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4STOKES VECTOR BASED POLARIZATION RESOLVED SECOND HARMONIC MICROSCOPY
NIRMAL MAZUMDER1 AND FU-JEN KAO2
Department of Biophysics, Manipal School of Life Sciences, Manipal Academy of Higher Education, India
*nirmaluva@gmail .com
ABSTRACT
We developed a four-channel photon counting based Stokes polarimeter for spatial characterization of polarization properties of Second Harmonic (SH) light. In this way, the critical polarization parameters can be obtained concurrently without the need of repeated image acquisition. Various polarization parameters, including the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP), are extracted from the reconstructed 2D Stokes vector based SH images in a pixel-by-pixel manner. The Stokes vector measurements are further extended by varying the polarization states of the incident light and recording the resulting Stokes parameters of the SH signal. In turn this allows the molecular structure and orientation of the samples including collagen fibers, skeletal muscle fiber, and starch granules. The combination of SHG microscopy and Stokes polarimeter hence makes a powerful tool to investigate the structural order of targeted specimens.
Keywords: Polarimetry, Second harmonic generation, nonlinear optics INTRODUCTION
Second harmonic generation (SHG) microscopy is an effective analytical tool for detailed investigation of microscopic structure and orders of non-centrosymmetric molecules [1]. Stokes vector based SHG microscopy resolves the polarization states of the SH signal and allows the deduction of the molecular organization of collagen, skeletal muscle, starch etc [2-4]. The technique is also implemented to characterize the polarization properties of the SH signal during starch gelatinization. Starch in the form of grains is the major storage compound in plants and so is an important part of our food [5]. Scientists are keen to understand the origins in plants, and how changes to the plants' genes could affect the composition and properties of the starch in the grains [6]. The finest features in the starch granule structure are due to the molecular packing of amorphous amylose and crystalline amylopectin lamellae [7]. Also, the sample preparation for the high resolution microscopy provides a complete structural elucidation of starch in its native form. The optical microscopy provides non-invasively the detail of the microscopic structural information of starch [8]. A strong SH signal from semi-crystalline amylopectin chains which are assumed to lie in the amorphous lamellae (amylose) form radially distributed amorphous growth rings in starch [9, 10]. A Stokes vector based SHG microscopy scheme is distinct from several other previously demonstrated polarization resolved approaches in that it uses a large number of images rather than a single shot measurement [2,11-13]. The complete polarization states of the SH light of starch granules were characterized from SHG Stokes micrographs [2,3]. In order to optimize the processing operations and obtain the desired quality of starch-based foods, a thorough understanding of the starch-water interaction through the gelatinization process is required [14,15]. In pixel by pixel SH image analysis, it is found that at room temperature the structural distribution of double helical amylopectin is self-organized upon hydration within starch granules [12]. In this article, the thermal behavior of these structurally complex materials is investigated by Stokes vector based polarization resolved SHG imaging. In addition, the chemical interactions between different components are observed from the reconstructed 2D SHG images using various polarization parameters, such as the degree of polarization (DOP), the degree of linear polarization (DOLP) and the degree of circular polarization (DOCP) from the acquired Stokes parameters [2].
MATERIALS AND METHODS
The experimental arrangement for measuring the polarization properties of SH signal via SHG microscopy is described in detail in [2,3]. A modified inverted Olympus IX81 confocal microscope is used as our imaging setup. A femtosecond Ti: sapphire (Coherent Mira Optima 900-F) laser oscillator was used as the excitation light source. The center wavelength was set at 800 nm and had a full width at half maximum (FWHM) spectral width of 15 nm which gave transform limited pulses of ~ 100 fs, with average power ~550 mW and repetition rate~76 MHz. Our polarization microscope includes a polarization state generator (PSG), sample and polarization state analyzer (PSA). The various polarization states are generated using the PSG formed from a polarizer and a half wave plate. Samples were mounted upside-down on an XYZ stage and scanned with a laser scanning unit (Olympus, FV300). An objective lens (UPlanFLN 40X/N.A. 1.3, Olympus Co., Japan) is used for focusing the laser beam. The measured signals were analyzed by means of a polarization state analyzer (PSA), specifically, a four-channel Stokes-polarimeter [2]. The SH signal is collected in the forward direction using a 20X, 0.75 N.A. objective lens. A band pass filter of 400 ± 40 nm (Edmund Optics Inc., Barrington, New Jersey) was also inserted into the SHG emission path. Details regarding calibration and performance of our Stokes-polarimeter are given in [2-4]. The four-channel Stokes-polarimeter microscope is a variation in that we reconstructed the 2D intensity images as well as the corresponding Stokes vector images. Again, the different polarization parameters are reconstructed from the acquired TSCPC data pixel by pixel with a specialized homemade routine in MATLAB (MathWorks, R2009b, Natick, MA) [2]. We report on measurements and characterization of polarization properties of (SH) signals using a four-channel photon counting based Stokes polarimeter. In this way, the
critical polarization parameters can be obtained concurrently without the need of repeated image acquisition. The critical polarization parameters, including the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP), are extracted from the reconstructed Stokes vector based SH images in a pixel-by-pixel manner [2].
RESULTS AND DISCUSSION
Stokes vector based SH microscopy was developed to investigate the molecular structure more precisely using polarization properties of SH. 2D Stokes vector images of collagen type-I are reconstructed to determine the image contrast and to examine molecular alignment in fiber [16]. It is evident that the horizontally polarized excitation beam is transformed into partially polarization light upon interaction with the collagen fibers. The spatial distribution of anisotropic and chiral properties from collagen type-I are differentiated using DOLP and DOCP parameters. The relative orientation of the optical axis of crystals with extraordinary and ordinary rays varies at different focal depth. Thus the chiral SHG response should depend on the variation in the contribution of chiral and achiral susceptibility elements [17]. This can, in turn reveal collagen-fiber orientation and structural order through SH detection. Therefore, the DOLP and DOCP values are complimentary; the region with higher/lower DOLP value shows lower/higher DOCP value. The measurements are further extended to angular dependence of Stokes parameters of the SH signal to characterize the molecular orientation more thoroughly [18]. The measurements are further extended by varying the polarization states of the incident light and recording the resulting Stokes parameters of the SH signal. In the previous study, it is demonstrated that due to type I phase matching and concentric shell like structure, starch granule acts as a polarization state analyzer [12]. Specifically, SH contrast depends on the polarization states of the excitation and reflects molecular arrangement accordingly. For example, starch granules are arranged in semi-crystalline shells, the amylopectin chains in the crystalline layers are strongly anisotropically ordered and thus yield strong SH [3, 12]. Right and left circularly polarized illumination is transformed into elliptically polarization, depending on the handedness and the absolute orientation of amylopectin molecules. The DOLP and DOCP distributions hence demonstrate the components of both linearly and circularly polarized light in the SH signal. The crystallized arrangement of collagen type-I and amylopectin seems to be an indispensable condition for efficient SH conversion. The optical nonlinearity in starch granules will facilitate further studies in food science and provide insights into bio-energy transformation dynamics.
CONCLUSION
In conclusion, this review has elucidated the uniqueness and the prospects of Stokes vector based polarization resolved SH imaging. Conventionally polarization microscopy usually characterized measured signals with a two-channel configuration. SH imaging, however, has the advantage of being highly sensitive to the structural order of targeted specimens. Generally, SH polarization analysis can be carried out with Jones calculus since SH is usually coherent and fully polarized. However, multiple or time-lapsed scans would be required if the phase relationship between the eigen-polarization vectors is to be uncovered. We have presented the basics and applications of linear and nonlinear polarization light microscopy techniques in details. The molecular orientation and retardance provides additional information on birefringent specimen with enhanced contrast. Nonetheless, deep imaging inside thick biological samples can distort the polarization linearity of the excitation laser beam before it reaches the focal volume. In SH anisotropy, birefringence of collagen may strongly affect the incident electric field. This effect is more pronounced in the forward geometry than the backward detection, which needs to be taken into account during image analysis. The integration of SH microscopy and Stokes polarimetry hence makes a powerful tool to investigate the complete polarization state of SH light as well as the structural order of collagen fiber, starch granules, skeletal muscle [2, 12, 18]. The analysis was therefore extended to include the orientation and degree of organization from type-I collagen by varying the incident laser polarization whilst detecting the resulting polarization state of SH light using the four-channel Stokes-polarimeter [19]. A full Mueller matrix formalism has long been shown a powerful method and applied under linear optics settings. PSA measures the polarization states of the signal beam. There is no need to control the incident beam polarization to a very specific state (such as being perfectly linearly or circularly polarized) on the samples. A specific polarization state, such as being "linearly horizontally polarized", is usually referred to the coordinate of the observer, instead of the relative orientation (and thus interaction) between the incident beam and the samples. The important parameters to be extracted from the polarization measurements are the degree of polarization (DOP), the degree of linear polarization (DOLP), and the degree of circular polarization (DOCP) [2, 3, 12] Characterizing the polarization states of the outgoing signal beam and thus deducing these parameters will be sufficient to infer the status of and the SH response from the samples, which is the core idea of our method. The measured SH signals and the reconstructed Stokes images are originated from the focal plane within the sample, attributing to the optical nonlinearity. Importantly, it should be noted that in SH microscopy Type I phase matching is assumed, that is hva, ordinary + hvm, ordinary^ hv2m, extraordinary, for the SH signal, which also indicates the polarization states of the SHG would faithfully reflect those of the incident excitation beam.
ACKNOWLEDGEMENT
NM thank Department of Science and Technology (DST) [Project Number-SERB/MTR/2020/000058] and Indian Council of Medical Research (ICMR) [ICMR, ID No. 2020-3286], Government of India for financial support. NM also thank Manipal School of Life Sciences, Manipal Academy of Higher Education, Manipal for providing the infrastructure and facilities.
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