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A theoretical model for spectral forward scatter patterns from a bacterial colony based on elastic light scatter is presented. The spectral forward scatter patterns are computed by scalar diffraction theory, and compared with experimental results of three discrete wavelengths (405 nm, 635 nm, and 904 nm). To provide quantitative analysis, spectral dependence of diffraction ring width, gap, maxima, minima, and the first deflection point are monitored. Both model and experiment results show an excellent agreement; a longer wavelength induces a wider ring width, a wider ring gap, a smaller pattern size, and smaller numbers of rings. Further analysis using spatial fast Fourier transform (SFFT) shows a good agreement; the spatial frequencies are increasing towards the inward direction, and the slope is inversely proportional to the incoming wavelength.
© 2015 Optical Society of America
1. Introduction
Optical interrogation of biological samples is popular in diverse fields from agriculture to clinical applications. Due to the inherent wide spectral window of the optical interrogation, strategic selections of appropriate wavelengths are critical for enhanced resolution and better classification of the biological samples. In biomedical application, multispectral techniques have been widely used in skin diagnostics [1,2] and microscopic dark-field imaging [3]. In agriculture and food science field, multispectral reflectance measurements have been used extensively to detect and monitor the quality of the harvested fruits [4], acquire the spectral reflection image from bacterial colonies for label-free classification [5], and surface contamination of food [6]. Recently, using a laser scatter patterns from a single colony were reported from diverse research groups [7–10]. The successful application is proven for classifying genera and species levels and some cases down to serovar levels [11,12]. The limitations of the single wavelength scatter, however, are the type of information acquired is limited by the single wavelength thus bacteria with lower hierarchical level have shown less discriminatory power [11,12].
For optical modeling of these applications, bacterial colonies are modeled as a biological spatial light modulator which changes the amplitude and phase of the outgoing wave, and the characteristics of the scatter patterns to the micro- and macroscopic morphological traits (diameter, elevation profile, individual cell shape) of the individual colonies are closely investigated [13]. The latest results of experiment reveal that elevation profile of Staphylococcus aureus ATCC 25923 colony shows good fitness with a Gaussian curve. The results are measured by a custom-built integrated colony morphology analyzer (ICMA) [14] that can measure the 3-D morphology of each colony and 2-D optical density (OD) map simultaneously. Therefore, S. aureus is chosen as a model bacterium for this study since it is one of the prevailing clinical microorganisms and also generates concentric circular diffraction patterns which are ideal for comparison with the diffraction theory.
The benefit of the multispectral approach can be summarized as: 1) capability to provide elastic light scatter (ELS) patterns in multiple wavelengths without a specimen movement, 2) leverage different spectral response via wavelength dependent refractive indices, and 3) simple installation for the current version of single wavelength BARDOT system. In this report, we will expand our scalar diffraction theory to model the ELS patterns across discrete visible range of spectrum. Detailed simulation and prediction of the multispectral ELS patterns will be presented. For experimental validation, a new system called multispectral Bacterial Rapid Detection using Optical scattering Technology (MS-BARDOT) is constructed.
2. Materials and methods
2.1 MS-BARDOT instrument
The first design of MS-BARDOT utilized the stepping motor and right angle gold mirror to physically translate the three lasers sequentially which were not appropriate for fast and reliable acquisition of images. Therefore, to both minimize the dimension and remove the ghost effect, we designed an optical cage system with pellicle beam splitters. Figure 1 shows the schematics and defined coordinate system of the proposed MS-BARDOT. The proposed instrument consists of two major parts: 1) multispectral forward scatterometer and 2) a sequence controller. The optical part is composed of two cage type R45:T55 pellicle beam splitters (Thorlabs Inc., NJ, USA) to reduce a ghost effect caused by typical plate beam splitters. Integrated two pellicle beam splitters for light source are positioned above the Petri dish at a distance of 67 mm from the top of the Petri dish to the center of the bottom pellicle beam splitter. For light sources, circular and collimated 1 mW, 405 nm and 635 nm (Coherent Inc., CA, USA), and 904 nm (Lasermate Group Inc., CA, USA) laser diode modules are selected and integrated to each port of the cage mounted pellicle beam splitter unit (Fig. 1(a)). Due to the stacked beam splitter unit design, multispectral ELS patterns from a single bacterial colony can be measured in less than 4 seconds. To capture forward scatter patterns of a bacterial colony, a monochromatic CMOS camera (Pixelink, PL-B741, ON, Canada) with 1280(H) × 1024(V) pixels and 6.7-µm-unit pixel size is located under the Petri dish at a distance of 9.7 mm from the bottom of the Petri dish to the surface of the image sensor. To normalize the incident light intensity, we have implemented a Si photodiode (PD; Thorlabs Inc., CA, USA) with active wavelength covered from 400 nm to 900 nm to the bottom pellicle beam splitter unit. Since the incident light intensity affects the gain of the CMOS camera, the intensity is simultaneously monitored and recorded for further verification.
Fig. 1 (a) Schematic of proposed in situ multispectral forward scatterometer. Three different wavelength laser diodes (light sources), a photo diode (PD) for intensity monitoring, and one CMOS camera (scatterometer) were integrated to two of stacked cage type pellicle beam splitters (R45:T55). d1 = 67 mm (collimated region) for an easy access and loading for a sample specimen, and d2 = 9.7 mm for scatter measurements with a small size CMOS camera. (b) Coordinate system of the proposed scatter model.
The sequence controller part includes a custom built MCU (Atmel, AVR128, CA, USA) as a data acquisition unit, and PC as a master controller. Using MCU’s internal 10 bit A/D conversion, a variable non-inverting amplified and 2nd low pass filtered photodiode signal is captured, transferred to PC through a RS232C communication, and computed to a light intensity considering both the spectral gain of the PD and the reflection/transmission ratio of the pellicle beam splitter along the incident wavelength. Three custom built intensity tunable diode laser drivers are connected to digital I/O of the MCU. The CMOS camera is connected to PC through IEEE1394, and controlled using SDK from manufacturer (Pixelink, ON, Canada). A custom built MFC based GUI, which was developed using MS Visual Studio 2008 controls all the sequences and records all synchronized information along the incident wavelength.
2.2 Sample preparation
For a better comparison with the theoretical model, S.aureus ATCC 25923 is selected as a model organism. For agar plate preparation, a frozen S. aureus stock is streaked on BHI (brain heart infusion) agar plate, and grown at 37 °C for 13 h. Single S. aureus colony is collected with a sterilized loop, and grown in 5 ml BHI broth (Difco, MD, USA) for 15 h at 37 °C at 130 rpm in an incubator shaker. Cultures were serially diluted and surface plated on BHI agar plate (100 mm x 15 mm) to achieve a bacterial counts of 50-100 CFU/plate. The plates are incubated at 37 °C until the size of the colonies reached to diameter range of 700~900 µm, which took around 11 – 13 h. The diameters of the bacterial colonies are measured using both a bright-field microscope (Leica Microsystems, Bannockburn, IL, USA) equipped with CCD camera (Leica Microsystems, Leica DFC310 FX, Bannockburn, IL, USA) and Leica Application Suite V4.20 build 607 (Leica Microsystems, Bannockburn, IL, USA) with a 10 × objective, and ICMA (Integrated Colony Morphology Analyzer, Purdue University, IN, USA). The agar thickness of each plate was controlled to keep 8 mm to avoid variation.
2.3 Spectral forward scatter model
Figure 1(b) shows a proposed coordinate system and schematic of spectral forward scatter model. The bacterial colony and the semi-solid media (BHI agar plate) are located at the aperture plane, and the forward scatter pattern was captured at the image plane which are defined as (xa, ya) and (xi, yi) respectively. A light propagation direction is defined as positive z axis. The distance between the aperture and the image plane is defined as zi, and the bacterial colony is considered as an amplitude and phase modulator. The ratio between center height of a colony and diameter is defined as an aspect ratio, and 1:6.7 is used based on the previous results of experiment [14]. From the Fresnel approximation and Huygens-Fresnel principle [13], the spectral electric field at the image plane, E(xi, yi, λ), is expressed as
where C is the proportionality constant, fx and fy are spatial frequencies, T(xi, yi, λ) represents an amplitude modulator which is the multiplication of the Gaussian laser beam profile and bacterial colony transmittance f(nbac,nair,nec,λ) [13]. nbac, nair, and nec represent the refractive indices for the bacteria, air, and an extracellular material respectively. We assume that nbac is wavelength dependent while the rest are constant. Then the overall phase term Фoverall which modifies the propagating light can be expressed as the summation of three components where Фc, Фq, and Фr are colony, quadratic, and Gaussian phase component respectively and represents the colony profile. Finally, two equations that relate the phase variation to the number of rings and maximum diffraction angle are modified as3. Experimental results
3.1 Morphology characterization
To verify and compare the theoretical predictions with experiment, several different measurement modalities are utilized to acquire the morphological parameters that were required for Eq. (1)-(5).
Figure 2 illustrates five different modalities of correlated measurements: camera image of plate (Fig. 2(a)), 3D morphology (Fig. 2(b)), optical density (Fig. 2(c)), a phase contrast microscope (PCM) image (Fig. 2(d)), and spectral forward scatter patterns for 405, 635, and 904 nm (Figs. 2(e)-2(g)). These correlated measurements from multiple modalities are shown for a thorough understanding of the morphological and optical characteristics of colonies of S. aureus. Considering the average aspect ratio of S. aureus colonies, diameter of approximately 800 µm colonies are selected, and verified by both PCM and ICMA since the lager diameter of the S. aureus colonies with the aspect ratio induced larger scatter patterns which were larger than dimension of the CMOS sensor. The spectral scatter patterns display periodic and circularly symmetric ring patterns, while the size of the pattern, the width and gap of the each ring, and the spatial frequency of the patterns vary depending on the interrogating wavelengths. Figure 2 (h) shows the cross sectional morphology and OD profile at center region of the colony. The morphology of the S. aureus colony is a bell curve with tailing edge which had center height of 120 µm, and the morphology data measured by ICMA are used for this simulation as colony shape. The spatial OD shows a Gaussian shape with a raised center area, a shoulder near the center area, and large slope near edge area. The OD of the bare BHI agar was measured approximately 0.2 using ICMA light source (675 nm), while the maximum OD of the colony was measured as 0.64.
Fig. 2 Comparison of five different measurement modalities for S. aureus; (a) Image of S. aureus on BHI agar plate, (b) 3D morphology map by ICMA, (c) OD map by ICMA, (d) PCM, (e-g) ELS (405 nm, 635 nm, and 904 nm), (h) cross sectional morphology and OD profile of center region of S. aureus.
3.2 Multispectral simulations
To regenerate and predict the periodic and circularly symmetric scatter patterns, we define several parameters of scatter patterns such as the first deflection point, ring gap, ring width, and local maxima and minima (Fig. 3) for a quantitative analysis. The first deflection point is defined as the outer most point of the pattern and defines the diameter of the scatter pattern. Ring gap and ring width are designated as the distance between adjacent local maxima and minima respectively. The order of local minima and maxima points is determined along the inward direction from the outer rim area, and the first local minimum is defined as the first deflection point, which is directly correlated with the pattern size.
Fig. 3 Definition of parameters for the multispectral forward scatter pattern analysis. The order of the minima and maxima is determined toward the inward direction from the outer most intensity; the first local minimum is specifically defined by the first deflection point.
Due to the asymptotically decreasing intensity at the edge, it is difficult to choose the first deflection point in a consistent manner. Therefore, the location of the first deflection point was estimated with the following three assumptions; 1) the predicted scatter pattern is circular symmetric, 2) the every maxima point was located at the middle of each minima point, and 3) frequency shift is negligible at the outer rim area. The location was computed by adding the distance in between the first maximum and minimum point to the location of the first maximum point. The theoretical results from this algorithm were compared with manual calculations for different wavelengths and also verified with and experimental results which showed good agreement.
Figure 4 shows the predicted characteristics of spectral forward scatter patterns for S. aureus colony. For model prediction, diameter of the colony, height of the colony, distance between the aperture and image plane, and diameter of the incident light are fixed as 800 µm, 120 µm, 9.7 mm, and 1 mm respectively. Refractive index of the S. aureus cell is assumed as a thin cellulous film which has 1.4850 to 1.4524 between 400 nm to 900 nm [15]. This spectral reference refractive index is curve fitted using two terms power equation as with coefficient , −1.789, and 1.455 for a, b, and c respectively, with the goodness of fit of SSE, R-square, and RMSE was , 0.9995, and 0.0001386 respectively. Figure 4(a) and (b) show the spectral dependency of the location of the first to third ring gap and ring width respectively. Each local maxima and minima was automatically found using analyzer program from the predicted patterns, and confirmed with manual calculation. Each of ring width and the ring gap was computed based on the location of these local maxima and minima. Figure 4(c) shows the computed results for the number of rings along the incident wavelength of the predicted model using Eq. (6). Number of the rings was decreased from 113 to 47 (57% decreased) for the incident wavelength shift from 400 nm to 900 nm. Figure 4(d) shows the comparison of the half diffraction angle estimated by algorithm (Eq. (7), blue triangle), manual calculation from predicted pattern (red square), and result of experiment (green star). All three results show good agreement that half maximum diffraction angle decreased from 0.048 to 0.046 rad (3.72% decreased by the algorithm), and diffraction angle from the experiment decreased by 4.4% from 405nm to 904nm. Similar to the number of rings, half maximum diffraction angle, which is directly correlated with the pattern size, is also inversely proportional to the incident wavelength. Meanwhile, ring gap and width increased by 40.1%, and 40.8% from 400 nm to 900 nm of the incident wavelength respectively, which are proportional to the wavelength. Second and third ring width and gap show similar trends with those of the first ring case.
Fig. 4 Analysis of spectral forward scatter patterns. Distance of the first to third (a) ring gap and (b) ring width, and (c) number of diffraction ring along incident wavelength. (d) Comparison of the half diffraction angle estimated by algorithm (blue triangle), manual calculation from predicted pattern (red square), and experiment result (green star). Both the ring gap and ring width were proportional to incident wavelength, while number of rings and half diffraction angle were inversely proportional.
3.3 Experimental verification
Figure 5(a) and 5(b) show the 1D cross section of spectral diffraction patterns for simulation and experiment. For comparison, full 2D patterns are shown in Fig. 5(c) and 5(d). Considering the pixel width of the CMOS camera, the x coordinate of Fig. 5(b) and (d) are converted from pixel to mm scale, and that of y coordinate was converted to normalized intensity considering the quantum efficiency of CMOS sensor along the incident wavelength. The cross section of simulation results show wider and sparser period of patterns for the longer incident wavelength, while the overall pattern size is decreasing.
Fig. 5 Comparison of spectral forward scatter pattern prediction and experimental result of S. aureus ATCC25923 measured by a proposed instrument. Cross sectional view of the spectral forward scatter pattern at boundary area of a) simulation model, b) experimental result, a quarter view of c) predicted model, and d) experimental measurement.
Even though experimental data showed unclear edge and peaks, both the prediction and experimental results showed an excellent agreement. The average of percent error in between the model predictions and results of experiment were computed as 3.54% (pattern size), 0.04% (location of the first to third maxima), and 7.66% (ring width). As the result indicates, longer wavelength induces smaller diffraction angle and smaller diameter which was verified with experimental results.
Figure 6 shows the comparison of spatial frequency changes of the spectral forward scatter patterns between theoretical model and experimental measurements. Even though the scatter patterns show periodic rings, the spatial frequency was not a constant value, but spatially shifted every two or three periods. It also can be observed at Fig. 4(a) and 4(b), however, the effect was not clearly shown since the figures only demonstrated the first three quantities. To verify the spatially shifting frequency effect, we applied the SFFT into the zoom-in patterns for better spatial resolution (Fig. 6(a) and 6(b)). X axis of the Fig. 6 stands for the radial direction of the patterns where center of the pattern is started at 0. Y axis is similar to that of X axis, while Y axis of Fig. 6(c) and 6(d) stands for spatial frequency. From the nature of SFFT, spatial frequency of the pattern can be separated by the window for each location and then visualized. Due to the inherent noise from experiments, the SFFT results of experimental measurements were not clear as the predicted cases. Particularly for 405 nm result, discontinuity on the SFFT result was observed (between 0.5 – 2.5 mm) due to the dominating speckle patterns in the center area. However, the comparison result showed good agreement on trend that the spatial frequency was linearly increased from outer bound to center region, while the slope was inversely proportional to the incident wavelength.
Fig. 6 Comparison of spatial frequency shift of the spectral forward scatter pattern in between predicted model and experimental measurement of S. aureus (1) 405nm, (2) 635 nm, and (3) 905 nm, and patterns from (a) predicted model, (b) experimental result. SFFT result of the center cross sectional area of (c) predicted model and (d) experimental result shows good agreement. Arrows have been added for better visualization.
4. Discussion
We designed a stackable type laser source module which incorporates three incident laser wavelengths, a single photodiode, and two of pellicle beam splitters. The benefits of this design provide: 1) a compact module (50 x 90 x 120 mm) which allows us to simply replace the single wavelength laser diode module in the current BARDOT system, 2) us to acquire multiple wavelength images quickly (less than 4 seconds per colony), and 3) the condition where additional photodiode in the same optical train to acquire simultaneous monitoring of the input intensity that affects the quality of the scatter patterns. One critical design point of the instrument was; two pellicle beam splitters allowed to remove the multiple reflection images from the two beam splitters, and the ghost effect by the thickness of a beam splitter. Typical plate beam splitters generate significant artifacts from the multiple reflections of the surface and deteriorate the quality of the captured scatter images. Due to the spectral nature of the new modeling approach, all the derived formulas (Eq. (1)–(7)) include the wavelength term. In addition, the spectral dependency of the refractive index plays an important role in calculating the two major characteristics of the scatter patterns from Eq. (6) and (7). The longer wavelength induces a lower refractive index of the bacteria cell, and it reduces the overall optical path difference of the bacterial colony model, which is correlated to Фoverall(xa, ya, λ). Therefore, the longer wavelength reduces the magnitude of the phase modulator, and this results in a smaller pattern size and a fewer number of ring patterns.
According to Fig. 4, both of the characteristics shows an inversely proportional relationship to the incoming wavelength majorly contributed by the trend of the spectral refractive indices. The comparison between the theoretical modeling and the experiments shows an excellent agreement in terms of the number of peaks and the locations for all three wavelengths tested. In addition, the width of the outermost ring is proportional to the incoming wavelength which matches well (within 7.6%) between the theory and the experiment. In Fig. 5(d), the experimental scatter patterns display not only the concentric ring structures but also the radial spoke features. Several previous studies show possible correlations between the variations of the internal cell density from the 3-D confocal microscope images with the presence of this spoke patterns [16] and also correlations with the swarming type of colony shape to the speckle characteristics [17]. However, further research is needed for better understanding of the biological origin of the structural density change.
From the SFFT analysis, theoretical spatial frequency shift along the cross sectional direction was visualized. As the Fig. 6(c) and 6(d) show, the spatial frequency is linearly increased from the outer bound to the center region, while the slope of the frequency is inversely proportional to the incident wavelength. The effect of spatial frequency shift also can be used as a spectral finger print of the pattern. One minor difference observed is originating from the intensity of the outer most ring where the experiment results show a somewhat lower value than the theoretical model. The main reason for this discrepancy is due to the biological growth nature of the bacterial colony. According to literature [16], a colony forms a highly dense core area and a rim area where cells are constantly dividing and expanding the boundary. Thus, biological structure in the rim area is somewhat different from the perfect Gaussian shape that we assumed in the theory. Multispectral forward scatter adds valuable information regarding the bacterial colony using their spectral response, such as a pattern size, ring gap and width, number of rings, and spatial frequency shift along the cross sectional direction. With the successful implementation of multispectral forward scatter, hyperspectral forward scatterometer based bacterial phenotyping can be designed with an acousto-optic tunable filters (AOTF) and super -continuum lasers.
Acknowledgment
This research was supported through a cooperative agreement with the Agricultural Research Service of the US Department of Agriculture project number 1935-42000-035 and the Center for Food Safety Engineering at Purdue University.
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