Direct single-shot phase retrieval from the diffraction pattern of separated objects.

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called 'diffraction before destruction' experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing the phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.

Structural Basis for the Brilliant Colors of the Sapphirinid Copepods.

Males of sapphirinid copepods use regularly alternating layers of hexagonal-shaped guanine crystals and cytoplasm to produce spectacular structural colors. In order to understand the mechanism by which the different colors are produced, we measured the reflectance of live individuals and then characterized the organization of the crystals and the cytoplasm layers in the same individuals using cryo-SEM. On the basis of these measurements, we calculated the expected reflectance spectra and found that they are strikingly similar to the measured ones. We show that variations in the cytoplasm layer thickness are mainly responsible for the different reflected colors and also that the copepod color strongly depends on the angular orientation relative to the incident light, which can account for its appearance and disappearance during spiral swimming in the natural habitat.

The mechanism of color change in the neon tetra fish: a light-induced tunable photonic crystal array.

The fresh water fish neon tetra has the ability to change the structural color of its lateral stripe in response to a change in the light conditions, from blue-green in the light-adapted state to indigo in the dark-adapted state. The colors are produced by constructive interference of light reflected from stacks of intracellular guanine crystals, forming tunable photonic crystal arrays. We have used micro X-ray diffraction to track in time distinct diffraction spots corresponding to individual crystal arrays within a single cell during the color change. We demonstrate that reversible variations in crystal tilt within individual arrays are responsible for the light-induced color variations. These results settle a long-standing debate between the two proposed models, the "Venetian blinds" model and the "accordion" model. The insight gained from this biogenic light-induced photonic tunable system may provide inspiration for the design of artificial optical tunable systems.

The structural basis for enhanced silver reflectance in Koi fish scale and skin.

Fish have evolved biogenic multilayer reflectors composed of stacks of intracellular anhydrous guanine crystals separated by cytoplasm, to produce the silvery luster of their skin and scales. Here we compare two different variants of the Japanese Koi fish; one of them with enhanced reflectivity. Our aim is to determine how biology modulates reflectivity, and from this to obtain a mechanistic understanding of the structure and properties governing the intensity of silver reflectance. We measured the reflectance of individual scales with a custom-made microscope, and then for each individual scale we characterized the structure of the guanine crystal/cytoplasm layers using high-resolution cryo-SEM. The measured reflectance and the structural-geometrical parameters were used to calculate the reflectance of each scale, and the results were compared to the experimental measurements. We show that enhanced reflectivity is obtained with the same basic guanine crystal/cytoplasm stacks, but the structural arrangement between the stack, inside the stacks, and relative to the scale surface is varied when reflectivity is enhanced. Finally, we propose a model that incorporates the basic building block parameters, the crystal orientation inside the tissue, and the resulting reflectance and explains the mechanistic basis for reflectance enhancement.

Direct phase retrieval in double blind Fourier holography.

Phase measurement is a long-standing challenge in a wide range of applications, from X-ray imaging to astrophysics and spectroscopy. While in some scenarios the phase is resolved by an interferometric measurement, in others it is reconstructed via numerical optimization, based on some a-priori knowledge about the signal. The latter commonly use iterative algorithms, and thus have to deal with their convergence, stagnation, and robustness to noise. Here we combine these two approaches and present a new scheme, termed double blind Fourier holography, providing an efficient solution to the phase problem in two dimensions, by solving a system of linear equations. We present and experimentally demonstrate our approach for the case of lens-less imaging.

Two-photon excitation in scattering media by spatiotemporally shaped beams and their application in optogenetic stimulation.

The use of wavefront shaping to generate extended optical excitation patterns which are confined to a predetermined volume has become commonplace on various microscopy applications. For multiphoton excitation, three-dimensional confinement can be achieved by combining the technique of temporal focusing of ultra-short pulses with different approaches for lateral light shaping, including computer generated holography or generalized phase contrast. Here we present a theoretical and experimental study on the effect of scattering on the propagation of holographic beams with and without temporal focusing. Results from fixed and acute cortical slices show that temporally focused spatial patterns are extremely robust against the effects of scattering and this permits their three-dimensionally confined excitation for depths more than 500 µm. Finally we prove the efficiency of using temporally focused holographic beams in two-photon stimulation of neurons expressing the red-shifted optogenetic channel C1V1.