# Polarization Optics to Differentiate Among Bioaerosols for Lidar Applications

Alain Miffre, Danaël Cholleton, Adrien Genoud, Antonio Spanu, Patrick Rairoux

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Alain Miffre, Danaël Cholleton, Adrien Genoud, Antonio Spanu, Patrick Rairoux. Polarization Optics to Differentiate Among Bioaerosols for Lidar Applications. Photonics, 2024, 11 (11), pp.1067. 10.3390/photonics1111067. [https://arxiv.org/abs/2011.06714](https://arxiv.org/abs/2011.06714)

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Article

# Polarization Optics to Differentiate Among Bioaerosols for Lidar Applications

Alain Miffre <fnref n="1" />,* , Danaël Cholleton <fnref n="1" />, , Adrien P. Genoud <fnref n="1" />, , Antonio Spanu <fnref n="2" /> and Patrick Rairoux <fnref n="1" />

**Abstract:** Polarization optics, which characterize the orientation of the electromagnetic field through Stokes vectors formalism, have been effectively used in lidar remote sensing to detect particles that differ in shape, such as mineral dust or pollen. In this study, for the first time, we explore the capability of polarization optics to distinguish the light-backscattering patterns of pollen and fungal spores, two complex-shaped particles that vary significantly in surface structure. A unique laboratory polarimeter operating at lidar backscattering at 180.0° was conducted to assess their light depolarization property in laboratory ambient air. If, at the precise lidar backscattering angle of 180.0°, the depolarization ratios of pollen and fungal spores were difficult to differentiate, slight deviations from 180.0° allowed us to reveal separate scattering matrices for pollen and fungal spores. This demonstrates that polarization optics can unambiguously differentiate these particles based on their light-(back)scattering properties. These findings are consistent at both 532 and 1064 nm. This non-invasive, real-time technique is valuable for environmental monitoring, where rapid identification of airborne allergens is essential, as well as in agricultural and health sectors. Polarization-based light scattering thus offers a valuable method for characterizing such atmospheric particles, aiding in managing airborne contaminants.

**Keywords:** polarization; Stokes vectors; Mueller matrices; lidar; backscattering

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**Citation:** Miffre, A.; Cholleton, D.; Genoud, A.P.; Spanu, A.; Rairoux, P. Polarization Optics to Differentiate Among Bioaerosols for Lidar Applications. *Photonics* **2024**, *11*, 1067. https://doi.org/10.3390/photonics1111067

Received: 7 October 2024

Revised: 7 November 2024

Accepted: 13 November 2024

Published: 14 November 2024

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**Copyright:** © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

The ability to differentiate biological particles in the atmosphere is crucial for various environmental and health-related applications, such as allergen monitoring, agricultural management, and public health [1–4]. Among the many bioaerosols present in the atmosphere, pollen and fungal spores are of particular interest due to their potential to trigger allergic reactions [1,4]. Fungal spores and pollen are indeed common bioaerosols found in the atmosphere. For instance, species from the genus *Cladosporium*, a major source of airborne fungal spores, release significant quantities during late summer and fall or in humid conditions [2–4]. Despite their shared relevance to allergen monitoring, pollen and fungal spores exhibit significant differences in origin and surface structure [1–5], with spikes, holes, and apertures for pollen [5], while fungal spores present cell walls and complex textures [2–4]. Hence, while pollen and fungal spores are airborne and have allergenic potential, their physical properties—such as surface texture, overall form or size—differ significantly. Scanning electron microscopic images such as that displayed in Figure 1 are then exploited to distinguish them. Additionally, molecular techniques are used to extract and sequence DNA from pollen and fungal spores, enabling precise identification [6]. While these two methodologies require either a substrate or/and air sampling, real-time and non-invasive techniques are interesting to develop in complement for environmental monitoring, as proposed by polarization lidar instruments [7–20].

<footnote n="1">¹ Universite Claude Bernard Lyon 1, CNRS, ILM UMR 5306, 69100 Villeurbanne, France; adrien.genoud@univ-lyon1.fr (A.P.G.); patrick.rairoux@univ-lyon1.fr (P.R.)</footnote>

<footnote n="2">² Réseau National de Surveillance Aérobiologique, 69690 Brussieu, France; antonio.spanu@rnsa.fr</footnote>

<footnote>* Correspondence: alain.miffre@univ-lyon1.fr; Tel.: +33-047-243-1087</footnote>
Polarization phenomena are ubiquitous in nature, offering a valuable resource for studying various environmental processes. In atmospheric science, polarization optics—which examines the orientation of the electric field through Stokes vectors [21]—has become a valuable tool. Ground-based [7–19] or satellite-based [20] lidar systems are typically configured with single- or dual-wavelength polarization lidar instruments, designed to analyze the polarization state of backscattered radiation precisely at the 180.0° backscattering angle, measuring both parallel and perpendicular polarization components [7–20]. Polarization lidar instruments quantify the changes in light polarization after light backscattering from mineral dust [7–14,20], volcanic ashes [14–17,20] or pollen [18,19]. These particles, which differ significantly in shape, indeed cause light depolarization that can be quantified through the so-called lidar particle depolarization ratio [7–20], a key quantity to classify among aerosols [22]. However, differentiating bioaerosols such as pollen and fungal spores through polarized light backscattering is still a research challenge that traditional remote sensing methods cannot address. Laboratory or field-based polarized light scattering measurements are crucial for assessing the polarimetric characteristics of these bioaerosols as analytical light scattering theories, such as the Lorenz–Mie theory, do not apply to such intricate biological structures. Notably, differences in the overall form and surface texture of these bioaerosols may cause variations in their light scattering and depolarization characteristics, offering a potential method for differentiating them using polarization optics, with valuable insights for remote monitoring of such airborne allergens.

The goal of this study is then to assess the ability of polarization optics to differentiate between pollen and fungal spores bioaerosols based on their light backscattering properties for further use in lidar applications. This study concentrates on pollen and fungal spores, as addressing other aerosols, such as mineral dust or volcanic ash, would require further additional research. Still, and as shown below, our study provides new insights for airborne allergens remote monitoring through a laboratory experiment conducted on pollen and fungal spores, revealing their intrinsic polarimetric light backscattering properties. It utilizes a π-polarimeter and the scattering matrix formalism to analyze the polarization state of the backscattered radiation [23,24]. The paper is structured as follows. Section 2 describes the experimental setup, including the π-polarimeter operating at both exact and near-backscattering angles. Section 2 begins by introducing the bioaerosols samples and ends by addressing the potential sources of uncertainty in the measurements. Section 3 presents the experimental results, including the polarimetric signatures and lidar particle depolarization ratios at 180.0° and near-backscattering angles. This analysis is then extended to 1064 nm wavelength and a discussion on the significance of the study is proposed. The paper concludes by summarizing the findings and proposing future research directions.

## 2. Materials and Methods

### 2.1. *Bioaerosol Samples*

Two commonly encountered proxies of bioaerosols are here considered: ragweed (*Ambrosia artemisiifolia*) representing pollen and *Cladosporium* representing fungal spores, as depicted in Figure 1. *Cladosporium* is a well-known allergen and its spores are among the most common fungal spores found in outdoor air [1–4]. Likewise, ragweed is an important allergenic pollen [1–4]. The bioaerosols used in this study accurately represent those found in the natural environment. The *Cladosporium herbarum* spores were cultivated under controlled conditions and harvested to ensure quality and consistency. The *Ambrosia artemisiifolia* pollen was collected directly from the plant, meticulously dried and sieved, then rigorously tested to ensure its quality and absence of contamination. Furthermore, a subsample of the bioaerosols underwent further quality control analysis using microscopy to confirm their identity and integrity. This rigorous approach ensures that the experimental findings are relevant to real-world scenarios and contribute valuable insights to the field of bioaerosol detection.
<figure><img src="image_5.png" /><figcaption>**Figure 1.** Microscopic images of two widely encountered bioaerosols: (a) Ragweed pollen (*Ambrosia artemisiifolia*, laboratory study at iLM), (b) Fungal spores (*Cladosporium herbarum*, from MycoBank, a comprehensive database of images of fungal species (https://www.mycobank.org/ (accessed on 14 October 2024)).</figcaption></figure>

## 2.2. Light Polarization States: Stokes Vectors and Mueller Matrices

Light polarization, which describes the orientation of the electric field, is extensively documented in various textbooks [25–27], including specialized books [28]. As introduced by G. Stokes himself [21], a polarization state can be described by its Stokes vector $\mathbf{St} = [I, Q, U, V]^T$, where the first Stokes parameter $I$ corresponds to the light intensity, $Q$ and $U$ describe linear polarization, while $V$ accounts for circular polarization (supercript $T$ represents the transpose vector). The Stokes parameters play a crucial role in laboratory measurements using photometric and polarimetric optical instruments, as these instruments do not directly measure the electric field, but quantities that are quadratic combinations of the electric field components [26,27]. Polarization states can be visualized in Figure 2 on the Poincaré sphere [28], where a polarization state is defined by its longitude $2\chi$ and latitude $2\omega$, while $\tan(2\omega)$ represents the ellipticity. Linear polarization states $(p, s, 45+, 45−)$ lie in the equatorial $(Q, U)$-plane while right and left circular polarization states $(RC, LC)$ are located at the poles, with respective Stokes vectors recalled in the caption of Figure 2 for clarity. Also, a $(p)$-polarized state can be transformed into a $(45+)$-state or a $(RC)$-state using half-wavelength plate (HWP) or a quarter-wave plate (QWP), respectively, with corresponding Mueller matrices [28]:

$$[\mathbf{HWP}] = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & C_{4\varphi} & S_{4\varphi} & 0 \\ 0 & S_{4\varphi} & -C_{4\varphi} & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix}, \quad [\mathbf{QWP}] = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & C_{2\psi}^2 & S_{2\psi}C_{2\psi} & -S_{2\psi} \\ 0 & S_{2\psi}C_{2\psi} & S_{2\psi}^2 & C_{2\psi} \\ 0 & S_{2\psi} & -C_{2\psi} & 0 \end{bmatrix} \quad (1)$$

where $C_x = \cos(x)$, $S_x = \sin(x)$ and the $\varphi$ and $\psi$ angles are defined with respect to the fast axis of the HWP and QWP plates, respectively. Additionally, polarizing beam-splitter cubes (PBCs) can be employed to adjust the polarization state to $(p)$-polarization with transmissivity $T_p$ and to $(s)$-polarization when used as a retroreflector with reflectivity $R_s$.
If $T_s \ll 1$ and $R_p \ll 1$ characterize the (PBC)-imperfections, the corresponding Mueller matrices are [28]:

$$[\mathbf{PBC}_T] = \frac{1}{2} \begin{bmatrix} T_p & T_p & 0 & 0 \\ T_p & T_p & 0 & 0 \\ 0 & 0 & 2T_s^{1/2} & 0 \\ 0 & 0 & 0 & 2T_s^{1/2} \end{bmatrix}, \quad [\mathbf{PBC}_R] = \frac{1}{2} \begin{bmatrix} R_s & -R_s & 0 & 0 \\ -R_s & R_s & 0 & 0 \\ 0 & 0 & 2R_p^{1/2} & 0 \\ 0 & 0 & 0 & 2R_p^{1/2} \end{bmatrix} \quad (2)$$

<figure><img src="image_6.png" /><figcaption>**Figure 2.** Visualization of polarization states on the Poincaré sphere [23]. A polarization state, defined by its longitude $2\chi$ and latitude $2\omega$, has $[1, \cos(2\omega) \cos(2\chi), \cos(2\omega) \sin(2\chi), \sin(2\omega)]^T$ for Stokes vector. Six degenerate polarization states can then be defined: (p) and (s)—polarized light with $\mathbf{St} = [1, \pm 1, 0, 0]^T$ with positive sign for (p)-state, $(45\pm)$—polarized light with $\mathbf{St} = [1, 0, \pm 1, 0]^T$, (RC) and (LC)—polarized light with $\mathbf{St} = [1, 0, 0, \pm 1]^T$ with positive sign for (RC)-state.</figcaption></figure>

## 2.3. Scattering Matrix Formalism

We here consider elastic light scattering by a particle ensemble, embedded in an unbounded host medium, the laboratory ambient air. To account for modifications of the polarization state of the electromagnetic radiation through the scattering process, the dedicated formalism is that of the scattering matrix [26,27], where the polarization state of the incident (subscript i) and scattered (no subscript) radiations, described with their respective Stokes vectors $\mathbf{St}_i$ and $\mathbf{St}$, relate with the scattering matrix [26,27]:

$$\mathbf{St} = \frac{\lambda^2}{4\pi^2 d^2} [\mathbf{F}(\theta)] \mathbf{St}_i \quad (3)$$

where $\lambda$ is the wavelength of the radiation, $d$ is the distance from the particle scattering medium to the photodetector, while $\theta = (k_i, k)$ is the scattering angle ($k = k_i = 2\pi/\lambda$), which defines the scattering plane, used as a reference plane for the Stokes vectors. The scattering matrix $[\mathbf{F}(\theta)]$ is a characteristic of the particle-scattering medium and describes how the intensity and polarization of light are altered as a function of the scattering angle. Depending on the particle's size, shape, and complex refractive index [27], it can serve as a polarimetric signature of these particles. Its expression at scattering angle $\theta$ can be found in light scattering textbooks [27]:

$$[\mathbf{F}(\theta)] = \begin{bmatrix} F_{11}(\theta) & F_{12}(\theta) & 0 & 0 \\ F_{12}(\theta) & F_{22}(\theta) & 0 & 0 \\ 0 & 0 & F_{33}(\theta) & F_{34}(\theta) \\ 0 & 0 & -F_{34}(\theta) & F_{44}(\theta) \end{bmatrix} \quad (4)$$

where the scattering matrix elements $F_{ij}(\theta)$ ($i, j = 1-4$) can be normalized with $F_{11}(\theta)$, the scattering phase function, to obtain reduced scattering matrix elements $f_{ij}(\theta) = F_{ij}(\theta)/F_{11}(\theta)$,
which are less or equal to one [18,20]. Lidar remote sensing applications concern the specific backscattering angle $\theta = 180.0^{\circ} = \pi$, where the backscattering theorem [25] leads to $f_{44}(\pi) = 1 - 2f_{22}(\pi)$, while $f_{33}(\pi) = -f_{22}(\pi)$ and $f_{12}(\pi) = f_{34}(\pi) = 0$. Hence, in Equation (4), only scattering elements $F_{11}(\pi)$ and $F_{22}(\pi)$ do not vanish and the scattering response of the particle medium is determined by the normalized scattering matrix element $f_{22}(\pi) = F_{22}(\pi)/F_{11}(\pi)$. This matrix element plays a key role in polarization lidar applications, as it governs the lidar particle depolarization ratio [27]:

$$PDR = (1 - f_{22}(\pi))/(1 + f_{22}(\pi)) \qquad (5)$$

Although lidar applications are limited to the exact backscattering angle of 180.0°, it is valuable to explore slight deviations from this angle. When the backscattering theorem no longer holds ($\theta < \pi$), the normalized scattering matrix elements $f_{33}(\theta)$ and $f_{44}(\theta)$ are no longer directly related to $f_{22}(\theta)$, offering additional insights into the scattering behavior. In particular, the following set of normalized scattering matrix elements ($f_{22}$, $f_{33}$, $f_{44}$, $f_{12}$, $f_{34}$) is then accessible.

## 2.4. Laboratory Polarimeter at Lidar Exact Backscattering Angle of 180.0° (π-Polarimeter)

To accurately evaluate the lidar PDR of bioaerosols, we use a unique laboratory π-polarimeter specifically developed by our group for that purpose [23]. This instrument operates at 180.0° lidar backscattering angle, a crucial feature for precise PDR evaluations, especially for non-spherical aerosols. Other existing laboratory light scattering setups only approximate the 180.0° lidar backscattering angle and hence the lidar PDR. Our laboratory π-polarimeter (see Figure 3) mainly comprises a polarizing beam-splitter cube (PBC), precisely aligned to set the lidar backscattering angle with accuracy (1 mm out of 10 m) and a (QWP), used to modulate the polarization state of the light, enabling exploration of the (Q, V)—plane on the Poincaré sphere. As in most lidar applications, the laser source of the π-polarimeter is a ns-pulsed laser emitting at wavelength $\lambda = 532$ nm. The laboratory experiment actually consists of two π-polarimeters operating simultaneously but at different wavelengths ($\lambda = 532$ nm, $\lambda = 1064$ nm). To avoid overloading Figure 3, only one is represented. Pollen and fungal spores indeed have sizes exceeding a few micrometers, with pollen being even larger, and light scattering is primarily governed by the size parameter, e.g., the size expressed in wavelength units.

Accurate evaluations of the lidar PDR can be obtained by accounting for the successive Mueller matrices encountered by the ns-pulsed laser source on the optical pathway from the PBC to the particle scattering medium, then back to the photodetector. Using Figure 3 and Equations (1)–(4), the Stokes vector $St_d$ of the detected backscattered radiation is then:

$$St_d = [PBC_R][QWP(-\psi)][F(\theta)]St_i \qquad (6)$$

where $St_i$ is the Stokes vector of the radiation entering the particle scattering medium. Following Figure 3, $St_i = [QWP(\psi)][PBC_T]St_0$ if $St_0 = [1, 1, 0, 0]^T$ stands for the Stokes vector emerging from the laser cavity. After a few calculations, we obtain $St_i = [1, \cos^2(2\psi), -\sin(4\psi)/2, -\sin(2\psi)]^T$. The detected backscattered light intensity $I_d$ on the photodetector can then be obtained by projecting the Stokes vector $St_d$ on the unitary projection raw vector $P_j = [1, 0, 0, 0]$ to finally obtain after detailed calculations:

$$I_d(\psi) = I_0 \times [a - c\cos(4\psi)] \qquad (7)$$

where the light intensity $I_0$ is directly proportional to the laser power density, the electro-optical efficiency of the photodetector, the distance $d$ and the polarization characteristics ($T_p, R_S$) of the retro-reflecting PBC. The coefficients $a$ and $c$ solely depend on $F_{11}(\pi)$ and $F_{22}(\pi) : 2a = F_{11}(\pi) + F_{22}(\pi)$, while $2c = 3F_{22}(\pi) - F_{11}(\pi)$. As a result, $f_{22}(\pi)$ can be
retrieved from Equation (7) by adjusting the recorded experimental variations of $I_d(\psi)$, to obtain quantitative evaluations of $c/a$, then $f_{22}(\pi)$:

$$f_{22}(\pi) = (1 + c/a)/(3 - c/a) \qquad (8)$$

As a result, we finally obtain the lidar particle depolarization ratio using Equation (5):

$$PDR = (1 - c/a)/2 \qquad (9)$$

<figure><img src="image_7.png" /><figcaption>**Figure 3.** Laboratory $\pi$-polarimeter operating at exact backscattering lidar angle ($\theta = \pi$, blue arrows), and at near backscattering angle ($\theta < \pi$, yellow arrows) [24]. The PBC is precisely aligned (1 mm out of 10 m) to cover the backscattering angle $\theta = 180.0 \pm 0.2^{\circ}$ with accuracy. The QWP modulates the polarization state of the incident ns-pulsed laser light to obtain accurate evaluations of $f_{ij}$ by adjusting the experimental variations of $I_d(\psi)$ with the $\psi$ rotation angle of the QWP, as quantified by Equation (7) (for $\theta = 180.0^{\circ}$) and (10) (for $\theta < 180.0^{\circ}$). Accurate values of the lidar PDR are then retrieved from $f_{22}(\pi)$ using Equation (5). For the sake of clarity, we add that the angle $\psi$ is measured counterclockwise between the QWP's fast axis and the laser scattering plane (x, z), as seen from the PBC toward the particles and that the (p, s) polarization components are defined relative to this plane. The experiment involves two laboratory polarimeters operating simultaneously at 532 and 1064 nm wavelengths (only one is represented to ease the reading).</figcaption></figure>

## 2.5. Laboratory Polarimeter at near Lidar Backscattering Angle of 180.0°

In the above section, the particle scattering medium was investigated using polarization states varying only from linear to circular; on the Poincaré sphere, only the $(Q, V)$-plane was explored as $2\chi = 0$. To probe the particle scattering medium with all points of the Poincaré sphere, we here examine slight deviations from the exact lidar backscattering angle of 180.0°, as depicted in Figure 3 in dark yellow, using the same light detector as for exact backscattering angles. To assess the set of matrix elements ($f_{22}$, $f_{33}$, $f_{44}$, $f_{12}$, $f_{34}$), the following light polarization states (p, 45+, RC) are successively considered. Following Figure 3 and Equations (1)–(4), by accounting for the successive Mueller matrices encountered by the ns-laser pulse, we derive the detected backscattered light intensity:

$$I_{d,pol}(\psi) = I_0 \times [a_{pol} - b_{pol}\sin(2\psi) - c_{pol}\cos(4\psi) - d_{pol}\sin(4\psi)] \qquad (10)$$

where subscript pol has been added to the detected light intensity $I_d$ to specify the considered incident polarization state pol = (p, 45+, RC). Compared with Equation (7), new coefficients $b_{pol}$ and $d_{pol}$ appear, which accounts for $f_{33}$, $f_{44}$ and $f_{34}$, as presented in Table 1 where the coefficients ($a_{pol}$, $b_{pol}$, $c_{pol}$, $d_{pol}$) are given. These coefficients solely depend on the normalized scattering matrix elements ($f_{22}$, $f_{33}$, $f_{44}$, $f_{12}$, $f_{34}$). Hence, by recording the variations of $I_{d,pol}(\psi)$, then adjusting these variations with Equation (10), quantitative eval-
uations of $(a_{pol}, b_{pol}, c_{pol}, d_{pol})$, then $(f_{22}, f_{33}, f_{44}, f_{12}, f_{34})$ are obtained using successive incident polarization states $pol = (p, 45+, RC)$. After a few calculations, the following set of equations is finally retrieved:

$$f_{33} = 2d_{45+} / (a_{45+} + c_{45+}), \quad f_{44} = -b_{RC} / (a_{RC} + c_{RC}) \quad (11)$$

$$f_{12} = 2c_{RC} / (a_{RC} + c_{RC}), \quad f_{34} = 2d_{RC} / (a_{RC} + c_{RC}) \quad (12)$$

$$f_{22} = [f_{12}(c_p - a_p) + 2c_p] (a_p + c_p) \quad (13)$$

<table><caption>**Table 1.** Expression of $a_{pol}$ to $d_{pol}$-coefficients as a function of the incident laser light polarization.</caption><thead><tr><th>Polarization State pol</th><th>a<sub>pol</sub></th><th>b<sub>pol</sub></th><th>c<sub>pol</sub></th><th>d<sub>pol</sub></th></tr></thead><tbody><tr><td>p</td><td>2 - f<sub>22</sub> + f<sub>12</sub></td><td>0</td><td>f<sub>12</sub> + f<sub>22</sub></td><td>0</td></tr><tr><td>45+</td><td>2 - f<sub>12</sub></td><td>2f<sub>34</sub></td><td>f<sub>12</sub></td><td>f<sub>33</sub></td></tr><tr><td>RC</td><td>2 - f<sub>12</sub></td><td>-2f<sub>44</sub></td><td>f<sub>12</sub></td><td>f<sub>34</sub></td></tr></tbody></table>

## 2.6. Accuracy in Retrieved Normalized Scattering Matrix Elements

### 2.6.1. At 180.0° Backscattering Angle: Lidar Applications

In the laboratory $\pi$-polarimeter, the polarization state of the ns-pulsed laser is precisely set to $[1, 1, 0, 0]^T$ (with no ellipticity) by employing two successive polarizing beam splitters (PBC), upstream of the retroreflector PBC to be seen in Figure 3. Moreover, to mitigate polarization cross-talk between the emitter and detector polarization axes, a secondary PBC is placed between the retro-reflecting PBC and the photodetector to correct for imperfections in the retro-reflecting PBC (with $T_p = 98.9\%$, $R_s = 99.6\%$). This configuration ensures that only a small fraction $R_p$ of the (p)- component is reflected. As a result, the set-up effectively eliminates unwanted p-component contributions from the backscattered radiation, making the laboratory $\pi$-polarimeter sensitive only to the s-component, as shown in Figure 3. The cross-talk ratio CT, representing the stray (p)- component contribution relative to the (s)- component, was found equal to $CT = R_p T_s / R_s T_p = 5 \times 10^{-5}$, which is negligible compared to other sources of uncertainties.

### 2.6.2. At near 180.0° Backscattering Angle

We here investigate the changes in $f_{ij}$ caused by potential deviations from ideal incident polarization states $pol = (p, 45+, RC)$. For that, slight modifications to the incident Stokes vectors are applied. At first order in $\omega$ and $\chi$, the modified Stokes vectors for the (p, 45+, RC) polarization states are $[1, 1, 2\chi, 2\omega]^T$, $[1, 2\chi, 1, -2\omega]^T$, $[1, -2\omega, 2\chi, 1]^T$, respectively. The induced modifications on the $(a_{pol}, b_{pol}, c_{pol}, d_{pol})$ coefficients can then be calculated as $\Delta a_{pol} = a_{pol}(\omega, \chi) - a_{pol}(0, 0)$, with similar expressions for $b_{pol}, c_{pol}$ and $d_{pol}$-coefficients. For RC-incident polarization for instance, we hence obtain $\Delta a_{RC} = 2\omega f_{22}$, $\Delta b_{RC} = 4\chi f_{34}$, $\Delta c_{RC} = -2\omega f_{22}$ and $\Delta d_{RC} = 2\chi f_{33}$. Interestingly, we note that $a_{RC}(\omega, \chi) + c_{RC}(\omega, \chi) = a_{RC}(0, 0) + c_{RC}(0, 0) = 2$. A similar conclusion can be drawn using 45+-polarized light: $a_{45+}(\omega, \chi) + c_{45+}(\omega, \chi) = a_{45+}(0, 0) + c_{45+}(0, 0) = 2$. Hence, in Equations (11) and (12), the denominator is insensitive to slight corrections in the first order in $\omega$ and $\chi$. By propagating the uncertainties in $\omega$ and $\chi$ into Equations (11)–(13), we assess the deviation $\Delta f_{ij}$ affecting each intrinsic $f_{ij}$ matrix element. The uncertainties on ($f_{33}, f_{44}, f_{34}$) are, at most, equal to $2\omega, 2\chi, 2\chi$, respectively. From an experimental point of view, the values of $2\omega$ and $2\chi$ can be calculated by considering the complementary incident polarization states (s, 45-, LC), in addition to polarization states (p, 45+, RC).
### 3. Results and Discussion

In this section, the recorded variations of backscattered light intensity as a function of the $\psi$-rotation angle of the QWP are presented for ragweed and fungal spores, to retrieve their corresponding polarimetric signatures with their normalized scattering matrix elements. We start by retrieving the normalized scattering element $f_{22}(\pi)$ and the corresponding particle depolarization ratio PDR for use in lidar applications.

#### 3.1. Depolarization Ratio of Pollen and Fungal Spores at 180.0° Lidar Backscattering Angle

Figure 4 displays the recorded variations of $I_d(\psi)$ for pollen (in green) and fungal spores (in brown). These curves exhibit constant extrema which are a clear sign that the size and shape distribution of the particles did not vary during the optical acquisition. The variations of these curves, which thus result from the rotation of the QWP, can be safely adjusted with Equation (7). Their scattering matrix element $f_{22}(\pi)$ and corresponding lidar PDR are presented in Table 2. Under such careful measurements and stable experimental conditions, pollen and fungal spores exhibit nearly identical lidar PDR. This similarity, even within our low experimental error bars, makes the differentiation of these two bioaerosols challenging based on this sole polarimetric signature.

<figure><img src="image_8.png" /><figcaption>**Figure 4.** Backscattered light intensity $I_d(\psi)/I_0$ as a function of the orientation of the QWP for pollen bioaerosol (in green) and fungal spores bioaerosol (in brown) at 180.0° lidar backscattering angle, allowing to retrieve their polarimetric signature $f_{22}(\pi)$ and lidar PDR, using Equations (8) and (9). The experiment is carried out at 532 nm wavelength, using the $\pi$-polarimeter presented in Section 2.3.</figcaption></figure>

<table><caption>**Table 2.** Laboratory evaluation of $f_{22}(\pi)$ and corresponding lidar PDR, using Equations (8) and (9) for pollen and fungal spores derived from Figure 4. The experiment is carried out at 532 nm wavelength.</caption><thead><tr><td>Species</td><td>$f_{22}(\pi)$</td><td>Lidar PD (%)</td></tr></thead><tbody><tr><td>Pollen</td><td>0.517 ± 0.005</td><td>31.8 ± 0.5</td></tr><tr><td>Fungal spores</td><td>0.521 ± 0.016</td><td>31.5 ± 1.3</td></tr></tbody></table>

#### 3.2. Polarimetric Signatures of Pollen and Fungal Spores at 177.5° Backscattering Angle

Figure 5 displays the recorded variations of $I_{d,pol}(\psi)$ for pollen (in green) and fungal spores (in brown), for the three successive incident polarization states pol = (p, 45+, RC) at
532 nm wavelength. In comparison with Figure 4, the light scattering curves of pollen and fungal spores now strikingly differ, regardless of the considered incident light polarization state. By adjusting these curves with the theoretical law established in Equation (10), ($a_{pol}, b_{pol}, c_{pol}, d_{pol}$) coefficients, then matrix elements ($f_{22}, f_{33}, f_{44}, f_{12}, f_{34}$) of pollen and fungal spores were evaluated, as presented in Table 3. The low uncertainties on $2\omega$ and $2\chi$ (0.024 and 0.006 on $2\omega$ and $2\chi$, respectively, for pollen, 0.028 and 0.027 for fungal spores) enable differentiation between pollen and fungal spores using light polarization. The diagonal matrix elements show the most significant differences. In particular, $f_{22}$ is noticeably different as it now ranges from 0.38 for pollen to 0.71 for fungal spores. Hence, and as a conclusion, light polarimetry is a valuable tool to differentiate among bioaerosols when a set of incident polarization states is taken into account, leading to a set of polarimetric signatures ($f_{22}, f_{33}, f_{44}, f_{12}, f_{34}$).

<figure><img src="image_9.png" /><figcaption>**Figure 5.** Backscattered light intensity $I_{d,pol}(\psi)/I_0$ as a function of the orientation of the QWP for pollen bioaerosol (in green) and fungal spores bioaerosol (in brown) for successive incident polarization states $pol = (p, 45^\circ, RC)$, respectively, labeled (**a**–**c**) in the figure. The experiment is carried out at 532 nm wavelength at $177.5^\circ$ angle, using the polarimeter presented in Section 2.4. The curves are adjusted with Equation (10) to derive the polarimetric signatures ($f_{22}, f_{33}, f_{44}, f_{12}, f_{34}$) of pollen and fungal spores using Equations (11)–(13).</figcaption></figure>
<table><caption>**Table 3.** Laboratory evaluation of ($f_{22}$, $f_{33}$, $f_{44}$, $f_{12}$, $f_{34}$) using Equations (10)–(13) for pollen and fungal spores derived from Figure 5. The experiment is carried out at 532 nm wavelength. The error bars are calculated by evaluating $2\omega$ and $2\chi$ as explained in Section 2.6.2.</caption><thead><tr><th>Species</th><th>f<sub>22</sub></th><th>f<sub>33</sub></th><th>f<sub>44</sub></th><th>f<sub>12</sub></th><th>f<sub>34</sub></th></tr></thead><tbody><tr><td>Pollen</td><td>0.38 ± 0.03</td><td>-0.33 ± 0.03</td><td>-0.18 ± 0.01</td><td>0.00 ± 0.02</td><td>-0.01 ± 0.02</td></tr><tr><td>Fungal spores</td><td>0.71 ± 0.07</td><td>-0.63 ± 0.07</td><td>-0.30 ± 0.05</td><td>-0.01 ± 0.05</td><td>-0.04 ± 0.05</td></tr></tbody></table>

### 3.3. Polarimetric Signatures of Pollen and Fungal Spores at Two Wavelengths

We now proceed to a similar study at 1064 nm wavelength. Though pollen and fungal spores have sizes in the micrometer range, the analysis at a 1064 nm wavelength (see Figure 6 and Table 4) reveals similar findings to those at a 532 nm wavelength. Despite a slight increase in the scattering matrix element at the largest wavelength, differentiating between pollen and fungal spores based solely on the lidar depolarization ratio remains challenging due to the similarity in their values.

<figure><img src="image_10.png" /><figcaption>**Figure 6.** Same as Figure 4 but at 1064 nm wavelength.</figcaption></figure>

<table><caption>**Table 4.** Laboratory evaluation of $f_{22}(\pi)$ and corresponding lidar PDR, using Equations (8) and (9) for pollen and fungal spores derived from Figure 6. The experiment is carried out at 1064 nm wavelength.</caption><thead><tr><th>Species</th><th>f<sub>22</sub>(π)</th><th>Lidar PDR (%)</th></tr></thead><tbody><tr><td>Pollen</td><td>0.543 ± 0.018</td><td>29.6 ± 1.5</td></tr><tr><td>Fungal spores</td><td>0.554 ± 0.016</td><td>28.7 ± 1.3</td></tr></tbody></table>

Figure 7 and Table 5 are the analogues of Figure 5 and Table 3 but at 1064 nm wavelength. Following Table 3, the retrieved scattering matrix elements make it possible to distinguish between pollen and fungal spores, at least for diagonal elements $f_{33}$ and $f_{44}$ and even $f_{34}$. The verification of this conclusion at two different wavelengths (532 nm, 1064 nm) highlights the importance of optical polarimetry in studying the surface structure of bioaerosols. However, $f_{22}$ and $f_{12}$ do not provide such clear differentiation. Therefore, among all polarization states examined, (45+) and circular polarization states appear particularly promising for discriminating between bioaerosols.
<figure><img src="image_11.png" /><figcaption>Figure 7. Same as Figure 5 but at 1064 nm wavelength.</figcaption></figure>
<table><caption>**Table 5.** Laboratory evaluation of ($f_{22}$, $f_{33}$, $f_{44}$, $f_{12}$, $f_{34}$) using Equations (10)–(13) for pollen and fungal spores derived from Figure 7. The experiment is carried out at 1064 nm wavelength.</caption><thead><tr><th>Species</th><th>f<sub>22</sub></th><th>f<sub>33</sub></th><th>f<sub>44</sub></th><th>f<sub>12</sub></th><th>f<sub>34</sub></th></tr></thead><tbody><tr><td>Pollen</td><td>0.47 ± 0.01</td><td>-0.41 ± 0.01</td><td>-0.30 ± 0.01</td><td>0.02 ± 0.04</td><td>0.06 ± 0.01</td></tr><tr><td>Fungal spores</td><td>0.51 ± 0.06</td><td>-0.58 ± 0.08</td><td>-0.25 ± 0.02</td><td>-0.02 ± 0.05</td><td>-0.01 ± 0.05</td></tr></tbody></table>

### 3.4. Significance of the Study

This research work is practically significant as it deals with bioaerosols which are widespread atmospheric allergens. Indeed, as explained in Section 2.1, the bioaerosols used in the experiment represent those found in the natural environment so that the laboratory experimental findings are relevant to real-world scenarios. Moreover, our study demonstrates that, using the conventional lidar configuration at a 180.0° backscattering angle, differentiating between pollen and fungal spores is challenging, based on the sole particle depolarization ratio (PDR), even at several wavelengths. This result is key for the lidar remote sensing community as the PDR and its spectral dependence are crucial parameters for aerosol typing [22]. In contrast, shifting the scattering angle slightly reveals distinct polarimetric signatures, enabling differentiation.

Nevertheless, under real outdoor conditions, a large diversity of aerosols may exist, that can be coped with polarization lidar instruments. In the literature [7,9,11,12], lidar aerosol partitioning algorithms have hence been developed to optically separate two or three-component aerosol particle mixtures into their individual optical backscattering components. Our group contributed to this research area by developing the dedicated formalism [15] and the three-component lidar aerosol partitioning algorithm [13,14]. These aerosol partitioning algorithms, which rely on the superposition principle derived from the linearity of Maxwell's equations, all require prior knowledge of the intrinsic PDR of each component, which is used as an input parameter for the algorithm. Hence, our ability to discern pollen/fungal spores in a complex mixture through lidar remote sensing is primarily governed by our knowledge of their intrinsic PDR, what our study uniquely provides (world first). Therefore, we believe that the revealed spectral and polarimetric signatures of pollen and fungal spores in the laboratory are likely to shed important light on our ability to differentiate these two bioaerosols under field outdoor conditions. Performing such lidar data acquisitions and partitioning algorithms is, however, clearly beyond the scope of our contribution; in this Special Issue on polarization optics, we rather assess the ability of polarization optics to differentiate between pollen and fungal spores bioaerosols based on their light backscattering properties and conclude that our new methodology shows the feasibility and perspective of the polarimetric approach for real-time remote observations of bioaerosols.

Our controlled laboratory environment also allows us to thoroughly investigate the fundamental interactions between the bioaerosols and the detection system, thus optimizing the performance of the latter before deployment in more complex outdoor environments. This laboratory study hence provides a crucial foundation for developing a robust bioaerosol detection method that can be implemented in commercial lidar systems for outdoor monitoring. To ensure the practical applicability of our laboratory device for lidar remote sensing, it is crucial to validate its performance in real-world environments. Future research will focus on comparing our device with established methods, including Hirst-type spore traps (the current gold standard for pollen and spore monitoring [29,30] and other automated sensor technologies. Additionally, we plan to conduct airborne measurements using pollen instruments carried by weather balloons to analyze the vertical distribution of bioaerosols, a key factor in understanding atmospheric transport and potential health impacts. This multi-faceted approach will ensure the robustness and applicability of the lidar technology for comprehensive bioaerosol monitoring in outdoor environments.
## 4. Conclusions

In this contribution to the Special Issue on polarization optics in photonics, a laboratory study is conducted to investigate the potential of light polarimetry to differentiate between pollen and fungal spores, two common bioaerosols with distinct allergenic properties, through their light backscattering patterns. Using the scattering matrix formalism, we analyze how these bioaerosols alter the polarization state of the light, using a unique (world-first) laboratory π-polarimeter, operating at the lidar backscattering angle of 180.0° and at two wavelengths (532 nm, 1064 nm) for further use in lidar remote sensing applications. The 1064 nm wavelength is particularly interesting because the sizes of pollen and fungal spores generally range within several micrometers, with pollen often being even larger. To accurately evaluate the lidar particle depolarization ratio (PDR) of pollen and fungal spores, a crucial parameter for aerosol typing [22], we adjusted the experimental variations of detected backscattered light intensity with the rotation of a retarder plate, using the theoretical law established by applying the scattering matrix formalism.

Our laboratory findings are threefold. Firstly, a differentiation based on the sole lidar PDR at 180.0° is difficult, even within our low experimental error bars. Secondly, probing the particle scattering medium with all points of the Poincaré sphere reveals distinct polarimetric signatures that enable differentiation, with $f_{33}$, $f_{44}$ and $f_{34}$ matrixelements exhibiting the largest differences. Thirdly, these findings are consistent at both 532 nm and 1064 nm wavelengths.

The outlooks of this work are numerous. For instance, our conclusion, highlighting the importance of light polarimetry, should be broadened to other pollen and fungal spores. This would enable a more precise discussion on the feasibility of a polarization lidar remote sensing experiment capable of distinguishing between pollen and fungal spores. This study hence encourages further research applying light polarimetry to a wider range of bioaerosols, including various pollen and fungal spores, mold, bacteria, algae, and viruses. This expanded scope will enhance our understanding of bioaerosol differentiation using polarization lidar for real-time atmospheric monitoring.

**Author Contributions:** Conceptualization, A.M., D.C., A.S. and P.R.; methodology, A.M.; software, D.C.; validation, D.C., A.M. and P.R.; formal analysis, D.C. and A.M.; investigation, A.M.; resources, D.C., A.P.G. and A.S.; data curation, D.C.; writing—original draft preparation, A.M.; writing—review and editing, A.P.G., P.R., A.S. and A.M.; visualization, D.C., A.S.; supervision, A.M.; project administration, P.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no specific funding during the last two years.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data supporting reported results can be asked to the corresponding author.

**Acknowledgments:** A. Spanu acknowledges the support of the French Ministry of Health and Prevention and the Ministry for the Ecological Transition and Territorial Cohesion.

**Conflicts of Interest:** The authors declare no conflicts of interest.

## References

1. Lake, I.R.; Jones, N.R.; Agnew, M.; Goodess, C.M.; Giorgi, F.; Hamaoui-Laguel, L.; Semenov, M.A.; Solomon, F.; Storkey, J.; Vautard, R.; et al. Climate Change and Future Pollen Allergy in Europe. *Environ. Health Perspect.* **2017**, *125*, 385–391. [CrossRef] [PubMed]

2. Šantl-Temkiv, T.; Sikoparija, B.; Maki, T.; Carotenuto, F.; Amato, P.; Yao, M.; Morris, C.E.; Schnell, R.; Jaenicke, R.; Pöhlker, C.; et al. Bioaerosol field measurements: Challenges and perspectives in outdoor studies. *Aerosol Sci. Technol.* **2020**, *54*, 520–546. [CrossRef]

3. Kim, K.-H.; Kabir, E.; Jahan, S.A. Airborne bioaerosols and their impact on human health. *J. Environ. Sci.* **2018**, *67*, 23–35. [CrossRef] [PubMed]

4. Weikl, F.; Radl, V.; Munch, J.; Pritsch, K. Targeting allergenic fungi in agricultural environments aids the identification of major sources and potential risks for human health. *Sci. Total. Environ* **2015**, *529*, 223–230. [CrossRef] [PubMed]

5. Hess, M. *Pollen Terminology: An Illustrated Handbook*; Springer: Berlin/Heidelberg, Germany, 2009.
6. Abrego, N.; Norros, V.; Halme, P.; Somervuo, P.; Ali-Kovero, H.; Ovaskainen, O. Give me a sample of air and I will tell which species are found from your region: Molecular identification of fungi from airborne spore samples. *Mol. Ecol. Resour.* **2018**, *18*, 511–524. [CrossRef]

7. Haarig, M.; Ansmann, A.; Engelmann, R.; Baars, H.; Toledano, C.; Torres, B.; Althausen, D.; Radenz, M.; Wandinger, U. First triple-wavelength lidar observations of depolarization and extinction-to-backscatter ratios of Saharan dust. *Atmos. Meas. Tech.* **2022**, *22*, 355–369. [CrossRef]

8. Freudenthaler, V.; Esselborn, M.; Wiegner, M.; Heese, B.; Tesche, M.; Ansmann, A.; Müller, D.; Althausen, D.; Wirth, M.; Fix, A.; et al. Depolarization ratio profiling at several wavelengths in pure Saharan dust during SAMUM 2006. *Tellus B Chem. Phys. Meteorol.* **2009**, *61*, 165–179. [CrossRef]

9. Müller, D.; Veselovskii, I.; Kolgotin, A.; Tesche, M.; Ansmann, A.; Dubovik, O. Vertical profiles of pure dust and mixed smoke–dust plumes inferred from inversion of multiwavelength Raman/polarization lidar data and comparison to AERONET retrievals and in situ observations. *Appl. Opt.* **2013**, *52*, 3178–3202. [CrossRef]

10. Miffre, A.; Cholleton, D.; Mehri, T.; Rairoux, P. Remote Sensing Observation of New Particle Formation Events with a (UV, VIS) Polarization Lidar. *Remote Sens.* **2019**, *11*, 1761. [CrossRef]

11. Tesche, M.; Ansmann, A.; Müller, D.; Althausen, D.; Engelmann, R.; Freudenthaler, V.; Groß, S. Vertically resolved separation of dust and smoke over Cape Verde using multiwavelength Raman and polarization lidars during Saharan Mineral Dust Ex-experiment. *J. Geophys. Res.* **2009**, *114*, D13202.

12. Burton, S.P.; Hair, J.W.; Kahnert, M.; Ferrare, R.A.; Hostetler, C.A.; Cook, A.L.; Harper, D.B.; Berkoff, T.A.; Seaman, S.T.; Collins, J.E.; et al. Observations of the spectral dependence of linear particle depolarization ratio of aerosols using NASA Langley airborne High Spectral Resolution Lidar. *Atmos. Meas. Tech.* **2015**, *15*, 13453–13473. [CrossRef]

13. Mehri, T.; Kemppinen, O.; David, G.; Lindqvist, H.; Tyynelä, J.; Nousiainen, T.; Rairoux, P.; Miffre, A. Investigating the size, shape and surface roughness dependence of polarization lidars with light-scattering computations on real mineral dust particles: Application to dust particles’ external mixtures and dust mass concentration retrievals. *Atmos. Res.* **2018**, *203*, 44–61. [CrossRef]

14. David, G.; Thomas, B.; Nousiainen, T.; Miffre, A.; Rairoux, P. Retrieving simulated volcanic, desert dust and sea-salt particle properties from two/three-component particle mixtures using UV-VIS polarization lidar and T matrix. *Atmos. Meas. Tech.* **2013**, *13*, 6757–6776. [CrossRef]

15. Miffre, A.; David, G.; Thomas, B.; Rairoux, P. Atmospheric non-spherical particles optical properties from UV-polarization lidar and scattering matrix. *Geophys. Res. Lett.* **2011**, *38*, L16804. [CrossRef]

16. Ansmann, A.; Tesche, M.; Groß, S.; Freudenthaler, V.; Seifert, P.; Hiebsch, A.; Schmidt, J.; Wandinger, U.; Mattis, I.; Müller, D.; et al. The 16 April 2010 major volcanic ash plume over central Europe: EARLINET lidar and AERONET photometer observations at Leipzig and Munich, Germany. *Geophys. Res. Lett.* **2010**, *37*, L13810. [CrossRef]

17. Miffre, A.; David, G.; Thomas, B.; Rairoux, P.; Fjaeraa, A.; Kristiansen, N.; Stohl, A. Volcanic aerosol optical properties and phase partitioning behavior after long-range advection characterized by UV-Lidar measurements. *Atmos. Environ.* **2012**, *48*, 76–84. [CrossRef]

18. Sicard, M.; Jorba, O.; Ho, J.J.; Izquierdo, R.; De Linares, C.; Alarcón, M.; Comerón, A.; Belmonte, J. Measurement report: Characterization of the vertical distribution of airborne Pinus pollen in the atmosphere with lidar-derived profiles—A modeling case study in the region of Barcelona, NE Spain. *Atmos. Meas. Tech.* **2021**, *21*, 17807–17832. [CrossRef]

19. Filioglou, M.; Leskinen, A.; Vakkari, V.; O’Connor, E.; Tuononen, M.; Tuominen, P.; Laukkanen, S.; Toiviainen, L.; Saarto, A.; Shang, X.; et al. Spectral dependence of birch and pine pollen optical properties using a synergy of lidar. *Atmos. Chem. Phys.* **2023**, *23*, 9009–9021. [CrossRef]

20. Winker, D.M.; Vaughan, M.A.; Omar, A.; Hu, Y.; Powell, K.A.; Liu, Z.; Hunt, W.H.; Young, S.A. Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms. *J. Atmos. Ocean. Technol.* **2009**, *26*, 2310–2323. [CrossRef]

21. Stokes, G. On the composition and resolution of streams of polarized light from different sources. *Trans. Camb. Philos. Soc.* **1852**, *9*, 399–416.

22. Illingworth, A.J.; Barker, H.W.; Beljaars, A.; Ceccaldi, M.; Chepfer, H.; Clerbaux, N.; Cole, J.; Delanoë, J.; Domenech, C.; Do-novan, D.P.; et al. The Earthcare Satellite: The Next Step Forward in Global Measurements of Clouds, Aerosols, Precipitation, and Radiation. *Bull. Am. Meteor. Soc.* **2015**, *96*, 1311–1332. [CrossRef]

23. Miffre, A.; Mehri, T.; Francis, M.; Rairoux, P. UV-VIS depolarization from Arizona Test Dust particles at exact backscattering angle. *J. Quant. Spectrosc. Radiat. Transf.* **2016**, *169*, 79–90. [CrossRef]

24. Miffre, A.; Cholleton, D.; Rairoux, P. Laboratory evaluation of the scattering matrix elements of mineral dust particles from 176.0° up to 180.0°-exact backscattering angle. *J. Quant. Spectrosc. Radiat. Transf.* **2019**, *222–223*, 45–59. [CrossRef]

25. Van de Hulst, H.C. Light scattering by small particles, New York (John Wiley and Sons), London (Chapman and Hall), 1957. Pp. xiii, 470; 103 Figs.; 46 Tables. 96s. Q. J. R. Meteorol. Soc. **1958**, *84*, 198–199.

26. Bohren, C.F.; Huffman, D.R. *Absorption and Scattering of Light by Small Particles*, 1st ed.; Wiley-VCH: Weinheim, Germany, 1983; 530p, ISBN 9783527618163.

27. Mishchenko, M.I.; Travis, L.D.; Lacis, A.A. *Scattering, Absorption, and Emission of Light by Small Particles*; Cambridge University Press: Cambridge, UK, 2002; 492p.

28. Shurcliff, W.A. *Polarized Light: Production and Use*; Harvard University Press: Cambridge, MA, USA; London, UK, 1962; 181p. [CrossRef]
29. Adamov, S.; Lemonis, N.; Clot, B.; Crouzy, B.; Gehrig, R.; Graber, M.-J.; Sallin, C.; Tummon, F. On the measurement uncertainty of Hirst-type volumetric pollen and spore samplers. *Aerobiologia* **2024**, *40*, 77–91. [CrossRef]

30. Maya-Manzano, J.M.; Tummon, F.; Abt, R.; Allan, N.; Bunderson, L.; Clot, B.; Crouzy, B.; Daunys, G.; Erb, S.; Gonzalez-Alonso, M.; et al. Towards European automatic bioaerosol monitoring: Comparison of 9 automatic pollen observational instruments with classic Hirst-type traps. *Sci. Total. Environ.* **2023**, *866*, 161220. [CrossRef]

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