Joint estimation of object and probes in vectorial ptychography

Mixed-state ptychography for quantitative optical properties measurement of vector beam

Recent advances in ptychography have extended to anisotropic specimens, but vectorial reconstruction of probes owing to polarization aliasing remains a challenge. A polarization-sensitive ptychography that enables full optical property measurement of vector light is proposed. An optimized reconstruction strategy, first calibrating the propagation direction and then performing faithful retrieval, is established. This method avoids multiple image acquisitions with various polarizer configurations and significantly improves the measurement accuracy by correlating the intensity and position of different polarization components. The capability of the proposed method to quantify anisotropic parameters of optical materials and polarization properties of vector probe is demonstrated by experiment.

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.

Extending the capabilities of vectorial ptychography to circular-polarizing materials such as cholesteric liquid crystals

The problem of imaging materials with circular-polarization properties is discussed within the framework of vectorial ptychography. We demonstrate, both theoretically and numerically, that using linear polarizations to investigate such materials compromises the unicity of the solution provided by this computational method. To overcome this limitation, an improved measurement approach is proposed, which involves specific combinations of elliptical polarizations. The effectiveness of this strategy is demonstrated by numerical simulations and experimental measurements on cholesteric liquid crystal films, which possess unique polarization properties. With the help of Pauli matrices algebra, our results highlight the technique's ability to discern between the different types of circular polarizers, uniform vs. non-uniform, and determine their handedness.

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.

Amorphous-to-crystal transition in the layer-by-layer growth of bivalve shell prisms

Biomineralization integrates complex physical and chemical processes bio-controlled by the living organisms through ionic concentration regulation and organic molecules production. It allows tuning the structural, optical and mechanical properties of hard tissues during ambient-condition crystallisation, motivating a deeper understanding of the underlying processes. By combining state-of-the-art optical and X-ray microscopy methods, we investigated early-mineralized calcareous units from two bivalve species, Pinctada margaritifera and Pinna nobilis, revealing chemical and crystallographic structural insights. In these calcite units, we observed ring-like structural features correlated with a lack of calcite and an increase of amorphous calcium carbonate and proteins contents. The rings also correspond to a larger crystalline disorder and a larger strain level. Based on these observations, we propose a temporal biomineralization cycle, initiated by the production of an amorphous precursor layer, which further crystallizes with a transition front progressing radially from the unit centre, while the organics are expelled towards the prism edge. Simultaneously, along the shell thickness, the growth occurs following a layer-by-layer mode. These findings open biomimetic perspectives for the design of refined crystalline materials. STATEMENT OF SIGNIFICANCE: Calcareous biominerals are amongst the most present forms of biominerals. They exhibit astonishing structural, optical and mechanical properties while being formed at ambient synthesis conditions from ubiquitous ions, motivating the deep understanding of biomineralization. Here, we unveil the first formation steps involved in the biomineralization cycle of prismatic units of two bivalve species by applying a new multi-modal non-destructive characterization approach, sensitive to chemical and crystalline properties. The observations of structural features in mineralized units of different ages allowed the derivation of a temporal sequence for prism biomineralization, involving an amorphous precursor, a radial crystallisation front and a layer-by-layer sequence. Beyond these chemical and physical findings, the herein introduced multi-modal approach is highly relevant to other biominerals and bio-inspired studies.

Broadband decoupling of intensity and polarization with vectorial Fourier metasurfaces

Intensity and polarization are two fundamental components of light. Independent control of them is of tremendous interest in many applications. In this paper, we propose a general vectorial encryption method, which enables arbitrary far-field light distribution with the local polarization, including orientations and ellipticities, decoupling intensity from polarization across a broad bandwidth using geometric phase metasurfaces. By revamping the well-known iterative Fourier transform algorithm, we propose "à la carte" design of far-field intensity and polarization distribution with vectorial Fourier metasurfaces. A series of non-conventional vectorial field distribution, mimicking cylindrical vector beams in the sense that they share the same intensity profile but with different polarization distribution and a speckled phase distribution, is demonstrated. Vectorial Fourier optical metasurfaces may enable important applications in the area of complex light beam generation, secure optical data storage, steganography and optical communications.

Polarization-sensitive differential phase-contrast microscopy

We present a novel, to the best of our knowledge, form of polarization microscopy capable of producing quantitative optic-axis and phase retardation maps of transparent and anisotropic materials. The proposed method operates on differential phase-contrast (DPC) microscopy that produces a phase image of a thin specimen using multi-axis intensity measurements. For polarization-sensitive imaging, patterned illumination light is circularly polarized to illuminate a specimen. The light transmitted through a specimen is split into two orthogonal polarization states and measured by an image sensor. Subsequent DPC computation based on the illumination patterns, acquired images, and the imaging model enables the retrieval of polarization-dependent quantitative phase images, which are utilized to reconstruct the orientation and retardation of the specimen. We demonstrate the validity of the proposed method by measuring the optic-axis and phase retardation maps of calibrated and various anisotropic samples.

Reference-free quantitative microscopic imaging of coherent arbitrary vectorial light beams

Precise spatial characterization of vectorial beams is crucial for many advanced optical experiments, but challenging when wavefront and polarization features are involved together. Here we propose a reference-free method aimed at extracting the map of the complex-amplitude components of any coherent beam at an optical-microscopy resolution. Our method exploits recent advances in ptychographic imaging approaches. We emphasize its versatility by reconstructing successfully various experimental vectorial beams including polarization and phase vortices, the exit field of a multicore fiber and a speckle pattern.

Analyzer-free linear dichroic ptychography

Linear dichroism is an important tool to characterize the transmission matrix and determine the crystal or orbital orientation in a material. In order to achieve high-resolution mapping of transmission properties, the linear-dichroism scattering model in ptychographic imaging is introduced, and an efficient two-stage reconstruction algorithm is developed. Using the proposed algorithm on a uniaxial material, the dichroic transmission matrix can be recovered without an analyzer by using ptychography measurements with as few as three different polarization angles, with the help of an empty region to remove phase ambiguities.

Ptychography retrieval of fully polarized holograms from geometric-phase metasurfaces

Controlling light properties with diffractive planar elements requires full-polarization channels and accurate reconstruction of optical signal for real applications. Here, we present a general method that enables wavefront shaping with arbitrary output polarization by encoding both phase and polarization information into pixelated metasurfaces. We apply this concept to convert an input plane wave with linear polarization to a holographic image with arbitrary spatial output polarization. A vectorial ptychography technique is introduced for mapping the Jones matrix to monitor the reconstructed metasurface output field and to compute the full polarization properties of the vectorial far field patterns, confirming that pixelated interfaces can deflect vectorial images to desired directions for accurate targeting and wavefront shaping. Multiplexing pixelated deflectors that address different polarizations have been integrated into a shared aperture to display several arbitrary polarized images, leading to promising new applications in vector beam generation, full color display and augmented/virtual reality imaging.

Controlling light with planar elements requires full polarization channels and reconstruction of optical signals. Here, the authors have demonstrated a general method relying on pixelated metasurfaces that enables wavefront shaping with arbitrary output polarization, allowing full utilization of polarization channels.

Confocal Bragg ptychography for bulk specimens: a numerical demonstration

We report on a new X-ray imaging method, which generalizes Bragg ptychography to 3D mapping of embedded crystalline volumes within thick specimens. The sample is probed by a pencil X-ray beam. The diffracted beam is magnified by an objective and passes through a slit in the image plane to be monitored by a 2D detector in the far-field of the image plane. The dimensions of the incoming beam and the slit opening define a confocal Bragg volume. Scanning the sample with respect to this probe volume, an iterative oversampling routine is used to reconstruct the shape and projected displacement field of extended internal volumes. This routine takes into account the pupil function and known aberrations of the lens. We demonstrate the method by a numerical study of a 3.5 µm grain comprising a wall of edge dislocations. With a probe volume of ∼0.12 µm³ and a compound refractive lens with a numerical aperture of 0.49×10^-3 as the objective, the dislocations are fully resolved with a displacement sensitivity of ∼10 pm. The spatial resolution is 26×27×123 nm³ (rms), with the poor resolution along the optical axis being limited by the probe size. With a four times larger numerical aperture, the resolution becomes 16×8×123 nm³ (rms). The lens aberrations are found to be not critical.