From Molecules to Classrooms: A Comprehensive Guide to Single-Molecule Localization Microscopy.

Single-molecule localization microscopy (SMLM) has revolutionized our ability to visualize cellular structures, offering unprecedented detail. However, the intricate biophysical principles that underlie SMLM can be daunting for newcomers, particularly undergraduate and graduate students. To address this challenge, we introduce the fundamental concepts of SMLM, providing a solid theoretical foundation. In addition, we have developed an intuitive graphical interface APP that simplifies these core concepts, making them more accessible for students. This APP clarifies how super-resolved images are fitted and highlights the crucial factors determining image quality. Our approach deepens students' understanding of SMLM by combining theoretical instruction with practical learning. This development equips them with the skills to carry out single-molecule super-resolved experiments and explore the microscopic world beyond the diffraction limit.

X-ray propagation through a kinoform lens.

Combining geometric ray tracing and wave optics propagation, a new simulation model named LWF is established to calculate the full coherent X-ray propagation through a kinoform lens. The LWF model is used to analyze the X-ray propagation through long and short kinoform lenses and calculate the intensity distribution at the focal plane. When the aperture is large, the focal spot for the long kinoform lens is smaller than that for the short kinoform lens. Due to the use of the geometric ray-tracing method to calculate the beam propagation inside the kinoform lens, the LWF model takes a low number of transversal wavefront segments, i.e. a short time, to achieve high accuracy. The simulation times for the one-dimensional and two-dimensional LWF models are 0.025 s and 5.3 s, respectively, with a calculation error of less than 0.5%. The high efficiency and high accuracy make the LWF model a strong tool in designing kinoform lenses.

A fast and lightweight tool for partially coherent beamline simulations in fourth-generation storage rings based on coherent mode decomposition.

A new algorithm to perform coherent mode decomposition of undulator radiation is proposed. It is based on separating the horizontal and vertical directions, reducing the problem by working with one-dimension wavefronts. The validity conditions of this approximation are discussed. Simulations require low computer resources and run interactively on a laptop. The focusing with lenses of the radiation emitted by an undulator in a fourth-generation storage ring (EBS-ESRF) is studied. Results are compared against multiple optics packages implementing a variety of methods for dealing with partial coherence: full two-dimension coherent mode decomposition, Monte Carlo combination of wavefronts from electrons entering the undulator with different initial conditions, and hybrid ray-tracing correcting geometrical optics with wave optics.

A wave optics model for the effect of partial coherence on coherent diffractive imaging.

With the development of fourth-generation synchrotron sources, coherent diffractive imaging (CDI) will be a mainstream method for 3D structure determination at nanometre resolution. The partial coherence of incident X-rays plays a critical role in the reconstructed image quality. Here a wave optics model is proposed to analyze the effect of partial coherence on CDI for an actual beamline layout, based on the finite size of the source and the influence of the optics on the wavefront. Based on this model, the light field distribution at any plane, the coherence between any two points on this plane and CDI experiments can be simulated. The plane-wave CDI simulation result also shows that in order to reconstruct good image quality of complex samples the visibility of the interference fringes of any two points in the horizontal and vertical directions of the incident light field at the sample needs to be higher than 0.95.

Fast convolution-based performance estimation method for diffraction-limited source with imperfect X-ray optics.

Although optical element error analysis is always an important part of beamline design for highly coherent synchrotron radiation or free-electron laser sources, the usual wave optics simulation can be very time-consuming, which limits its application at the early stage of the beamline design. In this work, a new theoretical approach has been proposed for quick evaluations of the optical performance degradation due to optical element error. In this way, time-consuming detailed simulations can be applied only when truly necessary. This approach treats the imperfections as perturbations that convolve with the ideal performance. For simplicity, but not by necessity, the Gaussian Schell-model has been used to show the application of this theoretical approach. The influences of the finite aperture size and height error of a focusing mirror are analysed using the proposed theory. The physical explanation of the performance degradation acquired from the presented approach helps to give a better definition of the critical range of error spatial frequencies that most affect the performance of a mirror. An example comparing two mirror surface errors with identical power spectral density functions is given. These two types of mirror surface errors result in very different intensity profiles. The approach presented in this work could help beamline designers specify the error tolerances on general optical elements more accurately.

Compensation of heat load deformations using adaptive optics for the ALS upgrade: a wave optics study.

A realistic wave optics simulation method has been developed to study how wavefront distortions originating from heat load deformations can be corrected using adaptive X-ray optics. Several planned soft X-ray and tender X-ray insertion-device beamlines in the Advanced Light Source upgrade rely on a common design principle. A flat, first mirror intercepts the white beam; vertical focusing is provided by a variable-line-space monochromator; and horizontal focusing comes from a single, pre-figured, adaptive mirror. A variety of scenarios to cope with thermal distortion in the first mirror are studied by finite-element analysis. The degradation of the intensity distribution at the focal plane is analyzed and the adaptive optics that correct it is modeled. The range of correctable wavefront errors across the operating range of the beamlines is reported in terms of mirror curvature and spatial frequencies. The software developed is a one-dimensional wavefront propagation package made available in the OASYS suite, an adaptable, customizable and efficient beamline modeling platform.

Null Wave Front and Ryu-Takayanagi Surface.

The Ryu-Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu-Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu-Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu-Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.

The wave optical whole process design of the soft X-ray interference lithography beamline at SSRF.

A new spatially coherent beamline has been designed and constructed at the Shanghai Synchrotron Radiation Facility. Here, the design of the beamline is introduced and the spatial coherence is analyzed throughout the whole process by wave optics. The simulation results show good spatial coherence at the endstation and have been proven by experiment results.

Atom-Diffraction from Surfaces with Defects: A Fermatian, Newtonian and Bohmian Joint View.

Bohmian mechanics, widely known within the field of the quantum foundations, has been a quite useful resource for computational and interpretive purposes in a wide variety of practical problems. Here, it is used to establish a comparative analysis at different levels of approximation in the problem of the diffraction of helium atoms from a substrate consisting of a defect with axial symmetry on top of a flat surface. The motivation behind this work is to determine which aspects of one level survive in the next level of refinement and, therefore, to get a better idea of what we usually denote as quantum-classical correspondence. To this end, first a quantum treatment of the problem is performed with both an approximated hard-wall model and then with a realistic interaction potential model. The interpretation and explanation of the features displayed by the corresponding diffraction intensity patterns is then revisited with a series of trajectory-based approaches: Fermatian trajectories (optical rays), Newtonian trajectories and Bohmian trajectories. As it is seen, while Fermatian and Newtonian trajectories show some similarities, Bohmian trajectories behave quite differently due to their implicit non-classicality.

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.

Wave optical simulation of retinal images in laser safety evaluations.

Lasers with wavelengths in the visible and near infrared region, pose a potential hazard to vision as the radiation can be focused on the retina. The laser safety standard IEC 60825-1:2014 provides limits and evaluation methods to perform a classification for such systems. An important parameter is the retinal spot size which is described by the angular subtense of the apparent source. In laser safety evaluations, the radiation is often described as a Gaussian beam and the image on the retina is calculated using the wave optical propagation through a thin lens. For coherent radiation, this method can be insufficient as the diffraction effects of the pupil aperture influence the retinal image. In this publication, we analyze these effects and propose a general analytical calculation method for the angular subtense. The proposed formula is validated for collimated and divergent Gaussian beams.

Periodic Stratified Porous Structures in Dynamic Polyelectrolyte Films Through Standing-Wave Optical Crosslinking for Structural Color.

Periodic porous structures have been introduced into functional films to meet the requirements of various applications. Though many approaches have been developed to generate desired structures in polymeric films, few of them can effectively and dynamically achieve periodic porous structures. Here, a facile way is proposed to introduce periodic stratified porous structures into polyelectrolyte films. A photo-crosslinkable polyelectrolyte film of poly(ethylenimine) (PEI) and photoreactive poly(acrylic acid) derivative (PAA-N3 ) is prepared by layer-by-layer (LbL) self-assembly. Stratified crosslinking of the PEI/PAA-N3 film is generated basing on standing-wave optics. The periodic stratified porous structure is constructed by forming pores in noncrosslinked regions in the film. Thanks to the dynamic mobility of polyelectrolytes, this structural controlment can be repeated several times. The size of pores corresponding to the layer spacing of the film contributes to the structural colors. Furthermore, structural color patterns are fabricated in the film by selective photo-crosslinking using photomasks. Although the large-scale structural controlment in thick (micron-scale and above) films needs to be explored further, this work highlights the periodic structural controlment in polymeric films and thus presents an approach for application potentials in sensor, detection, and ink-free printing.

Holographic Sampling Display Based on Metagratings.

Glasses-free three-dimensional (3D) display is considered as a potential disruptive technology for display. The issue of visual fatigue, mainly caused by the inaccurate phase reconstruction in terms of image crosstalk, as well as vergence and accommodation conflict, is the critical obstacle that hinders the real applications of glasses-free 3D display. Here we propose a glasses-free 3D display by adopting metagratings for the pixelated phase modulation to form converged viewpoints. When the viewpoints are closely arranged, the holographic sampling 3D display can approximate a continuous light field. We demonstrate a video rate full-color 3D display prototype without visual fatigue under an LED white light illumination. The metagratings-based holographic sampling 3D display has a thin form factor and is compatible with traditional flat panel and thus has the potential to be used in portable electronics, window display, exhibition display, 3D TV, as well as tabletop display.

Universal diffraction of atoms and molecules from a quantum reflection grating.

Since de Broglie's work on the wave nature of particles, various optical phenomena have been observed with matter waves of atoms and molecules. However, the analogy between classical and atom/molecule optics is not exact because of different dispersion relations. In addition, according to de Broglie's formula, different combinations of particle mass and velocity can give the same de Broglie wavelength. As a result, even for identical wavelengths, different molecular properties such as electric polarizabilities, Casimir-Polder forces, and dissociation energies modify (and potentially suppress) the resulting matter-wave optical phenomena such as diffraction intensities or interference effects. We report on the universal behavior observed in matter-wave diffraction of He atoms and He2 and D2 molecules from a ruled grating. Clear evidence for emerging beam resonances is observed in the diffraction patterns, which are quantitatively the same for all three particles and only depend on the de Broglie wavelength. A model, combining secondary scattering and quantum reflection, permits us to trace the observed universal behavior back to the peculiar principles of quantum reflection.

Semiclassical TEM image formation in phase space.

Current developments in TEM such as high-resolution imaging at low acceleration voltages and large fields of view, the ever larger capabilities of hardware aberration correction and the systematic shaping of electron beams require accurate descriptions of TEM imaging in terms of wave optics. Since full quantum mechanic solutions have not yet been established for, e.g., the theory of aberrations, we are exploring semiclassical image formation in the TEM from the perspective of quantum mechanical phase space, here. Firstly, we use two well-known semiclassical approximations, Miller's semiclassical algebra and the frozen Gaussian method, for describing the wave optical generalization of arbitrary geometric aberrations, including nonisoplanatic and slope aberrations. Secondly, we demonstrate that the Wigner function representation of phase space is well suited to also describe incoherent aberrations as well as the ramifications of partial coherence due to the emission process at the electron source. We identify a close relationship between classical phase space and Wigner function distortions due to aberrations as well as classical brightness and quantum mechanical purity.