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Influence of various growth conditions on Fresnel diffraction patterns of bacteria colonies examined in the optical system with converging spherical wave illumination

Igor Buzalewicz, Alina Wieliczko, and Halina Podbielska

Open Access Open Access

Abstract

The novel optical system based on converging spherical wave illumination for analysis of bacteria colonies diffraction patterns, is proposed. The complex physical model of light transformation on bacteria colonies in this system, is presented. Fresnel diffraction patterns of bacteria colonies Escherichia coli, Salmonella enteritidis, Staphylococcus aureus grown in various conditions, were examined. It was demonstrated that the proposed system enables the characterization of morphological changes of colony structures basing on the changes of theirs Fresnel diffraction patterns.

©2011 Optical Society of America

1. Introduction

One of the most important issues in many fields of life science, health safety and food production is the microbial contamination. The rapid, accurate and effective detection of pathogens is recently widely studied by many groups, also due to possible biohazard [1, 2]. Although the majority of microorganisms are able to coexist with humans, plants and animals with beneficial relations, many of them are responsible for various infectious diseases or may cause the contamination of food products. The increasing number of bacterial species identified as important food- and waterborne pathogens, is observed continuously. The big hazard are new laboratory-created pathogens [3, 4] and increased bacteria resistance to commonly used antibacterial agents (antibiotics, sterilization chemicals etc.). Especially, antibiotics resistance is frequently discussed in the medical literature [5–7]. The National Institute of Allergy and Infectious Diseases - NIAID warns that over 70% of various bacteria species, most often causing hospital infections, are already completely resistant to at least one kind of antibiotics commonly used for their treatment [8]. By these reasons the new modalities to detect and combat pathogenic microbes are in focus of many international and national initiatives.

Novel techniques for bacteria characterization to be applied in microbiological diagnosis, have to be developed and examined. Among chemical techniques for bacteria identification, the most popular is the polymerase chain reaction (PCR). Although the PCR method is very sensitive, it is time-consuming according to hours needed for molecular analysis and it requires very pure samples, which additionally makes it expensive. Therefore, some efforts are made towards the development of techniques that can reduce the cost of analysis and quickly detect bacterial pathogens in food, water or in clinical samples. Optical biosensors offer the non-invasive and non-destructive detection, since in this case the amplitude and phase of light modulated by pathogens are analyzed, instead of pathogens themselves. Optical techniques include infrared and fluorescence spectroscopy, flow cytometry, chromatography and chemiluminescence analysis [9, 10]. In the fluorescence spectroscopy bacteria pathogens can be detected directly by analyzing the fluorescence spectra of bacteria cells (e.g. laser induced fluorescence imaging, fluorescence lifetime measurements, laser induced breakdown spectroscopy and dual-wavelength fluorometry) [11–22] or indirectly, by examination of fluorescence spectra of bio-conjugated markers often containing antibodies [23–26]. It should be pointed out that the main disadvantages of these techniques include demanding and time-consuming preparation of high quality samples and necessity to use an equipment with high sensitivity and spectral resolution. The high percentage of false positives in this case may be caused by e.g. similar pathogens fluorescence signature generated by non-biological objects existed in the examined sample. There are also some attempts to use surface plasmon resonance (SPR) phenomena to detect bacterial cells in suspensions [27–29]. The SPR biosensor is an optical sensor exploiting surface plasmons to describe interactions between an analyte in solution and a biomolecular recognition element immobilized on the SPR sensor surface. Recently, techniques based on the analysis of light scattering by bacteria pathogens are examined, as well [30–35]. Generally, they are based on the inverse scattering theory, which relates to the identification of unknown pathogens from the scattering pattern generated by them. These methods include the differential light scattering techniques characterizing angular distribution of light scattered by bacteria cells in water solution [30], backscattered and two-dimensional angular optical scattering techniques for aerosols characterization [31–35]. Samples that may be analyzed by the above mentioned methods must be in form of single bacterial cells or bacterial cells in suspension, therefore appropriate preparation process of high quality samples, is required. These techniques offer label- free detection of bacterial pathogens by light scattering analysis without the need for a labeling reagent or immunological markers. Over the past few years, it was demonstrated that the analysis of forward light scattering on bacteria colonies, mostly affected by diffraction effects, can be used for identification of different bacteria species [36–42]. Diffraction patterns of bacterial colonies exhibit some specific features, which are suitable for bacteria species characterization and can be analyzed using scalar diffraction theory. Moreover, there is no need for special preparation of bacteria samples.

Experiments previously performed in our group have shown that analysis of bacteria colonies Fourier spectra, considered in general as diffraction patterns, can be used to estimate the bacteria colonies number and in consequence, to asses antimicrobial properties of different antimicrobial agents [43–45].

Here, a new approach towards examination of forward light scattering on bacteria colonies in a Fourier transform optical system with converging spherical wave, will be presented. According to our knowledge, this is a first attempt to exploit such a system for analyzing the bacteria colony diffraction signature, as well as to examine its Fresnel patterns. This new diffraction-based sensor offers more effective analysis of scatterograms. The proposed system possess some useful features as the possibility of diffraction patterns scaling and compression of the observation plane in the same setup. This solution offers also low level of optical aberrations. These factors can significantly improve the analysis of diffraction patterns of bacteria colonies. The complex physical model of light transformation on bacteria colonies grown on solid nutrient medium in Petri dish, will be presented. The influence of various growth conditions (temperature of incubation, time of incubation, kind of nutrient medium) on the Fresnel diffraction patterns, will be examined. Obtained results have demonstrated that there is a high correlation between the morphological structure of the colony and recorded diffraction patterns.

2. The physical model of light transformation on bacteria colonies in the optical system with converging spherical wave illumination

2.1 The wave field transformation

For simplicity, let assume that a coherent plane wave Uin.(x0,y0) = A with the amplitude A, propagating along optical axis z perpendicularly to the (x0,y0) plane, falls on the transforming lens L0. It means that the point light source is located in an infinite distance from the transforming lens (see Fig. 1 ). The lens L0 with the focal distance f is transforming the incident plane wave into the converging spherical wave, which can be described as [46]

Uout.(x0,y0)=AP(x0,y0)exp{−iπλf(x02+y02)}=AP(x0,y0)ψ(x0,y0;−F),
where λ is the wavelength of incident wave, F=1/f, P(x0,y0) is a pupil function of the transforming lens and the function ψ(x,y,p) represents Gaussian function:

 figure: Fig. 1

Fig. 1 Proposed optical system configuration for characterization of bacteria colonies diffraction patterns: L0 transforming lens in (x0,y0) plane, bacteria colonies on Petri dish in (x1,y1) plane, observation plane (x2,y2).

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ψ(x,y,p)=exp{iπpλ(x2+y2)}.

Between the lens L0 and the object plane (x1,y1) located in the distance z1 from the lens, the free propagation takes place, therefore the optical field can be described using the Fresnel diffraction approximation, as follows:

U(xm+1,ym+1)=exp(ikzm+1)iλzm+1×∫−∞+∞∫+∞−∞U(xm,ym)exp{iπλzm+1[(xm+1−xm)2+(ym+1−ym)2]}dxmdym=,=C(λ,Zm+1)∫−∞+∞∫−∞+∞U(xm,ym)ψ(xm+1−xm,ym+1−ym,Zm+1)dxmdym
where-Zm+1=1/zm+1.

Finally, the wave field illuminating the object plane can be expressed as:

Uin.(x1,y1)=C(λ,Z1)∫−∞+∞∫−∞+∞Uout.(x0,y0)ψ(x1−x0,y1−y0,Z1)dx0dy0,
where C(λ, Z1) is a constant characteristic for Fresnel approximation depending on the λ and Z1. Additionally, it was assumed that the finite object is totally illuminated by the converging spherical wave, therefore the pupil function can be ignored. By the substitution of the optical field Uout.(x0,y0) expressed by Eq. (1) to Eq. (4) and taking into account the properties of Gaussian function:
ψ(x1−x0,y1−y0,Z1)=ψ(x0,y0,Z1)ψ(x1,y1,Z1)exp{−i2πλZ1(x0x1+y0y1)},
and
ψ(x0,y0,Z1)ψ(x0,y0,−F)=ψ(x0,y0,Z1−F),
it is possible to transform the Eq. (4) to the following form

Uin.(x1,y1)=C(λ,Z1)Aψ(x1,y1,Z1)∫−∞+∞∫−∞+∞ψ(x0,y0,Z1−F)exp{−i2πλZ1(x0x1+y0y1)}dx0dy0.

Moreover, the Fourier transform of Gaussian function can be described by the following formula:

ℑ{exp{−πc(x2+y2)}}=1cexp{−πc(fx2+fy2)},
where fx, fy are the spatial frequencies and ℑ{...} denotes the two-dimensional Fourier transform. So finally, after simple transformations, the optical field Uin.(x0,y0) described by Eq. (7) can be now expressed, as follows:
Uin.(x1,y1)=iλAZ1−FC(λ,Z1)ψ(x1,y1,−Z1FZ1−F),
or after simple transformation, as:
Uin.(x1,y1)=(ff−z1A)exp{ikz1}ψ(x1,y1,−Z1FZ1−F),
The Eq. (10) represents a spherical wave converging towards the plane z = f and which amplitude changes proportionally to the ratio f/(f-z1), what is in agreement with geometrical optics predictions [46,47].

When this wave illuminates the single bacteria colony on Petri dish placed in the object plane (x1,y1), its amplitude and phase are modulated by analyzed object. The contribution of the nutrient medium is limited to the presence of exponential phase shift along optical axis, as well as to the attenuation of a primary amplitude of the incident wave. For simplicity at this stage of analysis, let assume that amplitude transmittance tb(x1,y1) of the bacteria colony is described by the following expression:

tb(x1,y1)=tb0(x1,y1)exp{iϕ(x1,y1)},
where tB0(x1,y1) expresses the two-dimensional transmission coefficient and φ(x1,y1) is the two-dimensional phase distribution [46]. The amplitude and phase transformations on bacteria colony of the wave field Uin.(x0,y0), can be simply presented by
U(x1,y1)=Uin.(x1,y1)tb(x1,y1)
Similarly, as in the case of the free propagation of the optical field from the lens L0 to the object plane, we are using the Fresnel approximation to obtain scattered wave field in the observation plane:
Uin.(x2,y2)=C2(λ,Z2)∫−∞+∞∫−∞+∞U(x1,y1)ψ(x2−x1,y2−y1,Z2)dx1dy2.
After rearrangement of Eq. (13) and appropriate substitutions according to the Gaussian function properties as described by Eq. (5), Eq. (6) and Eq. (8), the wave field in the observation plane takes a form:
Uin.(x2,y2)=C(λ,Z1,Z2)(fAf−z1)ψ(x2,y2,Z2)ℑ{tb(x1,y1)ψ(x1,y1,Z˜)}fx=x2Z2λ;fy=y2Z2λ
where
Z˜=Z2−Z1FZ1−F
It can be seen that for Z˜>0 Eq. (14) is describing the Fresnel transform of the bacteria colony amplitude transmittance. However, it should be pointed out that there exist some important differences between this expression and the conventional Fresnel diffraction formula known from scalar theory of diffraction. Presented above expression should be considered as a Fresnel diffraction formula for tb(x1,y1) alone, and not for entire scattered wave field U.(x1,y1), as it is commonly regarded. Moreover, the parameter Z˜ is not describing the distance to the observation plane, but rather the nature of diffraction pattern (Fresnel or Fraunhofer), which is observed.

If the observation plane will be shifted to the back focal plane of the transforming lens, then z1 + z2 = f and according to the Eq. (15), the parameter Z˜=0. As a result, the exponential quadratic phase term ψ(x1,y1,Z˜)=1 and the Eq. (14) takes a form of the Fourier transform of the bacteria colony amplitude transmittance alone, which represents the Fraunhofer diffraction formula:

Uin.(x2,y2)=C(λ,Z1,Z2)(fAf−z1)ψ(x2,y2,Z2)ℑ{tb(x1,y1)}fx=x2Z^λ;fy=y2Z^λ,
where
Z^=1z^=1f−z1=Z1FZ1−F
It can be seen that the converging spherical wave illumination eliminates the need for large observation distances for recording the Fraunhofer pattern. In [47] the extended analysis of the converging spherical wave illumination system properties is presented and it was shown that this system allows to compress and distort the observation space along optical axis into the finite region of the space between the diffracting object and the Fourier transform plane. If the location of the observation plane ranges from the object plane z = z1 to the Fourier transform plane z = f, then, it is possible to observe the Fresnel diffraction pattern of the object, which scale depends directly on the value of parameter Z˜ and indirectly on the relation between the distance z1 and f. If the observation plane is near the Fourier transform plane, then Z˜=0 and the Fraunhofer diffraction pattern of the object can be observed with the scaling factor of Z^ depending on the distance z^=f−z1. It means that by increasing the distance z^, the size of the diffraction pattern is larger until the object is directly behind the lens. If the distance z^ decreases, the size of the pattern is getting smaller. Moreover, when the point light source is moved closer to the front focal plane of the transforming lens, then the illuminating beam will converge less rapidly and the Fourier transform plane will be moved further from the lens. Therefore, the scale changes of the observed diffraction patterns will be larger. In such optical system the matrix size of used detectors may be smaller due to the possibility of adjusting an appropriate scale of the observed diffraction pattern.

Additionally, to the presented above properties of Fourier transform, the optical system with converging spherical wave illumination possess more advantages comparing to the other Fourier transform systems [48]. The transforming lens, which is placed in front of the object, must be corrected only for a pair of on-axis points to produce the spherical wave and not for all aberrations for the infinity – focal plane points pairs as in configuration with the plane wave illumination. Therefore, the setup with converging spherical wave illumination is more simple, so the level of coherence noises on optical elements is reduced. Moreover, choosing the same size of the lens as the size of the object allows to avoid the bandwidth limitation of the lens. These properties additionally lower the costs of the system construction.

2.2 The degeneration of Fraunhofer diffraction condition by phase modulation of bacteria colony

Presented above analysis did not take into consideration the phase modulation of the incoming wave field caused by the form of bacteria colony. In general, many bacteria colonies have spheroid shapes, therefore it will affect the validity of the above presented consideration, because no assumption about the object form was made there. In the literature various approaches to the bacteria colonies profile shape are presented: a convex shape [36], a thin film with decreasing tailing edge [49] or a Gaussian profile [41]. In our approach a convex shape with the single radius of curvature rb (see Fig. 2 ), will be analyzed. The total phase delay of the wave field passing through the bacteria colony may be expressed [46], as

ϕ(x1,y1)=k[To−Δ(x1,y1)−nbΔ(x1,y1)],
where nb is the refractive index of the bacteria colony, T0 is the thickness along optical axis and Δ(x1,y1) is the bacteria colony thickness function in the off-axis region.

 figure: Fig. 2

Fig. 2 Model of the convex shaped bacteria colony.

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Referring to the assumed geometry of the bacteria colony profile, the thickness Δ(x1,y1) can be written as

Δ(x1,y1)=T0−zb=T0−(rb−rb2−x12−y12)=T0−rb(1−1−x12+y12rb2).
If we expand the square root term in power series and simplify it, the thickness function can be described as
Δ(x1,y1)=T0−x12+y122(1r∞−1rb)
and the phase delay as
ϕ(x1,y1)=knbT0−k(nb−1)x12+y122(1r∞−1rb)=knT0−k(nb−1)x12+y122R,
where R=(n−1)(r∞−1−rb−1). It should be pointed that an additional phase delay along optical axis of a wave passing through the Petri dish and nutrient medium, occurs. Therefore, the refractive indices of the Pethri dish np and the nutrient medium na, as well as their thicknesses Tp and Ta, respectively, should be taken into account, as well. By the substitution of the Eq. (21) to Eq. (11) and further to the diffraction formula represented by Eq. (14), the following expression is obtained:
Uin.(x2,y2)=C˜×ℑ{tb0(x1,y1)ψ(x1,y1,Z˜′)}fx=x2Z2λ;fy=y2Z2λ,
where
Z˜′=Z2−Z1FZ1−F−R,
and the constant C˜can be expressed as:
C˜=(fAf−z1)exp(ikZ1−1)exp(ikZ2−1)ψ(x2,y2,Z2)exp(iknpTp)exp(iknaTa)exp(iknbT0)iλZ2−1.
Additional term R in the Eq. (23) indicates that the phase modulation of bacteria colony due to its convex shape and the refractive index nb, affects the conditions of Fraunhofer diffraction observation. Now, the location of the Fourier plane is shifted along the optical axis, respectively to the value of R. Moreover, this parameter affects as well the lateral scale changes of Fresnel pattern, which are correlated with the Z˜′. Therefore, it can be seen that for analysis of Fraunhofer patterns the additional information about bacteria colony profile is required.

3. Materials and methods

3.1 Preparation of bacteria samples

The experiments were performed on bacteria colonies of Escherichia coli (0119), Salmonella enteritidis (ATCC 13076) and Staphylococcus aureus (PCM 2267). The cultures were obtained from the microbiological laboratory of the Department of Epizootiology and Veterinary Administration with Clinic of Infectious Diseases of the Wroclaw University of Environmental and Life Science. Bacteria suspensions were first incubated for 24 hours at the temperature of 37°C. Respective dilutions were seeded on the surface of the solid nutrient medium in Petri dish, so as to obtain 12-20 colonies per plate, and were again incubated at 37 °C for next 12, 14, 22, 36 or 40 hours. Additionally, in order to examine the influence of the kind of nutrient medium on diffraction patterns, the Escherichia coli (0119) bacteria species were seeded on four different nutrient media: MacConkey (Biocorp), nutrient agar (Oxoid), tryptone soya agar (Oxoid) and Columbia agar (Oxoid). To analyze the influence of the structural changes of the bacteria colonies on the observed diffraction patterns some samples were exposed to low-temperature stress and were incubated at 15°C and 0°C, while the control samples were incubated at 37°C. First, morphological properties of bacteria colonies were examined by means of the optical microscope (Nikon Eclipse 2000, objective 4x, 10x). Then, the diffraction patterns of the colonies were recorded in the proposed optical system with converging spherical wave illumination.

3.2 The absorption properties of used nutrient media and selection of the light source

Examined bacteria colonies were grown on solid nutrient media that contain various nutrients for bacteria breeding. The variety of the nutrient media chemical composition can significantly affects their transmission properties. Particularly, it is important to choose an appropriate wavelength of light source. Therefore, the absorption properties of some mostly used nutrient media (MacConkey, agar and Columbia agar) were measured by means of the AvaSpec-3648 spectrometer in the spectral range 300-800 nm with the resolution 2 nm (see Fig. 3 ). It can be seen that generally nutrient media exhibit significant absorption in the UV-A and UV-VIS spectral range. Columbia and nutrient agar have absorbance maximum at ca. 400 nm. However, side lobes in VIS spectral range: 400-600 nm, are observed, as well. In the case of the MacConkey medium the strong absorbance occurs at 330 nm, as well as in the spectral range 400-600 nm. It can be seen that each nutrient medium at wavelengths longer than 600 nm, has lower absorbance. Therefore, as a light source the laser diode module (1mW, collimated beam, Thorlabs) with wavelength 635 nm was chosen for proposed diffraction experiments.

 figure: Fig. 3

Fig. 3 The absorption spectra of: (a) Columbia agar, (b) Nutrient agar,(c) MacConkey medium.

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3.3 The optical system configuration and calibration

The schema of the proposed optical system with converging spherical wave illumination is shown on Fig. 4 . It includes the laser diode module (635 nm, 1 mW, collimated Thorlabs), beam expander BE (Edmund Optics), transforming lens L (achromatic doublet, focal distance: 48.6 cm, clear aperture: 6.35cm, Edmund Optics), CMOS camera C (EO-1312, Edmund Optics) and XYZ sample positioning stage with Petri dish S, which enables the adjustment of uniform illumination of the single bacteria colony. By changing the position of sample holder along optical axis the diffraction patterns scale can be changed.

 figure: Fig. 4

Fig. 4 The schematic configuration of proposed optical system (explanation in text).

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Calibration of the system can be accomplished simply by analysis of the diffraction patterns of the exit pupil of the system. Without the object, when such a system is properly focused, so in another words, the detector is located exactly in the back focal plane of the transforming lens, then in the observation plane the Fraunhofer diffraction pattern of the exit pupil can be observed. These exemplary diffraction pattern are showing that optical system with converging spherical wave illumination can compress the observation space and both Fresnel and Fraunhofer patterns can be observed. The Fresnel diffraction pattern of the exit pupil indicates that this system is defocused and the observation plane is in the Fresnel region (see Fig. 5 ). By changing the position of the camera along the optical axis for fixed position of the object, the various diffraction patterns can be observed: from Fresnel pattern to Fraunhofer pattern. If the converging spherical wave illumination is applied, the lateral dimension of the diffraction pattern decreases with the increasing of the distance between the object and the transforming lens.

 figure: Fig. 5

Fig. 5 Different diffraction patterns of the exit pupil of the optical system: (a) z2=2 cm, (b) z2=9 cm,(c) z2=15 cm Fresnel patterns for increasing distance from the transforming lens, (d) z2=28.8 cm Fraunhofer pattern in the back focal plane of the transforming lens (aperture diameter: 2 mm).

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4. Results

4.1 Scaling Fresnel patterns of the bacteria colony

The main advantage of the proposed optical system with converging spherical wave illumination has the ability to control the diffraction patterns dimension by changing the sample location along the optical axis, respectively to the fixed positions of the transforming lens and camera.

In order to demonstrate it, Salmonella enteritidis and Staphylococcus aureus colonies on Tryptone soya agar were analyzed. The Fresnel diffraction patterns of single bacteria colony for various object’s positions, were recorded. Exemplary results are shown on Fig. 6 and Fig. 7 . If moving the object towards the transforming lens the pattern becomes larger and on the other hand, it becomes smaller if moving it away from the lens

 figure: Fig. 6

Fig. 6 The change of the dimension of Fresnel diffraction patterns in the case of Salmonella enteritidis colony with decreasing the distance z1:(a) 28 cm, (b) 26.5 cm, (c) 25.3 cm, (d) 24.5cm (bacteria colony diameter: approx. 0.8 mm, beam diameter: approx. 1 mm).

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 figure: Fig. 7

Fig. 7 The change of the of Fresnel diffraction patterns of Staphylococcus aureus colony with decreasing the distance z1.: (a) 28 cm, (b) 27cm (bacteria colony diameter: 2.1 mm, beam diameter: approx. 2.1 mm).

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4.2 Correlation between bacteria colony structure changes and observed Fresnel patterns

It is obvious that the chemical composition of nutrient media has an effect on the bacteria metabolism. The shape of bacteria colony depends, among others, also on bacteria metabolic processes. The shape, size, structure and color of the bacteria colony is widely analyzed in the microbiological diagnosis. These properties depend not only on the bacteria species, but also on various environmental factors such as growth conditions: kind of nutrient medium, temperature, growth media surface wettability etc. Therefore, these parameters should be taken under careful consideration in the procedure of bacteria species identification. In our experiments, Escherichia coli (0119) colonies grown on two different nutrient media (Columbia agar and Tryptone soya agar), were analyzed.

On the Fig. 8 different diffraction patterns of Escherichia coli (0119) colony grown in different temperatures, are presented. The used nutrient medium was Columbia agar. The samples of bacteria colonies after incubation at 37°C for 12 hours were grown in temperature 15°C for next 6 hours. Obtained results as presented on Fig. 8 have revealed some differences between the Fresnel diffraction patterns, depending on the incubation temperature. These changes are demonstrated by deformation of the second diffraction ring (Fig. 8(b), 8(c)). To quantitatively evaluate the differences between Fresnel diffraction pattern of bacteria colonies grown in different temperatures, additional image processing analysis was applied to determine the two-dimensional correlation coefficient in Matlab software environment, which is describing the similarity between two compared Fresnel patterns. The 2D correlation coefficient in the case of Fresnel patterns of bacteria colonies grown in the same conditions at 37°C, ranged from 0.79 to 0.88, which is understandable according to the random localization of bacteria cells and speckle effect commonly observed, if the coherent light sources are used The values of 2D correlation coefficients between reference Fresnel diffraction patterns of bacteria colonies grown at 37°C and at 15°C are lower values and are in the range from 0.59 to 0.67. Therefore, it can be seen that in this case the significant changes of Fresnel diffraction patterns of bacteria colonies grown at different temperatures are observed.

 figure: Fig. 8

Fig. 8 (a) Fresnel patterns of Escherichia coli colony incubated at 37°C, (b), (c) Fresnel patterns of bacteria colonies exposed on low- temperature stress at 15°C (bacteria colony diameter:. 2 mm, beam diameter: approx. 2.3 mm).

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Generally, Fresnel diffraction patterns of Escherichia coli colonies contain the central maximum inside the shadow of colony (bacteria colony shadow is indicated by red arrow), and second one outside this region, with radial spoke-likes intensity maxima. For bacteria colonies grown at 37°C, this second maximum has radial symmetry, but for colonies grown at 15°C this symmetry is broken, however, the general structure of Fresnel patterns is preserved. Therefore, it can be seen that Fresnel patterns are indeed sensitive for morphological changes of bacteria colony structure caused by growth conditions. To analyze more carefully this process, the microscopic images of bacteria colonies structure after low temperature stress at 0°C were recorded with using the spectral filter for 635 nm. The diffraction image of analyzed Escherichia coli (0119) (see Fig. 9(a) ) colony has shown some heterogeneities inside the structure of the colony exposed to the 0°C for 20 minutes. They are also observed on the microscopic image (see Fig. 9(b)). These heterogeneities caused the diffraction pattern changes seen in the region of second diffraction ring. Simultaneously, the colony internal structure, was also influenced (see Fig. 9(c), 9(d)). In analyzed case, the first ring maximum is not so evidently presented on Fig. 9(c), but after decreasing the diameter of the laser beam, it is observed in the center of the diffraction pattern on Fig. 9(d).

 figure: Fig. 9

Fig. 9 (a) Shadowgraph image of bacteria colony internal structure (the red circle indicates the area of bacteria colony shown on the microscopic image), (b) microscopic image of analyzed area of the colony, (c) Fresnel diffraction pattern of Escherichia coli colony (approx. beam diameter 2 mm), (d) the same Fresnel pattern in case of smaller diameter of the laser beam (approx. beam diameter 1.5 mm).

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The same behavior was observed in the case of Escherichia coli (0119) colonies grown on tryptone soya agar. The Fresnel pattern of bacteria colony grown on this nutrient medium has the similar form as in the case of Columbia agar broth (see Fig. 10(a) , 10(b)), what is caused by similar chemical composition. The red arrow indicates the colony shadow. In this case the 2D correlation coefficients between the Fresnel diffraction patterns of bacteria colonies grown at 37°C and at 0°C have the lower values than in previous case from 0.34 to 0.46. It means that the difference between the Fresnel diffraction patterns of colony of the same bacteria species increases, if the temperature of incubation is decreased. Morphology of bacteria colonies grown at lower temperatures is not the same as in the case of colonies exposed to warmer conditions. Therefore, the changes in the diffraction image (see Fig. 10(c)) and in the resulting Fresnel diffraction pattern, are observed, as well. The incubation temperature should be taken into consideration in the analysis of diffraction patterns of bacteria colonies and it should be standardized, if the diffraction patterns are used for characterization or identification of bacteria species.

 figure: Fig. 10

Fig. 10 (a), (b) Fresnel patterns of Escherichia coli incubated at 24°C (c) shadowgraph image of the internal structure of the colony exposed to 0°C (d) Fresnel pattern of bacteria colony exposed to 0°C.

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4.3 The influence of the nutrient medium on the Fresnel diffraction pattern of bacteria colony

As it was previously mentioned, various grown conditions can affect the morphological properties of bacteria colonies and in consequence their diffraction patterns. In this section, the dependence of the Fresnel diffraction patterns of the Escherichia coli (0119) colonies from the kind of the used nutrient medium, will be analyzed. Three nutrient media MacConkey, nutrient agar and Columbia agar, were examined. Bacteria colonies were incubated at 37 °C for 12 hours and their Fresnel diffraction patterns were recorded after 14, 22, 36 and 40 hours. The beam diameter was approximately equal to the diameter of illuminated bacterial colony. The diameter of the bacterial colony after 14, 22, 36 and 40 hours of incubation was approximately equal: 500 μm, 1000 μm, 1500 μm and 2100 μm for Columbia agar, 500 μm, 1200 μm, 1900 μm and 2500 μm for MacConkey medium; 850 μm, 1300 μm, 2000 μm and 2300 μm for nutrient agar, respectively.

Microscopic images of exemplary bacteria colonies also showed the differences between the colonies structures (see Fig. 11 ). The change of the bacteria colony diameter directly indicates the influence of the kind of used nutrient medium on the colony structure. The most significant differences in the colony transmission properties were observed in the case of bacteria colonies grown on MacConkey agar. It was caused by dyeing the bacteria colonies, because bacteria cells are decomposing the lactose contained in the nutrient medium.

 figure: Fig. 11

Fig. 11 Microscopic images of Escherichia coli colonies grown on: (a) Columbia agar, (b) MacConkey medium, (c) nutrient agar.

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The Fresnel diffraction patterns of Escherichia coli colonies grown on analyzed nutrient media are shown on Fig. 12 . One may see that the morphological changes of bacteria colonies are reflected by the spatial structure of diffraction patterns. For Columbia agar after 14 hours incubation the diffraction pattern contains one strong round central maximum outside the colony shadow with radial spokes, however for longer times of incubation the second round maximum occurs inside the region of the colony shadow. In the case of MacConkey medium the diffraction patterns for various incubation times were similar and they contain a lot of radial spokes outside the colony shadow region, however their structures were significantly different than these recorded for bacteria colonies grown on Columbia agar. For the nutrient agar the obtained Fresnel patterns were also different than in previous cases, after 22 hours of incubation the strong, round maximum with radial spokes occurred outside the region of the colony shadow. Presented results indicate that the kind of used growth medium is the most important factor, which should be taken into account in the analysis of bacteria colonies diffraction patterns.

 figure: Fig. 12

Fig. 12 Time depended changes of Fresnel diffraction patterns of Escherichia coli colonies grown on three different nutrient media at temperature 37°C.

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5. Discussion

The complex physical model of light transformation in optical system with converging spherical wave illumination, which was widely used in optical information processing for analysis of flat transparencies, can by applied for analysis of light diffraction by bacteria colonies. To prove the theoretical predictions of proposed model, the additional computational simulations were performed in MatLab environment. Achieved results (see Fig. 13 ) for circular aperture with the same radius and observation distances as presented on Fig. 5 have shown that our approach can predict the experimental diffraction patterns. It was demonstrated that it is possible to compress the observation space in proposed optical system to observe both Fresnel and Fraunhofer diffraction patterns, as well. However, it should be pointed out that some modification should be introduced taking into account the presence of additional phase modulation of bacteria colonies caused by their shapes. This modulation affects the main properties of the optical system, because the Fraunhofer patterns in general will be not observed in the back focal plane of the transforming lens, but the observation plane will be shifted to another location depending on the colony curvature.

 figure: Fig. 13

Fig. 13 The computational simulations of diffraction patterns of the circular aperture with the same observation distances as on Fig. 5.

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However, all other advantages of analyzed optical system as scaling, possibility of observation of Fresnel and Fraunhofer patterns, low level of optical aberrations etc. are preserved. Obtained experimental results have shown that in the proposed system it is possible to control the scale of bacteria colonies diffraction patterns by changing the location of the sample respectively to the fixed locations of the transforming lens and camera.

Performed experiments have shown that in the analysis of bacteria diffraction patterns growth conditions should be taken into the careful consideration. In the case of various incubation temperatures, it was shown that the observed Fresnel diffraction patterns exhibit significant differences. In general, basing on microscopic and phase contrast images one can distinguish in the bacteria colony two zones with different transmission properties in the center and edges areas. Central, circular shaped zone has low 2D transmission coefficient around 0.3-0.4 and second concentric zone has higher 2D transmission coefficient around 0.7-0.8. This corresponds to the colony state, since in the center of colony the oldest bacteria cells are located and the higher concentration of the extracellular material is observed. These factors are causing higher mass density in the center of the colony and in consequence lower transmission in this region than in the region near the colony edges. Therefore, the resulting diffraction patterns can be considered in term of knife edge diffraction phenomena on each transmission zone of bacteria colony. It is a similar effect as in the case of light diffraction on annular aperture or on Fresnel plate zones with different transmission coefficient. The structure of the diffraction patterns are generally affected by circular shape of these zones, as well as their transmission. Moreover, since the beam diameter slightly exceed the lateral size of bacteria colony, the part of the beam is attenuated and transmitted by the colony, therefore it means that bacteria colony can by treated as a phase and amplitude aperture, which is creating the diffraction rings in the observation plane. Additional radial spokes observed in Fresnel diffraction patterns are caused by arc-shaped features occurred near the region of colony edges, presented in the bacterial colony as it was already reported [36]. The effect of the influence of the incubation temperature on Fresnel patterns is more evident, in the case of bacteria colonies incubated in lower temperature, since in this case apart the lower diameter of the colony, the heterogeneity of their internal zones structure, particularly near their edges, is observed in comparison to the bacteria colonies grown in standard, higher temperature of incubation (see Fig. 9 and Fig. 10). In most cases, the deformation of the circular shape of the zone near the bacteria colony edges is observed, therefore the second diffraction ring observed in Fresnel patterns of bacteria colony is affected, what was experimentally demonstrated.

Results presented in the Section 4.3 have shown that the Fresnel diffraction patterns are also affected by the kind of used nutrient medium on which the bacteria cells were seeded. Different chemical compositions of the nutrient media cause the changes of bacterial colony morphology, size and its transmission properties. For Columbia agar for longer incubation times, the second round maximum occurs inside the region of the colony shadow and the diameter of the diffraction rings decreases. In our opinion, taking account the scalar theory of diffraction, this effect can be caused by the change of the size of bacterial colony, as well as the size of the zones with different 2D transmission coefficients inside the colony. According to the Eq. (22), the bacterial colony diffraction pattern can be treated as a Fourier transform of the colony amplitude transmittance (see Eq. (11)), therefore according to the similarity theorem of the Fourier transform [46], when the diameter of bacterial colony and diameter of internal zones of colony with different transmission properties are increased with the increasing of the incubation time, the diameter of the diffraction ring of Fresnel patterns decreased. This effect can explain the observed behavior of the diffraction patterns changes depending of the type of the incubation time. However, it should be pointed out that some significant influence of central thickness of bacterial colony on maximal diffraction angle and on number of diffraction rings, is observed [41]. Therefore, the maximum diffraction angle depends on the diameter of the colony, but as well on the central thickness of the colony. In the case of MacConkey medium, the additional effect of bacterial colony dyeing is observed. Therefore, practically the central zone of bacterial colony is completely attenuates the incident laser beam and the 2D transmission coefficient is around zero (see Fig. 14 ). This means that the central zone of the colony acts as a classical opaque obstacle.

 figure: Fig. 14

Fig. 14 The microscopic image of the Escherichia coli colony grown on MacConkey medium after 22 hours of incubation with additional spectral filter increasing the contrast.

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After 22 hours of the incubation this central zone does not exceed the diameter of bacterial colony, therefore the diffraction ring observed in the Fresnel pattern is located inside the colony shadow. However for longer times of incubation the entire colony is completely non-transparent, therefore the diffraction on the bacterial colony edges is dominating. Moreover, the presence of the additional precipitated bile salts near the colony edges are affecting the Fresnel diffraction pattern, as well.

In the case of nutrient agar, the difference of 2D transmission coefficients of the zones of the bacterial colony with different transmission properties were lower than 0.2, therefore the most significant factor is the difference of transmission coefficients between the bacteria colony and the agar, near the region of colony edges. The radial spokes observed in Fresnel diffraction patterns were caused by arc-shaped features and irregular shape of colony edges. These results additionally indicate that the kind of used nutrient media can affect the transmission properties of bacterial colony and in consequences the diffraction patterns.

Experimental results and theoretical considerations indicate that the incubation temperature, as well as the kind of used nutrient medium, significantly affect the colony morphology and in consequence diffraction patterns. These factors are crucial for the bacteria identification based on colonies diffraction patterns. One has to notice that standardization conditions must be introduced to ensure the repeatability of observed Fresnel diffraction patterns. Moreover, presented results have shown the potential of proposed optical system with converging spherical wave illumination to distinguish the morphological and physiological differences between analyzed bacterial colonies.

6. Conclusions

Proposed optical system with converging spherical wave illumination, which was not so far used for analysis of bacteria colonies diffraction patterns, has some significant advantages including diffraction pattern scaling, compression of observation space, low level of optical aberrations and simple calibration. Particularly important are the scaling properties, since the size of used camera matrix may be conveniently chosen. The complex model of light transformation, including the phase modulation of the bacteria colony profile, explaining the light diffraction in the proposed optical system, was presented. Obtained experimental results have shown high correlation between Fresnel diffraction patterns of the bacteria colonies and the morphological structure of the colony. Moreover, it was shown that bacteria culture conditions can affect the spatial structure of diffraction patterns. Proposed optical system enables the nondestructive and noninvasive optical examination of bacteria colonies under the most standard, microbiological procedure of bacteria breeding. Moreover, the bacteria samples can be used for further verification or investigation.

Acknowledgment

This work was partially supported by the Research Grant from the Polish Ministry of Science and Higher Education (No N N505 557739). The support of the European Union under the European Social Fund (No DG-G/2589/10) is gratefully acknowledged, as well.

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Figures (14)
Fig. 1
Fig. 1 Proposed optical system configuration for characterization of bacteria colonies diffraction patterns: L0 transforming lens in (x0,y0) plane, bacteria colonies on Petri dish in (x1,y1) plane, observation plane (x2,y2).

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Fig. 2
Fig. 2 Model of the convex shaped bacteria colony.

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Fig. 3
Fig. 3 The absorption spectra of: (a) Columbia agar, (b) Nutrient agar,(c) MacConkey medium.

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Fig. 4
Fig. 4 The schematic configuration of proposed optical system (explanation in text).

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Fig. 5
Fig. 5 Different diffraction patterns of the exit pupil of the optical system: (a) z2=2 cm, (b) z2=9 cm,(c) z2=15 cm Fresnel patterns for increasing distance from the transforming lens, (d) z2=28.8 cm Fraunhofer pattern in the back focal plane of the transforming lens (aperture diameter: 2 mm).

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Fig. 6
Fig. 6 The change of the dimension of Fresnel diffraction patterns in the case of Salmonella enteritidis colony with decreasing the distance z1:(a) 28 cm, (b) 26.5 cm, (c) 25.3 cm, (d) 24.5cm (bacteria colony diameter: approx. 0.8 mm, beam diameter: approx. 1 mm).

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Fig. 7
Fig. 7 The change of the of Fresnel diffraction patterns of Staphylococcus aureus colony with decreasing the distance z1.: (a) 28 cm, (b) 27cm (bacteria colony diameter: 2.1 mm, beam diameter: approx. 2.1 mm).

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Fig. 8
Fig. 8 (a) Fresnel patterns of Escherichia coli colony incubated at 37°C, (b), (c) Fresnel patterns of bacteria colonies exposed on low- temperature stress at 15°C (bacteria colony diameter:. 2 mm, beam diameter: approx. 2.3 mm).

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Fig. 9
Fig. 9 (a) Shadowgraph image of bacteria colony internal structure (the red circle indicates the area of bacteria colony shown on the microscopic image), (b) microscopic image of analyzed area of the colony, (c) Fresnel diffraction pattern of Escherichia coli colony (approx. beam diameter 2 mm), (d) the same Fresnel pattern in case of smaller diameter of the laser beam (approx. beam diameter 1.5 mm).

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Fig. 10
Fig. 10 (a), (b) Fresnel patterns of Escherichia coli incubated at 24°C (c) shadowgraph image of the internal structure of the colony exposed to 0°C (d) Fresnel pattern of bacteria colony exposed to 0°C.

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Fig. 11
Fig. 11 Microscopic images of Escherichia coli colonies grown on: (a) Columbia agar, (b) MacConkey medium, (c) nutrient agar.

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Fig. 12
Fig. 12 Time depended changes of Fresnel diffraction patterns of Escherichia coli colonies grown on three different nutrient media at temperature 37°C.

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Fig. 13
Fig. 13 The computational simulations of diffraction patterns of the circular aperture with the same observation distances as on Fig. 5.

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Fig. 14
Fig. 14 The microscopic image of the Escherichia coli colony grown on MacConkey medium after 22 hours of incubation with additional spectral filter increasing the contrast.

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Equations (24)

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U out. ( x 0 , y 0 )=AP( x 0 , y 0 )exp{ −iπ λf ( x 0 2 + y 0 2 ) }=AP( x 0 , y 0 )ψ( x 0 , y 0 ;−F ),
ψ( x,y,p )=exp{ iπp λ ( x 2 + y 2 ) }.
U( x m+1 , y m+1 )= exp( ik z m+1 ) iλ z m+1 × ∫ −∞ +∞ ∫ +∞ −∞ U( x m , y m )exp{ iπ λ z m+1 [ ( x m+1 − x m ) 2 + ( y m+1 − y m ) 2 ] }d x m d y m =, =C( λ, Z m+1 ) ∫ −∞ +∞ ∫ −∞ +∞ U( x m , y m ) ψ( x m+1 − x m , y m+1 − y m , Z m+1 )d x m d y m
U in. ( x 1 , y 1 )=C( λ, Z 1 ) ∫ −∞ +∞ ∫ −∞ +∞ U out. ( x 0 , y 0 )ψ( x 1 − x 0 , y 1 − y 0 , Z 1 )d x 0 d y 0 ,
ψ( x 1 − x 0 , y 1 − y 0 , Z 1 )=ψ( x 0 , y 0 , Z 1 )ψ( x 1 , y 1 , Z 1 )exp{ −i2π λ Z 1 ( x 0 x 1 + y 0 y 1 ) },
ψ( x 0 , y 0 , Z 1 )ψ( x 0 , y 0 ,−F)=ψ( x 0 , y 0 , Z 1 −F),
U in. ( x 1 , y 1 )=C( λ, Z 1 )Aψ( x 1 , y 1 , Z 1 ) ∫ −∞ +∞ ∫ −∞ +∞ ψ( x 0 , y 0 , Z 1 −F )exp{ − i2π λ Z 1 ( x 0 x 1 + y 0 y 1 ) }d x 0 d y 0 .
ℑ{ exp{ −πc( x 2 + y 2 ) } }= 1 c exp{ − π c ( f x 2 + f y 2 ) },
U in. ( x 1 , y 1 )=iλ A Z 1 −F C( λ, Z 1 )ψ( x 1 , y 1 ,− Z 1 F Z 1 −F ),
U in. ( x 1 , y 1 )=( f f− z 1 A )exp{ ik z 1 }ψ( x 1 , y 1 ,− Z 1 F Z 1 −F ),
t b ( x 1 , y 1 )= t b 0 ( x 1 , y 1 )exp{ iϕ( x 1 , y 1 ) },
U( x 1 , y 1 )= U in. ( x 1 , y 1 ) t b ( x 1 , y 1 )
U in. ( x 2 , y 2 )= C 2 ( λ, Z 2 ) ∫ −∞ +∞ ∫ −∞ +∞ U ( x 1 , y 1 )ψ( x 2 − x 1 , y 2 − y 1 , Z 2 )d x 1 d y 2 .
U in. ( x 2 , y 2 )=C( λ, Z 1 , Z 2 )( fA f− z 1 )ψ( x 2 , y 2 , Z 2 )ℑ { t b ( x 1 , y 1 )ψ( x 1 , y 1 , Z ˜ ) } f x = x 2 Z 2 λ ; f y = y 2 Z 2 λ
Z ˜ = Z 2 − Z 1 F Z 1 −F
U in. ( x 2 , y 2 )=C( λ, Z 1 , Z 2 )( fA f− z 1 )ψ( x 2 , y 2 , Z 2 )ℑ { t b ( x 1 , y 1 ) } f x = x 2 Z ^ λ ; f y = y 2 Z ^ λ ,
Z ^ = 1 z ^ = 1 f− z 1 = Z 1 F Z 1 −F
ϕ( x 1 , y 1 )=k[ T o −Δ( x 1 , y 1 )− n b Δ( x 1 , y 1 ) ],
Δ( x 1 , y 1 )= T 0 − z b = T 0 −( r b − r b 2 − x 1 2 − y 1 2 )= T 0 − r b ( 1− 1− x 1 2 + y 1 2 r b 2 ).
Δ( x 1 , y 1 )= T 0 − x 1 2 + y 1 2 2 ( 1 r ∞ − 1 r b )
ϕ( x 1 , y 1 )=k n b T 0 −k( n b −1) x 1 2 + y 1 2 2 ( 1 r ∞ − 1 r b )=kn T 0 −k( n b −1 ) x 1 2 + y 1 2 2 R,
U in. ( x 2 , y 2 )= C ˜ ×ℑ { t b 0 ( x 1 , y 1 )ψ( x 1 , y 1 , Z ˜ ′ ) } f x = x 2 Z 2 λ ; f y = y 2 Z 2 λ ,
Z ˜ ′ = Z 2 − Z 1 F Z 1 −F −R,
C ˜ = ( fA f− z 1 )exp( ik Z 1 −1 )exp( ik Z 2 −1 )ψ( x 2 , y 2 , Z 2 )exp( ik n p T p )exp( ik n a T a )exp( ik n b T 0 ) iλ Z 2 −1 .
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