Open AccessArticle

Optical Bacteria Recognition: Cross-Polarized Scattering

Riccardo Pepino

Hamed Tari

Alessandro Bile

Arif Nabizada

and

Eugenio Fazio

Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, 00161 Rome, Italy

Author to whom correspondence should be addressed.

Symmetry 2025, 17(3), 396; https://doi.org/10.3390/sym17030396

Submission received: 23 January 2025 / Revised: 27 February 2025 / Accepted: 3 March 2025 / Published: 6 March 2025

(This article belongs to the Special Issue Symmetry/Asymmetry in Neuromorphic and Intelligent Photonics)

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Abstract

The rapid identification of bacteria is extremely important for controlling infections and enabling swift and effective action. Light scattering has proven to be a highly versatile technique for identifying bacteria, as it does not require long colony growth times. In this article, we present a study on the use of cross-polarized optical scattering (CPS). Despite a relatively low scattering efficiency (10⁻⁵ to 10⁻⁶), working with cross-polarization enhances contrast by eliminating a highly intense background of scattered light. CPS has been applied to four bacteria, with three similar in shape. Moreover, two of them are Gram+ and two Gram-. The obtained images have been reduced in size down to a 16-bit images and camera noise has been added. Although bacteria are symmetrical in principle, in reality rotations of their orientation generate asymmetries in the CPS patterns that were exploited precisely to recognize and classify the different species. The classification of bacteria by a t-SNE algorithm in a reduced-dimension space shows that their features are grouped into specific clusters. However, such classification is not completely decisive due to partial cluster overlapping.

Keywords:

light scattering; cross-polarized scattering; light polarization; bacteria; bacterial detection; rapid testing

1. Introduction

Optical recognition of bacteria represents an emerging field at the intersection of microbiology, optical engineering, and artificial intelligence. This technology aims to quickly and accurately identify bacteria through the analysis of their optical characteristics, without the need for bacterial cultures, thereby reducing diagnostic times and improving the efficiency of medical, environmental, and industrial applications.

The potential applications of optical bacterial recognition are numerous. In the medical field, this technology could be used for the rapid diagnosis of bacterial infections [1] and for monitoring antibiotic resistance [2,3,4]. Traditionally, bacterial identification has relied on microbiological culture techniques, which, although accurate, require significant time and resources [5]. Recently, approaches based on optical technologies have gained attention for their ability to provide rapid and non-invasive results. These methods exploit the unique properties of bacteria, such as their cell shape, cell wall composition, and responses to specific light spectra [6].

Among the most commonly used optical technologies, there is advanced optical microscopy [7,8,9,10,11,12], flow cytometry [13,14,15,16], and Raman spectroscopy [17]. Raman spectroscopy, in particular, has been extensively studied for bacterial recognition due to its ability to detect the unique chemical fingerprints of bacteria. For example, it has been demonstrated that Raman spectra can distinguish between different bacterial species and, in particular, can detect variations in the composition of proteins, lipids, and nucleic acids [17].

The main drawback of these techniques is their complexity, which is due to the instrumentation.

On the contrary, light scattering [17,18,19,20,21] has been successfully used for bacterial classification and has been shown to assess a bacterium’s antimicrobial resistance [22]. It is a relatively simple technique that can be easily automated by combining it with classification algorithms. All this makes it easily portable, applicable even outside the laboratory with relative ease, and usable by less experienced personnel.

In this paper, we study Cross-Polarization Scattering (CPS), i.e., the interaction between polarized light and individual bacteria and the detection of the cross-polarization signal. Despite a relatively low efficiency (10⁻⁵ to 10⁻⁶), working with CPS allows to us obtain good sensitivity by completely eliminating the unscattered residue.

2. Materials and Methods

2.1. Bacteria Structure

Bacteria are prokaryotic organisms, that is, unicellular organisms whose genetic material is not enclosed within a specific membrane, and the compartmentalization of cellular functions in specific organelles is missing in the cytoplasm. Bacteria are divided into two macrogroups: Gram-positive (Gram+) and Gram-negative (Gram-), and their difference is based on the structure of their cell walls [5]. Gram+ bacteria have a cell wall made up of three layers: the first external layer of peptidoglycan, a small periplasma film [r], and an internal cell membrane, made up of phospholipids and proteins. Gram- bacteria instead have a complex cell wall made up of five layers: an external membrane, made up of phospholipids, proteins and lipopolysaccharides, a periplasma region, a thin layer of peptidoglycan, another thin layer of periplasma, and an internal cell membrane made up of phospholipids and proteins [5].

The cytoplasm of bacteria is a gelatinous solution that fills the inside of the cell, containing all of the components necessary for cellular functions, such as enzymes, nutrients, ribosomes and DNA. Although bacteria, unlike eukaryotes, do not have a nuclear membrane that encloses their genetic material, the DNA is mainly concentrated in a central region called the nucleoid [5].

In this work, we analyzed bacillus-shaped bacteria, i.e., rod-shaped, which are guaranteed to have an anisotropic shape and therefore can originate a characteristic diffusion of light. In particular, two Gram+ bacteria were analyzed (Bacillus subtilis and Bacillus globigii, also known as Bacillus atrophaeus) and two Gram- bacteria (Bacillus salmonella and Cholera vibrio). These bacilli have more or less the same shape, but differ in their size and membrane composition.

The scheme of the internal structures is shown in Figure 1, while in Table 1, the geometric parameters are reported.

2.2. Refractive Indices

An important and indeed critical parameter in optical studies is the knowledge of the refractive indices of the various elements that make up the system. As bacteria are complex and non-homogeneous structures that are composed of many substances, the various elements of a bacterium can have different refractive indices due to their composition, thicknesses, and the concentration of water they contain. We have therefore carried out a detailed and in-depth evaluation of these refractive indices.

2.2.1. Nucleotide

Using a non-absorbed wavelength, the internal composition of the cell can be considered to be approximately the same for all bacteria and, consequently, the associated refractive index is also the same [29]. For this reason, the nucleotide is the same for all of the analyzed bacteria and is mainly composed of RNA (with a nominal concentration of 0.5 g/mL), DNA (with a concentration of 6.8 g/mL), and proteins (with a concentration of 8.6 g/mL) [30]. To calculate its refractive index (n_NCT) we used the incremental formula [31], which describes the influence of the various components of the solution as a function of the concentration of the solutes:

n_{N C T} = n_{0} + \sum_{i} δ n_{i} \cdot c_{i}

(1)

where n₀ is the refractive index of the solvent,

δ n_{i}

are the index variations due to different concentrations of solutes

c_{i}

. Water with index

n_{0} =

1.333 was used as solvent [32]; from the literature we find that

δ n_{p r o t e i n}

= 0.17 mL/gr [31],

δ n_{R N A} =

0.20 mL/gr [33], and

δ n_{D N A} =

0.16 mL/gr [34]. Consequently,

n_{N C T} =

1.3639 remains constant for all of the bacteria used.

2.2.2. Cytoplasm

The cytoplasm was also analyzed within a non-absorptive spectral range; thus, its composition can be considered to be approximately identical across all of the bacteria examined. Consequently, its refractive index was uniformly calculated for all samples using the incremental Formula (1), based on the concentrations of the various components. The macromolecular concentration within the cytoplasm ranges between 255 and 289 g/L [35,36,37]. Of this, approximately 60–68 g/L consists of RNA, with 9–10 g/L attributed to tRNA, and the remainder, amounting to 51–57.8 g/L, comprising ribosomal RNA. The protein component accounts for approximately 165–187 g/L, while a smaller fraction, ranging between 30 and 34 g/L, is composed of metabolites and polysaccharides.

Applying the incremental Formula (1), the refractive index of the cytoplasm was determined to lie between 1.3883 and 1.3935. This range is consistent with values reported in the literature, which approximate 1.39 [38,39].

2.2.3. Bacterial Membrane

The calculation of the refractive index of the cell wall is complex since, as shown in Figure 1, bacterial cell walls of both Gram-positive and Gram-negative are multilayered structures that alternate components, such as peptidoglycan, periplasmic space, plasma membrane, and, in the case of Gram-negative bacteria, an additional outer membrane. For this reason, we first determined the refractive index of each region and then calculated an overall index as a weighted average of the multilayer structures, taking into account the thickness of each individual component.

Plasma and Outer Membranes

The plasma membrane and outer membrane are primarily composed of proteins and phospholipids in an approximate ratio of 4:6 [40]. However, the outer membrane of Gram-negative bacteria also contains lipopolysaccharides, located on the outermost surface [41].

The phospholipids and lipopolysaccharides present can vary in both the polar head and the length of the hydrophobic tail [5]. Depending on the polar head, they may include molecules, such as cardiolipin (CL), phosphatidylethanolamine (PE), phosphatidylglycerol (PG), lysophosphatidylethanolamine (LyslPE), lysophosphatidylglycerol (LysilPG), and diphosphatidylglycerol (DPG). Additionally, each phospholipid and lipopolysaccharide can have a hydrophobic tail composed of fatty acids of varying types and quantities. This variability means that membranes, while appearing structurally simple, exhibit highly diverse compositions, making their chemistry exploitable for bacterial identification [42]. To calculate the refractive index of the membranes, the Bruggeman Equation (5) [43,44] was used:

\sum_{i = 1}^{m} f_{i} \frac{ε_{i} - ε_{e f f}}{ε_{i} + 2 * ε_{e f f}} + \sum_{i = 1}^{m'} f_{i} (\sum_{j = 1}^{3} \frac{ε_{i} - ε_{e f f}}{ε_{i} + {L_{j} * (ε}_{i} - ε_{e f f})}) = 0

(2)

which requires as inputs the volume fraction

f_{i}

of each component, their dielectric constant

ε_{i}

, and, if necessary, the depolarization

L_{j}

. Regarding the volume fractions, the typical chemical compositions of various bacteria found in the literature [45,46,47,48,49,50,51,52,53,54,55,56,57,58] do not account for the presence of possible water molecules. However, molecular dynamics simulations reveal that, on average, 11.7 water molecules bind to each phospholipid head [53], while approximately 39 water molecules bind to each membrane protein [59]. Therefore, an accurate estimation of the volume fractions must consider water in the calculation of the chemical composition.

By initially approximating the membrane mass as the product of the effective density and the membrane volume as follows:

m_{m e m b r a n e} = ρ_{e f f e c t i v e} \cdot v o l

(3)

and assuming the additivity of volumes, the effective density can be calculated using the following relationship:

ρ_{e f f e c t i v e} = m_{t o t} \sum_{i} \frac{ρ_{i}}{m_{i}} = \sum_{i} \frac{ρ_{i}}{c_{i}}

(4)

where

c_{i}

represents the concentrations. From the effective density, the total mass and the mass of individual components are calculated, which are then used to determine the number of moles of each macromolecule and, consequently, the number of water molecules bound to the membrane. Subsequently, using the newly calculated concentrations, the volume fractions for each component were obtained. The values of the dielectric constants and the densities of the various macromolecules [60,61,62,63,64] are listed in Table 2.

Phospholipids can be considered cylindrical in shape and are therefore anisotropic, necessitating the calculation of the depolarization factor

L_{j}

. To this end, they were modeled as randomly oriented cylinders, with a length equal to half the thickness of the membrane and a cross-sectional area of 0.65 nm² [53]. Similarly, lipopolysaccharides, when present, were treated analogously but with a cross-sectional area of 2.32 nm² [65].

The refractive index ranges for each membrane are reported in Table 3. As can be observed, these values fall within the expected range of 1.35–1.60, as documented in the literature [39,40,66,67,68].

Periplasm

The refractive index of the periplasm was calculated using Equation (1). For Vibrio cholerae and Salmonella, the thin peptidoglycan layer was considered as a solute within the periplasm, and the values reported in [69] were used. For bacilli, the values provided in [70] were employed. The maximum and minimum values obtained are shown in Table 3.

Peptidoglycan

Finally, the refractive index of the thick peptidoglycan layer in bacilli is 1.351, as reported in [71].

2.2.4. Membrane Refractive Indices

Once the refractive index values for the various membrane compartments were determined, the overall refractive index n_tot of the cell wall was calculated (Table 3) as the weighted average based on the thicknesses S_i of the individual walls:

G R A M - : n_{t o t} s_{t o t} = n_{o m} s_{o m} + n_{p e r} s_{p e r} + n_{i m} s_{i m}

(5)

G R A M + : n_{t o t} s_{t o t} = n_{p e p} s_{p e p} + n_{p e r} s_{p e r} + n_{i m} s_{i m}

(6)

2.3. Numerical Simulation Model

The light scattering by bacteria was simulated using the COMSOL Multiphysics software (v. 6.2) with the Wave Optics module. The 3D models were divided into nucleoid, cytoplasm, and cell wall, with different characteristics for Gram-negative and Gram-positive bacteria (see Table 1). In the model, individual bacteria (Figure 2) are positioned within water cylinders with their axis parallel to the x-axis, which also corresponds to the propagation direction of a plane wave with a wavelength of 532 nm, linearly polarized along the z-axis. The cylinders represent the numerical integration volumes for the scattered electromagnetic field.

The walls of the cylinders were designed to be at a distance of at least λ/2 from the bacterium (which is why the cylinders have different dimensions), to prevent the absorption of scattered field components that could affect the diffraction image. At the edges of the cylinder, a Perfectly Matched Layer (PML) with a thickness of λ/2 was applied to control spurious numerical reflections. In the simulation of the system, variable tetrahedral meshes were employed, with a maximum size of

\frac{λ}{5 n_{i}}

The numerical model simulates the interaction between vertically polarized radiation (z-polarization) and an anisotropic object, which is the bacterium. First, it solves Maxwell’s equations within a cylinder to determine the component of polarization converted to the horizontal (y-polarization). Subsequently, this component is propagated using the Fresnel equation under the near-field approximation:

I_{y} (y, z) = \frac{1}{Ω} {|\frac{1}{i λ d} \iint E_{y} (u, v) e^{- i \frac{π}{λ X} (y^{2} + z^{2})} e^{i \frac{2 π}{λ X} (u y + z v)} d v d u|}^{2}

(7)

where X represents the propagation distance and Ω s the electromagnetic impedance of the vacuum.

Several simulations were conducted, varying the refractive index between its maximum and minimum values for each region and modifying, as shown in Figure 3, the orientation of the bacterium both around the propagation axis and the angle relative to the xz plane. In this way, 720 images were generated for each bacterium, resulting in a total of 2880 images.

3. Results

3.1. Cross-Polarization Scattering Images Generated by Rotating the Bacteria Around the x-Axis

Initially, we simulated the scattering of linearly polarized light along the z-axis in the far field by rotating the bacteria around the x-axis, which corresponds to the propagation axis of the light. Figure 4 shows the intensity maps for y-polarization obtained for Salmonella and Vibrio cholerae bacteria for rotations ranging from 0° to 170°. As can be observed, the two maps are distinctly different due to the differing morphology of the bacteria. The CPS efficiency was estimated to be on the order of 10⁻⁵ ÷ 10⁻⁶. The maximum scattering efficiency was observed for bacterial rotations near 45°/135°, where the coupling between the two cross-polarizations is most efficient.

Figure 5 presents a comparison of the normal-incidence images (x-angle 0°, z-angle 0°) for Salmonella and the two bacilli, as they produce diffraction patterns with similar characteristics due to their similar geometric structures. Despite their similar morphology, the differing membranes and biochemical compositions render them optically distinct.

The images exhibit symmetry with respect to any axis passing through their center. Specifically, the two resulting halves are identical but rotated by 180° relative to each other. Additionally, they display concentric ellipses (dashed lines in the figure), with the shorter radius aligned along the horizontal direction and the longer radius parallel to the vertical direction, resulting in a 90° rotation compared to the original orientation of the bacteria. This rotation can be explained by drawing a parallel with diffraction through a rectangular slit: light tends to diverge more along the direction of the smaller axis [72]. Similarly, in the case of bacteria, their geometry leads to broader diffraction along the shorter axis, generating ellipses that vary in number and size based on the geometric characteristics of the bacteria.

Finally, the intensity of the diffraction images progressively increases from the center toward the edges, indicating that the higher spatial frequencies of the object contribute more significantly to light scattering and polarization conversion. This trend partially depends on the exposed surface area: larger bacteria, such as Bacillus subtilis, scatter more light than smaller bacteria, such as Bacillus globigii, due to greater interaction with the incident radiation. However, the intensity differences observed between bacteria of similar sizes, such as Bacillus subtilis and Salmonella, are attributable to the refractive index. Salmonella, having a higher refractive index, amplifies the intensity of the peaks without altering the shape of the diffraction pattern, thereby converting light polarization more efficiently.

Figure 6b,d show the images of Vibrio cholerae with rotations around the x-axis of 0° and 45°. At a zero angle, the image exhibits characteristics similar to those of Salmonella at 45°, with peaks distributed along an axis inclined at −45° relative to the center of the image and clear symmetry along this axis. This occurs because, as shown in Figure 6a, Vibrio cholerae is aligned along an axis inclined at 45°. Rotating it by 45°, as in Figure 6c, aligns it along the vertical axis, producing a pattern similar to those of the other bacteria, albeit with some differences. The Vibrio cholerae pattern is symmetric only along the horizontal axis. Additionally, although it has geometric parameters similar to other bacteria, its intrinsic curvature compacts its geometric dimensions compared to others, resulting in a greater angular divergence of light. Consequently, its diffraction patterns exhibit broader and fewer peaks, mostly confined to those near the center, with overall lower intensity compared to other bacteria.

3.2. Cross-Polarization Scattering Images Generated by Rotating the Bacteria Around the z-Axis

Figure 7 presents a comparison of the CPS intensity maps for the four bacteria, obtained at the angles x:0°/z:0°, x:90°/z:0°, and x:0°/z:90°. The images corresponding to x:90°/z:0° are simply rotated by 90 degrees relative to those at x:0°/z:0°, which were previously analyzed, and exhibit similar characteristics. In contrast, the images for x:0°/z:90° demonstrate different behaviors. For Salmonella and the bacilli, the patterns exhibit radial symmetry and resemble those obtained from spherical objects or objects with circular cross-sections. The distribution of the peaks follows a trend similar to that observed at a zero x-angle, directly depending on the radial size of the object and increasing as this dimension grows.

In the case of Vibrio cholerae, a different trend is observed. Due to its curvature, its structure closely resembles that of rod-shaped bacteria with a z-angle of 45°, and consequently, its diffraction patterns are very similar to theirs.

3.3. CPS Images Generated by Varying the Refractive Indices Between the Calculated Maximum and Minimum Values

CPS signals exhibit some variability in the refractive index values of the membranes for both Gram-positive and Gram-negative bacteria. The influence of the refractive index on the intensity mapping of cross-polarized scattered light is shown in Figure 8. As observed, variations in the refractive index do not alter the geometry of the mapping but only its contrast, making the peaks and valleys more or less pronounced. This allowed us to simplify the image analysis, maintaining the information obtained for one refractive index equivalent to that of another.

4. Discussion

4.1. 16-Bit Image Reduction and the t-SNE Algorithm for Reducing the Information Dimension

To simulate real-world behavior, we converted the obtained mappings to a 16-bit dynamic range, which is typical of most commercial cameras. In doing so, we considered a quantum efficiency of 0.8, which is standard for 16-bit cameras [r]. The images obtained using this procedure are shown in Figure 9. In this case as well, it was observed that three of the classes appear very similar, while the fourth is distinctly different.

The most evident characteristic of the transformed images is the marked difference that persists among them: at the same refractive index, the images of the bacteria remain distinct, reflecting their unique structural properties. However, the discretization—necessary because the number of photons cannot be a decimal value—leads to the elimination of many peaks that are present in the original images. This effect is particularly noticeable for polar angles that are multiples of 90° or equal to 0°: under these conditions, some peaks are significantly flattened, and the images are characterized by a few dominant peaks. Despite the reduction in the amount of information contained in the images, the 16-bit transformation preserves the main features required to analyze the differences between the bacteria and for their potential classification. For instance, a possible numerical approach to extracting new information from the mappings, making them unique and distinguishable, can be achieved by applying a dimensionality reduction using the nonlinear t-SNE (t-distributed Stochastic Neighbor Embedding) algorithm.

4.2. Application of the t-SNE Algorithm for Reducing the Information Dimension

The obtained images are all different from each other, due to different orientations or different bacteria. The variation between the bacteria is a positive aspect because it favors recognition. The problem arises with the similarities, for example, in images belonging to the same bacterium but at different orientations. Moreover, images have extremely complex characteristics, which is indeed not very intuitive for direct observation. To better manage the large amount of information derived from these images, we applied the t-SNE algorithm to reduce multidimensional vectors (such as images) to a lighter space where image differences can be easily highlighted. Therefore, the t-SNE algorithm allows us to represent a very large dataset in a reduced space in order to qualitatively estimate the different characteristics of the data and therefore of the scattering sources.

The nonlinear t-SNE algorithm is an unsupervised neural technique for dimensionality reduction: it separates dissimilar information (representing it as distant points with a low probability on a new two-dimensional map) and clusters similar information (representing it as closely grouped points with a high probability). We have applied the t-SNE algorithm to the 2880 images obtained from the CPS simulations, whose results are shown in Figure 10A. The algorithm mapped the CPS intensity distributions into a lower-dimensional space while preserving the pairs of points with a high similarity. Using this technique, the Vibrio cholerae cluster is localized in a well-defined region, completely separated from the others. Bacillus globigii forms small distinct clusters, while the Salmonella and Bacillus subtilis classes almost entirely overlap. This makes it challenging to define a curve that precisely distinguishes the four classes. Indeed, we anticipate good classification performance for Vibrio cholerae, given its clear separation from the other classes. Bacillus globigii is expected to be classified with moderate accuracy, thanks to the formation of small clusters. In contrast, distinguishing between Salmonella and Bacillus subtilis is problematic: the points in both classes follow similar and closely aligned trajectories, making their differentiation complex.

When a logarithmic transformation of the images is applied, it can be observed that although the t-SNE representation appears different (Figure 10B), it retains the same characteristics as the one obtained with untransformed images, while enhancing the positional differentiation between the bacteria. Using the logarithmic-scale t-SNE representation, not only does Vibrio cholerae exhibit a unique mapping position, but Bacillus globigii also becomes distinguishable from the others. For Salmonella and Bacillus subtilis, however, the maps show significant overlaps that necessitate the use of artificial intelligence techniques for discrimination [73]. Thus, this representation is able to discriminate different species by identifying clusters of typical features. Such classification has proven, however, not to be completely conclusive, requiring more sophisticated techniques to resolve the conflicts.

To further contextualize our findings, we compared the performance of CPS with other optical bacterial recognition techniques, such as Raman spectroscopy and flow cytometry. Raman spectroscopy provides detailed molecular fingerprints of bacteria and has been extensively studied for bacterial recognition due to its ability to detect unique biochemical signatures [17]. However, its application in real-time diagnostics is limited by the need for complex instrumentation and extensive post-processing [17]. On the other hand, flow cytometry enables rapid classification of bacterial populations and has been successfully applied in bacterial identification [13,14,15,16], but it often requires fluorescent labeling, making it less suited for label-free applications [13]. CPS, despite its relatively low scattering efficiency (10⁻⁵ to 10⁻⁶), offers the advantage of background suppression, significantly improving the signal-to-noise ratio without requiring external markers. The preliminary classification using the t-SNE algorithm demonstrates that CPS can capture structural differences in bacterial morphologies, though partial cluster overlap indicates that further optimization is required. These results suggest that CPS, when integrated with machine learning techniques, could provide a balance between speed, simplicity, and accuracy in bacterial identification, complementing existing methodologies in scenarios where label-free, rapid screening is required.

5. Conclusions

In this paper, we show that Optical Cross-Polarized Scattering can be an effective and rapid technique for bacterial recognition. The technique provided a very large dataset of images from the same bacterium or from different bacteria useful for the purpose of characterization and classification. To reduce the amount of data without losing information, we used the t-SNE algorithm, which allowed us to group all of the data into a single map to compare them. This application allowed the data to cluster into ensemble of characteristics of single bacteria and thus make them identifiable within reduced-dimensional maps. However, this representation has not proven to be conclusive because of several overlapping clusters caused by the extreme variability of the data. This study has highlighted the need to use more complex classification codes, for example, with the direct use of machine learning techniques.

Author Contributions

Conceptualization, E.F. and R.P.; software, R.P., H.T., A.N. and A.B.; formal analysis, R.P. and E.F.; investigation, E.F. and R.P.; writing—review and editing, E.F. and R.P.; supervision, E.F.; funding acquisition, R.P. and E.F.; revision R.P., E.F. and A.B. All authors have read and agreed to the published version of the manuscript.

Funding

Sapienza Università di Roma—Avvio alla Ricerca (B83C23004760001). Sapienza Università di Roma—Avvio alla Ricerca (AR224190029D8129).

Data Availability Statement

Data are available upon request.

Acknowledgments

The authors are indebted to M. Iodice of ISASI-CNR for the use of the COMSOL Multiphysics program machine time.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Schematic structure of Gram+ and Gram- bacteria.

Figure 2. Three-dimensional models of individual bacteria. (A) Salmonella enterica. (B) Vibrio cholerae. (C) Bacillus globigii. (D) Bacillus subtilis.

Figure 3. The simulations were performed by rotating the bacteria around the x and z axes to capture all possible orientations.

Figure 4. CPS maps for Salmonella and Vibrio cholerae bacteria for rotations from 0° to 170° around the x-axis (blue color corresponds to zero light intensity).

Figure 5. Cross-polarized optical scattering (CPS) images for Salmonella and Bacilli (globigii and subtilis) bacteria at normal incidence. Images display concentric elliptical structures (dashed lines), whose dimensions depend on size of bacteria (blue color corresponds to zero light intensity).

Figure 6. Orientations (a,c) and corresponding CPS images (b,d) for Vibrio cholerae at angles around the x-axis of 0° and 45° (blue color corresponds to zero light intensity).

Figure 7. Comparison of CPS images of the four bacteria for 90° rotations around the main axes x and z (blue color corresponds to zero light intensity).

Figure 8. Salmonella bacterium: x-angle of 45°, z-angle of 0°. Variation in CPS images for the refractive index values of the membranes as reported in Table 3: (A)

n_{c i t} = 1.3883, n_{m e m b} = 1.43

; (B)

n_{c i t} = 1.3883, n_{m e m b} = 1.45

; (C)

n_{c i t} = 1.3935, n_{m e m b} = 1.43

; and (D)

n_{c i t} = 1.3935, n_{m e m b} = 1.45

. (blue color corresponds to zero light intensity).

Figure 8. Salmonella bacterium: x-angle of 45°, z-angle of 0°. Variation in CPS images for the refractive index values of the membranes as reported in Table 3: (A)

n_{c i t} = 1.3883, n_{m e m b} = 1.43

; (B)

n_{c i t} = 1.3883, n_{m e m b} = 1.45

; (C)

n_{c i t} = 1.3935, n_{m e m b} = 1.43

; and (D)

n_{c i t} = 1.3935, n_{m e m b} = 1.45

. (blue color corresponds to zero light intensity).

Figure 9. 16-bit CPS images (all with same orientation at z = 0°). (blue color corresponds to zero light intensity).

Figure 10. (A) TSNe normal images and (B) TSNe logarithmic scale images.

Table 1. Geometric parameters of bacteria.

Bacterium	GRAM	Radius	Length	Internal Membrane Thickness	External Membrane Thickness	Periplasmatic Thickness	Cytoplasm Radius	Nucleotide Length	Peptidoglycan Thickness
Cholera	Gram-	215 nm [23]	1.21 µm [24]	10 nm [5]	10 nm [5]	15 nm [25]	150 nm	0.657 µm	-
Salmonella	Gram-	375 nm [26]	2.56 µm [26]	8 nm [5]	8 nm [5]	15 nm [25]	250 mm	1.559 µm	-
Subtilis	Gram+	435 nm [27]	2.3 µm [27]	10 nm [5]	-	22.3 nm [24]	300 nm	1.267 µm	34 nm [22]
Globigii	Gram+	250 nm [28]	2 µm [28]	10 nm [5]	-	22.3 nm [24]	150 mm	1.527 µm	34 nm [22]

Table 2. Density and refractive index values of membrane components.

	PE	PG	CL	LPS	MP	NL	DPG	LYSOPE	LPG	RNA	DNA	DAG	DGDG	H₂O
$ρ$	1.3	1.3	1.6 [r]	1.1	1.32	0.9	1.6	1.1	1.4	2	1.4	0.9	1.5	1
$n$	1.475	1.475	1.505	1.512	1.621	1.480	1.460	1.527	1.533	1.635	1.587	1.472	1.590	1.3337

Table 3. Calculated refractive indices for the cell wall and its components.

Bacterium	External Membrane	Peptidoglycan	Periplasm	Internal Membrane	Cell Wall
Salmonella	1.50–1.55	-	1.35–1.37	1.52–1.53	1.43–1.45
Vibrio cholera	1.52–1.54	-	1.34–1.36	1.52–1.53	1.45–1.46
Bacillus subtilis	-	1.351	1.35–1.36	1.54–1.59	1.38–1.39
Bacillus globigii	-	1.351	1.35–1.36	1.54–1.59	1.38–1.39

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Pepino, R.; Tari, H.; Bile, A.; Nabizada, A.; Fazio, E. Optical Bacteria Recognition: Cross-Polarized Scattering. Symmetry 2025, 17, 396. https://doi.org/10.3390/sym17030396

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Pepino R, Tari H, Bile A, Nabizada A, Fazio E. Optical Bacteria Recognition: Cross-Polarized Scattering. Symmetry. 2025; 17(3):396. https://doi.org/10.3390/sym17030396

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Pepino, Riccardo, Hamed Tari, Alessandro Bile, Arif Nabizada, and Eugenio Fazio. 2025. "Optical Bacteria Recognition: Cross-Polarized Scattering" Symmetry 17, no. 3: 396. https://doi.org/10.3390/sym17030396

APA Style

Pepino, R., Tari, H., Bile, A., Nabizada, A., & Fazio, E. (2025). Optical Bacteria Recognition: Cross-Polarized Scattering. Symmetry, 17(3), 396. https://doi.org/10.3390/sym17030396

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