Birefringence is an inherent optical property of a material that indicates different refractive index depending on the polarization and direction of the incident light. Such materials are also known as (optically) anisotropic materials. In some materials, birefringence can be introduced or modified using external applied electric, magnetic, or mechanical field. This includes, for instance, liquid crystal (LC) materials-based planar devices, the birefringence of which can be tuned by changing the strength of electric field across them. Furthermore, optical anisotropy property can be used for defect detection in semiconductor wafers. Likewise, for nanotubes, anisotropic optical scattering has been used for inferring their orientation variations, which can be applied to develop single particle tracking techniques. For biological structures, birefringence measurements can reveal the architecture of cytoskeletons, and can measure the orientation of single molecules in live cells.
By measuring changes in polarization, which describes the oscillation direction of E-field vector, one can map birefringence distribution within an anisotropic sample. Recently, researchers at LBRC have started to make concerted efforts in this area to develop interferometry-based systems for birefringence measurements in biological samples. To this end, we have developed a method that enables polarization measurements, i.e., retardance and orientation angle of linear birefringence, combined with single-shot quantitative phase microscopy. Figure 1 shows the corresponding experiment setup that uses collimated light from a 633 nm fiber-coupled source. A circular polarizer (CP) is used to convert the linearly polarized collimated laser beam into right-handed circular polarization before illuminating the sample. After transmitting through the sample, the beam is collected by an objective lens (Olympus, 4X, numerical aperture (NA) = 0.16). A Wollaston prism (WP), placed at the intermediate image plane, decomposes the sample beam into horizontally and vertically polarized beams. These two beams are symmetrically separated along the optical axis with a separation angle of ~20 degrees. Next, the two beams pass through a 4f system and impinge on a linear polarizer (LP) at 45 deg before interfering on a CMOS camera. The measurement involves recording a fringe pattern that is used to retrieve the complex field, which in turn is are further used to extract the birefringence parameters using a new polarization recovery algorithm described in Ref. .
To demonstrate working principle of the system shown in Fig. 1, we measured wide-field distribution and orientation of a custom-made liquid crystal (LC) device developed by our collaborator, Hamamatsu Corporation. In this sample, the LC molecules are uniformly distributed between two quartz glass plates and divide into two regions. Each region has a separate pair of electrodes to control strength of applied electric field. When the light polarization is along the long axis of an LC molecules, the refractive index is ne while the refractive index is no when the light polarization is orthogonal to the long axis. The LC sample thickness is 20 µm whereas the birefringence (difference of ne and no) is 0.2. Therefore, the maximum possible retardance is 39.7 radians.
Figure 2(a) shows the measured interferogram of the LC device. Note that electric field is applied only to the right side of the device, decreasing its retardance down to 13.3 rad. No voltage was applied to the left region; thus, the retardance of this region remained at the original value of 39.7 rad. Figure (b) illustrates the phase delay between the left and right regions. The orientation angle distribution was also retrieved, and was determined as 116.3±1.5 degrees. Furthermore, Fig. 2(c) and 2(d) show spatially averaged orientation angle and retardance, respectively, of the right-hand side region plotted as a function of the applied voltage. As expected, the orientation angle does not change whereas the retardance decreases as a function of applied voltage.
Quantitative phase or holographic imaging at visible wavelengths provides limited molecular information for cellular biomolecules such as proteins, carbohydrates, lipids, and small molecules. It is, therefore, important to realize molecular-specific polarization holographic imaging at ultraviolet (UV) or infrared (IR) wavelengths. However, high performance wide-field imagers at UV and IR wavelengths have limited availability. To remedy this situation, we have recently developed a single-pixel camera based approach to measure UV or IR optical fields in collaboration with the Biomedical Optics Lab, Korea Advanced Institute of Technology (KAIST).
Figure 3 shows the experimental setup for polarization-sensitive holographic microscopy without the use of an image sensor. By employing polarization-dependent point measurements, the patterns maximizing the focused intensities corresponding to the polarization states can be found. From the obtained patterns, optical fields corresponding to the polarization states can be determined. A digital micromirror device (DMD) is utilized to achieve fast and polarization-independent modulations. A linearly polarized plane wave (λ = 532 nm) impinges onto a sample via a polarizer, lens (L1), and a condenser lens (63X, NA = 1.0). The scattered field from the sample is collected and relayed onto the DMD by an objective lens (100X, NA = 1.4), a tube lens, and additional 4-f relay lenses (L2-3). The relayed scattered field is modulated by the DMD, and a polarization-maintaining single mode fiber (PMSMF) transmits the focused light after a lens (L4) to polarization-sensitive point detection, which consists of a polarizing beamsplitter (PBS) and two avalanche photodiodes (APDs).
To effectively find the pattern maximizing focused intensity after a lens, binary patterns displayed on the DMD are constructed using phase shifts and a Hadamard basis. Next, we can find the optical phase conjugation pattern by analyzing recorded intensities corresponding to the displayed patterns. Since a DMD modulates light regardless of its incident polarization state, the optical phase conjugationpatterns with respect to the polarization states can be simultaneously found from the measured intensities using two APDs. Furthermore, a spatially resolved Jones matrix of the sample is determined from the measured scattered fields (details provided in Ref. ).
To demonstrate the applicability of our approach, we have analyzed anisotropic optical properties of a maize starch granule by reconstructing its Jones matrix [see Fig. 4]. Maize starch granules have strong birefringence and optical activity due to the two major molecular constituents, namely, amylose (28.7%) and amylopectin (71.3%). In particular, amylopectin, that has a double helix molecular structure, forms extensively branched supramolecular crystallite structure in a starch granule [Fig. 4(a)]. From a hilum inside the starch granule, branched chains of amylopectin grow in radial directions [Fig. 4(a)]. Due to the chiral molecular and the supramolecular structure, a maize starch granule shows distinctive anisotropic optical properties which have been investigated by various methods including polarized light microscopy, second harmonic generation microscopy, and circular dichroism spectroscopy. Although the present experiments were performed in the visible regime, the method can be readily expanded to polarization-dependent holographic imaging in the invisible wavelengths that will enable molecular-specific optical measurements of chiral molecules.