Starch is an essential and widely distributed natural material, but its detailed conformation and thermal transition properties are not yet well understood. We present a rapid Mueller matrix imaging system to explore the structural characteristics of starch granules by using 16 measurements with different incoming and outgoing polarizations. Due to the minimum rotation of the optical elements and the self-calibration ability of this system, the full Mueller matrix images can be accurately obtained within ten-odd seconds. Both structural and molecular features of the starch granule were investigated in the static state and gelatinization process by means of multiple optical characteristics deduced from the Mueller matrix. The experimental results for the structural changes during the gelatinization were close to other nonlinear optical approaches; moreover, the crystallinity and optical rotation of the starch granule are also determined through the use of this approach.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Biophotonic techniques have gained much interest in the last decade for exploring the functional and structural characteristics of organisms in a non-invasive manner from the macro to micro levels. Optical polarization characteristics of organisms are helpful in diagnosing their features at cell or tissue levels due to the ability to enhance the conformational transitions in the cell or morphological change signals in the tissue [1–4]. Mueller matrix provides comprehensive information of the sample by the interaction of polarized light with matter; therefore, the full Mueller polarimetric imaging technique is a powerful metrology not only for quantitative analysis of biological tissues, but also for aerosol monitoring, wafer inspection, etc [5–7]. By further decomposing the Mueller matrix via various decomposition methods, specific polarization characteristics of the sample such as, diattenuation, retardance and depolarization can be quantitatively analyzed, and those polarization characteristics have been proven to be associated with changes in collagen content and organization, muscular hypertrophy, or cellular orientations. Given the fundamental and clinical importance of these and related changes, the measuring and decomposing the tissue Mueller matrix has gained much interest and rapid progress in the field of biological tissue assessment.
Starch is a major polysaccharide in the form of granules within plant cells, and is an important raw material used in food and other industries . Starch granules are mainly composed of two glucose polymers, linear amylose, and branched amylopectin, which are usually organized in alternating amorphous and crystalline concentric configurations [9, 10]. The functional properties of starch can be improved by modification processes with chemicals, heat, or extensive mechanical treatment. However, the size, shape, and crystalline structures of starch granules are species specific; the processing condition for different types of starches and their functionality in various industrial applications are multifarious during the modification process. Therefore, developing a simple, easy, and comprehensive approach to predict the reaction behavior during production is a major challenge in starch industry.
Structural investigations of starch granules have been carried out by many approaches. Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) have been used to study starch granule ultrastructure or granule morphology, but require many preparation processes before the examination . Atomic force microscopy (AFM) is also a popular technique to study surface features and internal structure of the starch granule but limited in a small area . The optical microscope remains the most commonly used apparatus to study the morphology of starch granules. When observed under polarized light microscopy, most starch granules show a Maltese cross due to the crystallinity of amylopectin [13, 14]. In order to have a better understanding of the structural conformation and the starch-water interaction behavior, nonlinear optical microscopic techniques such as Coherent anti-Stokes Raman Scattering (CARS) and second harmonic generation (SHG) are useful for investigating the molecular orientation, internal structure, and local bond density of the starch granule [15–18]. In addition, the second-harmonic generation circular dichroism (SHG-CD) technique provides better chiral sensitivity to obtain three-dimensional chiral information of the starch granule; the internal structure, hilum, can be clearly observed by this technique . While polarization modulation involving SHG microscopy, usually known as Stokes vector resolved second harmonic generation microscopy, increased orientation and degree of structural characterization of starch granules can be acquired. An image of the Stokes vector describes the polarization state of an outgoing light wave from the sample; however, determination of the full Mueller matrix of a sample can provide optical characteristics quantitatively that facilitate the measurable examination of the sample.
In previous studies about optical characteristics of the starch granule, radial distribution of amylopectin chains in the crystalline layers were thought to cause polarization anisotropy . Since double helical structures are formed by short amylopectin branches, the macroscopic optical rotation also can be observed in some specific amylopectin molecules [20, 21]. Circular dichroism is also an important feature of the starch granule due to macroscopic molecular packing . As a result, starch granules have multiple optical polarization properties, but the above nonlinear optical microscopic techniques had only the capability of determining one or two optical features of the starch granule. Here, we present the polarization optical properties of starch granules by their Mueller matrix images to examine their structural transformation over a range of temperatures, often referred to as the gelatinization process. After obtaining the Mueller matrix images of starch granules, we further quantitatively determined their depolarization, dichroism, and retardance characteristics by Lu-Chipman polar decomposition methods both in static and gelatinization conditions . Not only the conformational change of three predominant structures, e.g., hilum, growth ring, and crystallized regimes in the starch, are discussed, but also their optical polarization characteristics during the heat treatment process.
2. Theory and experiment
2.1 Optical configuration for the Mueller matrix measurement
Conventionally, the Mueller matrix polarimeter consists of two main components: a polarization state generator (PSG), where the incident polarization is systematically varied, and a polarization state analyzer (PSA), where the polarization of the outgoing light is determined. The schematic setup of the proposed optical system for imaging is almost the same as our previous work, as shown in Fig. 1 .
The light source installed, a 100 mW laser diode @658 nm then passed through a spatial filter with the beam expander feature, is able to modify the beam diameter about 5 mm. The PSG is composed of one polarizer and two liquid crystal variable retarders (LCVRs) (LCC1113-A, Thorlabs, Newton, NJ, USA) whose retardations (δ1, δ2) are dependent on their driving voltages. As for the azimuth angle of the polarizer, it was set at −45° and the slow axis of the two LCVRs were oriented to an angle of 90° and 45°, respectively. The PSA was made up of a PEM and an analyzer. Here, the PEM was modulated as δ0sinθp, and its azimuth was set at 0°. While the amplitude of modulation δ0 is set at π, and the temporal phase angle is represented as θp, the total Mueller matrix of the system is given by:
In practice, the four phase retardations (δ1, δ2) = (90°, 0°), (0°, 0°), (75.5°, 206.5°), and (75.5°, 153.5°) were set by driving the voltages for both LCVRs in a time sequence, so that four specific polarization states were generated from the PSG. In order to characterize the Stokes vector of the outgoing light from the sample, four conditions were also set up for the PSA by changing the azimuth of the analyzer A and the temporal phase angle θp of the PEM, with the following conditions: (A, θp) = (0°, 0), (45°, 0°), (45°, 30°) and (45°, 90°). While capturing the images with different conditions of the PSG and the PSA, the modulated pulse is achieved by a DC bias current equal to the threshold value coupled with a programmable pulse generator (Agilent Technologies 8110A) to drive the laser diode. A square wave generated by the PEM controller can be used to trigger the three specific temporal phases 0°, 30°, and 90° for the stroboscopic illumination with a pulse width of 110 ns (~2° phase change of the modulator) . Except for the polarization optical elements, an objective, imaging lenses and a CCD camera (Pike F145B ASG16, 1388x1038 pixels with a 14-bit gray scale) were installed to magnify and capture images. The objective and lenses produced a total magnification of about 100X to meet the requirements for the measurement, while the exposure time of the CCD camera was set to be around one-tenth second to maintain enough intensity in its linear range. In order to minimize the measuring time due to mechanical rotation, the images were taken at the optimal optical settings in the sequence from I1 to I16 as shown in Table 1, while the details for determining individual Mueller matrix elements are listed in Table 2. The system was operated through LabVIEW and controlled by a personal computer which made it possible to obtain one set of Mueller matrix image about within ten-odd seconds.
2.2 Decomposition of the Mueller matrix
Mueller matrix decomposition enables the separation of the depolarization effects due to multiple scattering and heterogeneities from other polarization properties, such as the retardance for structural or compositional anisotropy. Various kinds of decompositions of Mueller matrices have been proposed throughout the years, Lu-Chipman polar decomposition and the differential matrix formalism of Mueller matrix were the most frequently used methodologies for interpretation of the intrinsic polarimetry characteristics of biological tissues. Generally, Lu-Chipman polar decomposition is involved in decomposing a given Mueller matrix into three elementary matrices in sequence, namely, diattenuation (MD), retardation (MR) and depolarization (MΔ) . Due to the noncommuting nature of the matrix multiplication, the deduced results are thus expected to be influenced by the sequence adoption of the three elementary matrices. However, the characteristics of the polarization are usually exhibited simultaneously in the biological sample; therefore, the decomposing sequence of the elementary matrices is not able to be designated. The differential matrix formalism represents the both polarization and depolarization properties of a sample in a single matrix, and it implies the polarization properties take place simultaneously; therefore, it is regarded as a precious algebraic tool for understanding the polarization characteristics of anisotropic materials, nanostructures, or biological samples. Nevertheless, in terms of the decomposed parameters and their definition, the linear retardation (δ), its orientation angle (θ), and optical rotation (ψ) from Lu-Chipman polar decomposition are more intuitive and commonly used in conventional optical metrology [26–28]. Therefore, we employed Lu-Chipman polar decomposition approach for understanding the polarization characteristics of starch granules. Once the Mueller matrix is deduced from 16 images, the quantitative individual polarization medium properties, such as depolarization, retardance, linear retardation, and optical rotation, will capture much attention for discussion . Before decomposing a Mueller matrix M, the experimental normalized Mueller matrix can be expressed as follows:
2.3 Starch preparation for the gelatination process
After installation and calibration of the optical system, we examined the optical characteristics of starch granules which were isolated from peeled potatoes. The freshly cut pieces of potato were ground thoroughly by a homogenizer for one minute. About 0.25 ml of a dilute starch-water suspension solution was pipetted and a droplet placed on a coverslip. Subsequently, the sample was placed in the hood for water evaporation, but not in a totally dry state, for about 10 min. A small amount of glycerol surrounded the droplet and then the specimen was covered with a coverslip. For examining the gelatinization course, a temperature-controlled resistive heated-tip was installed at a fixed temperature. While the heated-tip reached at thermal equilibrium state, the element was placed 3 mm away from the cover glass to investigate the starch-water interaction behavior every 90 seconds, including 20 seconds of image capturing and transfer. Before each image capturing operation, the surface temperature of the coverslip is recorded by an infrared thermometer (Fluke 561) to study the starch granule structure transformation behavior in relation to the temperature.
3. Results and discussion
3.1 Images of various polarization
In order to obtain the full Mueller matrix images, at least 16 individual polarization-state measurements are required. The measurements are usually performed by generating four specific polarization states from the PSG, and the Stokes vectors of the light after passing through the sample can thus be analyzed through four settings of the PSA. Figure 2 shows the images of 16 individual polarization-state measurements with 4 basis states of the PSG and the PSA. Three starch granules enclosed by glycerin can be clearly observed in Fig. 2, and the backgrounds of I11 and I15 are totally dark. Those two particular images resulted from the orthogonal polarizations between the PSG and PSA; the dark background in I11 was ± 45° linear orthogonal polarizations, and I15 was crossed circular polarizations, respectively. However, while illuminated with different orthogonal polarizations, the images of starch granules revealed unlike features.
In I11, a Maltese cross is seen in starch granules due to its linear birefringence originating from the crystalline structure of anisotropically aligned amylopectin, which suggests its crystalline axis is distributed in the radial direction . I15, examined under crossed circular polarization, shows the birefringent structures to be equally bright at all orientations of the optic axis, and the non-birefringent structures show a dark background. Two features in I15 are noted: 1. a dark spot can be found in each starch granule, and it is regarded as hilum and bulk amorphous region. We find it helpful to compare the spot locations in I15 with those in I11. Since the hilum is a hollow structure and the bulk amorphous region is mainly composed of amylose and disordered reducing ends of amylopectin, both structures are without or with very weak birefringence characteristics that make the obvious dark spot. As a result, the location of dark spot in I15 is also the center of the Maltese cross in I11. 2. Alternating light and dark rings, known as growth rings, can be viewed in I11 and I15. Concentric shells can be barely observed with conventional optical microscopy but was not noted in previous studies under crossed polarization microscope. The observed concentric shells pattern was analogous to growth ring model of the starch granule. The growth rings were organized in alternating concentric thick amorphous and semi-crystalline domains, which results in the spatial variation of the refractive index in the starch granule. This makes rings clearly visible and yields excellent contrast with the dark background.
3.2 Images of Mueller matrix
After 16 images with various polarization conditions were taken, the Mueller matrix image of the starch granule is deduced. To account for non-uniform illumination across the field of view, elements in Mueller matrix are normalized by the m00; therefore, 15 different matrix elements are experimentally determined, as shown in Fig. 3. In general, Mueller matrix of a sample contains the information of elementary polarimetry characteristics, such as diattenuation, retardance, polarizance and depolarization . For a nondepolarizing Mueller matrix, the magnitudes of polarizance vector (p) from Eq. (4) and the magnitudes of diattenuation vector (d) from Eq. (5) should be identical, which equals to its Mueller matrix: m012 + m022 + m032 = m102 + m202 + m302 [23,32]. By comparing the images of (p) with (d) in Fig. 4(a) and 4(b), both images show different patterns, which indicates that starch granule has the property of depolarization. Moreover, we found that the images of the off-diagonal elements m12, m13, m23, m21, m31, m32, m30 and m31 shows that these elements have some values and are not relative to certain symmetry axes [33–35], which implies that the starch granule is an optical anisotropic case. Thus, we can conclude that the starch granule is with somewhat appreciable depolarization nature and the optical anisotropic characteristics. The above finding shows Mueller matrix offers the possibility of quantifying the polarimetry characteristics of a sample, but complexities arise when all properties are mixed and thus the quantitative optical anisotropic features are interpreted by matrix decomposition approach.
3.3 Polar decomposition of Mueller matrix images under static condition
Mueller matrix decomposition enables the separation of the depolarization effects due to multiple scattering and heterogeneities from other polarization properties, such as the retardance for structural or compositional anisotropy. Many researchers have used Lu-Chipman polar decomposition of the Mueller matrix for developing diagnostic metrics based on the structural properties. Polar decomposition is an efficient approach to quantitatively determine the sample polarization properties from the measured Mueller matrix; The values for diattenuation (d), retardance (R), and depolarization (Δ) can be deduced from the decomposed MD, MR, and MΔ matrices.
Diattenuation refers to the difference in transmittance between two orthogonal components of the incident waves. Some polarization elements show strong diattenuation, such as the diattenuation is 1 for a linear polarizer ; however, diattenuation inside biological organisms is typically small in the visible spectrum owing to weak absorption, and a large proportion of diattenuation of a biological sample is attributed to interface effects. As shown in Fig. 4(b), the starch granules show larger diattenuation values than the surrounding medium. This occurs as a result of difference in Fresnel coefficients at normal incidence between the starch granules and surrounds so that the boundary of starch granules can be readily observed. For the same reason, growth ring structures in the starch granule are also clearly recognized due to its dense and loose architecture.
The second examined optical feature was depolarization, represented by depolarization coefficient (Δ) from Eq. (10). While depolarization coefficient equals 1 for a non-depolarizing medium and 0 for an ideal depolarizer. This characteristic usually comes from retardance varying in space or wavelength, diattenuation, multiple reflections, multiple scatterings, and etc. Since the thickness of the starch granule was less than 50 µm, the overall depolarization effect was not significant in Fig. 4(c), which shows that the depolarization coefficient in most parts of the starch granule is close to 1. Larger depolarization coefficient was observed at the boundary of the starch granule and a small portion of growth ring structure owing to the rapidly change of the refractive index. Since some media may not depolarize the input polarization states equally, the coefficient of linear and circular depolarization is further analyzed in Fig. 5. In general, circularly polarized light is preserved to a greater extent than linearly polarized light in turbid samples, but it shows greater depolarization effect of the circularly polarized light at the border of the starch granule. We need to continue studying the relationship between the helical structure of amylopectin in the starch granule and depolarization effect of the circular polarized light.
The last optical characteristic is the retardance, which contains linear and circular birefringence properties. As shown in Fig. 4(d), the hilum of the starch granule can be clearly recognized through the characteristics of the retardance by reason of very weak signal, and this consequence is likely due to less or non-crystalline material in the hilum. We further decomposed the total retardance into linear retardation and optical rotation from Eqs. (8) and (9), as shown in Fig. 6. Generally, a starch granule exhibits positive birefringence due to the crystallinity which aligned in a radial direction. In Fig. 6(a), the pattern of linear retardation of the largest starch granule is almost in the same pattern as radial symmetry. Optical rotation signals are also found in Fig. 6(b). Since amylose and amylopectin are polysaccharides that are mainly composed of glucose units, the chirality is also one of the fundamental optical properties that can be found in the starch granule. In this experiment, the thickness of starch granules is dozens of micrometers and the deduced optical rotation was much bigger than normally recognized value. This result may attribute to three reasons: 1. the optical path length increment caused by multiple scattering in the starch granule, resulting in accumulation of optical rotation; 2. the helical structure of the amylopectin may also largely raise the value of optical rotation; 3. overestimation of optical rotation due to adoption of Lu-Chipman polar decomposition and its associated analysis . However, structural features of helical amylopectin and chiral side-chain liquid-crystalline are also related to an external stimulus, such as temperature, pH, and solvent and are worthy of further examination by comparison with other methods. Recently, analytical relationships between Lu-Chipman polar decomposition and the differential matrix decomposition for either simultaneous or sequential occurrence of the linear retardation and optical rotation effects has been established; hence, the detailed comparative examination of both characteristic is an important issue for future research.
3.4 Polarization and Mueller matrix images during the gelatinization process
Starch gelatinization is the process in which, as heating continues, starch granules take up water irreversibly and swell, resulting in more viscosity and clarity. A previous report described the internal crystalline structure and birefringence characteristics of the starch granule that are gradually lost during the gelatinization process . The crossed linear and circular polarization characteristics of the starch granule during the heat treatment is shown in Fig. 7. Through the observation of I11, the Maltese cross has gradually disappeared from the center of all the granules at the 4th examination. Such behavior is in agreement with previous reports indicating that the disruption of crystallinity began from the hilum of the B-type starches granule, such as potato [18,37]. The course of gelatinization can be more clearly examined by the I15 images. Before the heat treatment, the hilum was clearly recognized by the dark spot, which became larger with increased heating time, especially after the 4th examination. This behavior means the dissolution of starch granule in water was not from the outside in, but rather from the inside out. Previous AFM studies confirmed that some pores on the starch granule surface form channels connecting an internal cavity at the granule hilum . While the starch granule starts to swell, the inflow of water and outflow of amylose were through these channels. However, these channels are beyond the resolution of the light microscope. The proof of the existence of small channels was observed under macroscopic view as the granule began to swell from the inside out. SHG and CARS signals lead to the same result but with advanced requirements for the light source and detector.
Polarization characteristics of retardance (R) during the course of gelatinization demonstrated distinct variation and access capability for crystalline and chirality properties of starch granules [19,22,38]; therefore, we mainly discussed the R variation during the gelatinization process and further decomposed R into linear retardation (δ) and optical rotation (ψ) from Eqs. (4) and (5) to explore structural transformation of the starch granule. The images of retardance characteristics at different timeline are shown in Fig. 8. According to the timeline and recorded temperature in Fig. 7, the temperature of the surrounding area has been reached at 80°C in the 2nd examinations, exceeding the gelatinization temperature (about 55°C); however, starch granules showed their intact shapes during the first three examinations, and we believe this development is attributed to the time needed for water flowing into the helium.
In the 4th and 5th examination, the starch granules obviously absorbed water and revealed a partially swelling, their retardance faded away after the initiation of the gelatinization, as shown in Fig. 8. In this period, the physical properties of the starch granules indicated that they have reached an irreversible structural change whose intermolecular bonds were broken down and crystalline structures were destabilized [39, 40], especially after the 4th examination. In addition, this structural transition can be explored by linear retardation (δ) and optical rotation (ψ), as shown in Fig. 9. The δ is positively relative with the proportion of amylopectin molecules, which are the main composition of the crystalline region and have a radial orientation . As a result, the crystalline variation of the starch granule can be examined by analyzing the δ, and one can observe the loss of δ on heating, indicative of disordering processes, suggested the loss of radially aligned structure began at the weakest crystallites region after the 4th examination . The appearance was further analyzed and proved through use of the histogram, as shown in Fig. 10. The behavior of the retardance was similar to I15 which demonstrated the hilum was getting larger, along with the continuum of heat treatment for the starch granule. Moreover, the ψ is also deduced from the retardance, as shown in Fig. 9, revealing non-uniform distribution to the orientation. The loss of double-helical order of the starch granule was also a sign for the gelatinization. The pattern of the ψ also demonstrated a signification change after the 4th examination.
The last stage of the gelatinization, the 6th to 8th examination, demonstrated the crystallinity continued to disrupt up to the outer part of the granule through the examination of R, δ and ψ. During this period, starch granules were burst and completely disrupted; their shape almost can't recognize in the final examination, which means soluble amylose was leached into the surroundings.
In general, nonlinear optical techniques applied to cellular and tissue images usually result in higher molecular contrast than the linear optical approach. In this study, we employed a Mueller matrix imaging polarimetry system with the hybrid modulation technique in a linear optical range. The developed Mueller matrix polarimetry system with the hybrid modulation technique recorded full field images without scanning apparatus and achieved the image acquisition interval within ten-odd seconds; therefore, this method is sufficient to both spatial and time resolutions for cell or tissue real-time monitoring. Although this system explores the light–matter interaction in the linear optical regime, the optical properties of starch granules during the gelatinization still can be determined through use of this Mueller matrix imaging system. Apart from that, a time delay of crystalline structure destabilization and helium enlargement was observed while the surrounding temperature of the starch granule reached the gelatinization temperature, because it takes time to let the water inflow into the inner part of the starch granule through the small channels. Based on the Lu-Chipman polar decomposition of the Mueller matrix, three predominant structures in the starch granule are characterized; moreover, the anisotropy and optical rotation of the starch granule were further investigated. However, only one or two structural features of the starch granule can be determined by conventional linear or non-linear optical approach.
Two improvements of this system are underway. One is the multi-wavelength capability for the system to increase the wavelength dependent scattering information between the light and materials. This goal can be achieved by an equivalent phase retardation technique for the PEM that the retardation dispersion settings of the PEM for different wavelengths were not required . The other issue is the rotation of the analyzer. Although the mechanical rotation in this system is only once, this issue may impede the measurement for the tissue or cell polarimetry imaging system that should be fast and robust. The light path of this system will be adjusted to build a movement free configuration. A full Mueller matrix imaging polarimetry configuration should reveal additional structural details, allowing a quick molecular characterization of samples for bioengineering applications.
The authors declare that there are no conflicts of interest related to this article.
Ministry of Science and Technology (MOST 105-2221-E-035-045).
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