One-step Jones matrix polarization holography for extraction of spatially resolved Jones matrix of polarization-sensitive materials

Object alignment in spatially multiplexed holograms applied to polarization sensing

The paper presents a new algorithm for object alignment in digital holography with multiple spherical reference waves. The algorithm was applied to polarization sensing with two orthogonally polarized reference waves. A novel holographic setup was built using a diffraction grating to generate two symmetric reference waves, keeping the setup simple and highly adjustable. The angles of rotation of the polarizing elements were calculated with mean absolute errors of 0.71° and 2.96° based on intensity and phase measurements, respectively. The same algorithm can be applied to any digital holographic measurement with multiple spherical reference waves.

Single-shot measurement of the Jones matrix for anisotropic media using four-channel digital polarization holography

Dynamic measurement of the Jones matrix is crucial in investigating polarization light fields, which have wide applications in biophysics, chemistry, and mineralogy. However, acquiring the four elements of the Jones matrix instantly is difficult, hindering the characterization of random media and transient processes. In this study, we propose a single-shot measurement method of the Jones matrix for anisotropic media called "four-channel digital polarization holography" (FC-DPH). The FC-DPH system is created by a slightly off-axis superposition of reference light waves, which are modulated by a spatial light modulator (SLM), and signal light waves that pass through a Ronchi grating. The SLM enables flexible adjustment of the spatial carrier frequency, which can be adapted to different anisotropic media. The four elements of the Jones matrix can be obtained from the interferogram through the inverse Fourier transform. Optical experiments on anisotropic objects validate the feasibility and accuracy of the proposed method.

Polarization-sensitive intensity diffraction tomography

Optical anisotropy, which is an intrinsic property of many materials, originates from the structural arrangement of molecular structures, and to date, various polarization-sensitive imaging (PSI) methods have been developed to investigate the nature of anisotropic materials. In particular, the recently developed tomographic PSI technologies enable the investigation of anisotropic materials through volumetric mappings of the anisotropy distribution of these materials. However, these reported methods mostly operate on a single scattering model, and are thus not suitable for three-dimensional (3D) PSI imaging of multiple scattering samples. Here, we present a novel reference-free 3D polarization-sensitive computational imaging technique-polarization-sensitive intensity diffraction tomography (PS-IDT)-that enables the reconstruction of 3D anisotropy distribution of both weakly and multiple scattering specimens from multiple intensity-only measurements. A 3D anisotropic object is illuminated by circularly polarized plane waves at various illumination angles to encode the isotropic and anisotropic structural information into 2D intensity information. These information are then recorded separately through two orthogonal analyzer states, and a 3D Jones matrix is iteratively reconstructed based on the vectorial multi-slice beam propagation model and gradient descent method. We demonstrate the 3D anisotropy imaging capabilities of PS-IDT by presenting 3D anisotropy maps of various samples, including potato starch granules and tardigrade.

Spatially multiplexed dielectric tensor tomography

Dielectric tensor tomography (DTT) enables the reconstruction of three-dimensional (3D) dielectric tensors, which provides a physical measure of 3D optical anisotropy. Herein, we present a cost-effective and robust method of DTT using spatial multiplexing. Exploiting two orthogonally polarized reference beams with different angles in an off-axis interferometer, two polarization-sensitive interferograms were multiplexed and recorded using a single camera. Then, the two interferograms were demultiplexed in the Fourier domain. By measuring the polarization-sensitive fields for various illumination angles, 3D dielectric tensor tomograms were reconstructed. The proposed method was experimentally demonstrated by reconstructing the 3D dielectric tensors of various liquid-crystal (LC) particles with radial and bipolar orientational configurations.

Time-Resolved Four-Channel Jones Matrix Measurement of Birefringent Materials Using an Ultrafast Laser

A method for ultrafast time-resolved four-channel Jones matrix measurement of birefringent materials using an ultrafast laser is investigated. This facilitated the acquisition of a four-channel angular multiplexing hologram in a single shot. The Jones matrix information of a birefringent sample was retrieved from the spatial spectrum of a hologram. The feasibility of this approach was established by measuring the Jones matrix of starch granules in microfluidic chips and the complex amplitude distribution and phase delay distribution of liquid crystal cell at different voltages. Moreover, when the picosecond laser was switched to a femtosecond laser, ultrafast measurements were possible provided that the time interval between two detection pulses was larger than the pulse width.

Single-Shot Quantitative Polarization Imaging of Complex Birefringent Structure Dynamics

Polarization light microscopes are powerful tools for probing molecular order and orientation in birefringent materials. While a number of polarization microscopy techniques are available to access steady-state properties of birefringent samples, quantitative measurements of the molecular orientation dynamics on the millisecond time scale have remained a challenge. We propose polarized shearing interference microscopy (PSIM), a single-shot quantitative polarization imaging method, for extracting the retardance and orientation angle of the laser beam transmitting through optically anisotropic specimens with complex structures. The measurement accuracy and imaging performance of PSIM are validated by imaging a birefringent resolution target and a bovine tendon specimen. We demonstrate that PSIM can quantify the dynamics of a flowing lyotropic chromonic liquid crystal in a microfluidic channel at an imaging speed of 506 frames per second (only limited by the camera frame rate), with a field-of-view of up to 350 × 350 μm² and a diffraction-limit spatial resolution of ~2 μm. We envision that PSIM will find a broad range of applications in quantitative material characterization under dynamical conditions.

Polarization-sensitive imaging based on incoherent holography

The polarization-sensitive imaging technology is proposed based on incoherent holography. The distribution of state of polarization (SoP) of the object light field can be reconstructed by measuring the phase difference and amplitude ratio of two components of the Jones vector on the basis of incoherent self-interference theory and the accurate point spread function (PSF) of the incoherent holographic system. In the analysis of Fresnel diffraction, we develop a new method to greatly simplify the calculation of the accurate PSF by means of imaging property of lens and symbolic mathematics tools. In the recording process, we utilize the automation of phase shift, photography, and synthesization of color hologram to greatly shorten the total recording time of a group of phase-shifted holograms. The experimental results show that the proposed technology can accurately realize polarization-sensitive imaging and it is much simpler for complete linearly polarized light.

Six-pack holographic imaging for dynamic rejection of out-of-focus objects

Six-pack holography is adapted to reject out-of-focus objects in dynamic samples, using a single camera exposure and without any scanning. By illuminating the sample from six different angles in parallel using a low-coherence source, out-of-focus objects are laterally shifted in six different directions when projected onto the focal plane. Then pixel-wise averaging of the six reconstructed images creates a significantly clearer image, with rejection of out-of-focus objects. Dynamic imaging results are shown for swimming microalgae and flowing microbeads, including numerical refocusing by Fresnel propagation. The averaged images reduced the contribution of out-of-focus objects by up to 83% in comparison to standard holograms captured using the same light source, further improving the system sectioning capabilities. Both simulation and experimental results are presented.

System design and error correction for 300 mm aperture vertical Fizeau spatial-temporal phase-shifting interferometer

With the development of high-power lasers for aerospace, electronics, etc., the demand for large-aperture planar optical elements has become more urgent, along with the demand for measurement methods. In this paper, the design of a 300 mm aperture vertical Fizeau spatial-temporal phase-shifting interferometer is discussed. Based on position difference between laser sources, the spatial phase-shifting technique is achieved by generating a laser source array on the focal plane of the collimation lens, and four pairs of coherent beams with different phase shifts are integrated in a vertical Fizeau interference system. Combined with a tunable laser diode, a temporal phase-shifting technique can be realized in any pair of coherent beams through wavelength tuning. The key techniques, which include laser duplication to introduce different phase shifts, conjugate imaging, and separation for interferograms, and assembly for a transmission flat, are demonstrated. The systematic error and position mismatch error of interferograms are eliminated. Comparison experiments are conducted between spatial and temporal phase-shifting techniques. A dynamic water surface is also measured to verify its capacity for detecting dynamic objects.

Speckle-field digital polarization holographic microscopy

We present a new polarization holographic microscopy technique based on speckle-field illumination with enhanced spatial resolution and controlled coherent noise reduction. The proposed technique employs a spatial light modulator for the generation of a sequential speckle pattern for the illumination of the sample. The developed microscope is capable of simultaneous extraction of orthogonal polarization components of the field emanating from the sample. We demonstrate the potential features of the technique by presenting spatially resolved images of the known samples and the inhomogeneous anisotropic samples. The technique has substantial significance in biomedical imaging with digital auto-focusing and complex field imaging.

Real-time measurement of the liquid-crystal optic-axis angle and effective refractive index distribution based on a common-path interferometer

A common-path interferometer for the real-time measurement of the liquid-crystal (LC) optic-axis angle and effective refractive index distribution is proposed. This method involves adding a polarizer and polarization camera to a general optical microscope. This requires only single-exposure imaging without changing any optical elements, and greatly simplifies the measurement process and system. In addition, the measurement results are unaffected by light-source power fluctuations or a non-uniform spatial distribution. Therefore, this method is suitable for measuring the LC optic-axis angle and effective refractive index of electrically controlled LC devices. Finally, the feasibility and validity of the proposed method are verified by simulation and experimentation.

Single-shot quantitative birefringence microscopy for imaging birefringence parameters

A method for realizing 2D single-shot measurements of birefringence parameters (including both retardation and optic axis orientation) of anisotropic materials using a simple recording setup and an efficient processing algorithm is proposed. The recording setup can be built simply by inserting a circular polarizer and a polarization beam splitter, respectively, in the object path and reference path of a conventional off-axis holographic imaging system, with no need for other adjustments. An algorithm for quantitatively retrieving the birefringence parameters from one single-shot hologram is proposed and demonstrated, in which a new quantity describing the birefringence, called complex birefringence parameter, is introduced, and a set of formulas used to extract the birefringence parameters is derived. Some experimental results are given for demonstrating the feasibility of the method that reveal that the method may provide another effective approach for investigating the birefringence properties of dynamic anisotropic materials, especially the birefringence induced by ultrafast pulse lasers.

Measurements of polarization-dependent angle-resolved light scattering from individual microscopic samples using Fourier transform light scattering

We present a method to measure the vector-field light scattering of individual microscopic objects. The polarization-dependent optical field images are measured with quantitative phase imaging at the sample plane, and then numerically propagated to the far-field plane. This approach allows the two-dimensional polarization-dependent angle-resolved light scattered patterns from individual object to be obtained with high precision and sensitivity. Using this method, we present the measurements of the polarization-dependent light scattering of a liquid crystal droplet and individual silver nanowires over scattering angles of 50°. In addition, the spectroscopic extension of the polarization-dependent angle-resolved light scattering is demonstrated using wavelength-scanning illumination.

Jones matrix microscopy from a single-shot intensity measurement

Quantitative measurement of Jones matrix elements is crucial for the study of light polarization with the wide range of applications. Here, we propose and experimentally demonstrate a novel method of Fourier space sharing to determine spatially resolved all four elements of the Jones matrix from a single-intensity frame. This is achieved by applying a holographic approach and making use of two triangular polarization Sagnac interferometers in the sample and reference arms. The proposed technique is flexible to adjust carrier frequencies in order to meet the varying demand of different anisotropic samples. A Jones matrix microscopy system is developed and applied to transparent samples. Experimental implementation of the proposed technique is demonstrated by determining the Jones matrix elements of commercially available known samples and liquid crystal droplets.

Double-channel angular-multiplexing polarization holography with common-path and off-axis configuration

We propose a double-channel angular-multiplexing polarization holographic imaging system with common-path and off-axis configurations. In the system, its input plane is spatially divided into three windows: an object window and two reference windows, and two orthogonal linear polarizers are attached, respectively, on the two reference windows; a two-dimensional cross grating is inserted between the input and output planes of the system. Thus the object beam passing through the object window and the two orthogonal polarized reference beams passing through the two reference windows can overlap each other at the output plane of the system and form a double-channel angular-multiplexing polarization hologram (DC-AM-PH). Using this system, the complex amplitude distributions of two orthogonal polarized components from an object can be recorded and reconstructed by one single-shot DC-AM-PH at the same time. Theoretical analysis and experimental results demonstrated that the system can be used to measure the Jones matrix parameters of polarization-sensitive or birefringent materials.

Fiber-based lensless polarization holography for measuring Jones matrix parameters of polarization-sensitive materials

We report a fiber-based lensless holographic imaging system to realize a single-shot measurement of two dimensional (2-D) Jones matrix parameters of polarization-sensitive materials. In this system, a multi-source lensless off-axis Fresnel holographic recording geometry is adopted, and two optical fiber splitters are used to generate the multiple reference and illumination beams required for recording a four-channel angular-multiplexing polarization hologram (AMPH). Using this system and the method described in this paper, spatially resolved Jones matrix parameters of a polarization-sensitive material can be retrieved from one single-shot AMPH. We demonstrate the feasibility of the method by extracting a 2-D Jones matrix of a composite polarizer. Applications of the method to measure the Jones matrix maps of a stressed polymethyl methacrylate sample and a mica fragment are also presented. Benefit from the fiber-based and lensless off-axis holographic design, the system possesses a quite compact configuration, which provides a feasible approach for development of an integrated and portable system to measure Jones matrix parameters of polarization-sensitive materials.

Single-shot digital holographic microscopy for quantifying a spatially-resolved Jones matrix of biological specimens

Field-based polarization measurements are essential for the completeness of information when exploiting the complex nature of optical responses of target objects. Here, we demonstrate digital holographic microscopy for quantifying a polarization-sensitive map of an object with a single-shot measurement. Using the image-splitting device generating four different copies of an object image and a separate reference beam of an off-axis configuration enables single-shot and multi-imaging capability. With the use of two polarization filters, four complex field images containing an object's polarization response are obtained simultaneously. With this method, we can construct a complete set of 2-by-2 Jones matrix at every single point of the object's images, and thus clearly visualize the anisotropic structures of biological tissues with low level of birefringence. This method will facilitate the high-precision measurements for fast dynamics of the polarization properties of biological specimens.

Inverse polarizing effect of an elliptical-polarization recorded hologram at a large cross angle

We report on the inverse polarizing effect (IPE) of an elliptical-polarization recorded hologram at a large recording angle. The IPE is a polarizing phenomenon in which the reconstructed signal switches the major and minor axes and keeps the original polarization, direction compared, to that of the signal wave. In reviewing the case of a linear-polarization and circular-polarization recorded hologram, we found that the IPE is a unique phenomenon for elliptical polarization. The IPE was observed at the cross angle of 38° experimentally, and was theoretically explained using tensor theory to remove paraxial limitation.