Enhanced nearfield resolution of small phase objects using a priori knowledge

Optimizing phase contrast in transmission electron microscopy with an electrostatic (Boersch) phase plate

Several suggestions involving physical phase plates in a transmission electron microscope have emerged recently to enhance contrast of (weak) phase objects. One option is a (half-plane) Hilbert phase plate which is positioned the back focal plane of the objective lens [1].

Under the “weak phase object” approximation, the component of the electron wave scattered by an object is phase shifted by π/2 with respect to the unscattered component. This phase shift has been confirmed for thin carbon films by many experiments dealing with image contrast and the contrast transfer theory. There is also an additional phase shift which is a function of the atomic number of the scattering atom. This shift is negligible for light atoms such as carbon, but becomes significant for heavy atoms as used for stains for biological specimens. The light elements are imaged as phase objects, while those atoms scattering with a larger phase shift may be imaged as amplitude objects. There is a great deal of interest in determining the complete object wave, i.e., both the phase and amplitude components of the electron wave leaving the object.

Many useful materials such as Permalloy exhibiting a very small magneto-optic Kerr-effect (MOKE), are in a class called weak phase objects (WPOs). Polarized light microscopy converts a WPO’s phase distribution into a viewable and recordable intensity map. Nearly crossing the polars is necessary to convert a WPO to an amplitude image. Therefore, digital image processing procedures are usually necessary to enhance MOKE images. In order to increase efficiency and throughput, three methods to increase light intensity are described and demonstrated. All three methods conduct laser light to the conventional source spot in the microscope by imaging the output face of a multimode optical fiber onto the objective’s rear focal plane. Dithering the fiber or its image more rapidly than video scan rates, average illumination nonuniformities caused by fiber modes and diminishes short-range artifacts due to laser coherence. With a third method the long-range nonuniformity is avoided by dithering the location of the fiber-face image. Time-averaged distributions of fiber-face output and corresponding patterns of illumination on the air bearing surface of a recording head, are presented together with polar Kerr contrast images as evidence of the quality, resolution, and stability of the improved method. A combination of all three methods synchronized at a multiple of the video scan rate, produced the most uniform, steady and incoherent source, making it suitable for efficient, real-time, Kerr-effect video microscopy of magnetic materials and devices.

Distributions of amplitude and phase for bivariate distributions

The phase extraction neural network (PhENN) [Optica 4, 1117 (2017)] is a computational architecture, based on deep machine learning, for lens-less quantitative phase retrieval from raw intensity data. PhENN is a deep convolutional neural network trained through examples consisting of pairs of true phase objects and their corresponding intensity diffraction patterns; thereafter, given a test raw intensity pattern, PhENN is capable of reconstructing the original phase object robustly, in many cases even for objects outside the database where the training examples were drawn from. Here, we show that the spatial frequency content of the training examples is an important factor limiting PhENN's spatial frequency response. For example, if the training database is relatively sparse in high spatial frequencies, as most natural scenes are, PhENN's ability to resolve fine spatial features in test patterns will be correspondingly limited. To combat this issue, we propose "flattening" the power spectral density of the training examples before presenting them to PhENN. For phase objects following the statistics of natural scenes, we demonstrate experimentally that the spectral pre-modulation method enhances the spatial resolution of PhENN by a factor of 2.

Two properties of a wave, its intensity and colour, are familiar to all of us. A third property, phase, is less familiar and carries shape information. Quantitative Phase Imaging (QPI), the method discussed in this paper, measures phase information. It utilises the fact that a phase distribution in one plane effects the intensity distribution after propagation. Many samples at the nanoscale are phase objects. For nanostructures, the phase change of the incident wave is strong, while the modulation of amplitude may be negligible. QPI generates the refractive and thickness structure of these transparent samples in a transmission imaging geometry.

The formation of instantaneous speckle-modulated interference images of thin transparent layers in an optical microscope under an illuminating quasi-monochromatic or frequency broadband wave field with wide angular spectra and coherent effects are considered. Instantaneous speckle-modulated interference images of the layer in the transverse and longitudinal sections of the total wave field reflected by the layer are obtained by numerical simulation of the spatial distributions of the complex amplitude of the wave fields reflected by the layer faces and their superposition. The results of computer simulation of instantaneous speckle-modulated and experimentally observed averaged interference images of the layer under quasi-monochromatic and frequency broadband illuminating layer field with different width of the angular spectrum are presented. The mutual correlation of instantaneous speckle fields reflected by the layer faces and the effects of the influence of the width of the angular and frequency spectra of the illuminating field on the contrast of experimentally observed interference images of the layer are studied numerically. On the basis of the instantaneous speckle-modulation of the wave field the physical mechanism of the influence of angular width and the width of the frequency spectra of the illuminating field on the mutual coherence of the interfering wave fields is investigated.

We inv estigate the problem in which a volume hologram is produced by two waves of arbitrary amplitude and phase distribution (the only restriction being that they must obey the rules of geometrical optics), and the developed hologram is illuminated by one of the waves having the same phase distribution but not necessarily the same amplitude distribution. Coupled partial differential equations are derived and solved in the form of an infinite series valid for both transmission and reflection holograms. For transmission holograms a simple approximate solution is given for the amplitude of the reconstructed wave in the immediate vicinity of the input surface.

For defect detection or undesired object in commercial products, it is required to develop a fast measurement system that can obtain three-dimensional distribution of surface of the opaque medium such as metal or inside of the transparent medium. For this purpose, we fabricated a digital holographic microscope using a fast image sensor when the phase object is put on a fast movable stage. In the fabricated system, an image sensor operated at maximum frame rate of 2000 fps and a movable stage operated at maximum speed of 300 mm/s are introduced. Under the continuous wave illumination, motion-blurred phase object is reconstructed. By using numerical processing such as deconvolution filter, the reconstructed phase distribution is much improved. Numerical results are presented.

Diffractive optical elements able to generate on-axis (zero-order) phase as well as amplitude distributions are described. The proposed elements are surface-relief plates, that is phase-only elements, that are based on concepts of computer-generated masks followed by lithographic and etching processes. The proposed encoding method assumes variable spatial partitioning of the cell and a fixed phase value allocated to each subcell. This method requires the minimal number of etching levels needed for full representation of the wave front, that is three, but can be applied with improved efficiency using more etching levels. The reconstructed amplitude and phase distributions contain some noise owing to the encoding process. Discussion of the error sources is given.

The feasibility of using a Kerr magneto-optic-effect display as the input to a coherent optical computer is discussed and experimentally verified. Simple amplitude and phase distributions were generated on a continuous ferromagnetic thin film and their Fourier transforms were displayed with a lens. An experiment was performed demonstrating spatial filtering of a magneto-optically generated amplitude distribution. Magneto-optic generation of more complicated amplitude distributions requires a matrix-type thin-film structure and this input must be treated as sampled data.

A compact quadriwave lateral shearing interferometer (QWLSI) with strong adaptability and high precision is proposed based on a novel randomly encoded hybrid grating (REHG). By performing the inverse Fourier transform of the desired ±1 Fraunhofer diffraction orders, the amplitude and phase distributions of the ideally calculated quadriwave grating can be obtained. Then a phase chessboard is introduced to generate the same phase distribution, while the amplitude distribution can be achieved using the randomly encoding method by quantizing the radiant flux on the ideal quadriwave grating. As the Faunhofer diffraction of the REHG only contains the ±1 orders, no order selection mask is ever needed for the REHG-LSI. The simulations and the experiments show that the REHG-LSI exhibits strong adaptability, nice repeatability, and high precision.

Effort has been made for sensitive detection of reaction products in histochemistry at electron microscopic level. Phase contrast electron microscopy utilizing phase plates has been considered suitable for high contrast observation of weak phase objects. This novel technique was newly applied to histochemically stained strong phase objects of osmificated biological specimens. Sections of various thicknesses, specifically stained for the Golgi apparatus by the ZIO technique using the heavy metals Zn and Os, were observed with a phase contrast electron microscope in Zernike and Hilbert imaging modes. Quantitative analysis of image contrast in real space and the power spectrum in Fourier space showed a high contrast gain even for strong phase objects. This result indicates that phase contrast electron microscopy is useful for effective detection of reaction products in histochemistry.

Visualization and investigation of supersonic air micro jets (SAMJ) as weak phase objects present serious problems when done through classical visualizing methods. Usage of advanced holographic interference techniques would make the study and evaluation of characteristic densities, density gradients and jet’s structure (weak shocks followed by expansion waves) more successful. It should be remarked, that the applications of Mach-Zehnder (reference) and shear dual-hologram techniques, which were performed in earlier works, have been done separately and have a demonstrative character. In the present paper, the authors have tried to apply both the dual-hologram techniques, simultaneously. This approach makes it possible to measure the same phase object under study by reference beam and shear interference techniques using only Mach-Zehnder holograms. Finally, experimental data obtained from both the techniques were numerically compared and found to be more applicable. It was first experimentally shown that sensitivity of shear interference approach during evaluations of radial component of density gradients in a micro jet can be enhanced by using the technique of re-recording holograms. The effect of fast transition to a transonic regime accompanied by expansion and later on with disintegration of a jet was observed and jet’s densities and radii in transition region were evaluated. As a whole, method of co-joint application of reference beam and shear dual-hologram interferometry has shown its self-descriptiveness, flexibility and utility for optical diagnostics of a weak gas dynamic micro object, the supersonic air micro jet.