Phase Retrieval Based on Shaped Incoherent Sources

Current ghost imaging phase reconstruction schemes require either complex optical systems, iterative algorithms, Fourier transform steps, or entangled photon pairs. These factors may increase the difficulty of system design, lead to phase retrieval errors, or result in excessive time consumption. To tackle this challenge, we propose a five-step phase-shifting method that eliminates the need for complex optical systems, Fourier transform steps, entangled photon pairs, or iterative algorithms. Using five specifically designed incoherent sources, we can generate five distinct ghost imaging patterns. Subsequently, the phase information of the object can be calculated from these five speckle patterns. Additionally, we offer a detailed theoretical explanation for choosing the five-step phase-shifting method over the more commonly used three-step or four-step phase-shifting methods. We demonstrate the applicability of this theoretical proposal through numerical simulations involving two types of complicated objects. The results illustrate that the phase information of the complex object can be successfully and quantitatively reconstructed.

Temporal coherence envelope function of field emission in electron microscopy

Imaging in electron microscopy is adversely affected by partial electron spatial and temporal coherence. Temporal coherence has been treated theoretically in the past using the method pioneered fifty years ago by Hanßen and Trepte, who assumed a Gaussian energy distribution. However, state-of-the-art instruments employ field emission (FE) sources that emit electrons with a non-Gaussian energy distribution. We have updated the treatment of temporal coherence to describe the effects of an arbitrary energy distribution on image formation. The updated approach is implemented in Fourier optics simulations to explore the effect of FE on image formation in conventional, non-aberration-corrected (NAC) and aberration-corrected (AC) low energy electron microscopy. It is found that the resolution that can be achieved for the FE distribution is only slightly degraded compared to a Gaussian distribution with the same energy spread. FE also produces a focus offset. These two effects are weaker for AC than for NAC microscopy. These and other insights may be relevant to the selection of the aperture size that optimizes resolution and to analyses that make use of focal image series. The approach developed here is also applicable to transmission electron microscopy.

PUMA - An open-source 3D-printed direct vision microscope with augmented reality and spatial light modulator functions

3D-printed microscopes are a topical emerging field in the literature. However most microscopes presented to date are quite novel re-imaginings of the microscope's mechanical design and they are either solely dependent on, or primarily geared towards, camera-based observations rather than ergonomic direct vision screening through an ocular lens. The reliance on camera, computer and monitor for observation introduces a compromise between portability, cost and the quality of an instant wide field of view. In this report, I introduce the Portable Upgradeable Modular and Affordable (PUMA) microscope which is an open-source 3D-printed multimodality microscope that employs a traditional upright design for ease of human direct visual observations and slide screening. PUMA uses standard RMS or C-mount objectives, with a tube length 160 mm, 170 mm or infinity and wide field high eye point ocular lenses. PUMA can use simple mirror-based illumination or can be configured to a full Köhler system with Abbe condenser for high numerical aperture observations including oil immersion. PUMA also has advanced digital/optical imaging features such as a digital spatial light modulator and - unique to any 3D printed microscope to date - an augmented reality heads-up display for interactive calibrated measurements. Digital camera imaging can also be used with PUMA - in fact PUMA can take up to three separate digital cameras simultaneously. PUMA can also function as a direct vision multi-header microscope for teaching or discussion. The illumination system is also modular and includes transillumination, epi-illumination, fluorescence, polarisation, dark ground and also Schlieren-based phase contrast and other Fourier optics filtering modalities. All these advanced features are available through an on-board, battery operated, microprocessor so no mains supply, smartphone, network connection, PC or external monitor are required making PUMA a truly portable system suitable for remote field work.

High order phase contrast and source divergence in low energy electron microscopy

We present experimental observations of high order phase contrast in aberration corrected low energy electron microscopy (AC-LEEM). Phase contrast produced by atomic steps on a Ag (111) surface exhibits prominent high order interference fringes, which have not been reported before. These phase contrast features depend upon defocus and incident electron energy, similar to the prominent first order fringes observed previously and in agreement with Fourier optics (FO) model predictions. The comparison of experimental results and FO model simulations demonstrates that fringe amplitudes are strongly affected at large defocus by the source divergence. This effect is exploited to quantitatively determine the divergence, 0.055 ± 0.005 mrad, of the field emission source in AC-LEEM under the imaging conditions used. Although the divergence determines the spatial coherence of the illumination in microscopy, it has not been possible to characterize this key instrumental parameter in LEEM before.

High-Throughput, High-Resolution Interferometric Light Microscopy of Biological Nanoparticles

Label-free, visible light microscopy is an indispensable tool for studying biological nanoparticles (BNPs). However, conventional imaging techniques have two major challenges: (i) weak contrast due to low-refractive-index difference with the surrounding medium and exceptionally small size and (ii) limited spatial resolution. Advances in interferometric microscopy have overcome the weak contrast limitation and enabled direct detection of BNPs, yet lateral resolution remains as a challenge in studying BNP morphology. Here, we introduce a wide-field interferometric microscopy technique augmented by computational imaging to demonstrate a 2-fold lateral resolution improvement over a large field-of-view (>100 × 100 μm²), enabling simultaneous imaging of more than 10⁴ BNPs at a resolution of ∼150 nm without any labels or sample preparation. We present a rigorous vectorial-optics-based forward model establishing the relationship between the intensity images captured under partially coherent asymmetric illumination and the complex permittivity distribution of nanoparticles. We demonstrate high-throughput morphological visualization of a diverse population of Ebola virus-like particles and a structurally distinct Ebola vaccine candidate. Our approach offers a low-cost and robust label-free imaging platform for high-throughput and high-resolution characterization of a broad size range of BNPs.

Energy-Tailorable Spin-Selective Multifunctional Metasurfaces with Full Fourier Components

Compact integrated multifunctional metasurface that can deal with concurrent tasks represent one of the most profound research fields in modern optics. Such integration is expected to have a striking impact on minimized optical systems in applications such as optical communication and computation. However, arbitrary multifunctional spin-selective design with precise energy configuration in each channel is still a challenge, and suffers from intrinsic noise and complex designs. Here, a design principle is proposed to realize energy tailorable multifunctional metasurfaces, in which the functionalities can be arbitrarily designed if the channels have no or weak interference in k-space. A design strategy is demostrated here with high-efficiency dielectric nanopillars that can modulate full Fourier components of the optical field. The spin-selective behavior of the dielectric metasurfaces is also investigated, which originates from the group effect introduced by numerous nanopillar arrays. This approach provides straightforward rules to control the functionality channels in the integrated metasurfaces, and paves the way for efficient concurrent optical communication.

Comparing Fourier optics and contrast transfer function modeling of image formation in low energy electron microscopy

A theoretical understanding of image formation in cathode lens microscopy can facilitate image interpretation. We compare Fourier Optics (FO) and Contrast Transfer Function (CTF) approaches that were recently adapted from other realms of microscopy to model image formation in low energy electron microscopy (LEEM). Although these two approaches incorporate imaging errors from several sources similarly, they differ in the way that the image intensity is calculated. The simplification that is used in the CTF calculation advantageously leads to its computational efficiency. However, we find that lens aberrations, and spatial and temporal coherence may affect the validity of the CTF approach to model LEEM image formation under certain conditions. In particular, these effects depend strongly on the nature of the object being imaged and also become more pronounced with increasing defocus. While the use of the CTF approach appears to be justified for objects that are routinely imaged with LEEM, comparison of theory to experimental observations of a focal image series for rippled, suspended graphene reveals one example where FO works, but CTF does not. This work alerts us to potential pitfalls and guides the effective use of FO and CTF approaches. It also lays the foundation for quantitative image evaluation using these methods.

Orbital angular momentum light in microscopy

Light with a helical phase has had an impact on optical imaging, pushing the limits of resolution or sensitivity. Here, special emphasis will be given to classical light microscopy of phase samples and to Fourier filtering techniques with a helical phase profile, such as the spiral phase contrast technique in its many variants and areas of application.This article is part of the themed issue 'Optical orbital angular momentum'.

WavePropaGator: interactive framework for X-ray free-electron laser optics design and simulations

This article describes the WavePropaGator (WPG) package, a new interactive software framework for coherent and partially coherent X-ray wavefront propagation simulations. The package has been developed at European XFEL for users at the existing and emerging free-electron laser (FEL) facilities, as well as at the third-generation synchrotron sources and future diffraction-limited storage rings. The WPG addresses the needs of beamline scientists and user groups to facilitate the design, optimization and improvement of X-ray optics to meet their experimental requirements. The package uses the Synchrotron Radiation Workshop (SRW) C/C++ library and its Python binding for numerical wavefront propagation simulations. The framework runs reliably under Linux, Microsoft Windows 7 and Apple Mac OS X and is distributed under an open-source license. The available tools allow for varying source parameters and optics layouts and visualizing the results interactively. The wavefront history structure can be used for tracking changes in every particular wavefront during propagation. The batch propagation mode enables processing of multiple wavefronts in workflow mode. The paper presents a general description of the package and gives some recent application examples, including modeling of full X-ray FEL beamlines and start-to-end simulation of experiments.

On-chip photonic Fourier transform with surface plasmon polaritons

The Fourier transform (FT), a cornerstone of optical processing, enables rapid evaluation of fundamental mathematical operations, such as derivatives and integrals. Conventionally, a converging lens performs an optical FT in free space when light passes through it. The speed of the transformation is limited by the thickness and the focal length of the lens. By using the wave nature of surface plasmon polaritons (SPPs), here we demonstrate that the FT can be implemented in a planar configuration with a minimal propagation distance of around 10 μm, resulting in an increase of speed by four to five orders of magnitude. The photonic FT was tested by synthesizing intricate SPP waves with their Fourier components. The reduced dimensionality in the minuscule device allows the future development of an ultrafast on-chip photonic information processing platform for large-scale optical computing.

Non-moving Hadamard matrix diffusers for speckle reduction in laser pico-projectors

Personal electronic devices such as cell phones and tablets continue to decrease in size while the number of features and add-ons keep increasing. One particular feature of great interest is an integrated projector system. Laser pico-projectors have been considered, but the technology has not been developed enough to warrant integration. With new advancements in diode technology and MEMS devices, laser-based projection is currently being advanced for pico-projectors. A primary problem encountered when using a pico-projector is coherent interference known as speckle. Laser speckle can lead to eye irritation and headaches after prolonged viewing. Diffractive optical elements known as diffusers have been examined as a means to lower speckle contrast. This paper presents a binary diffuser known as a Hadamard matrix diffuser. Using two static in-line Hadamard diffusers eliminates the need for rotation or vibration of the diffuser for temporal averaging. Two Hadamard diffusers were fabricated and contrast values measured showing good agreement with theory and simulated values.

Partially coherent X-ray wavefront propagation simulations including grazing-incidence focusing optics

X-ray beamlines in modern synchrotron radiation sources make extensive use of grazing-incidence reflective optics, in particular Kirkpatrick-Baez elliptical mirror systems. These systems can focus the incoming X-rays down to nanometer-scale spot sizes while maintaining relatively large acceptance apertures and high flux in the focused radiation spots. In low-emittance storage rings and in free-electron lasers such systems are used with partially or even nearly fully coherent X-ray beams and often target diffraction-limited resolution. Therefore, their accurate simulation and modeling has to be performed within the framework of wave optics. Here the implementation and benchmarking of a wave-optics method for the simulation of grazing-incidence mirrors based on the local stationary-phase approximation or, in other words, the local propagation of the radiation electric field along geometrical rays, is described. The proposed method is CPU-efficient and fully compatible with the numerical methods of Fourier optics. It has been implemented in the Synchrotron Radiation Workshop (SRW) computer code and extensively tested against the geometrical ray-tracing code SHADOW. The test simulations have been performed for cases without and with diffraction at mirror apertures, including cases where the grazing-incidence mirrors can be hardly approximated by ideal lenses. Good agreement between the SRW and SHADOW simulation results is observed in the cases without diffraction. The differences between the simulation results obtained by the two codes in diffraction-dominated cases for illumination with fully or partially coherent radiation are analyzed and interpreted. The application of the new method for the simulation of wavefront propagation through a high-resolution X-ray microspectroscopy beamline at the National Synchrotron Light Source II (Brookhaven National Laboratory, USA) is demonstrated.

k-space imaging of the eigenmodes of sharp gold tapers for scanning near-field optical microscopy

We investigate the radiation patterns of sharp conical gold tapers, which were designed as adiabatic nanofocusing probes for scanning near-field optical microscopy (SNOM). Field calculations show that only the lowest order eigenmode of such a taper can reach the very apex and thus induce the generation of strongly enhanced near-field signals. Higher-order modes are coupled into the far field at finite distances from the apex. Here, we demonstrate experimentally how to distinguish and separate between the lowest and higher-order eigenmodes of such a metallic taper by filtering in the spatial frequency domain. Our approach has the potential to considerably improve the signal-to-background ratio in spectroscopic experiments at the nanoscale.