Small Defocus Research Articles

Two-dimensional beam scanning by tunable photonic spin Hall effect

To the best of our knowledge, a novel tunable photonic spin Hall effect is proposed based on a pair of liquid crystal Pancharatnam-Berry (PB) lenses. Owing to the spin-dependent geometric phases, a PB lens focus or defocus the incident light field according to its spin angular momentum. By cascading two PB lenses with a small gap, the focus and defocus effects can be suppressed, and the transmitted light fields with opposite spin will be deflected toward opposite directions when the two PB lenses have a relative lateral displacement. The deflection angles vary linearly with the displacements, thus double-lines two-dimensional continuous beam scanning is achieved with a scanning angle of 39o × 39° and a beam diverging angle of 0.028o × 0.028°. The scanning beam is used to write different patterns on a 200 nm thick gold film. We believe this beam scanning system can find wide applications ranging from laser processing, Lidar, particle manipulation, to free space optical communications.

Single-shot wavelength-multiplexed phase microscopy under Gabor regime in a regular microscope embodiment

Phase imaging microscopy under Gabor regime has been recently reported as an extremely simple, low cost and compact way to update a standard bright-field microscope with coherent sensing capabilities. By inserting coherent illumination in the microscope embodiment and producing a small defocus distance of the sample at the input plane, the digital sensor records an in-line Gabor hologram of the target sample, which is then numerically post-processed to finally achieve the sample’s quantitative phase information. However, the retrieved phase distribution is affected by the two well-known drawbacks when dealing with Gabor’s regime, that is, coherent noise and twin image disturbances. Here, we present a single-shot technique based on wavelength multiplexing for mitigating these two effects. A multi-illumination laser source (including 3 diode lasers) illuminates the sample and a color digital sensor (conventional RGB color camera) is used to record the wavelength-multiplexed Gabor hologram in a single exposure. The technique is completed by presenting a novel algorithm based on a modified Gerchberg–Saxton kernel to finally retrieve an enhanced quantitative phase image of the sample, enhanced in terms of coherent noise removal and twin image minimization. Experimental validations are performed in a regular Olympus BX-60 upright microscope using a 20X 0.46NA objective lens and considering static (resolution test targets) and dynamic (living spermatozoa) phase samples.

Differential programming enabled functional imaging with Lorentz transmission electron microscopy

Lorentz transmission electron microscopy is an advanced characterization technique that enables the simultaneous imaging of both the microstructure and functional properties of materials. Information such as magnetization and electric potentials is carried by the phase of the electron wave, and is lost during image acquisition. Various methods have been proposed to retrieve the phase of the electron wavefunction using intensities of the acquired images, most of which work only in the small defocus limit. Imaging at strong defoci not only carries more quantitative phase information, but is essential to the study of weak magnetic and electrostatic fields at the nanoscale. In this work we develop a method based on differentiable programming to solve the inverse problem of phase retrieval. We show that our method maintains a high spatial resolution and robustness against noise even at the upper defocus limit of the microscope. More importantly, our proposed method can go beyond recovering just the phase information. We demonstrate this by retrieving the electron-optical parameters of the contrast transfer function alongside the electron exit wavefunction.

Defocus-dependent Thon-ring fading

The brightness of modern Schottky field-emission guns can produce electron beams that have very high spatial coherence, especially for the weak-illumination conditions that are used for single-particle electron cryo-microscopy in structural biology. Even so, many users have observed defocus-dependent Thon-ring fading that has led them to restrict their data collection strategy to imaging with relatively small defocus values. In this paper, we reproduce the observation of defocus-dependent Thon-ring fading and produce a quantitative analysis and clear explanation of its causes. We demonstrate that a major cause is the delocalization of high-resolution Fourier components outside the field of view of the camera. We also show that, to correctly characterize the phenomenon, it is important to make a correction for linear magnification anisotropy. Even when the anisotropy is quite small, it is present at all defocus values before circular averaging of the Thon rings, as is also true before merging data from particles in many orientations. Under the conditions used in this paper, which are typical of those used in single-particle electron cryomicroscopy, fading of the Thon rings due to source coherence is negligible. The principal conclusion is that much higher values of defocus can be used to record images than is currently thought to be possible, keeping in mind that the above-mentioned delocalization of Fourier components will ultimately become a limitation. This increased understanding should give electron microscopists the confidence to use higher amounts of defocus to allow, for example, better visibility of their particles and Ewald sphere correction.

Volta phase plate data collection facilitates image processing and cryo-EM structure determination.

A current bottleneck in structure determination of macromolecular complexes by cryo electron microscopy (cryo-EM) is the large amount of data needed to obtain high-resolution 3D reconstructions, including through sorting into different conformations and compositions with advanced image processing. Additionally, it may be difficult to visualize small ligands that bind in sub-stoichiometric levels. Volta phase plates (VPP) introduce a phase shift in the contrast transfer and drastically increase the contrast of the recorded low-dose cryo-EM images while preserving high frequency information. Here we present a comparative study to address the behavior of different data sets during image processing and quantify important parameters during structure refinement. The automated data collection was done from the same human ribosome sample either as a conventional defocus range dataset or with a Volta phase plate close to focus (cfVPP) or with a small defocus (dfVPP). The analysis of image processing parameters shows that dfVPP data behave more robustly during cryo-EM structure refinement because particle alignments, Euler angle assignments and 2D & 3D classifications behave more stably and converge faster. In particular, less particle images are required to reach the same resolution in the 3D reconstructions. Finally, we find that defocus range data collection is also applicable to VPP. This study shows that data processing and cryo-EM map interpretation, including atomic model refinement, are facilitated significantly by performing VPP cryo-EM, which will have an important impact on structural biology.

Hollow Cone Electron Imaging for Single Particle 3D Reconstruction of Proteins.

The main bottlenecks for high-resolution biological imaging in electron microscopy are radiation sensitivity and low contrast. The phase contrast at low spatial frequencies can be enhanced by using a large defocus but this strongly reduces the resolution. Recently, phase plates have been developed to enhance the contrast at small defocus but electrical charging remains a problem. Single particle cryo-electron microscopy is mostly used to minimize the radiation damage and to enhance the resolution of the 3D reconstructions but it requires averaging images of a massive number of individual particles. Here we present a new route to achieve the same goals by hollow cone dark field imaging using thermal diffuse scattered electrons giving about a 4 times contrast increase as compared to bright field imaging. We demonstrate the 3D reconstruction of a stained GroEL particle can yield about 13.5 Å resolution but using a strongly reduced number of images.

三维激光雷达发射/接收共光路光学系统设计

For the measurement needs of space three-dimensional coordinates, a 3D laser radar optical system was designed. This system used the structure of transmitting/receiving common path and based on Gaussian optics theory. It can not only improve system concentricity, reduced external interference, and also simplify the system structure, reduce the volume of the instrument. The system uses expanded beam collimation structure to achieve eight times beam expander. Through small defocus, by changing the distance between 28.203-14.671 mm of the transmission optical system between a first lens and the second, it can achieve ranging accuracy 0.02 mm+10m/m when the measuring range of 2-18 m.

Truncation of the series expressions in the advanced ENZ-theory of diffraction integrals

The point-spread function (PSF) is used in optics for design and assessment of the imaging capabilities of an optical system. It is therefore of vital importance that this PSF can be calculated fast and accurately. In the past 12 years, the Extended Nijboer-Zernike (ENZ) approach has been developed for the purpose of semi-analytic evaluation of the PSF, for circularly symmetric optical systems, in the focal region. In the earliest ENZ-years, the Debye approximation of the diffraction integral, by which the PSF is given, was considered for the very basic situation of a low-NA optical system and relatively small defocus values, so that a scalar treatment was allowed with a focal factor comprising a quadratic function in the exponential. At present, the ENZ-method allows calculation of the PSF in low- and high-NA cases, in scalar form and for vector fields (including polarization), for large wave-front aberrations, including amplitude non-uniformities, using a quasi-spherical phase focal factor in a virtually unlimited focal range around the focal plane, and no limitations in the off-axis direction. Additionally, the application range of the method has been broadened and generalized to the calculation of aerial images of extended objects by including the finite distance of the object to the entrance pupil. Also imaging into a multi-layer is now possible by accounting for both forward and backward propagation in the layers. In the advanced ENZ-approach, the generalized, complex-valued pupil function is developed into a series of Zernike circle polynomials, with exponential azimuthal dependence (having cosine/sine azimuthal dependence as special cases). For each Zernike term, the diffraction integral reduces after azimuthal integration to an integral that can be expressed as an infinite double series involving spherical Bessel functions, accounting for the parameters of the optical system and the defocus value, and Jinc functions comprising the radial off-axis value. The contribution of the present paper is the formulation of truncation rules for these double series expressions, with a general rule valid for all circle polynomials at the same time, and a dedicated rule that takes into account the degree and the azimuthal order of the involved circle polynomials to significantly reduce computational cost in specific cases. The truncation rules are based on effective bounds and asymptotics (of the Debye type) for the mentioned spherical Bessel functions and Jinc functions, and show feasibility of computation of practically all diffraction integrals that one encounters in the ENZ-practice. Thus it can be said that the advanced ENZ-theory is more or less completed from the computational point of view by the achievements of the present paper.

Design, Simulation, and Characterization of a Bimorph Varifocal Micromirror and Its Application in an Optical Imaging System

A 1.2-mm-diameter gold-silicon bimorph varifocal micromirror (VFM) has been designed and investigated for imaging applications. Several prototypes have been fabricated in a 10-μm-thick single-crystal silicon-on-insulator material. Controlled variation of the radius of curvature using electrothermal and optothermal actuation has been demonstrated. A finite-element-based simulation of the device behavior has been undertaken. Experimental characterization has shown that the device focusing power varied from an initial 87 dioptre to 69 dioptre by applying dc electrical power of 33 mW and produced a focusing power value of 59 dioptre when optothermally actuated with a normally incident laser beam of 488-nm wavelength and 43 mW. When electrothermally driven, the mechanical rise and fall times of the device were measured as 130 and 120 ms, respectively. Experimental and theoretical analyses using Zernike coefficients show that, throughout the actuation range, the aberration of the VFM is mainly a small defocus term, with negligible higher order aberrations. A compact active imaging system incorporating the VFM has been also demonstrated. This system was capable of focusing several objects located along the optical axis with a maximum tracking range of 134 mm.

Average intensity of tilted and off-axis Gaussian Schell-model beams propagating through a cat-eye optical lens in atmospheric turbulence

The influences of atmospheric turbulence and the beam coherence on the average intensity of tilted and off-axis laser beams propagating through a cat-eye optical lens in the turbulence are studied. It is shown that the oscillatory behavior and the skewness of average intensity may appear because there exist apertures and active detection laser beams are tilted or off-axis. The skewness is independent of turbulence, but the oscillatory behavior disappears due to turbulence. For a small positive defocus of a cat-eye optical lens, the on-axis average intensity reaches its maximum. The a positive defocus value becomes small as the focal length of the cat-eye optical lens decreases, but it is independent of atmospheric turbulence and the coherence of active detection laser beams. And the average intensity becomes an off-Gaussian-like profile when the propagation distance is large enough in turbulence. However, less beam spreading may occur with increasing propagation distance for active detection laser beams with less coherence, which is quite different from the behavior of laser beams propagating in free space. The better the coherence of active detection laser beams is, the more the average intensity is affected by the turbulence, but the difference is small. The results obtained in this paper are very useful for the applications is active laser detection.

Advanced analytic treatment and efficient computation of the diffraction integrals in the extended Nijboer-Zernike theory

The computational methods for the diffraction integrals that occur in the Extended Nijboer-Zernike (ENZ-) approach to circular, aberrated, defocused optical systems are reviewed and updated. In the ENZ-approach, the Debye approximation of Rayleigh’s integral for the through-focus, complex, point-spread function is evaluated in semi-analytic form. To this end, the generalized pupil function, comprising phase aberrations as well as amplitude non-uniformities, is assumed to be expanded into a series of Zernike circle polynomials, and the contribution of each of these Zernike terms to the diffraction integral is expressed in the form of a rapidly converging series (containing power functions and/or Bessel functions of various kinds). The procedure of expressing the through-focus point-spread function in terms of Zernike expansion coefficients of the pupil function can be reversed and has led to the ENZ-method of retrieval of pupil functions from measured through-focus (intensity) point-spread functions. The review and update concern the computation for systems ranging from as basic as having low NA and small defocus parameter to high-NA systems, with vector fields and polarization, meant for imaging of extended objects into a multi-layered focal region. In the period 2002-2010, the evolution of the form of the diffraction integral (DI) was dictated by the agenda of the ENZ-team in which a next instance of the DI was handled by amending the computation scheme of the previous one. This has resulted into a variety of ad hoc measures, lack of transparency of the schemes, and sometimes prohibitively slow computer codes. It is the aim of the present paper to reconstruct the whole building of computation methods, using consistently more advanced mathematical tools. These tools are explicit Zernike expansion of the focal factor in the DI, Clebsch-Gordan coefficients for the omnipresent problem of linearizing products of Zernike circle polynomials, recursions for Bessel functions, binomials and for the coefficients of algebraic functions that occur as pre-factors of the focal factor in the DI. This results in a series representation of the DI involving (spherical) Bessel functions and Clebsch-Gordan coefficients, in which the dependence of the DI on parameters of the optical configuration, on focal values, on spatial variables in the image planes, and on degree and azimuthal order of the circle polynomials are separated. This separation of dependencies, together with bounds on Clebsch-Gordan coefficients and spherical Bessel functions, facilitate the error analysis for the truncation of series, showing that in the new scheme the DI can be computed virtually without loss-of-digits. Furthermore, this separation allows for a modular implementation of the computation scheme that offers speed and flexibility when varying the various parameters and variables. The resulting scheme is pre-eminently appropriate for use in advanced optical simulations, where large defocus values, high NA and Zernike terms of high order and degree occur.

The Glenn A. Fry Award Lecture 2011

There has been a low level of interest in peripheral aberrations and corresponding image quality for over 200 years. Most work have been concerned with the second-order aberrations of defocus and astigmatism that can be corrected with conventional lenses. Studies have found high levels of aberration, often amounting to several dioptres, even in eyes with only small central defocus and astigmatism. My investigations have contributed to understanding shape changes in the eye with increases in myopia, changes in eye optics with ageing, and how surgical interventions intended to correct central refractive errors have unintended effects on peripheral optics.My research group has measured peripheral second- and higher-order aberrations over a 42° horizontal × 32° vertical diameter visual field. There is substantial variation in individual aberrations with age and pathology. While the higher-order aberrations in the periphery are usually small compared with second-order aberrations, they can be substantial and change considerably after refractive surgery.The thrust of my research in the next few years is to understand more about the peripheral aberrations of the human eye, to measure visual performance in the periphery and determine whether this can be improved by adaptive optics correction, to use measurements of peripheral aberrations to learn more about the optics of the eye and in particular the gradient index structure of the lens, and to investigate ways of increasing the size of the field of good retinal image quality.

Laplacian and caustic imaging theories of MEM work-function contrast

We apply geometrical, Laplacian, and caustic imaging theories to simulate the mirror electron microscope (MEM) contrast arising from a surface phase boundary associated with a discontinuity in work function. The key approximations inherent in the theories are highlighted and investigated within strong and weak scattering regimes from the work-function test object. For strongly varying potentials, the approximation that the electron classical turning distance is unchanged fails, invalidating the quantitative accuracy of the geometrical and Laplacian approaches. For sufficiently small defocus and surface height or potential variations, the Laplacian approach facilitates an intuitive interpretation of MEM contrast.

Cryogenic EBSD on ice: preserving a stable surface in a low pressure SEM

Naturally deformed ice contains subgrains with characteristic geometries that have recently been identified in etched surfaces using high-resolution light microscopy (LM). The probable slip systems responsible for these subgrain boundary types can be determined using electron backscattered diffraction (EBSD), providing the etch features imaged with reflected LM can be retained during EBSD data acquisition in a scanning electron microscope (SEM). Retention of the etch features requires that the ice surface is stable. Depending on the pressure and temperature, sublimation of ice can occur. The equilibrium temperature for a low pressure SEM operating at 1 × 10(-6) hPa is about -112°C and operating at higher temperatures causes sublimation. Although charging of uncoated ice samples is reduced by sublimation, important information contained in the etch features are removed as the surface sublimes. We developed a method for collecting EBSD data on stable ice surfaces in a low pressure SEM. We found that operating at temperatures of <-112°C reduced sublimation so that the original etch surface features were retained. Charging, which occurred at low pressures (<1.5 × 10(-6) to 2.8 × 10(-5) hPa) was reduced by defocusing the beam. At very low pressures (<1.5 × 10(-6) hPa) the spatial resolution with a defocused beam at 10 kV was about 3 μm in the x-direction at -150°C and 0.5 μm at -120°C, because at higher temperature charging was less and only a small defocus was needed to compensate it. Angular resolution was better than 0.7° after orientation averaging. Excellent agreement was obtained between LM etch features and EBSD mapped microstructures. First results are shown, which indicate subgrain boundary types comprised of basal (tilt and twist) and nonbasal dislocations (tilt boundaries).

Effect of nearwork-induced transient myopia on distance retinal defocus patterns

The purpose of the current study was to assess the effect of nearwork-induced transient myopia (NITM) on retinal defocus patterns during distance viewing. An empirically derived, conceptual model of human blur perception and related retinal defocus patterns has been extended to determine the effect of NITM on the relative contributions of myopic and hyperopic retinal defocus during distance viewing. Under the normal hyperfocal refractive condition during distance viewing with isolated stimulus conditions, there is very small myopic defocus (∼0.25 diopters), and no hyperopic defocus, present. After sustained nearwork generating NITM, a moderate increase in this myopic defocus contribution takes place. In the normal isolated distance viewing situation with only very small myopic defocus present, as would occur with many far outdoor activities, the paucity of overall retinal defocus may provide a “protected” condition against myopia development. In contrast, with the addition of NITM producing increased myopic retinal defocus only, there is an imbalance of retinal defocus that may be myopigenic, especially in the context of foveal and peripheral retinal interactions.

Atomic structure imaging of L1-type FePd nanoparticles by spherical aberration corrected high-resolution transmission electron microscopy

The atomic structure of FePd nanoparticles has been studied by spherical aberration (Cs) corrected high-resolution transmission electron microscopy. The periodic arrangement of atoms arising from chemical order is clearly seen as bright contrast due to the small negative value of corrected Cs. The amount of optimal defocus (Scherzer defocus) is markedly reduced by the small Cs value. The interface between crystalline particles and the amorphous matrix can also be observed, free of imaging artifacts, at a small defocus value. The reconstructed phase image directly shows the projected potential distribution within the specimen and reveals the elemental differences due to chemical order. The clear-cut long-range order is lost when particle size is smaller than about 5 nm, at which locally ordered mixed-phase particles begin to dominate.

On the transport of intensity technique for phase retrieval

The Transport of Intensity technique is becoming a viable alternative to electron holography for phase retrieval in Transmission Electron Microscopy. However, several issues are still to be clarified in order to ascertain the applicability of the technique; among them, the controversy regarding its geometrical or wave-optical nature, as related to the phase detection limit. We show here that the Transport of Intensity is a wave-optical technique that works in a special regime of small defocus where the image intensity is linear with the defocus parameter. By a simple analytical example we show that the Transport of Intensity correctly reconstructs the electron optical phase shift even when the phase is smaller than π, a value defining the boundary between the geometrical and wave approaches. Another example is given, the reconstruction of a phase jump, accompanied with experimental support showing that phase retrieval by Electron Holography and Transport of Intensity techniques yields results in good agreement.

Improving image quality by zero‐loss energy filtering: quantitative assessment by means of image cross‐correlation

Fourier ring correlation and root‐mean‐square contrast of pairs of images, taken under identical conditions, were used as criteria of image quality for comparing unfiltered with zero‐loss energy‐filtered imaging using a TEM equipped with a post‐column energy filter. For three different specimens (amorphous carbon film, macromolecules in light negative stain, virus particles in deep negative stain) the dependence of these quantities on electron dose, specimen thickness and defocus was investigated. A model, based on simple assumptions, was used to describe quantitatively their dependence on electron dose and specimen thickness. It was found that energy filtering is most advantageous for low‐dose imaging and small defocus values. The gain due to energy filtering strongly increases with specimen thickness, whereby the dependence is linear for light scattering elements. For thick specimens, the gain by energy filtering is more pronounced in the resolution range between 4 and 2 nm than for lower spatial frequencies.

Shadow images for in‐line holography in a STEM instrument

In a dedicated STEM instrument equipped with a field emission gun, shadow images are easily obtained and have many uses. They are very sensitive to misalignment of the instrument and astigmatism, and therefore can be used for rapid and accurate alignment of the microscope. For crystalline materials, the shadow image contains both the bright-field and dark-field images. It is a summation of the transmitted and diffracted beams, and is basically a kind of Gabor's in-line hologram. Under small or medium defocus, shadow images of a thin, well-orientated crystalline specimen take the characteristic form of Ronchigrams, which offer a unique means to calibrate the microscope operation parameters, such as the spherical aberration coefficient Cs and defocus settings of the objective lens, with high accuracy. With the calibrated values of Cs and delta, a transfer function of the objective lens may be generated. In the stage of numerical reconstruction, by adapting this transfer function to the experimentally recorded hologram the lens aberration introduced in forming the hologram may be corrected and an improved resolution may be achieved for electron microscope images.

Galilean invariance in Fourier optics

The invariance of amplitude distribution due to a converging wave front under Galilean transformation is found to lead to shift invariance of amplitude distribution. It is also established that an aberration-free off-axis converging spherical wave satisfies the Fokker-Planck equation, which reduces to the Bloch equation in the image plane. The effect of a small defocus is to reproduce periodically the image-plane amplitude distribution. Finally, the amplitude distribution and the ambiguity function of the amplitude distribution are the same in the image plane.