exp}({ikR} )}}{R}$, followed by backpropagation to the object plane based on the Kirchhoff-Helmholtz integral transformation [14,15]:

The wavefront reconstructed from the hologram ${H_0}({x,y} )$ corresponds to the transmission function $\tilde{t}({x,y} )$. The transmission function $t({x,y} )$ can be thereby obtained by the summation of 1. As is obvious, the reconstructed term $t({x,y} )$ itself does not explicitly give the absorption and phase information of the object. The object-introduced absorption is given by the absolute value of $({1 + \tilde{t}({x,y} )} )$:

Similarly, the object-introduced phase shift can then be extracted as the phase of

4. Result

4.1 Spatial resolution and instrumentation calibration of the holographic imaging platform

To evaluate the spatial resolution of the holographic imaging platform and calibrate the imaging platform, a dedicated resolution board is devised. This resolution board features as a glass slide with a vacuum-deposited chromium pattern, which is composed of a series of disks with varying diameters and spacings, aiming to emulate practical spherical particles. In our initial demonstrations, we have fabricated micro disks of two distinct diameters: 4.5 and 9 μm. The schematic design and a microscopy image of the customized resolution board are depicted in Figs. 3(a-b), respectively. This procedure can be considered as a preliminary assessment of the imaging resolution and a system calibration for accurate particle sizing in the following. The hologram of the resolution board, acquired through the holographic imaging system, is visualized in Fig. 3(c). Subsequently, the process of image reconstruction is initiated. Figure 3(d) provides an illustration of the reconstructed image, which is generated using the methodology expounded in Section 2. Notably, the reconstructed image is marred by various noise factors (e.g., twin-image artifacts, sample imperfection, and experimental noise). These factors inevitably pose challenges to efficient and robust particle recognition. A straightforward strategy is to employ thresholding prior to particle recognition. A global thresholding turns to be insufficient, since the image remains significantly impacted by noises. This results in numerous local maxima points being identified as potential particles, as depicted in Fig. 3(e). In contrast, the utilization of adaptive thresholding proves to be a more effective approach [16]. Adaptive thresholding involves dynamically adjusting the threshold value in different image regions to effectively distinguish desired particles from background noises. This approach successfully mitigates the influence of various noise factors, which is particularly advantageous when dealing with noisy backgrounds and experimental uncertainties. In fact, as will be demonstrated in the following, by employing an iterative procedure, twin-image free images can be retrieved from a single holographic registration. Figures 3(f and g) present the obtained images that are free from the disruptive artifacts, and the disks/particles that have been recognized. Figure 3(h) depicts the particle statistics (e.g., size, count, and shape). To establish a benchmark, the sizing statistics extracted from our platform are compared with those obtained using traditional microscopy, as presented in Fig. 3(i). A good agreement between the two sets of data is observed, validating the effectiveness and reliability of the platform for particle detection.

 

Fig. 3. Spatial resolution test. (a) Design of the resolution board with periodic disk patterns in order to mimic micro-sized particles. (b) Customized glass slide with vacuum deposited chromium pattens. (c) Raw hologram of the resolution board. (d) Reconstructed image of the resolution board. (e) Reconstructed image after regular thresholding. (f) Reconstructed image after adaptive thresholding. (g) Image with cropped disk patterns marked in pink. (h) Extracted shape factor (aspect ratio) of the captured disks(particles). (i) Disk count and sizing statistics obtained with the holographic method and traditional microscope. The scale represents 20μm.

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4.2 Twin-image free image reconstruction and particle metrology based on an iterative approach

As observed in previous section, the reconstruction process in digital inline holography encounters a challenge due to the inherent inability to spatially separate the superposition of the conjugate image and DC-term. This leads to the manifestation of an interference pattern known as the “twin image,” which significantly compromises the quality of the reconstructed image. Consequently, the presence of the twin image impedes the extraction of comprehensive information from a holographic recording. The attainment of twin-image-free reconstruction is pivotal for accurate and reliable particle detection.

To date, several strategies have been proposed to mitigate the twin-image noise in digital in-line holography. Some of these typical approaches include the utilization of the phase-shifting method [17] and the acquisition of recordings at multiple wavelengths or multiple angles [18,19]. However, these methods primarily suppress the twin image noise without completely eliminating it. Moreover, these approaches frequently necessitate multiple exposures and involve intricate setups. This complexity makes their experimental implementation challenging, particularly when endeavoring to construct compact and portable sensors.

A better alternative, capable of achieving twin-image free reconstruction, is based on an iterative algorithm, which is based on the fundamental physical principle that the object absorption should not lead to an increased amplitude due to scattering of the object, in accordance with the conservation of energy principle [20]. This process involves propagating the field back and forth between the image plane and the object plane, iteratively, until all artifacts resulting from the twin image are eliminated. During each iteration, negative values of object absorption are interpreted as a consequence of interference between the twin image and the reference wave. These negative values are subsequently replaced by zeros, while the phase values remain unaltered. Through several iterations, the twin image artifact diminishes, leading to the attainment of an optimized object image. This approach effectively tackles the twin image challenge and facilitates the generation of high-quality object reconstructions.

To provide an illustrative example, we conducted an experiment to test the iterative routine for the elimination of twin image artifacts using captured holograms of particle samples. The sample comprised spherical silica particles with sizes ranging from 4 to 6 μm. In Figs. 4(a) and (b), we present the field distributions of the raw hologram and the background prior to loading the particles. Before initiating the reconstruction process, we performed hologram normalization by dividing it with the background field. This normalization step was crucial for mitigating the influence of various experimental conditions, including speckle noise, background imperfections, and laser diode intensity fluctuations. In Fig. 4(c), we display the reconstructed hologram before the commencement of numerical iterations. Subsequently, we depict the reconstructed field intensities after the first, fifth, tenth, and twentieth iterations in Figs. 4(d)-(g), respectively. It is evident that the twin image artifact diminishes progressively with each iteration, a fact further confirmed by examining the intensity distributions along the blue line (as shown in the insert). The phase distribution of the sample approaches its true value after the iterative process, resulting in an image almost devoid of the disruptive twin image artifact, as demonstrated in Fig. 4(h).

 

Fig. 4. Image processing schematics for twin-image artifact elimination. (a) Experimental hologram of a sample with multiple particles. (b) Background image. (c) Reconstructed image before iterations. (d)-(g) Reconstructed image after the 1, 5, 10 and 20 iterations. The insert shows the intensity profiles along the blue lines. (h) Phase distribution of the sample after the 20 iterations. Green scale represents 20μm.

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The iterative procedure for particle identification and measurement offers significant advantages. In particular, compared to the adaptive thresholding method, the iterative approach inherently eliminates intensity ripples and fluctuations caused by the twin-image artifact. Additionally, it has the potential to prevent local maxima regions from being erroneously identified as potential particles. This results in an improved particle recognition and cropping accuracy, especially in scenarios where the background is noisy and subject to experimental uncertainties.

4.3 Demonstration of the platform for particle classification and mass density estimation

Notably, the capabilities of this imaging platform extend beyond capturing particle size and shape; it also records their precise locations. This leads to the intriguing possibility of establishing a correlation between particle locations and their inertia. This correlation could then be leveraged to estimate particle mass density and classify them concurrently.

To explore this concept further, we address the challenge of classifying particles with different mass densities by integrating on-chip holography with an inertial spectrometer, as depicted in Fig. 1. In a conventional inertial spectrometer, the determination of mass density typically involves manually inspecting particle positions and sizes, a process that is labor-intensive and time-consuming. In contrast, the integrated platform proposed in this study offers the simultaneous benefits of sizing, classifying, and potentially identifying particles in a remote manner. This innovative approach streamlines the classification process and promises to significantly enhance efficiency in particle analysis.

We then proceed to develop a theoretical model that establishes a relationship between particle location, size, and density using the configuration depicted in Fig. 1. The motion of a particle adheres to Newton's second law, where the particle's mass multiplied by its acceleration is equal to the force acting on it. Within a fluid flow field, the particle experiences the dominant effect of the Stokes drag force [21,22]. The two-dimensional trajectory of particles within the impactor can be described by the following equation [22].

In this equation, the coordinates ($x$, $y$) represent the instantaneous position of a particle at time t. The Stokes number ($Stk$) is intricately connected to both the particle mass density and diameter, according to the fluid-dynamic theory [23]. Notably, $Stk$ significantly influences particle trajectory and deposition sites. Particles possessing larger $Stk$ values have a propensity to promptly impact the deposition area, whereas those with smaller $Stk$ values persist along streamlines and ultimately settle on the collecting plate with a larger radius. The expression for $Stk$ can be described as follows:

In order to visualize the classification capabilities of the inertia spectrometer, we conducted preliminary simulations using COMSOL Multiphysics 5.6 software to calculate the trajectories of particles within the impactor. Taking into account factors such as gravity, Brownian motion, Stokes drag force, and pressure gradient, allowing us to simulate the trajectories and settling positions of particles on the deposition section.

The pressure contour and flow streamlines are shown in Figs. 5(a-b) to provide an understanding of the fluid dynamics within the device. The dimension of the impactor is also inserted in Fig. 5(a). In the simulation scenario depicted in Fig. 5(c), particles with varying inertia are introduced at the inlet with an initial velocity of 1 m/s, and the pressure at inlet is set to be 1atm. Over a short time period ($t$ = 0.01s), the particles are impacted and separated onto the deposition section based on their inertia, as shown in Fig. 5(d). As a preliminary demonstration, we perform simulation involving four particle mass densities (i.e., 1 g/cc, 2 g/cc, 3 g/cc, and 4 g/cc), and calculate the deposition position of each particle. In Fig. 5(e), we present the simulated characteristic curves of the designed inertial impactor for particles with different inertia. As expected, by registering the particle deposition locations and the particle size, we can extract the particle density by fitting these values to the characteristic curves. It is easy to rationalize that by calibrating the platform with interested particle sizes and mass density ranges, a look-up table can therefore be conveniently constructed which translates the particle diameter and deposition distance into its mass density. Here, the dynamic range of the proposed platform, which refers to the range of particle sizes and/or densities that can be effectively captured and classified, is a critical feature. It is relatively easy to rationalize that this range depends on factors such as the active area of the imager and the cut-off size or densities of the impactor. Figure 5(f) presents the dynamic range for particle sizes based on the current configuration, assuming a fixed particle density. The dynamic range is influenced by the cut-off particle diameter (${d_{50 - lower}}$) of the inertial impactor and the upper limit (${d_{50 - upper}}$), which defines the range of particle diameters captured by the imager. While an ideal step-function-like efficiency curve would be optimal, practical efficiency curves may exhibit an “S-shaped” behavior due to geometrical constraints and microfluidic designs. The dynamic range can be adjusted by manipulating geometrical parameters and microfluidic configurations. The platform's flexibility in adjusting the dynamic range is illustrated by modifying the inlet speed of the impactor. As inlet velocities increase from 1.0 m/s to 2.0 m/s, the dynamic range shifts towards a larger size range (defined between purple curves), demonstrating the platform's adaptability for different particle size/density ranges with relatively low complexity.

 

Fig. 5. (a),(b) The schematic configuration of the inertial impactor and its pressure map and flow streamlines. The dimension of the impactor is also inserted for clarity. (c),(d) Illustration of the particle release and impaction on the deposition section over a short time period. (e) Simulated correlation of the particle location, mass density, and particle size on the sample plate. (f) Illustration of the dynamic sizing range of the platform, considering a fixed particle mass density. (g),(h) The deposition map and corresponding histogram of particles with different mass densities when the particle sizes are fixed to be 5μm.

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Once the look-up table (or characteristic curve) of the inertia impactor is constructed, it can be applied for practical implementation. In this context, we employ the impactor for classification of three common types particles (i.e., PMMA, PSL, and Silica), with respective mass densities of 1.18 g/cc, 1.05 g/cc, and 2 g/cc. These spheres were obtained from a commercial sample with a nominal diameter of 5μm (Polysciences, Inc.). As expected, these particles can be effectively classified based on their inertia. Particles with lower inertia tend to travel along the streamline and impact the sticky plate at a greater stopping distance, while particles with higher mass are collected closer to the inlet, resulting in a smaller stopping distance, as depicted in Fig. 5(g). It's worth noting that the distribution of lighter particles, characterized by smaller inertia, tends to have a larger standard deviation due to the uncertainties associated with their longer flying path. Additionally, it's evident that the separation between particles with distinct inertial behavior is more prominent. However, when particles have similar mass densities, there is certain overlap in their deposition distribution. This is well observed in the histogram (Fig. 5(h)), where particles like PMMA and PSL exhibit a noticeable overlap, making it challenging to distinguish between them. This underscores the difficulty in practically identifying particles at the individual species level when their mass densities are similar. To address this challenge, the subsequent analysis demonstrates that incorporating another independent parameter, namely refractive index, can enhance the accuracy of particle identification and classification.

4.4 Demonstration of the platform for particle discrimination based on refractive index measurement

The refractive index of a particle serves as an additional independent parameter that can be effectively employed for particle material identification. In the following section, we outline an alternative application of the holographic platform to discriminate particles based on their refractive index measurements. This approach becomes particularly valuable in situations where discrimination based solely on mass density characterization proves to be challenging or insufficient.

As well observed in Section 4.2, each individual particle scatters a fraction of the incident beam. The scattered light interacts with the un-scattered portion, resulting in interference. The measured field can be described using the Lorenz-Mie theory [24]. This description takes into account not only the radius of the particle, ${a_p}$, but also its refractive index, ${n_p}$, among other parameters.

In fact, in this model [25,26], the hologram ($\mathrm{{\cal H}}$) can be written as a function of six parameters:

The captured raw hologram undergoes a normalization process by dividing it with a reference hologram acquired before the particle is immobilized. The reference hologram essentially represents the background, and it should closely match the intensity of the reference wave, with the only difference being the light scattered by the particle of interest. Therefore, we can approximate the background as having the same intensity as the reference hologram. This approximation allows us to express the normalized hologram as:

In order to infer the parameter, one typically needs a model for ${E_{scat}}$ and an inference method. In our work, we infer the parameters by minimizing the sum of the squared differences between the model and the measured hologram across all pixels. Using a set of parameters denoted as $\mathrm{\Theta }$, our objective can be expressed as:

This minimization process involves finding the parameter values in Θ that result in the best match between the model and the actual holographic measurements. By optimizing these parameters, we aim to achieve a more accurate representation of the scattered electric field and, consequently, the particle properties.

In the process of least-squares fitting, we employ an iterative non-linear algorithm, specifically the Levenberg-Marquardt method [25,26]. This algorithm necessitates the provision of initial parameter estimates by the user. It's essential to provide reasonably accurate initial guesses for the algorithm to effectively reach a solution. To prevent the algorithm from diverging into unrealistic parameter spaces, there are a few strategies that can be employed. One option is to set certain parameters as fixed, meaning they remain constant throughout the optimization process. Alternatively, one may allow parameters to vary within specific ranges.

In the subsequent steps, we conduct numerical fits to digitized and normalized holographic images using Monte Carlo fitting techniques. During this process, we consider the particle's radius (${a_p}$) and refractive index (${n_p}$) as adjustable parameters. We systematically scan through the anticipated parameter range to identify the optimal values that best fit the observed data. This iterative Monte Carlo fitting approach allows us to iteratively adjust these parameters to minimize the discrepancies between the simulated and actual holographic images, enabling us to obtain the most accurate values for the particle's radius and refractive index [27,28].

As a practical demonstration, we then apply the methodology for the determination of particle refractive index. Three types of particles (i.e., PMMA, PSL, Silica) with equivalent diameters (i.e., 5μm) used in previous section are employed. In Figs. 6(a)-(i), we present the raw holograms, numerical fit to Lorenz-Mie theory, and azimuthally averaged radial profiles for these particles, respectively. The disparities between the experimental profiles and the simulated counterparts can be primarily ascribed to two factors. Firstly, it is a well-established phenomenon that the intensity of peripheral ring patterns substantially diminishes as one moves away from the central area. This renders these regions notably susceptible to the influence of experimental noise and uncertainties, thereby introducing variations in the measured profiles when compared to their simulated counterparts. Secondly, the fitting procedure is inherently reliant on a crucial normalization step, imperative for accurate parameter estimation. Nevertheless, it should be noted that during the experimental process, particles may experience minor shifts or rotations in their positions. These slight alterations exert an impact on the accuracy of the normalization process, as the background reference may not precisely correspond to the background conditions of the particle's adjusted position. It is this deviation in normalization that further contributes to the discernible disparities observed in the results.

 

Fig. 6. Fitting to normalized holograms. (a)-(c) Normalized hologram, numerical fit to Lorenz-Mie theory, and azimuthally averaged radial profile for a 5 μm diameter Silica sphere. All scale bars indicate 20 μm. Red curve in the radial profile is obtained from experimental data, blue curve is obtained from the fit. (d)-(f) Data for a 5 μm PMMA sphere. (g)-(i) Data for a 5 μm PSL sphere. (j) The retrieved particle diameter and refractive index, the horizontal and vertical bars mark the deviation from the reference values provided by the manufacturer. (k) The histogram of particles with different refractive indices when the particle sizes are fixed to be 5μm.

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Figure 6(j) depicted the retrieved particle diameter and refractive index for the PMMA, PSL, and silica particles, which are consistent with values reported in [29–31]. The dashed lines mark the refractive indices and diameters specified by the manufacturer. The error-bars mark the estimated measurement precision in particle diameter and refractive index. For a 5 µm silica particle, the measurement errors are as small as ± 0.6% for the diameter and ± 0.4% for the refractive index. In Fig. 6(k), the histogram presents the refractive index distribution of multiple measurements of three particles. Interestingly, even though PMMA and PSL have closely matched mass densities, their distinctive variations in optical density become more prominent. This shift in focus from mass density to optical density significantly reduces the ambiguity in discrimination that arises from relying solely on mass density characteristics. Consequently, the particle classification becomes more accurate and robust, as the unique optical properties provide a complementary dimension for effective particle differentiation. This combined utilization of multiple parameters, such as mass density and optical density, underscores the potential of the proposed approach in enhancing particle identification accuracy across particles with similar mass densities.

4.5 Combination of mass density and refractive index characterization for accurate classification

Combination of mass density and refractive index information of particles offers a powerful approach for material classification. By combining these two independent parameters, a more comprehensive and accurate characterization of particles can be achieved, particularly in scenarios where discrimination based on a single parameter might be challenging due to overlapping values. The fusion of mass density and refractive index data enables a multidimensional analysis that enhances the ability to distinguish between different particle materials. The basic concept involves creating a multidimensional feature space where each particle is represented by its mass density and refractive index values. This creates a unique signature for each particle material, allowing for more effective discrimination.

As a preliminary demonstration, we present a two-dimensional visualization of the measured mass density and optical density values for different particle types: PSL (yellow dots), PMMA (red dots), and Silica (blue dots). An interesting observation from the scatterplot depicted in Fig. 7 is that, as the feature dimension increases due to the incorporation of both mass density and optical density parameters, the classification ambiguity that was evident when relying solely on one-dimensional data diminishes significantly. This improvement in accuracy underscores the power of combining multiple independent parameters for particle classification and discrimination. The scatterplot and visually demonstrate the enhanced discriminatory capability of the proposed approach, enabling more precise differentiation between particle types that would otherwise present challenges when using only a single parameter.

 

Fig. 7. Two-dimensional scatterplot of mass density and refractive index for polystyrene, PMMA and silica particles, together with histograms for polystyrene particles.

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In our current demonstration, we've focused on three specific particle types. However, the concept of fusing data from mass density and refractive index measurements offers a compelling avenue for material classification. By integrating these two independent parameters and employing machine learning-based data fusion algorithms, it is potential to achieve a more comprehensive and universal differentiation of diverse particles.

5. Discussion

5.1 Novelty and impact of this work

In this work, we demonstrate a holography microscopy for particle metrology, classification and identification. This integrated platform captures data from both the inertia-based impactor and the holographic imaging system in parallel, thereby enables simultaneous measuring the mass density and refractive index of particles at single species level. The collected data would then be fused and analyzed together to classify particles based on their mass density and refractive index. This would not only improve the accuracy of particle classification but also enable more robust identification, particularly in cases where particles have similar mass densities but distinctive refractive indices or vice versa. This duality opens up possibilities for discriminating particles, bubbles, binding events, hollow structures, and even uniformity and inhomogeneity in particles. A compact prototype and a customized App have been developed with practical applications.

The impact of this work extends into the design and creation of versatile particle sensors. For instance, in the pharmaceutical industry, the ability to perform on-site monitoring and classify the percentage of active pharmaceutical ingredient (API, i.e., lactose, naproxen, acetaminophen) along with its background is crucial for ensuring drug efficacy. Unfortunately, there's currently a lack of efficient methods to address such applications. To address this gap, we're collaborating closely with our industrial partners (Nanozen industries Co. Ltd, headquartered in Vancouver) to develop a tailored and integrated prototype. This prototype will include advanced electronic components and sophisticated algorithms to tackle these complex challenges in pharmaceutical manufacturing, showcasing the practical potential of our approach.

5.2 Accuracy of the inertial separation and the influencing factors

Here, we would like to discuss another critical feature of the platform: the accuracy of the inertial impactor for particle separation. As discernible in Figs. 5(g-h), even when monodispersed particles are employed, the distribution histogram exhibits certain deviations. These discrepancies are primarily attributed to non-uniform pressure contours and the inherent uncertainties that manifest during the experimental process. Notably, this phenomenon becomes more conspicuous when particles traverse longer flying paths, consequently impacting the accuracy of this modality in particle discrimination. In practical applications necessitating heightened precision, a preference for a narrower distribution arises. This objective can be attained and optimized by tailoring the device's geometry to confine target particle groups within a deposition section characterized by uniform pressure contours.

Furthermore, it's essential to acknowledge that the distribution uncertainty is also influenced by particle speed/flow rate, and pressure gradients. For a more comprehensive view of this effect, we conducted simulations involving adjustments to particle flow speed and pressure settings. From the results portrayed in Fig. 8, several key observations can be made. Firstly, elevating particle speed from 1 m/s to 1.5 m/s leads to a widening of the distribution of lighter particles, with a notably larger standard deviation. This effect can be ascribed to the longer flight paths of smaller and lighter particles, rendering them more susceptible to flow non-uniformities and the uncertainties inherent to the setup. Moreover, with increased particle speed, denser particles tend to impact closer to the inlet, which can be reasonably attributed to their greater inertia, making them less prone to altering their flight direction. Lastly, when the pressure is amplified from 1 atm to 3 atm, the deposition pattern of denser particles experiences discernible shift towards the outlet direction. This is probably due to the fact that the deposition section closer to the throat and bend experience a more pronounced pressure change. These observations underscore the significance of maintaining consistent experimental conditions in practical applications.

 

Fig. 8. Influence of particle flow speed and pressure gradients on the particle trajectory inside the impactor. The deposition map and corresponding histogram of particles with different mass densities when the particle sizes are fixed to be 5μm. (a),(b) Speed: 1 m/s, pressure: 1atm. (c),(d) Speed: 1.5 m/s, pressure: 1atm. (e),(f) Speed: 1 m/s, pressure: 3atm.

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5.3 Limitations of the platform and future direction

While our current demonstration has centered on standard micro-spheres, the practical world often involves irregular, non-spherical, or even inhomogeneous particles. The unique shape, homogeneity, and orientation of such particles can introduce considerable variations in their aerodynamic and optical properties, thereby influencing the precision of particle metrology and identification. In scenarios involving inhomogeneous particles, traditional methods based on Mie theory become less effective, the focus may shift towards their inertial differences for better discrimination. On the other hand, when dealing with irregular, non-spherical particles, inertial separation methods might face challenges, and optical techniques could provide a more robust approach. In fact, in order to better represent the irregular particle shapes, one may approximate these complex particles with simpler, idealized geometries like spheroids, cylinders, flakes, or cubes [32]. This simplification allows the application of established mathematical models and algorithms designed for these specific shapes. Another promising avenue involves leveraging machine learning algorithms to enhance accuracy. Techniques like Support Vector Machines (SVM), k-Nearest-Neighbor (k-NN), Artificial Neural Networks (ANN), or more advanced Convolutional Neural Networks (CNN) can be trained using diverse particle shapes and properties [33–35]. These algorithms learn patterns and relationships from the data, enabling them to make accurate predictions and classifications, even for irregular and complex particle geometries. By integrating these techniques, one can extend the capability of our platform to handle a wider variety of particle shapes and structures, making it more adaptable and effective in real-world applications.

5.4 Two promising automated implementation schemes

Finally, we note that our preliminary demonstration employs a manually fixed sticky plate on the 3D printed impactor, with a focus on stationary particle analysis. Nonetheless, our vision extends to two promising implementation schemes for future automation. The first involves the meticulous analysis of captured holograms on a frame-by-frame basis, enabling the real-time tracking of individual particle trajectories. This approach integrates existing hardware and leverages software optimization techniques [36], offering the potential for near-real-time analysis at frame rates conducive to practical applications. The second avenue centers on the development of an automatic and integrated system for sticky plate replacement, akin to replacing a film roll in photography. Our ongoing efforts in prototyping this solution reflect our commitment to enhancing the platform's usability and deployment in unattended, continuous operation scenarios. We anticipate that the integration of these features into our low-cost, large field-of-view, and user-friendly microscopy platform, coupled with in-situ inertial classification and optical characterization capabilities, presents a superior alternative to conventional filter paper collection and analysis methods, and will be of interest to a wide array of industries.

6. Summary

In summary, we demonstrate a holography platform for simultaneous characterization of mass density and refractive index of particles at single species level. The proposed approach involves utilizing calibrated models to estimate particle mass density based on the information obtained from particle location and size. Furthermore, since this classification strategy may face challenges when dealing with particle types with similar mass densities, we therefore, interrogate an additional independent parameter, namely the refractive index, which is extracted by employing Monte Carlo fitting to Lorenz-Mie theory. The combination of both aerodynamic and optical modalities within the holographic imaging platform enables versatile and unambiguous particle discrimination capabilities. In order to demonstrate such a methodology for practical implementation, a proof-of-concept prototype with a customized iOS-based App is developed for remote controlling the CMOS imager, image acquisition and reconstruction, as well as image analysis and data processing. The integration of the holographic imaging platform with the App interface ensures ease of use and remote accessibility, making the technology more practical and user-friendly. This capability opens doors to a wide range of applications, from industrial quality control to environmental monitoring and beyond. The resulting prototype demonstrates the potential for this approach to revolutionize particle analysis and classification methodologies.