2.1.

Design of Reflective Scatterometer

Figure 1(a) shows a schematic diagram of a newly designed reflective BARDOT system. A high-resolution digital camera (D810, Nikon Corp., Tokyo, Japan) with $7360(\mathrm{H})\times 4912(\mathrm{V})\text{pixels}$ and an AF-S NIKKOR 85 mm $\mathrm{f}/1.8\mathrm{G}$ lens (Nikon Corp., Tokyo, Japan) is positioned over the Petri dish at a distance of 490 mm (19.5′′), measured from the top surface of the Petri dish to the surface of the camera image plane [Fig. 1(b)]. Exposure program, ISO, F-number, exposure bias value, and focal length of the camera are fixed in manual mode, 800, f 8, 0.00 eV, and 85 mm, respectively. A black curtain covers the instrument completely to block unexpected environment light, and a 2-s shutter speed is used for the experiments. The shutter time is selected based on scattering pattern intensity, tested over a variety of shutter time options from 0.3 s to 3 s. A collimated, circular 5-mW beam from a 532-nm laser diode module (GLM-R1IB-05 Innovam Lasers, Montreal, Canada) acts as the light source [Fig. 1(c)]. As shown in Fig. 1(a), an R50:T50 plate beam splitter (BS) (BTF-VIS-30-SQW-5001M-C IDEX Optics & Photonics Marketplace, Albuquerque, New Mexico) is located over the agar plate at a 45-deg angle to deflect the incoming light to the sample. To avoid interference from an edge of the BS for the pattern, a $50\times 50\times 1\mathrm{mm}$ rectangular BS is selected. The light from the source is reflected and backscattered by the bacterial colony and forms a pattern on a screen located in between the BS and the camera; this pattern is captured by the camera as an RAW format for analysis.

Fig. 1

(a) Schematic diagram and experiment setup. Due to the oversized diameter of the backward-scatter patterns, wide screen, and $50:50$ (R/T) BS was used to realize the reflection setup. (b) Photograph of the actual setup. (c) Comparison of the different wavelength lasers on the blood agar media: (left) 532 nm and (right) 635 nm. As clearly seen, 635-nm wavelength light diffusively penetrates the blood agar and spreads out inside the media rather than reflecting off the surface.

As with the forward scatterometer, direct scatter-pattern capture without passing through any optical component guarantees the best quality; however, the screen is adapted owing to the larger pattern size produced by a larger diffraction angle (scattering angle) and the spatial limitation of the commercial large-area CMOS sensors. The screen was a diffuser film $279.4\times 355.6\mathrm{mm}$ (${11}^{\prime \prime }\times {14}^{\prime \prime }$) mounted in a monitor. Since the quality of the screen-captured pattern from the reflection-type instrument is also suitable for the custom-built pattern-analyzer program, we utilized the screen rather than installing an expensive wide-imaging sensor. The screen is located 140 mm ($\sim {5.5}^{\prime \prime }$) above the sample to ensure the high spatial resolution and quality of the scatter patterns.

2.2.

Sample Preparation

E. coli K12, L. innocua, S. typhimurium, and S. aureus were selected as model organisms. All genera were prepared by subculturing from frozen stocks stored in a freezer that was kept at $-80°\mathrm{C}$. From the frozen stock, each genus was cultured on trypticase soy agar (Bacto™, BD Diagnostics, Sparks, Maryland), and incubated at 37°C until colonies were able to be visibly located. One of the colonies was randomly selected to be subcultured on blood agar. The selected culture was then diluted serially two to three times with $100\mu \mathrm{L}$ for each dilution. From the final diluted tube, $50\mu \mathrm{L}$ was surface plated on a trypticase soy agar plate with 5% sheep blood ($100\mathrm{mm}\times 15\mathrm{mm}$), (TSA II™, BD Diagnostics, Sparks, Maryland) to obtain bacterial colony counts of 50 to $100\mathrm{CFU}/\text{plate}$. The plates were incubated at 37°C until the colonies reached a diameter of 700 to $900\mu \mathrm{m}$. Colony diameter and elevation were measured using both a confocal microscope equipped with a Leica DFC310 FX CCD camera and Leica Application Suite V4.20 build 607 (all from Leica Microsystems, Bannockburn, Illinois) using a $2\times$ objective, and a custom-built colony morphology analyzer.¹⁶

2.3.

Optical Modeling

To predict the pattern size, a geometric optics was utilized as a first-order approach. It is assumed that only a reflection by the curvature of the colony is deflecting the incoming light.¹⁷ Figure 2 shows the coordinate system of the analysis. Subscripts s, a, and i denote a source, an aperture, and an image plane, respectively.

Fig. 2

Schematic diagram of the coordinate definition. Incoming photons $(X_{\mathrm{s}},Y_{\mathrm{s}})$ from source are reflected from the colony surface $(X_{\mathrm{a}},Y_{\mathrm{a}})$ where its profile is defined as Eq. (1). At each incidence of reflected photons, the tangential and respective normal line is computed by ${\mathrm{P}}_{\mathrm{A}}$ and ${\mathrm{P}}_{\mathrm{C}}$. Then intersection between ${\mathrm{P}}_{\mathrm{B}}$ and imaging plane $(X_{\mathrm{i}},Y_{\mathrm{i}})$ was calculated to estimate the maximum half diffraction angle.

A bacterial colony is considered to be an optical reflector like a convex mirror. The curvature of the colony is modeled as a Gaussian profile with tailing edge as

2.4.

Time-Lapse Backward-Scatter Patterns

All four bacteria samples were incubated (I2400 Incubator Shaker, New Brunswick Scientific, Edison, New Jersey) and $\sim 15$ colonies per plate were measured. The first measurement was taken when E. coli, S. typhimurium, L. innocua, and S. aureus were incubated for 6, 6, 11, and 8 h, respectively. The time-dependent data were collected by the following steps every hour for 5 h. First, utilizing the integrated colony morphology analyzer (ICMA),¹⁶ colony diameter and elevation were accurately measured for each colony. Second, backward-scatter patterns were captured using the reflection-type instrument. The thickness of the agar for each plate was maintained at $\sim 8\mathrm{mm}$.

2.5.

Image Processing and Analysis

Since the shutter speed is fixed at 2 s, each pattern was captured, cropped to $512\times 512\text{pixels}$, and converted to gray-scale using the “Luminance” algorithm.¹⁹ The captured scatter patterns were analyzed by Baclan™, a stand-alone quantitative image-processing software that utilizes different types of features and provides a supervised learning-based classification of the captured pattern.^10,20,21 After extracting features by rotationally invariant Zernike moments (order 10) and Haralick texture moments (minimum of 1 and maximum of 4 pixels) from each scatter pattern, a classifier was constructed by SVM. Compared to the well-known linear discriminant analysis, SVM is able to construct decision hyperplanes in a multidimensional space that provides the best separation distances among the data classes.^22,23 For validation, 10-fold cross-validation with repetition of 30 times was performed to calculate the five statistical parameters (PPV, NPV, specificity, sensitivity, and accuracy). Detailed derivation for scatter pattern analysis was previously reported.^20,24 Using the captured data, an SVM algorithm was used for training; the performance of the classifier was provided by the cross-validation matrix. Based on the CV matrix, five statistical parameters were calculated: sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and accuracy (Table 1).

Table 1

Statistical performance of the Baclan™ software for the reflection scatter patterns.

3.1.

Forward- and Backward-Scattering Pattern

Figure 3 shows a comparison of forward- and backward-scatter pattern, for E. coli K12 both on a transparent medium (TSA) and opaque mediums (black inked TSA and blood agar plate) The green solid line shows the incoming light, while the red and green dotted lines represent light propagation for the forward- and backward-scatter patterns, respectively. A forward-scattering pattern is observed only with a transparent medium [Fig. 3(c)], whereas the backward-scattering pattern is observed regardless of the opacity of the medium. A red-dashed line shows the reflection of the forward-scatter pattern by the Petri-dish surface, which propagates in a backward direction [Fig. 3(a)]. Since the forward-scattering pattern is not generated in the opaque-medium case [Figs. 3(b) and 3(d)], this backward pattern is observed only with transparent media. The shape of the reflection and the forward scattering from the colony are identical. Even when the pattern is observed in the backward direction, however, it is not considered an actual backward-scatter pattern since the origin of the pattern is forward scatter. The half-diffraction angle of the reflection against the incoming laser has a similar value (0.17 rad) to that of its forward-scatter pattern (0.07 rad), which is $\sim 3.72$-fold smaller than the diffraction angle of the backward-scatter pattern (0.633 rad).

Fig. 3

Comparison of backscatter pattern of bacterial colony (E. coli K12) on both (a) transparent (TSA) and (b) opaque media (black ink added under TSA). For transparent media, both reflection of forward-scatter pattern from the bottom of agar plate (indicated by red-dashed arrow) and actual backscatter pattern (indicated by green-dotted arrow) are captured simultaneously, while only a backward-scatter pattern is captured for opaque media. In both cases, size of a backscattering pattern is larger ($\sim 3.7$ times) than the forward-scattering and the reflection of the forward-scattering pattern. (c) The forward-scatter patterns from the same colony on TSA media. In the red-circled area, we can observe the similar pattern of (c) embedded in the backward-scatter pattern. (d) Backscatter pattern from a bacterial colony plated on blood agar media. (blood agar with 5% sheep blood).

3.2.

General Level Backward-Scatter Patterns

Figure 4 shows snapshots of backward-scatter patterns for the four bacteria genera on 5% sheep blood agar as measured by the reflective BARDOT system. On visual inspection, the backward-scatter patterns for the genera show distinguishable characteristics. For example, the pattern of E. coli shows an overlapped comb with a spoke-shaped pattern. A small number of ring-shaped patterns appears at the periphery. Unlike other patterns, the boundary between the inner and outer sections of the pattern is unclear. For L. innocua, a speckle cloud with tilde-shaped patterns is observed in the center area, with thin rim patterns with overlapped comb-shaped patterns in the peripheral area. Note that the outermost boundary area of L. innocua shows only outward spoke patterns without a circular rim pattern. For Salmonella, very small speckles are observed in the center area, while relatively thick rims overlapped with spoke patterns are observed at the boundary. For S. aureus, interference of the outgoing wave generated the most unique patterns among the four genera tested; center regions were dominated by speckle-like patterns, while the outer rims showed typical ring patterns with irregular edges.

Fig. 4

Representative reflection scatter patterns captured from the reflection-type system. (a) E. coli K12, (b) L. innocua, (c) S. typhimurium, and (d) S. aureus.

3.3.

Simulation of the Reflected Scatter Dimension

Figure 5 displays the pattern size predicted from the bacterial colony model. This calculation was based on Eq. (1)⁵ and the maximum normal vector from the surface was used as the pattern size at the imaging plane. Figure 5(a) displays the predicted ray-tracing from the incoming laser assuming that each line represents a photon from the 2-mm-diameter laser source that completely covers the $>1\text{-}\mathrm{mm}$-diameter bacterial colony. The green-dotted line represents the maximum reflected angle that occurs at the deflection point of the bacterial colony profile. Figure 5(b) shows a close-up of the bacterial colony area. Figure 5(c) displays a comparison of the theoretical calculation and the experimental results for all four organisms tested. Yellow circles represent the geometrical optics model while the three crossbars show the corresponding experimental data for E. coli (red), S. typhimurium (green), and L. innocua (blue). The other crossbar, S. aureus (purple), is a prediction of half diffraction angle based on its aspect ratio, which was not able to be measured due to its excessively larger pattern size. In this study, all four bacterial genera was plated and incubated in order to achieve diameter size of $700\mu \mathrm{m}$ to $900\mu \mathrm{m}$. The aspect ratio and diffraction angle are natural characteristics of each genus for a certain growth rate. When the colony diameter size is kept as specified, E. coli, S. typhimurium, and L. innocua result in a smaller aspect ratio of colony along with smaller pattern size. In contrast to the other three, the aspect ratio of S. aureus has the irregular characteristic of an enormously large sized pattern due to its large aspect ratio. Obviously, the model indicates the half diffraction angle of reflection is increasing as the aspect ratio of the colony increases. Furthermore, the experiment data also well-correlates to the model in spite of minor error. Therefore, a legitimate pattern size prediction can be made by the model, as large diffraction of S. aureus is predicted by its high aspect ratio.

Fig. 5

Theoretical backward pattern size simulation from bacterial colonies by geometrical optic calculation. (a) using Eqs. (1)–(7), laser source is defined as point array of rays across 2 mm span. Distance from bacterial colony to the screen was set to 127 mm and patterns size was measured to be 203 mm in diameter which are provided from the experimental measurements. (b) The close-up view of the reflection phenomena from colony. Orange horizontal line represents the width of the laser and red parallel lines represents the photon arrays in collimated fashion. Blue dashed line shows normal reflection of the incoming photons while green dashed light shows the reflection from the colony surface. (c) Comparison of the aspect ratio and the half diffraction angle. The data clearly indicate a positive correlation between aspect ratio and pattern size. For better comparison, experimental data of aspect ratio and pattern size combination are displayed for four genera.

3.4.

Time-Lapse Backward-Scattering Patterns

Figure 6(a) shows a cross-sectional view of E. coli K12 on blood ager; Fig. 6(b) shows the aspect ratio and pattern size (half diffraction angle). Each profile corresponds to an elevation from a single colony on the same plate with the same incubation time. Variation in diameter and aspect ratio is observed even on the same plate. Once the respective aspect ratio and backward-scatter pattern size are plotted for the colonies tested, we can observe a positive correlation between the aspect ratio and pattern diameter [Fig. 6(b)]. An exception can be noted at E. coli colony #4. The aspect ratio of the colony is 0.0482 which should have been higher than what is shown. The purple line in Fig. 6(a) is the morphological profile of E. coli colony #4. The lower aspect ratio can be explained by the tailing edges of the profile at $-550$ to $-450\mu \mathrm{m}$ and 400 to $550\mu \mathrm{m}$ region because the diameter of the colony was overestimated compared to the slope of E. coli colony #4. Therefore, similar to the forward-scatter experiments,²⁵ a high aspect ratio produces a larger backward-scatter pattern. Figure 7 displays the time-dependent aspect ratio for all four genera. Starting from time point $t_0$, 5 to 15 colonies of each genus at each time point were collected and statistics were calculated. E. coli shows a maximum aspect ratio at $t_0+2$ hours and then decreases, while L. innocua and S. typhimurium plateau after $t_0+2$. Meanwhile, S. aureus begins with the largest aspect ratio (0.15) and gradually decreases at each time point.

Fig. 6

(a) Quantitative profile measurement data from ICMA using E. coli K12 at 8 h incubation as an example. Even in the same plate and same incubation time, their growth morphology can be varying, which results in different diameter and center elevation. (b) The aspect ratio and pattern size [in diffraction angle (rad)] of corresponding colonies of (a). Good correlation is shown between the aspect ratio and pattern sizes.

Fig. 7

Statistical aspect ratio variation for all four genera of bacteria for five different time points. After initial measurement, each plate with one genera of bacteria was interrogated with ICMA and reflection scatterometer for every 1 h. Each time point represents the average of 5 to 15 colonies with respective standard deviations. E. coli shows a maximum aspect ratio at $t_{0+2}$ and after that decrease which means colony is expanding in horizontal direction faster than the expansion in vertical direction. S. typhimurium and L. innocua both shows initial increase of aspect ratio and plateau after $t_{0+2}$ or $t_{0+3}$ hours. S. aureus monotonically decreases its aspect ratio after time $t_0$.

3.5.

Performance of the SVM-Based Classifier

One interesting result is that the combination of Zernike moments and Haralick texture patterns was critical to ensure high classification rates on the backward-scatter patterns (Fig. 8). In contrast to the forward-scatter patterns, all four genera generate highly disordered patterns in which the Haralick texture patterns are contributing to a more accurate classification than the Zernike patterns, which are responsible for circularly symmetric patterns. When the analysis was performed with only the Zernike polynomial, average PPV decreased to $\sim 83\%$ for Listeria and E. coli. Therefore, all results were obtained using the optimal parameter setting given in Sec. 2.5. Table 1 shows the five statistical parameters calculated from the CV matrix whose diagonal elements resulted in more than 95% classification for all four classes. All five statistical measures calculated by Eqs. (6)–(11) provided excellent results of 94% to 100% for each genera.

Fig. 8

Comparison of the PPVs (a) without and (b) with the Haralick texture features in order to show the effect of Haralick feature along increase of Zernike polynomial order (3 to 13). Combination of the Zernike polynomial and Haralick texture features clearly increase the correct classification rates for the four genera sample collected by the reflection scatterometer. The Haralick texture feature resulted in a significant difference. However, when Haralick texture feature is applied, the PPV value does not vary much along Zernike polynomial order. Average of 83% PPVs was achieved without Haralick texture features while the result was boosted to 93% when the Haralick features were applied.

3.6.

Comparison Between Forward- and Backward-Scatter Patterns

Forward- and backward-scatter patterns from the same microorganisms were compared using two different instruments. Forward-scatter patterns were captured by the standard BARDOT instrument on TSA media while the backward-scatter patterns were acquired by the reflection-type instrument. Based on the qualitative observation, the former generates more circularly symmetric ring patterns than the latter. For example, forward-scatter patterns of E. coli, L. innocua, and S. typhimurium display dominating ring patterns along with additional radial spoke patterns. In particular, S. aureus generated perfectly concentric ring patterns due to their smooth and high aspect ratio colony profile. Meanwhile, backward-scatter patterns predominantly expressed web-like random interference patterns even though their characteristic length or density was different among the genera. Interestingly, backward-scatter pattern of S. aureus was completely different from the rest of the three samples and showed a brighter center and weaker edge portion of the interference patterns.